ECONPress of Northeastern University
ECONPress is a publication for undergraduate compositions in economics. We publish twice a year during each fall and spring semester. ECONPress invites the highest quality submissions from undergraduate students in various economics related disciplines. It provides a forum for the undergraduate economics community to engage in active discussion and debate about the topics, theories, and applications they’ve learned in the classroom.
Editorial Board Alec Loudenback Editor-in-Chief , President Robert Dent Director of Finance, Editor Victor Martinelli Director of Content, Editor Tala Borno Director of Logistics, Editor Pooja Trivedi Director of Public Relations and Marketing, Editor Michael Onore Director of Programming, Editor
Selection Committee
Advisory Board
Eric Johnston Anna Mandell Jason Fertig Li Pan Yi Liu Xinyi Zhu Sam Kasuli
Dr. Peter J. Simon Dr. Daniel Greenfield
Special Thanks Edward J. Meehan Marcel Landesmann Prof. Steven Morrison
ECONPress of Northeastern University
Spring 2012
Volume II, Number II
Letter from the Editors...................................................... 5
Voting with Bidirectional Elimination ..........................6 Matthew Stephen Cook
Edited and published at Northeastern University Editorial Offices: ECONPress 360 Huntington Avenue 301 Lake Hall Boston, MA 02115-5000 ISSN: 2158-8864 (Print) 2158-8872 (Online) Electronic Mail:
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth.........................23 Brian Joel Feldman
Equity Volatility across Industries from IPO Day........35 Andrew Nielsen Lewis
Should Punitive Damages be Scaled to Wealth?...........51 Harrison A Seitz
International Collective Action on Climate Change....58 Evan Richards Sankey
Submissions Process and Guidelines............................66
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ECONPress
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Letter from the Editors
Letter from the Editors The greatest insights into our world are often not revolutionary, but evolutionary. Progress is not made in leaps and bounds but by small, determined steps. The authors that we present you in this edition of ECONPress have all taken well-founded topics, approached them with new questions and set into motion a process of researching answers that have not been given before. We at ECONPress have not developed the research within, but instead provide an outlet for such work to be distributed and recognized. Non-published research is akin to a tree fall not heard. We seek to make the work heard.
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Submitting to ECONPress is perhaps the easiest part of the entire research process and the labor of “rethinking our world” the most difficult. Yet all of the authors who submitted to ECONPress should be commended in their confidence and determination because as undergraduates we have not traditionally had such a way to share our work before. Each submission requires a modest confidence that one’s work is quality research - quality that each one of us undergraduates possess. The authors and research here are distinguished for hard work, unique insights, economic understanding, and adept prose - qualities that all other undergraduates like you possess and that are waiting to be shared. Let the research presented within inspire and instigate a debate in your own mind. Put that question to the test and build upon the work of those that have come before us. “Rethink your world” and share it with all of us. Such is a process to continue throughout your lifetime, and we at ECONPress hope to be but a small part. Thank you for reading, Alec Loudenback Robert Dent Michael Onore
Victor Martinelli Pooja Trivedi Tala Borno
The Editorial Board of ECONPress
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Voting with Bidirectional Elimination Matthew Stephen Cook Stanford University Abstract
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Two important criteria for judging the quality of a voting algorithm are strategyproofness and Condorcet efficiency. While, according to the Gibbard-Satterthwaite theorem, we can expect no voting mechanism to be fully strategy proof, many Condorcet methods are highly susceptible to compromising, burying, and bullet voting. In this paper I propose a new algorithm which I call “Bidirectional Elimination,” a composite of Instant Runoff Voting and the Coombs Method, which offers the benefit of greater resistance to tactical voting while nearly always electing the Condorcet winner when one exists. A sophisticated program was tailor-made and used to test IRV, the Coombs Method, and Bidirectional Elimination on tens of billions of social preference profiles in combinations of up to ten voters and ten candidates. I offer mathematical proofs showing the new algorithm meets the Condorcet criterion for up to 4 voters and N candidates, or M voters and up to 3 candidates; beyond this, program results show Bidirectional Elimination offers a significant advantage over both IRV and Coombs in approaching Condorcet efficiency.
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Voting with Bidirectional Elimination
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of Bidirectional Elimination was born. Jon also independently created his own proof of Condorcet efficiency for the [3 candidates, M voters] case. Tyler Mullen showed me the first set of conditions under which my algorithm would not elect the Condorcet winner. This led me to design the specifications for the program Jaehyun coded. Thanks to the four of you for your support of this stimulating project.
“This scheme, [known as] instant-runoff voting, doesn’t necessarily get you the movie (or the candidate) with the most committed supporters, but it does get you a winner that a majority can at least countenance. It favors consensus. Now here’s why it may also favor The Hurt Locker. A lot of people like Avatar, obviously, but a lot don’t—too cold, too formulaic, too computerized, too derivative. . . . Avatar is polarizing. So is James Cameron. He may have fattened the bank accounts of a sizable bloc of Academy members—some three thousand people drew Avatar paychecks— but that doesn’t mean that they all long to recrown him king of the world. . . . These factors could push Avatar toward the bottom of many a ranked-choice ballot.
mechanism. The purpose of this paper is to define important criteria, explain their importance, and evaluate a new voting mechanism using these criteria. The mechanism I will analyze is called Bidirectional Elimination and is conducted in a manner similar to IRV. The criteria I will use are the Condorcet criterion and strategy proofness. I will primarily analyze the mechanism based on the Condorcet criterion, using mathematical proofs and experimental data from computer simulations. I will discuss strategy proofness briefly, and recommend an experimental methodology one could use for a rigorous analysis.
1. Introduction For decades, the Academy of Motion Picture Arts and Sciences used a plurality vote to determine Best Picture: Over five thousand voters would submit a single vote among just a few nominees, and the movie with the most votes would win. In 2010, the Academy replaced plurality voting with a new system called Instant Runoff Voting (IRV). Instead of submitting a single choice, voters were asked to submit a preferential ranking of ten nominees. After all ballots were cast, the mechanism would systematically eliminate candidates with the fewest first-place votes until one winner remained.
IRV offered several advantages over a simple plurality vote. The plurality mechanism could have easily elected candidates many voters strongly disliked, and it also allowed for the spoiler effect—the negative effect a weaker candidate has over a stronger candidate by stealing away votes. To compensate for the spoiler effect, voters in the plurality elections were able to strategize by failing to report actual first choices; voters could compromise by voting for the Acknowledgments candidate they thought realistically had the best chance of winning. IRV eliminated I am grateful to Jonathan Levin for his the spoiler effect and reduced the chance instructive insights, engaging discussions, and of electing candidates whom a majority thoughtful guidance. A special thanks to Jae- disliked. hyun Park for lending his world class coding talents in creating the program used on tens In his February 15, 2010 article for The of billions of samples. Discussions with Jona- New Yorker, Hendrik Hertzberg explains than Zhang were enlightening: It was dur- the effects of IRV in the context of that ing conversation with him that the concept year’s Academy Awards:
On the other hand, few people who have seen The Hurt Locker—a real Iraq War story, not a sci-fi allegory—actively dislike it, and many profoundly admire it. Its underlying ethos is that war is hell, but it does not demonize the soldiers it portrays, whose job is to defuse bombs, not drop them. Even Republicans (and there are a few in Hollywood) think it’s good. It will likely be the second or third preference of voters whose first choice is one of the other ‘small’ films that have been nominated.” As a process, voting requires design. According to Allan Gibbard and Mark Satterthwaite, no voting mechanism is fully strategy proof, and according to Kenneth Arrow, no voting mechanism meets all reasonable criteria of fairness. A theoretical framework must be constructed to evaluate methods of aggregating individual interests into a collective decision. This theoretical framework, dating back to the work of French philosopher and mathematician Condorcet, is called social choice theory. Within this framework, criteria exist for evaluating the justness of a voting
The paper is organized as follows. Section 2 reviews criteria, background, terminology, and theorems related to social choice theory that are necessary for analyzing a voting mechanism. Section 3 dissects Instant Runoff Voting, the Coombs Method, and Condorcet Methods. Section 4 introduces Bidirectional Elimination, runs the algorithm step by step on a given set of preferences, and analyzes based on certain criteria presented in section 2. Section 5 offers logic proofs related to Condorcet efficiency. Section 6 presents and analyzes experimental results from a computer simulation. Section 7 offers concluding remarks. Results from the computer simulation show that Bidirectional Elimination comes very close to meeting Condorcet efficiency. Given the susceptibility of most Condorcet methods to tactical voting, and given that failure to elect the Condorcet winner occurs less than .6% of the time for up to 10 voters and 10 candidates using Bidirectional Elimination, I find this new algorithm may offer a significant advantage over Condorcet methods, and certainly a strict advantage over Instant Runoff Voting and over the similar Coombs Method. The importance: Bidirectional Elimination has the potential to improve justice in democratic systems.
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ECONPress 2. Background and Terminology
Failure to meet certain criteria creates susceptibility to strategic voting. Among these criteria is the monotonicity criterion, which states that a candidate X must not be harmed—that is, changed from being a winner to a loser—if X is raised on some ballots without changing the orders of the other candidates. Conversely, the later-noharm criterion states that giving a more positive ranking, or simple an additional ranking, to a less preferred candidate must not cause a more preferred candidate to lose.
The first key term is Condorcet winner. The Condorcet winner is the candidate who, when paired against any other individual candidate, will always capture a majority vote. A voting method that always elects the Condorcet winner when one exists is called Condorcet efficient, or is said to meet the Condorcet criterion. The Condorcet loser is one who always loses such pairwise runoffs. A system that never elects the Condorcet loser is said to meet the Condorcet loser criterion. A Condorcet method is a mechanism that will always elect the Condorcet winner. A Condorcet winner does not always exist. Sometimes there will be a tie, or a cycle; the latter is an example of 3. Relevant Voting Methods Condorcet’s paradox. For example, three voters with preferences (A>B>C), (B>C>A), Instant Runoff Voting and (C>A>B) cause a cycle; in this case, the group chooses A over B, B over C, and C Instant Runoff Voting is a system using over A, so there is no clear winner. ranked preferences to elect a single winner. The procedure works as follows. Voters subA second criterion for evaluating voting mit ranked preferences, and the candidate systems is strategy proofness. A voting system with the fewest first choice votes is systemis said to be strategy proof if, given full in- atically eliminated until only the winner formation over everyone else’s preferences, remains. In some cases, candidates will be no individual can improve his outcome tied for the position of “fewest first choice by misreporting his own preferences. Such votes.” If this happens, special tiebreaker misreporting is called tactical voting. Ac- rules must be constructed. IRV satisfies the cording to the Gibbard-Satterthwaite theo- later-no-harm criterion and the Condorcet rem, no preferential voting system is fully loser criterion but fails monotonicity, indestrategy proof. pendence of irrelevant alternatives, and the Condorcet criterion. IRV is susceptible to Various types of tactical voting can push-over voting. occur. The first is called push-over voting, in which a voter ranks a weak alternative Coombs Method higher, but not in the hopes of getting that alternative elected. The second is called The Coombs Method is a system simicompromising, which occurs when voters lar to IRV using ranked preferences to elect dishonestly rank an alternative higher than a single winner. Instead of systematically their true alternative in hopes of getting it eliminating the candidate with the fewest elected. The third strategy, called burying, first choice votes, Coombs systematically occurs when a voter dishonestly ranks a eliminates the candidate with the most last candidate lower in hopes of seeing it de- choice votes until one remains. Similarly, a feated. The last form is called bullet voting, special tiebreaker must be devised to deal which means voting for only one candidate with cases in which candidates are tied for in a preferential system when submitting a the position of “most last choice votes.” The list of ranked preferences is an option. Coombs Method satisfies the Condorcet
Voting with Bidirectional Elimination
loser criterion but fails monotonicity, independence of irrelevant alternatives, and the Condorcet criterion. The Coombs Method is susceptible to compromising and burying. Condorcet Methods Condorcet methods, methods that will always elect the Condorcet winner, include Copeland’s method, the Kemeny-Young Method, Minimax, Nanson’s method, ranked pairs, and the Schulze method. No Condorcet method satisfies the laterno-harm criterion or independence of irrelevant alternatives. The methods vary in monotonicity.
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until one is eliminated; then continue with regular IRV. If potential losers ever tie in the rightmost column containing potential losers, all potential losers are eliminated then. Under certain tiebreaker conditions, no winner will be elected; all candidates are eliminated.
Stage 2: Use the Coombs Method to elect a potential winner Y. If in any round of elimination two or more candidates share the highest number of last choice votes, a special tiebreaker is performed. To perform the tiebreaker, create a set of “potential losers” consisting of all the candidates sharing the highest number of last choice votes in the rightmost column. Then move to the Condorcet methods are generally quite next column to the left and reiterate this susceptible to tactical voting—in particular, form of the Coombs Method among pocompromising, burying, and bullet voting. tential losers only, possibly narrowing the set of potential losers, until one is eliminated; then continue with the regular Coombs Method. If potential losers are ever tied in 4. Bidirectional Elimination the leftmost column containing any potential losers, all potential losers are eliminated I now propose a new voting mechanism at once. Under certain tiebreaker condiusing ranked preferences. I call this new tions, no winner will be elected; all candimechanism “Bidirectional Elimination,” as dates are eliminated. it is a hybrid of both Instant Runoff Voting and the Coombs Method. The algorithm Stage 3: If X and Y are the same canworks as follows. (Note: The tiebreaker pro- didate, X = Y= winner; if X and Y are difcedure described in stages 1 and 2 is impor- ferent candidates, a simple pairwise runoff tant in preventing premature elimination between X and Y determines the winner; if of the Condorcet winner.) only one of the stages elects a potential winner, the potential winner is the final winThe Bidirectional Elimination Algorithm ner; if neither former stage elects a potential winner, there is no final winner. Stage 1: Use regular IRV to elect potential winner X. If in any round of elimiNon-Monotonic nation two or more candidates share the least number of first choice votes, a special Bidirectional Elimination fails the tiebreaker is performed. To perform the monotonicity criterion and is therefore tiebreaker, create a set of “potential los- not strategy-proof. The social preference ers” consisting of all candidates sharing the profiles below are examples susceptible to least number of first choice votes in the tactical voting. leftmost column. Then move to the next column to the right and reiterate this form of IRV among potential losers only, possibly narrowing the set of potential losers,
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# Voters
True Preferences
4
A>B>C
3
B>C>A
2
C>A>B
IRV and Coombs would each elect A in this case, so Bidirectional Elimination also elects A. However, a voter with preferences (B>C>A) could simply state falsely that his preferences were (C>A>B). Preferences would then look like this: # Voters Reported Preferences
A: Instant Runoff Voting elects candidate A, but Coombs Method does not.
4
A>B>C
2
B>C>A
B: Both Instant Runoff Voting and Coombs Method elect candidate A.
3
C>A>B
C: Coombs Method elects candidate A, but Instant Runoff Voting does not.
Now, IRV elects C; Coombs elects A; and C wins with Bidirectional Elimination when compared pairwise with A. By misreporting preferences, a voter was able to improve his outcome, now getting his second choice instead of his third choice. Visualization The circle below, not to scale, represents an arbitrary space for N>3 candidates and M>4 voters containing permutations of voter preferences. A + B + C + D: Permutations of preferences such that candidate A is a Condorcet winner. A + B + C: Bidirectional Elimination elects candidate A. A + B: Instant Runoff Voting elects candidate A. B + C: Coombs Method elects candidate A.
D: Bidirectional Elimination fails to elect candidate A.
Voting with Bidirectional Elimination
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pending on the nature of the collective deBidirectional Elimination may not cision, either no winner should be elected, eliminate cycles, but the mechanism does or an alternative method should be used to satisfy other pleasant, though informal, criarbitrarily select a winner. teria. The IRV stage of the mechanism will rarely eliminate a candidate whom voters Electoral cycles can be similar to ties in find appealing, while the Coombs stage will that no mathematically just winner exists. rarely elect a candidate whom voters find The classic example of Condorcet’s para- unappealing, and between the two stages, dox—three voters with profiles (A>B>C), the better candidate is chosen. (B>C>A), and (C>A>B) has no clear winner (this is an example of a circular tie). But what if votes are not as symmetrical? What if we add a fourth voter with preferences 5. Logic Proofs for IRV, Coombs (A>B>C)? Now, A is strictly preferred over Method, and Bidirectional Elimination B, which is strictly preferred over C; but A and C are tied in a pairwise runoff. This is IRV, Coombs Method, and Bidirecno longer a circular tie. While there may tional Elimination meet the Condorcet cristill be no clear winner, electing an arbitrary terion in certain specific combinations of N candidate seems less than ideal: One could candidates and M voters. In this section I argue that B should be eliminated since it is examine for which sets of [N candidates, M strictly dominated by A; and one could de- voters] each voting system meets the critebate whether C should be eliminated, since rion. while tied with A, C is still strictly dominated by B. Establishing criteria for justice For consistency and ease of notation, is more difficult given an asymmetric cycle candidate “A” refers to the Condorcet winlike this one. ner.
When no Condorcet winner exists, there must be new criteria for evaluating the justness of a voting algorithm. No Condorcet winner exists in the presence of a tie or a cycle.
A Condorcet completion method is required to elect a winner when ambiguities like these arise. One such completion method uses the “minimax rule” developed by Simpson and Kramer. This rule gives a score to each candidate as follows. Candidate A1 is paired against A2-N. For each pairwise comparison, a score is given to A1 equal to the number of votes his opponent has, minus the number of his own votes. The maximum of these scores is recorded as W1 (there are various ways of calculating a W score; this one, called using margins, is the simplest). The minimum of (W1…N) corresponds to the winner.
When votes are tied—such as in the simplest case, when two voters disagree over which of two candidates to elect—there is no mathematically “just” way of choosing between candidates. Bidirectional Elimination does not choose a winner in cases of ultimate ties. This is not a bad thing; de-
Andrew Caplin and Barry Nalebuff proposed a system based on Simpson and N candidates, 2 voters Kramer’s minimax using a “64%-majority rule” that can in fact eliminate all electoral When only two voters are present, a cycles given a restriction on individual pref- Condorcet winner can exist only when a tie erences, and on the distribution of prefer- does not exist; that is, when the voters agree ences. on the candidate to be chosen. Both candi-
When No Condorcet Winner Exists While Bidirectional Elimination fails to meet the Condorcet criterion, it comes very close, as shown in section 6. However, as the number of N candidates or M voters increases, the number of Condorcet winners generally decreases.
We will ignore two trivial cases, [1 candidate, M voters] and [N candidates, 1 voter], in which voters have no choice between candidates, or one voter has the ultimate choice (a situation similar to dictatorship). Tie and cyclical cases are not discussed here. I am primarily concerned with electing the Condorcet winner when one exists. Logic Proofs: Instant Runoff Voting Instant Runoff Voting, the weakest of the three voting mechanisms studied here, meets the Condorcet criterion for up to 2 voters and N candidates, or M voters and up to 2 candidates.
-12dates have therefore ranked this candidate (candidate A) as their first choice. All other N-1 candidates will be eliminated at once, leaving A as the winner from IRV. 2 candidates, M voters When only two candidates are present, a Condorcet winner exists when either M is odd, or M is even but the two candidates are not tied in their votes received. In both cases, candidate A captures more than 50% of the voters. If this is the case, the non-A candidate will be eliminated in the first and only iteration of IRV. Logic Proofs: Coombs Method
ECONPress follows that A can appear in the rightmost column at most once. If A were to appear in the rightmost column more than once, at least one non-A would be preferred in majority over A. This is impossible, as A is the Condorcet winner. If A does appear in the rightmost column once, either (1) the same non-A is now ranked in last-place by two voters, in which case this non-A is eliminated, or (2) three different candidates appear in the last column, in which case A cannot be eliminated in the tiebreaker, because one of the other two potential losers will be eliminated first. This is because as we move leftward through columns, A cannot appear before another candidate: At least three voters rank every other candidate below A.
The Coombs method, which meets the Condorcet criterion in a larger set of candidate/voter combinations, works consisIf A appears in the rightmost column tently for up to 4 voters and N candidates, zero times, it will not be eliminated in this or M voters and up to 2 candidates. round of the Coombs Method. N candidates, 2 voters
Candidate A can never be eliminated as the algorithm iterates. Under [N canWhen only two voters are present, a didates, 3 voters] conditions, Candidate A Condorcet winner can exist only when a tie can never be eliminated using the Coombs does not exist; that is, when the voters agree method. A will always win. on the candidate to be chosen. Both candidates have therefore ranked this candidate N candidates, 4 voters (candidate A) as their first choice, and the losing candidates (candidate non-A) as This proof is directly parallel to the [N their second and last choice. All other N-1 candidates, 3 voters] proof. To preserve candidates will be eliminated systematically the existence of a Condorcet winner ununtil only A remains from the Coombs der these conditions, only one of the four Method. voters may rank a given non-A candidate above A; otherwise, a tie could exist, or a N candidates, 3 voters majority of the voters could prefer a non-A candidate over A. To preserve the existence of a Condorcet winner under these conditions, only When columns of preferences are one of the three voters may rank a given drawn, while N>1 (a winner as not yet been non-A candidate above A; otherwise, at found, as multiple candidates remain), it least two-thirds of the voters would prefer follows that A can appear in the rightmost a non-A candidate over A. column at most once. If A were to appear in the rightmost column more than once, When columns of preferences are at least one non-A would be preferred in drawn, while N>1 (a winner as not yet been majority over A. This is impossible, as A is found, as multiple candidates remain), it the Condorcet winner.
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Voting with Bidirectional Elimination
If A does appear in the rightmost column once, either (1) a non-A is eliminated right away, or (2) all different candidates appear in the last column, in which case A cannot be eliminated in the tiebreaker, because one of the other three potential losers must be eliminated first. This is because as we move leftward through columns, A cannot appear before another candidate: At least three voters rank every other candidate below A. If A appears in the rightmost column zero times, it will not be eliminated in this round of the Coombs Method. Candidate A can never be eliminated as the algorithm iterates. Under [N candidates, 4 voters], Candidate A can never be eliminated using the Coombs method. A will always win. Logic Proofs: Bidirectional Elimination
Additionally, Bidirectional Elimination meets the Condorcet criterion for 3 candidates and M voters, which is more than either IRV or the Coombs Method can accomplish alone. 3 candidates, M voters Here we use an example with a total number of voters equal to X1+X2 . . . +X6 choosing between candidates A, B, and CÂ. A is given as the stable Condorcet winner. We wish to prove that Bidirectional Elimination will always elect candidate A given the [3 candidates, M voters] condition. Proving that Bidirectional Elimination will never eliminate A is the same as proving that Bidirectional Elimination will always elect A if and only if a candidate is eliminated each round. Since one candidate is eliminated each round, I will prove Bidirectional Elimination will never eliminate A—in order to show that Bidirectional Elimination will always elect A.
Bidirectional Elimination meets the Condorcet criterion for up to 4 voters and The table below represents all possible N candidates, or M voters and up to 3 can- permutations of voter preferences. didates. Since we are given that A is the stable Since Bidirectional Elimination utilizes Condorcet winner, to satisfy the stable IRV and the Coombs Method in electing Condorcet condition, A must have more two potential winners who eventually face votes than either B or C in pairwise counts. off in a pairwise election, when IRV or the The following two statements must be true: Coombs Method elects a Condorcet winner, so will Bidirectional Elimination. Thus X3 + X4 + X6 < X1 + X2 + X5 from the proofs above, we have already established that Bidirectional Elimination (1, implies A > B) meets the Condorcet criterion for up to 4 voters and N candidates, or M voters and up to 2 candidates. Number of Ballots X1 X2 X3 X4 X5 X6
First Choice A A B B C C
Second Choice B C A C A B
Third Choice C B C A B A
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X4 + X5 + X6 < X1 + X2 + X3
nates B; the second round eliminates A.
Coombs Case 2: The first round eliminates C; the second round eliminates A.
(2, implies A > C)
If the Condorcet condition is to be satisfied by Bidirectional Elimination, then we must show that A cannot be eliminated by both IRV and the Coombs Method. For this to be true, if the stable Condorcet winner A is eliminated in one of these two mechanisms, the other mechanism must not eliminate it. Candidate A could be eliminated in the IRV stage in one of three ways:
IRV Case 1 is impossible: If B is eliminated in the first round, only A and C remain in the final pairwise runoff. By (2), A would win this runoff and C would be eliminated, not A.
IRV Case 2 is impossible: If C is elimiX6 < X5 (7) nated in the first round, only A and B remain in the final pairwise runoff. By (1), From (7) and (6), we can show algebraA would win this runoff and B would be ically, eliminated, not A. X2 < X4 (8) Let us continue unraveling IRV Case 3. If first-round IRV eliminates A, then we From (6) and (1), we can show algebraknow: ically,
X1 + X2 < X5 + X6 (4) Given these conditions, can candidate A now also lose in a Coombs election? A loss could happen in one of three ways:
Candidate A, the Condorcet winner, is eliminated in the IRV stage in one of three ways:
Coombs Case 3: The first round eliminates A.
IRV Case 2 is impossible: If C is eliminated in the first round, only A and B reIRV Case 1: The first round eliminates main in the final pairwise runoff. By (1), B; the second round eliminates A. A would win this runoff and B would be eliminated, not A. IRV Case 2: The first round eliminates C; the second round eliminates A. This leaves us with only Coombs Case 3—the first round eliminates A—which IRV Case 3: The first round eliminates would require the following to hold: A. X1 + X3 < X4 + X6 (5) IRV Case 1 is impossible: If B is eliminated in the first round, only A and C reX2 + X5 < X4 + X6 (6) main in the final pairwise runoff. By (2), A would win this runoff and C would be From (1) and (3), we can show algebraeliminated, not A. ically,
X1 + X2 < X3 + X4 (3)
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Voting with Bidirectional Elimination
X3 < X1 From (4) and (2), we can show algebraically, X4 < X3
(10)
From (5) and (10), we can show algeCoombs Case 1: The first round elimi- braically,
Candidate B is eliminated in the first round. Candidate A is eliminated in the second round.
Candidate C is eliminated in the first round. Candidate A is eliminated in the second round.
Candidate A is eliminated in the first round.
Impossible
Impossible
Possible
Candidate A is also eliminated in the Coombs stage one of three ways:
X1 < X6
Candidate B is eliminated in the first round. Candidate A is eliminated in the second round.
Candidate C is eliminated in the first round. Candidate A is eliminated in the second round.
Candidate A is eliminated in the first round.
Impossible
Impossible
Impossible
6. Experimentation via Computer Simulation
(11) always elects the Condorcet winner given
the [3Voting candidates, M voters] condition. A Program to Simulate
From (5) and (2), we can show algebraically, Jaehyun Park generously wrote a program according The proof can be visualized in a tree to my specifications to test the (above). results of IRV, the Coombs Method, and Bidirectional Elimination for various social preference X5 < The X2 simulation in three inputs: (12) profiles. takes N candidates, M voters, and X cases. Here we
define “social preference profile” as the set of ranked preferences for all voters V0…M. When a chain can be all derived userThe entersfollowing X=0, the program will test possible permutations of social preference profiles from numbers through (12) 6. Experimentation Computer 6 possible exactly once and(7) output results. (Forabove: example, for 2 voters and 3 candidates, Vvia 1 has preference profiles. rankings, and V2 has 6 possible rankings, for a total of 36 possible social Simulation Entering When a user enters X>0, the program will create X X5 < X=0 X 2 <tests X4 <each X3 one < Xof <these.) X6 < X 1 5 random social preference profiles and perform the algorithms on each Since Voting these profiles A Program to one. Simulate are random when X>0, it is possible, though rare as M and N increase, for duplicate profiles to Since X5 cannot appear on both sides be tested. This duplication is generally expected of Monte Carlo experiments, and in this a proof the inequality, Coombs Case 3 must also Jaehyun Park generously wrote experiment does not significantly affect results. be impossible. We have just shown that it is gram according to my specifications to test Outputs of the simulation include: impossible for candidate A to be eliminated the results of IRV, the Coombs Method, and
by IRV, and also by the Coombs Method. Bidirectional Elimination for various social It is therefore impossible for A to be elimi-17 preference profiles. The simulation takes in nated by Bidirectional Elimination under three inputs: N candidates, M voters, and these conditions. Bidirectional Elimination X cases. Here we define “social preference
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profile” as the set of ranked preferences for all voters V1…M. When a user enters X=0, the program will test all possible permutations of social preference profiles exactly once and output results. (For example, for 2 voters and 3 candidates, V1 has 6 possible rankings, and V2 has 6 possible rankings, for a total of 36 possible social preference profiles. Entering X=0 tests each one of these.) When a user enters X>0, the program will create X random social preference profiles and perform the algorithms on each one. Since these profiles are random when X>0, it is possible, though rare as M and N increase, for duplicate profiles to be tested. This duplication is generally expected of Monte Carlo experiments, and in this experiment does not significantly affect results (only by thousandths of a percent).
winner. By symmetry, we can multiply R by the number of candidates to determine for how many permutations a Condorcet winner exists.
Outputs of the simulation include:
T, the Coombs Method success figure. This is equal to the number of times that A is the Condorcet winner, and the Coombs Method elects A.
Q, number of total cases, or social preference profiles, tested. Q is equal to X when X>0, or (N!)M when X=0. Individual preferences were restricted to include only sets in which each voter gave a ranking to every candidate. That is, if options A through E were available, each voter included options A through E in his individual preference profile, omitting no option from his ordering. Removing this domain restriction would expand the total number of possible social preference profiles to (N! + N!/2! + N!/3! . . . + 1)M, making the program unfeasible.
(N*R)/Q, percentage of cases with a Condorcet winner. Dividing N*R by the total number of cases tells us the percentage of cases for which a Condorcet winner exists. S, the IRV success figure. This is equal to the number of times that A is the Condorcet winner, and Instant Runoff Voting elects A. S/R, the IRV success ratio. Dividing S by the number of cases where A is the Condorcet winner returns a valuable percentage.
T/R, the Coombs Method success ratio. Dividing R by the number of cases where A is the Condorcet winner returns a valuable percentage. U, the Bidirectional Elimination success figure. This is equal to the number of times that A is the Condorcet winner, and Bidirectional Elimination elects A. U/R, the Bidirectional Elimination success ratio. Dividing U by the number of cases where A is the Condorcet winner returns a valuable percentage.
R, number of cases with A as Condorcet winner. The program labels one of the candidates as A and tests preference permutations to determine if A is a Condorcet winThe program reports the most accurate ner. results when X=0, and all cases are tested exactly once. However, since Q grows asR/Q, percentage of cases with A as Con- tronomically as N or M increase, the prodorcet winner. This calculation performs gram can take years to run beyond a [N=5 R/Q, the number of times that A is a Con- candidates, M=5 voters] simulation. We dorcet winner divided by the number of approximate by setting X equal to a large cases tested. number—in this case, one billion—when necessary to shorten the simulation. When N*R, number of cases with a Condorcet (N!)M < 1 billion, we test all possible samples
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Voting with Bidirectional Elimination
Table 1: Number of Cases Tested (Q)
Voters 1 2 3 4 5 6 7 8 9 10
Candidates 1 2 1 2 1 4 1 8 1 16 1 32 1 64 1 128 1 256 1 512 1 1024
3 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176
4 24 576 13824 331776 7962624 191102976 1000000000 1000000000 1000000000 1000000000
5 120 14400 1728000 207360000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
6 720 518400 373248000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
7 5040 25401600 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
8 40320 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
9 362880 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
10 3628800 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
7 14.286% 2.041% 10.866% 2.839% 10.054% 3.425% 9.736% 3.857% 9.562% 4.208%
8 12.500% 1.559% 9.111% 2.176% 8.318% 2.633% 8.006% 2.985% 7.841% 3.262%
9 11.111% 1.221% 7.786% 1.712% 7.024% 2.091% 6.727% 2.377% 6.570% 2.604%
10 10.000% 0.998% 6.759% 1.389% 6.030% 1.695% 5.745% 1.935% 5.595% 2.125%
7 100.000% 14.286% 76.060% 19.875% 70.375% 23.974% 68.153% 27.001% 66.935% 29.459%
8 100.000% 12.473% 72.884% 17.410% 66.543% 21.066% 64.051% 23.881% 62.729% 26.098%
9 100.000% 10.988% 70.071% 15.406% 63.217% 18.821% 60.540% 21.396% 59.132% 23.435%
10 100.000% 9.983% 67.587% 13.889% 60.304% 16.955% 57.452% 19.346% 55.949% 21.252%
Number of cases to test equals = ((number of candidates)!)^(number of voters) Cases tested capped at 1 billion.
Table 2: Percentage of Cases where A is a Condorcet Winner (R/Q)
Voters 1 2 3 4 5 6 7 8 9 10
Candidates 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000%
2 50.000% 25.000% 50.000% 31.250% 50.000% 34.375% 50.000% 36.328% 50.000% 37.695%
3 33.333% 11.111% 31.481% 14.815% 31.019% 16.958% 30.833% 18.397% 30.734% 19.447%
4 25.000% 6.250% 22.222% 8.550% 21.528% 10.002% 21.248% 11.034% 21.099% 11.781%
5 20.000% 4.000% 16.800% 5.535% 16.001% 6.571% 15.694% 7.295% 15.526% 7.876%
6 16.667% 2.778% 13.296% 3.862% 12.474% 4.623% 12.148% 5.180% 11.977% 5.620%
Table 3: Percentage of Cases where a Condorcet Winner Exists (N*R/Q)
Voters 1 2 3 4 5 6 7 8 9 10
Candidates 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000%
2 3 100.000% 100.000% 50.000% 33.333% 100.000% 94.444% 62.500% 44.444% 100.000% 93.056% 68.750% 50.874% 100.000% 92.498% 72.656% 55.190% 100.000% 92.202% 75.391% 58.340%
4 100.000% 25.000% 88.889% 34.201% 86.111% 40.008% 84.992% 44.136% 84.395% 47.122%
5 100.000% 20.000% 84.000% 27.675% 80.005% 32.857% 78.469% 36.474% 77.632% 39.382%
6 100.000% 16.667% 79.778% 23.172% 74.845% 27.738% 72.888% 31.083% 71.863% 33.723%
and set X=0; when (N!)M > 1 billion, we set with repeat simulations. X=1,000,000,000. This way, the program will never test more than a billion samples. Tables from Sample Runs Although for a [N=10 candidates, The tables of results from Park’s voting M=10 voters] simulation one billion tri- simulator appear below. als represent an extremely small fraction of the total possible permutations, (exactly Table 1 reports the number of social 2.53x10-52), the results are still closely ac- preference profiles tested. When the numcurate and change in the thousandths place ber is less than a billion, all possible social
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ECONPress
Table 4: IRV Success Ratio (S/R) Percentage of Cases where a Condorcet Winner Exists, and IRV Elects the Condorcet Winner Candidates Voters 1 2 3 4 5 6 7 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 3 100.000% 100.000% 100.000% 98.438% 96.429% 94.359% 92.349% 4 100.000% 100.000% 100.000% 100.000% 99.729% 99.241% 98.560% 5 100.000% 100.000% 97.512% 95.758% 93.947% 92.078% 90.172% 6 100.000% 100.000% 100.000% 99.970% 99.768% 99.313% 98.668% 7 100.000% 100.000% 99.676% 98.360% 96.815% 95.143% 93.403% 8 100.000% 100.000% 99.275% 98.377% 97.563% 96.748% 95.890% 9 100.000% 100.000% 98.332% 96.598% 94.941% 93.309% 91.677% 10 100.000% 100.000% 99.893% 99.613% 99.031% 98.309% 97.493%
Graph 1: Probability of Existence of Condorcet Winner Given Odd Number of Voters
8 100.000% 100.000% 90.466% 97.839% 88.326% 97.883% 91.644% 94.986% 90.066% 96.594%
9 100.000% 100.000% 88.720% 97.019% 86.560% 96.989% 89.938% 94.099% 88.497% 95.621%
10 100.000% 100.000% 87.070% 96.168% 84.800% 96.030% 88.212% 93.001% 86.938% 94.627%
Table 5: Coombs Method Success Ratio (T/R) Percentage of Cases where a Condorcet Winner Exists, and the Coombs Method elects the Condorcet Winner Candidates Voters 1 2 3 4 5 6 7 8 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 3 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 4 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 5 100.000% 100.000% 100.000% 95.758% 97.755% 96.672% 95.820% 95.161% 6 100.000% 100.000% 100.000% 100.000% 99.862% 99.630% 99.374% 99.143% 7 100.000% 100.000% 98.054% 96.663% 95.709% 94.863% 93.999% 93.130% 8 100.000% 100.000% 100.000% 99.716% 99.450% 99.255% 99.060% 98.847% 9 100.000% 100.000% 98.698% 97.232% 95.775% 94.569% 93.613% 92.827% 10 100.000% 100.000% 99.429% 99.034% 98.565% 98.082% 97.661% 97.320%
N Candidates
120.000%
10 100.000% 100.000% 100.000% 100.000% 94.183% 98.779% 91.516% 98.305% 91.431% 96.765%
Percentage of Cases where a Condorcet Winner Exists, and Bidirectional Elimination Elects the Condorcet Winner Candidates Voters 1 2 3 4 5 6 7 8 9 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 3 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 4 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 5 100.000% 100.000% 100.000% 100.000% 99.979% 99.947% 99.905% 99.855% 99.798% 6 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 99.999% 7 100.000% 100.000% 100.000% 99.994% 99.968% 99.925% 99.865% 99.787% 99.689% 8 100.000% 100.000% 100.000% 100.000% 99.999% 99.998% 99.995% 99.993% 99.990% 9 100.000% 100.000% 100.000% 99.983% 99.942% 99.881% 99.804% 99.713% 99.609% 10 100.000% 100.000% 100.000% 100.000% 99.999% 99.995% 99.990% 99.981% 99.971%
10 100.000% 100.000% 100.000% 100.000% 99.731% 99.998% 99.577% 99.983% 99.485% 99.956%
Table 6: Bidirectional Elimination Success Ratio (U/R)
Table 4 tells us how often an existing Condorcet winner will be elected by IRV.
Table 2 divides the number of social preference profiles for which A is the ConTable 5 tells us how often an existing dorcet winner by the total number of social Condorcet winner will be elected by the preference profiles tested. The result is the Coombs Method. percentage of cases for which candidate A is the Condorcet winner. Table 6 tells us how often an existing Condorcet winner will be elected by Bid. Multiplying Table 2 by number of can- Elim. didates tells us how often a Condorcet winner exists. Analysis of Results
Graph 2: Probability of Existence of Condorcet Winner Given N Candidates and Odd M Voters
1
120.000%
100.000%
2
100.000%
80.000%
3
80.000%
1
60.000%
4
60.000%
3
40.000%
5
40.000%
5
20.000%
6
20.000%
7
0.000%
7
0.000%
1
3
5
7
9
M Voters
9 1
8
M Voters
2
3
4
9
Graph 3: Probability of Existence of Condorcet Winner Given Even Number of Voters
N Candidates 1
120.000%
9 100.000% 100.000% 100.000% 100.000% 94.637% 98.944% 92.286% 98.593% 92.118% 97.039%
preference profiles were tried.
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Voting with Bidirectional Elimination
5
6
7
8
9
10
N Candidates
Graph 4: Probability of Existence of Condorcet Winner Given N Candidates and Even M Voters 120.000%
100.000%
2
100.000%
80.000%
3
80.000%
2
60.000%
4
60.000%
4
40.000%
5
40.000%
6
20.000%
6
20.000%
8
0.000%
7
0.000%
2
4
6
8
10
M Voters
2
3
4
5
6
7
8
9
10
N Candidates
9
Table 3 reveals interesting trends relating to the existence of Condorcet winners for various combinations of N candidates and M voters.
10 1
8
Existence of a Condorcet Winner
M Voters
voters:
Observe the major difference between Tables 3A and 3B, or Graphs 1 and 3. For an odd number of voters, the probability of the existence of a Condorcet winner starts high and decreases with the addition of votIn the row with 2 voters, we observe ers. For an even number of voters, the same that the result (percentage of cases where a probability starts low and increases with the Condorcet winner exists) is equal to 1/N. addition of voters. This interesting result Probabilistically this makes sense: With two leaves room for further study; probabilistic voters, a Condorcet winner can exist only analysis could lead to a theorem that would when both voters rank the same candidate answer these questions: in first place; that is, when the second voter chooses the same candidate as the first voter, Why does p, the probability of the exwhich happens with a probability of 1/N. istence of a Condorcet winner given a specific even number of voters and arbitrary N For two candidates and an odd number candidates, increase with more voters? Why of voters, a Condorcet winner will always does q, the probability of the existence of exist because even splits or ties are not pos- a Condorcet winner given a specific odd sible. number of voters and arbitrary N candidates, decrease with more voters? Except for the dictatorship case when M=1, the addition of candidates lowers the Why does p follow a linear pattern as N probability of the existence of a Condorcet increases, while q bows steeply? winner. As M approaches infinity, what do p The results become quite interesting and q approach? when we split Table 3 into odd and even
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Table 3A: Percentage of Cases where a Condorcet Winner Exists (N*R/Q); Odd Voters Only
Voters 1 3 5 7 9
Candidates 1 100.000% 100.000% 100.000% 100.000% 100.000%
2 100.000% 100.000% 100.000% 100.000% 100.000%
3 100.000% 94.444% 93.056% 92.498% 92.202%
4 100.000% 88.889% 86.111% 84.992% 84.395%
5 100.000% 84.000% 80.005% 78.469% 77.632%
6 100.000% 79.778% 74.845% 72.888% 71.863%
7 100.000% 76.060% 70.375% 68.153% 66.935%
8 9 100.000% 100.000% 72.884% 70.071% 66.543% 63.217% 64.051% 60.540% 62.729% 59.132%
10 100.000% 67.587% 60.304% 57.452% 55.949%
Table 3B: Percentage of Cases where a Condorcet Winner Exists (N*R/Q); Even Voters Only
Voters 2 4 6 8 10
Candidates 1 100.000% 100.000% 100.000% 100.000% 100.000%
2 50.000% 62.500% 68.750% 72.656% 75.391%
3 33.333% 44.444% 50.874% 55.190% 58.340%
4 25.000% 34.201% 40.008% 44.136% 47.122%
Approaching Condorcet Efficiency
5 20.000% 27.675% 32.857% 36.474% 39.382%
6 16.667% 23.172% 27.738% 31.083% 33.723%
7 14.286% 19.875% 23.974% 27.001% 29.459%
8 12.473% 17.410% 21.066% 23.881% 26.098%
9 10.988% 15.406% 18.821% 21.396% 23.435%
10 9.983% 13.889% 16.955% 19.346% 21.252%
very close to meeting the Condorcet criterion and may in fact be a more just alterTables 4, 5, and 6 show success ratios native to Condorcet methods—depending for IRV, Coombs, and Bidirectional Elimi- on the designer’s emphasis on Condorcet nation. efficiency versus strategy proofness. While there are some possible arrangements of The success ratio is rather poor for voter preferences such that the mechanism Instant Runoff Voting. The column with will fail to elect the Condorcet winner, eight candidates already drops below 90% these cases comprise less than .6% of the (when M=5). total in a 10x10 matrix of candidates and voters. The success ratio is much improved with the Coombs Method, never once Bidirectional Elimination is probably dropping below 90% throughout the entire less susceptible to strategic voting, but this 10x10 matrix. It is more difficult to arrange should be proven rigorously. I say “probapreferences in such a way that A remains bly” because IRV and the Coombs Method the Condorcet winner, but is eliminated us- are each individually less susceptible than ing the Coombs Method. most Condorcet methods; it seems logical Bidirectional Elimination would be as The success ratio for Bidirectional Elim- well. This question leaves room for future ination is even stronger than the former, study and experimentation: Given most not once dropping below 99.4%. Through- Condorcet methods’ vulnerability to tactiout the 10x10 matrix, Bidirectional Elimi- cal voting, Bidirectional Elimination may nation comes extremely close to Condorcet ironically be more successful at electing efficiency. the Condorcet winner. I encourage future economists to rigorously examine the susceptibility of Bidirectional Elimination to strategic voting, and compare with that of 7. Conclusion Condorcet methods, as well as IRV and the Coombs Method individually. The system of Bidirectional Elimination, an algorithm using IRV and the Experimentation for Strategy-Proofness Coombs Method in various stages, comes
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Voting with Bidirectional Elimination
This study could be facilitated with a program similar to Jaehyun Park’s, that would work as follows. Given inputs for N candidates and M voters, the program would generate (N!)M permutations of true preferences for voters V1 through VM. A “case counter” would start at zero. For each possible permutation of true preferences, the following would happen (a nested for loop): (1) The voting algorithm in question would be performed on true preferences, and a winner W would be elected. (2) Holding all other voters’ preferences constant, the program would then generate all remaining (N!-1) false permutations of voter V1’s preferences, and perform the algorithm on each of these. If at least one set of false preferences existed for V1 such that reporting these false preferences would elect a candidate whom V1 preferred over W, one would be added to a “case counter,” and the program would move onto the next set of true preferences, skipping steps 3 and 4. (3) If nothing had been added to the case counter after trying all permutations of false preferences for V1, the program would repeat step 2 for V2…M. If at least one set of false preferences existed for any Vi such that reporting these false preferences would elect a candidate whom Vi preferred over W, one would be added to a “case counter,” and the program would move onto the next permutation of true preferences. (4) If after step 3 no set of false preferences were found for any voter Vi that could improve his outcome, the “case counter” would remain at its current value, and the next permutation of true preferences would be tested similarly, until all permutation of true preferences had been tested. (5) Dividing the final “case counter” value by (N!)M would output the percentage of cases, given N and M as inputs, for which the voting algorithm in question is susceptible to tactical voting. The program would need to be designed, as Park designed his, to be capable of random sampling in addition to testing all cases. As N and M grow, (N!)M grows astronomically—and given the number of
operations required to conduct this simulation, testing all cases could require vast amounts of time. A Monte Carlo method will be necessary. Bidirectional Elimination’s robustness should come as promising news to economists. The algorithm holds potential to significantly improve democratic processes. Moreover, this new simulation method for testing criteria can be applied to other voting methods, enabling further experimentation and eventual comprehensive, datadriven comparisons of voting methods.
R
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ECONPress Works Cited
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
Arrow, Kenneth (1963). Social Choice and Individual Values. New York: John Wiley & Sons Inc., Second Edition. Caplin, Andrew and Nalebuff, Barry (1988). “On 64% Majority Rule.” Econometrica, Vol. 56, No. 4. 787-814.
Brian Joel Feldman
Dennis, Gregory (2008). “Why I Prefer IRV to Condorcet.” Fairvote: The Center for Voting and Democracy.
Northeastern University
Gehrlein, William (2006). Condorcet’s Paradox. Theory and Decision Library. Series C: Game Theory, Mathematical Programming, and Operations Research. Springer.
With the ever expanding debate over economic wealth raging on around the world, many countries (especially developing ones) have gone under-microscope to see what stimulates growth and what hinders it, but are social scientists and economists looking at the right things? So much of their time is spent talking about the technologies, workforces, and governments of these countries that often the religious profiles and cultures of developing countries get shoved aside, tossed into footnotes, or are all together omitted from the conversation. With this in mind, the emerging field of economics of religion is under immense pressure to come forward and possibly answer the question on many peoples’ minds, “Why are these developing countries not growing?”
Gibbard, Allan (1973). “Manipulation of Voting Schemes: A General Result.” Econometrica, Vol. 41, 587-601.
Introduction
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Review of the Literature Numerous studies have been produced during the brief history of economics of religion, all of which have asked important questions about the impact of religion on the surrounding world. The most notable topics and papers that arose in my research for this original study include: Robin Grier’s “The Effect of Religion on Economic Development: A Cross National Study of 63 Former Colonies”1, Rachel M. Mc1
Robin Grier, “The Effect of Religion on
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Cleary’s “Religion and Economic Development: The advantage of moderation”2, and Marcus Noland’s “Religion, Culture, And Economic Performance”3. It was these articles that laid the framework for this study by setting forth a precedent on which to build. In her study on “a pooled sample of 63 ex-colonial states” Grier contributed significantly to the argument of religion as a significant factor in real GDP growth. In her argument, Grier opposes the hypotheses of Weber, most notably the ‘Protestant Ethic’ (which states that the industrial revolution boom and subsequent rise of capitalism in Europe can be attributed to the strong Protestant roots of the area) , by saying “my results show that religion is not the sole determinant of differential development and growth.” Although Grier aims to refute the points of Weber’s ‘Protestant Ethic,’ she clearly suggests the effect of religion on national wealth to be a significant one4. This is later reflected in her econometric analysis of her collected data. “The results support my hypothesis that the growth rate of ProtEconomic Development: A Cross National Study of 63 Former Colonies” Kyklos: International Review for Social Sciences, 50, (1997). Accessed Oct 2011. http://faculty-staff.ou.edu/G/ Robin.M.Grier-1/religion.pdf 2 Rachel M. McCleary, “Religion and Economic Development: The advantage of moderation”, Hoover Institution, Stanford University, 147 (March 28, 2008) Accessed Oct. 2011 http://www.hoover.org/publications/policyreview/article/5729 3 Marcus Noland, “RELIGION, CULTURE, AND ECONOMIC PERFORMANCE” (Working Paper), The Peterson Institute for International Economics Accessed Oct. 2011 http://www.iie.com/ publications/wp/03-8.pdf 4 Robin Grier, “The Effect of Religion on Economic Development: A Cross National Study of 63 Former Colonies” Kyklos: International Review for Social Sciences, 50, (1997). Accessed Oct 2011. http://faculty-staff.ou.edu/G/ Robin.M.Grier-1/religion.pdf
-24estantism is significantly correlated with real GDP growth, and that Protestantism is one of many determinants of development.”4 As she has implied with her arguments, and stated explicitly with her analysis, religion clearly has a significant impact on national economies. The information in Grier’s study has been adapted into this study in the form of the inclusion of specific religions, which Grier had proved relevant in her conversation specifically about Protestantism. The second study to be analyzed is McCleary’s study on religious moderation. One of the stronger topics the article discusses is the ‘two-way causation’5 of religion and development in which McCleary states “The more educated a person is, the more likely he is to turn to science for explanations of natural phenomena… [a]ccording to this view, the higher the levels of educational attainment, the less religious people will be… On the other hand, an increase in education will also spur participation in religious activities, because educated people tend to appreciate social networks and other forms of social capital.”5 This two-way causation, from the viewpoint of the study at hand, suggests that variable literacy would share in the effect of religion on per capita GDP possibly creating a bias. But more importantly what McCleary suggests is the possibility that the full effect of religion very well may not be felt until the population is educated, and although questions of causality arise, this increasing returns in wealth presents a situation of exponential returns to religion, possibly observing a sort of economies of scale in which wealth increases faster as more people capture their human capital potentials. 5 Rachel M. McCleary, “Religion and Economic Development: The advantage of moderation”, Hoover Institution, Stanford University, 147 (March 28, 2008) Accessed Oct. 2011 http://www.hoover.org/publications/policyreview/article/5729
ECONPress Another important point that McCleary makes is on religious terrorism, where she says “Religious terrorists feel a sense of alienation from the larger society... [Krueger] found that the deterioration in economic conditions over time is associated with the likelihood of educated men becoming terrorist attackers.”5 This spurs an intriguing argument into the effects of religious diversity and tolerance. Although the two are not perfectly correlated, it is presumed that the more diverse religious bodies are the less likely they are to breed religious extremism because of the increases in tolerance and decrease of the sense of ‘alienation’. This, according to McCleary’s article and Krueger’s quoted research would mean that less religiously diverse populations would hinder economic stability and growth. Ultimately, McCleary’s findings on religious diversity within populations suggest that my four religion ratio should have both a large and statistically significant impact on per capita GDP, as well as fitting into a larger context of religious variables that have significance. Finally, in the article most similar and relevant to this one, Noland states that there is “[a]bundant evidence affirm[ing] that religious belief affects a wide range of behavioral outcomes (Iannaccone 1998), and religious activity can affect economic performance at the level of the individual, group, or nation.” 6 As Noland goes through the observations of Weber, Greif, and Solow though, he goes into extensive detail about historical examples only to conclude by saying “What does this have to do with economic performance? … [T]hese cultural measures [can’t] directly explain economic performance, and indeed, they do not appear to be correlated with economic growth 6 Marcus Noland, “RELIGION, CULTURE, AND ECONOMIC PERFORMANCE” (Working Paper), The Peterson Institute for International Economics Accessed Oct. 2011 http://www.iie.com/ publications/wp/03-8.pdf
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
rates.”6 This allusion to his results suggests that religion’s impact is insignificant on his dependent variables (total factor productivity)6, and ultimately this suggests that religious variables might not be significant in studies of religious variables impact on national wealth. This of course is not reason enough to halt since there are a few major distinctions to be made between this study’s model and Noland’s, most notably the difference in dependent variables. It is clear that although economics of religion is still emerging, a great amount of research has been brought forth, but even more clear is the room for expansion and improvement on previously existing models. This is made obvious in the contradictory points of many articles in the field, such as McCleary’s and Roland’s articles that have been analyzed here.
Explanation of the Model For this model pertaining to per capita gross domestic product (GDP) numerous independent variables were chosen for several reasons. The variables nominated have been consider either because of research done by prominent economists in the field of economics of religion, or because they have been suggested as relevant through economic theory. These bases exclude the explanatory variables on religion, which are the focus of this study, because the correlations of these variables are currently only speculative; meaning these were not chosen from either previous studies or from theory since they are believed to be novel and therefore have not been explored directly through any previously existing works.
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have been included in the model because economic theory suggests a strong correlation between these variables and per capita GDP or because their omission may have led to a bias in the coefficients of other independent variables. Since there are various major religions in the world, an observed country’s religious identity has been captured with variables in a few different forms. The first form that the observed country’s religious makeup, or religious profile, was included as, was a direct measure of what religions made up the population of the observed country. Since there was little to no unbiased literature on the specific economic effect of one religion over another, numerous specific religions have been included in the model independently of one another as to test their specific effects on per capita GDP. These specified religions include: Christianity, Buddhism, Islam, Hinduism, Sikhism, Judaism, and Irreligion. The second form chosen to incorporate a country’s religious profile was a four religion ratio within an observed country. This measurement, adapted from the ‘four firm concentration ratio’ measurement common in industrial organization, serves as a quantification of the religious diversity within an observed country. Since it was observed that more oppressive governments often reduce religious tolerance, as well as the same corrupted regimes also hindering wealth, it was expected that as this measure of religious diversity will be negatively correlated with GDP per capita.
Finally, the last form that was chosen to incorporate religious profiles in to the The variables chosen to explain the model was the measurement of years of invariation in per capita GDP included the dependence that the observed country had real GDP growth rate, the inflation rate, experienced. This measurement was include the unemployment rate, urbanization, because it was theorized that a country that the literacy rate, and finally the industrial has been occupied by a foreign power most makeup of the country. These variables likely would have had its religious identity
Industrial Makeup (e.g. Service) -26 Industrial Makeup (e.g.
Service) Industrial Makeup (e.g. Urbanization Industrial Makeup (e.g. Industrial Makeup (e.g. Service) Industrial Makeup (e.g. Service) Service) Industrial Makeup Service) Urbanization
(e.g. Service)
Urbanization Urbanization Urbanization Literacy Rates Urbanization Urbanization Literacy Rates
Literacy Rates Literacy Rates Literacy Rates Literacy Rates Literacy Rates Percent of Population (by religion)(e.g. Islam) Percent of Population (by religion)(e.g. Islam) Percent of Population Percent of Population Percent of Population (by religion)(e.g. Islam) Percent of Population Percent of Population (by religion) (by religion)(e.g. Islam) (by religion)(e.g. Islam) (by religion)(e.g. Islam) Four religion ratio (FRR) (e.g. Islam) Four religion ratio (FRR) Four religion ratio
ݑ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫൌ
ܲܦܩௌ௩ ܲܦܩ௧௧
ECONPress
ܲܦܩௌ௩ ݑ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫൌ ܲܦܩ ܲܦܩ ௧௧ ௌ௩ ܲ݊݅ݐ݈ܽݑ ݅݊ ܷ ݏܽ݁ݎܣ ܾ݊ܽݎ ܲܦܩௌ௩ ݑ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ ൌ ܲܦܩ ௌ௩ ܷ݊݅ݐܽݖܾ݅݊ܽݎ ܴܽ݁ݐ ൌ ݈ܽ݅ݎݐݏݑ݀݊ܫ ݑ݁݇ܽܯ ൌ ܲܦܩ ܲܦܩ ௧௧ ݈ܽ݅ݎݐݏݑ݀݊ܫ ݑ݁݇ܽܯ ൌ ௌ௩ ݈ܶܽݐ ܲ݊݅ݐ݈ܽݑ ܲܦܩ ௧௧ ݑ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫൌ ܲܦܩ௧௧ ܲ݊݅ݐ݈ܽݑ ݅݊ ܷ ݏܽ݁ݎܣ ܾ݊ܽݎ ܲܦܩ௧௧ ܷ ݁ݐܴܽ ݊݅ݐܽݖܾ݅݊ܽݎൌ ݈ܶܽݐ ܲ݊݅ݐ݈ܽݑ ܲ ݏܽ݁ݎܣ ܾ݊ܽݎܷ ݊݅ ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ݅݊ ܷ ݏܽ݁ݎܣ ܾ݊ܽݎ ܷ ݁ݐܴܽ ݊݅ݐܽݖܾ݅݊ܽݎൌ ܲ ݏܽ݁ݎܣ ܾ݊ܽݎܷ ݊݅ ݊݅ݐ݈ܽݑ ݈ܶ݊݅ܽݐ ܲ݊݅ݐ݈ܽݑ ܷ݁ݐܴܽ݊݅ݐܽݖܾ݅݊ܽݎ ܴܽ݁ݐൌൌܲ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ܷ ݏܽ݁ݎܣ ܾ݊ܽݎ ܷ݊݅ݐܽݖܾ݅݊ܽݎ ܶ ݈ܽݐௗ ௧ ଵହǡ ௗ ܲ݊݅ݐ݈ܽݑ ܷ݊݅ݐܽݖܾ݅݊ܽݎ ݁ݐܴܽ ݕܿܽݎ݁ݐ݅ܮ ܴܽ݁ݐൌൌ ݈ܶܽݐ ܲ݊݅ݐ݈ܽݑ ݈ܶܽݐ ܲ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ௧௧ ܲ݊݅ݐ݈ܽݑௗ ௧ ଵହǡ ௗ ݁ݐܴܽ ݕܿܽݎ݁ݐ݅ܮൌ ܲ݊݅ݐ݈ܽݑ ௧௧ ܲ݊݅ݐ݈ܽݑ ௗ ௧ ଵହǡ ௗ ܲ݊݅ݐ݈ܽݑௗ ௧ ଵହǡ ௗ ݁ݐܴܽ ݕܿܽݎ݁ݐ݅ܮൌ ܲ݊݅ݐ݈ܽݑ ௗ ௧ ଵହǡ ௗ ܲ݊݅ݐ݈ܽݑ ݁ݐܴܽݕܿܽݎ݁ݐ݅ܮ ܴܽ݁ݐൌൌܲ݊݅ݐ݈ܽݑ ௧௧ ௗ ௧ ଵହǡ ௗ ݕܿܽݎ݁ݐ݅ܮ ܲ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ௧௧ ݁ݐܴܽ ݕܿܽݎ݁ݐ݅ܮൌ ூ௦ ܲ݊݅ݐ݈ܽݑ ௧௧ ܲ݁݊݅ݐ݈ܽݑܲ ݂ ݐ݊݁ܿݎ ܲ݊݅ݐ݈ܽݑ ூ௦ ൌ ௧௧ ܲ݊݅ݐ݈ܽݑ ௧௧ ܲ݊݅ݐ݈ܽݑ ூ௦ ܲ݁݊݅ݐ݈ܽݑܲ ݂ ݐ݊݁ܿݎூ௦ ൌ ܲ݊݅ݐ݈ܽݑ ௧௧ ܲ݊݅ݐ݈ܽݑ ூ௦ ܲ݁݊݅ݐ݈ܽݑܲ ݂ ݐ݊݁ܿݎூ௦ ൌ ܲ݊݅ݐ݈ܽݑூ௦ ܲ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ூ௦ ܲ݁݊݅ݐ݈ܽݑܲ ݂ ݐ݊݁ܿݎூ௦ ൌ ௧௧ ூ௦ ܲ݁ݐ݊݁ܿݎ ݊݅ݐ݈ܽݑ݂ܲ ܲ݊݅ݐ݈ܽݑூ௦ൌൌܲ݊݅ݐ݈ܽݑ ܲ݊݅ݐ݈ܽݑ ௧௧ ݂ܲ݁ ݐ݊݁ܿݎ ூ௦ ܲ݊݅ݐ݈ܽݑ௧௧ ݅ݐܴܽ ݈ܴ݊݅݃݅݁ ݎݑܨ ܲ݊݅ݐ݈ܽݑ ௧௧
ݎݑܨ ൌ ܴ݈݁݅݃݅݊ ͳݐݏǡ ʹ݊݀ǡܴܽ݅ݐ ͵݀ݎǡ Ͷ ݏ݈ܴ݊݅݃݅݁ ݐݏ݁݃ݎܽܮ ݄ݐሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ
Four religion ratio (FRR) (FRR) Four religion ratio (FRR) ൌ ͳݐݏǡ ʹ݊݀ǡ ͵݀ݎǡ Ͷ ݏ݈ܴ݊݅݃݅݁ ݐݏ݁݃ݎܽܮ ݄ݐሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ ݎݑܨ ܴ݈݁݅݃݅݊ ܴܽ݅ݐ Four religion ratio (FRR) Four religion ratio (FRR) ݅ݐܴܽ ݈ܴ݊݅݃݅݁ ݎݑܨ ݎݑܨ ܴ݈݁݅݃݅݊ ܴܽ݅ݐ ൌ ͳݐݏǡ ʹ݊݀ǡ ͵݀ݎǡ Ͷ ݏ݈ܴ݊݅݃݅݁ ݐݏ݁݃ݎܽܮ ݄ݐሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ ܴ݈݁݅݃݅݊ ܴܽ݅ݐ Years Independent ݎݑܨ ൌ ͳݐݏǡ ʹ݊݀ǡ ͵݀ݎǡ Ͷ ݏ݈ܴ݊݅݃݅݁ ݐݏ݁݃ݎܽܮ ݄ݐሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ Years Independent ൌ ͳݐݏǡ ʹ݊݀ǡ ͵݀ݎǡ Ͷݐݏ݁݃ݎܽܮ݄ݐ ܴ݈݁݅݃݅ݏ݊ ሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ Years Independent ܻ݂݁ܽ ݏݎ ݁ܿ݊݁݀݊݁݁݀݊ܫ ൌݐݏ݁݃ݎܽܮ ʹͲͳʹ െ ܻ݁ܽ ݂ ݎሺݏ݁݃ܽݐ݊݁ܿݎ݁ሻ ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ ൌ ͳݐݏǡ ʹ݊݀ǡ ͵݀ݎǡ Ͷ݄ݐ ܴ݈݁݅݃݅ݏ݊ ܻ݁ܽ ݁ܿ݊݁݀݊݁݁݀݊ܫ ݂ ݏݎൌ ʹͲͳʹ െ ܻ݁ܽ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ ݂ ݎ Years Independent Years Independent ܻ݁ܽ ݁ܿ݊݁݀݊݁݁݀݊ܫ ݂ ݏݎൌ ʹͲͳʹ െ ܻ݁ܽ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ ݂ ݎ Years Independent Years Independent ܻ݂݁ܽ ݏݎ Table 1. Formulae of calculated ݁ܿ݊݁݀݊݁݁݀݊ܫൌ ʹͲͳʹ െ ܻ݁ܽ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ ݂ ݎ variables. ܻ݁ܽ݁ܿ݊݁݀݊݁݁݀݊ܫ݂ ݏݎ ݁ܿ݊݁݀݊݁݁݀݊ܫൌൌʹͲͳʹ ʹͲͳʹെെܻ݁ܽݎ ܻ݂݁ܽݎ ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ݂ ݁ܿ݊݁݀݊݁݁݀݊ܫ ݀݁ݎ݈ܽܿ݁ܦ ܻ݂݁ܽ ݏݎ Since much of the data collected is directly related to the definition of the collector, an Since much of the data collected is directly related to the definition of the collector, an
stripped or suppressed in that time of oc- and estimates when available. important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, Since much of the data collected is directly related to the definition of the collector, an cupation, such as the 15 countries formerly important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, Since much of the data collected is directly related to the definition of the collector, an the Soviet Union in which religion As noted above, some of the variables Since much of the data collected is directly related to the definition of the collector, an part ofSince much of the data collected is directly related to the definition of the collector, an important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, unemployment rate, urbanization, literacy, and years of independence were all calculated using data was objectively abolished and replaced with specified in my model required calculation. unemployment rate, urbanization, literacy, and years of independence were all calculated using data important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, 7 atheism. Below is a table of formulas explaining each important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, unemployment rate, urbanization, literacy, and years of independence were all calculated using data collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been variable’s calculation (see table). collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been unemployment rate, urbanization, literacy, and years of independence were all calculated using data
unemployment rate, urbanization, literacy, and years of independence were all calculated using data unemployment rate, urbanization, literacy, and years of independence were all calculated using data collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been 8 8. This data was deemed “best” since it was based of data collected by the World Christian Encyclopedia Since much of the data collected is di. This data was deemed “best” since it was based of data collected by the World Christian Encyclopedia collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been Description of the Data rectly8 related to the definition of the colcollected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been based of data collected by the World Christian Encyclopedia the most thorough and large‐scale of any data source in the field since it had estimates for every lector,8. This data was deemed “best” since it was an important note is the sources of the most thorough and large‐scale of any data source in the field since it had estimates for every . This data was deemed “best” since it was based of data collected by the World Christian Encyclopedia 88 The data collected for this study conthe data. The industrial makeup, GDP real . This data was deemed “best” since it was based of data collected by the World Christian Encyclopedia . This data was deemed “best” since it was based of data collected by the World Christian Encyclopedia the most thorough and large‐scale of any data source in the field since it had estimates for every country in the world, which, even if estimated, makes for an even playing field on which to compare all country in the world, which, even if estimated, makes for an even playing field on which to compare all sists of a cross-sectional collection from growth rate, inflation rate, unemployment the most thorough and large‐scale of any data source in the field since it had estimates for every the most thorough and large‐scale of any data source in the field since it had estimates for every 188 of the 196 countries in the world. The rate, urbanization, literacy, and years of inthe most thorough and large‐scale of any data source in the field since it had estimates for every country in the world, which, even if estimated, makes for an even playing field on which to compare all religions, even in countries without proper census data. This was also important because the definition religions, even in countries without proper census data. This was also important because the definition omitted eight were left out due to either dependence were all calculated using data country in the world, which, even if estimated, makes for an even playing field on which to compare all country in the world, which, even if estimated, makes for an even playing field on which to compare all country in the world, which, even if estimated, makes for an even playing field on which to compare all unreliable gross domestic product (GDP) collected from the CIA World Factbook. religions, even in countries without proper census data. This was also important because the definition of irreligion differed from source to source particularly since different sources defined irreligion of irreligion differed from source to source particularly since different sources defined irreligion figures, missing religious profile estimates, The remainder of the data (religious profiles religions, even in countries without proper census data. This was also important because the definition religions, even in countries without proper census data. This was also important because the definition religions, even in countries without proper census data. This was also important because the definition orof irreligion differed from source to source particularly since different sources defined irreligion because of other anomalies in the data. and FRR) has been based of data collected differently, so using data from multiple sources would have been out of the question. differently, so using data from multiple sources would have been out of the question. All of the data, religious or economic, was by the World Christian Encyclopedia8. of irreligion differed from source to source particularly since different sources defined irreligion of irreligion differed from source to source particularly since different sources defined irreligion of irreligion differed from source to source particularly since different sources defined irreligion publishing This data was deemed “best” since it was the derived from the most recent differently, so using data from multiple sources would have been out of the question. 8 David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. 8 most thorough and large-scale of any data differently, so using data from multiple sources would have been out of the question. David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. differently, so using data from multiple sources would have been out of the question. differently, so using data from multiple sources would have been out of the question. source in the field since it had estimates for 8 David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. 7 ”Revelations from the Russian Archives: 8 David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. CAMPAIGNS”. Library of 88ANTI-RELIGIOUS David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. Congress. July 22, 2010. Web accessed October 8 David B. Barrett, et.al, “World Christian 2011. http://www.loc.gov/exhibits/archives/anti. Encyclopedia”. Oxford University Press. 2001.
html
Web Accessed 2011.
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
GDP/capita ($) Mean Standard Error
Unemployment (%) 15431.15 Mean 1572.54 Standard Error
Median 8400.00 Mode 2500.00 Standard Deviation 21272.98 Minimum 300.00 Maximum 179000.00 % of GDP Services Mean 56.43 Standard Error 1.13 Median 57.90 Mode 58.20 Standard Deviation 15.46 Minimum 3.80 Maximum 92.50 Literacy Mean 82.28 Standard Error 1.49 Median 91.80 Mode 99.00 Standard Deviation 20.08 Minimum 21.80 Maximum 100.00 Buddhism% Mean 3.25 Standard Error 0.95 Median 0.02 Mode 0.00 Standard Deviation 12.89 Minimum 0.00 Maximum 85.27 Judaism % Mean 0.50 Standard Error 0.39 Median 0.01 Mode 0.00 Standard Deviation 5.28 Minimum 0.00 Maximum 71.39 Years of independence Mean 127.82 Standard Error 18.81 Median 52.00 Mode 21.00 Standard Deviation 253.75 Minimum 0.00 Maximum 2000.00
Inflation rate (%) 14.00 Mean 1.20 Standard Error
Median 8.50 Mode 6.70 Standard Deviation 15.21 Minimum 0.50 Maximum 95.00 % of GDP Industry Mean 29.63 Standard Error 1.04 Median 26.60 Mode 24.40 Standard Deviation 14.25 Minimum 5.40 Maximum 93.90 Urbanization (% in cities) Mean 56.52 Standard Error 1.72 Median 58.00 Mode 52.00 Standard Deviation 23.17 Minimum 11.00 Maximum 100.00 Muslim % Mean 24.12 Standard Error 2.60 Median 3.47 Mode 0.00 Standard Deviation 35.14 Minimum 0.00 Maximum 99.09 Sikhism % Mean 0.04 Standard Error 0.01 Median 0.00 Mode 0.00 Standard Deviation 0.20 Minimum 0.00 Maximum 2.19 Four-firm concentration (of religions) Mean 92.00 Standard Error 0.995 Median 97.96 Mode 100.00 Standard Deviation 13.464 Minimum 32.01 Maximum 100.00
Table 2. Summary Statistics of the Data.
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4.88 0.34
Median 3.70 Mode 2.30 Standard Deviation 4.55 Minimum -2.40 Maximum 28.20 % of GDP Agriculture Mean 13.85 Standard Error 1.03 Median 9.50 Mode 2.40 Standard Deviation 13.99 Minimum 0.00 Maximum 76.90 GDP real growth rate (%) Mean 3.80 Standard Error 0.27 Median 3.85 Mode 4.20 Standard Deviation 3.70 Minimum -13.00 Maximum 16.30 Christian % Mean 56.16 Standard Error 2.81 Median 70.14 Mode None Standard Deviation 38.07 Minimum 0.10 Maximum 98.07 Hinduism % Mean 2.26 Standard Error 0.68 Median 0.01 Mode 0.00 Standard Deviation 9.26 Minimum 0.00 Maximum 72.82 Irreligion % Mean 5.88 Standard Error 0.66 Median 1.99 Mode None Standard Deviation 8.94 Minimum 0.00 Maximum 49.76
-28every country in the world, which, even if estimated, makes for an even playing field on which to compare all religions, even in countries without proper census data. This was also important because the definition of irreligion differed from source to source particularly since different sources defined irreligion differently, so using data from multiple sources would have been out of the question. Table 2 contains a summary of the data that has been collected and entered for all of the independent variables from this model testing the effect of religious profiles on per capita GDP. There are a few major clarifications that need to be made about the data specifically. The first difference is described by the discrepancy in average populations by religion from their counterparts that reflect the world’s population. According to adhearents.com, 33% of the world’s population is Christian9, whereas the data for this model shows the average country at 56.16%. This difference arises because the data collected was based on each country producing an unweighted percent of the population that does not take into account the relative size of the country, so for the purposes of this study, the Cook Islands have the same weight as United States or India.
ECONPress not a per country average like suggested in this study’s data. Similar observations can be made about the 56.16% Christian that was mentioned before. Some numbers from the above table have some very interesting implications. The variation in the dependent variable (GDP per capita) was expectedly great from prior knowledge of poor wealth distribution of society and was reflected as such in the standard deviation of $21,272, which compared to the mean of $15,431 was very large. The median of $8,400 per capita GDP has the most interesting implications though. The median suggests that the majority of countries around the world are struggling (portrayed by a median well less than the mean, suggesting that more that 50% of countries in the world live below the world average) and the mean statistic was so high likely because of some outliers skewing the data upwardly, suggesting that a few countries have abnormally high levels of wealth.
Another set of data worth discussing is the data retaining to the variable describing Sikhism in a population. This variable’s data has relatively low variation and therefore is expected to have little to no explanatory power over GDP per capita. This is important to keep in mind since it will like lead to the variables omission. The same The second clarification that needs to be can be said for Judaism since the mean is made refers to the interpretation of means only 0.5, meaning a sum of Jewish percentfrom the above data. Since smaller coun- ages is only 94 (since there are 188 observatries have larger impacts on this data set, tions) and 71.39 of that comes from one a variable with a mean above what is sepa- country hinting at relatively low variance, rately published should be interpreted dif- particularly if you were to exclude the outferently. This means that the $15,431 GDP lying observation. per capita mean should not be compared to the $9,216 published by the World Bank. This is because the World Bank’s publications are based on a per person average and Estimation of the Model 9 “Major Religions of the World Ranked by Number of Adherents”.Adherents.com. August 9, 2007. Web. Accessed Oct. 2011. http://www. adherents.com/Religions_By_Adherents.html
When initially estimating the model for religion’s impact on Gross Domestic Product (GDP) per capita, seventeen variables were incorporated including eight variables
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
that economic theory considers to be strong factors that account for GDP. The remaining nine variables have been included to account for the suspected impact that religion would have on the model. With all seventeen variables included, initial estimates of the model did not live up to expectations and immediately raised major questions about possible error. With all seventeen variables incorporated, the model was only able to account for 26.62% of the variation found in GDP per capita. This relatively low adjusted R2 did not meet expectations since variables were included that were expected to be strong indicators of GDP per capita. This hinted towards the possible existence of a specification error and more specifically that the wrong form function may have been chosen. This was supported by a graphical presentation of the data collected for GDP per capita, which portrays the dependent variable as exponentially growing from observation to observation, suggesting that the log-level form should be used.
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be accounted for by the other independent variables then we assume multicollinearity exists. This creates issues with the VIFs associated with the industrial makeup variables (the measurement of GDP from the agricultural, service, and industrial sectors of an observed countries economy), and the variables representing the Christian percentage of the population of a country and a Muslim percentage of the population of a country. The VIFs for these problem variables were calculated as 105.9, 150.73, 123.79, 20.1, and 15.97 respectively; all of which are substantially over the accepted rule of thumb amount.
To correct for multicollinearity in the model, the culprit variables were examined to determine the root causes of the multicollinearity and to establish which variables should be removed to correct the model. Since the VIFs on the industrial makeup of the observed country were so high, and the three make up an identity in which the three must equal 100% since the entirety of GDP is generated through either agriculture, service, or industry and therefore represent a Once the model was specified in the textbook example of multicollinearity. To log-level form, suggested to be the correct solve for this, the variables representing the form from the graphical depiction of GDP percent of GDP from service and percent per capita, some of the expectations that of GDP from industry were removed. This were previously unmet became fulfilled. left just the variable measuring the percent The new model accounted for 77.07% of of GDP from agriculture which, with the the variation of the dependent variable other two variables excluded, had a VIF of (now the natural log of GDP per capita just 2.24; a great improvement from 105.9. and therefore not comparable to the original model in which GDP per capita was the The correction for multicollinearity asdependent variable) but still showed signs sociated with the religious variables (specifiof some major econometric issues includ- cally the variables measuring the percentage ing multicollinearity (as suggested through of the population that is Christian in the variance inflation factors), irrelevant vari- observed country and the percentage of the ables, and heteroskedasticity (as suggested population that is Muslim in the observed through White’s test). country) was achieved in a slightly different method than that of the industrial makeup The first of the issues addressed, multi- solution since the multicollinearity was not collinearity, was identified by creating vari- as obvious as the identity observed in the ance inflation factors (VIFs) which can be industrial makeup variables. compared against the rule of thumb of 5. This means that if more than 80% of the To investigate which variables might variance of one independent variable can be causing the high VIFs for the Christian
-30and Muslim variables, separate regressions were run in which the Christian and Muslim variables were set as the dependent variables. The variables that most likely caused the multicollinearity, which would be represented by high t-statistics in both models, included the other specific religions measured (Sikhism, Judaism, Hinduism, Buddhism, and Irreligion) and the variable measuring the number of years independence the observed country had experienced. These variables, particularly Judaism, Sikhism, and Irreligion, were not statistically significant in measuring GDP per capita and did not contain a great amount of variation in the data collected, leading me to believe they were weak indicators of the observed GDPs and could be readily dropped from the model. Similarly, the t-statistic associated with the years of independence, like the t-statistics of Judaism and Sikhism, were relatively low meaning that we (as researchers) could not accept the variable to be statistically different from zero, leading me to believe that the best course of action would be to drop the variable. With the above corrections made, the VIFs for the variables Christian and Muslim both dropped below 10, but were unable to drop below 5 without omitting the other variable. In the best interest of the investigatory power of the model both variables were left in since the effect of specific religions would be best observed in the two largest religions in the world. This of course doesn’t completely rule out the possibility of multicollinearity, but because the VIFs were low enough, suggested that the effect that the multicollinearity has on the variable’s standard errors is low enough to proceed with the regression analysis and more specifically hypothesis testing.
ECONPress the White test to test for heteroskedasticity, to test for the problem, and indeed the results suggested that heteroskedasticity did exist. To fix this issue, the model was estimated again with robust standard errors. This new model using robust standard errors saw all of the standard errors increase, except for the standard errors of the four religion ratio variable and the Hinduism variable. Although the Hinduism variable remained at a level of insignificant impact on the dependent variable, the four religion ratio variable went from insignificant to significant with the inclusion of robust standard errors. Oppositely, the variable accounting for urbanization became insignificant with the increase in its standard error. This ultimately led me to the realization that urbanization was the variable creating heteroskedasticity in the model, and led me to omit the variable. Omitting the variable resulted in a correction of the results from the White test, as well as the same desired result that the robust standard errors generated with regard to four religion ratio.
Now down to nine independent variables, the model accounting for variation in the natural log of GDP per capita was significantly stronger as it was cleared of multicollinearity and heteroskedasticity following the above fixes. The last specification test that was run was the Ramsey’s RESET test to test for omitted variables. The results of the RESET test suggested that there was in fact an omitted variable, which is believed to be the omitted measure of religiosity for each country. This variable would affect each variable in the model differently, by giving weight to the religions on a country by country basis instead suggesting that all members of a religion practice with the same devotedness from country to country. The next issue that arose in the model Unfortunately this data is not available, and accounting for variations in the natural log admittedly leaves something to be desired of GDP per capita is in reference to hetero- for future expansion of the model as more skedasticity. The model, which now incor- countries conduct extensive censuses. porated eleven variables, was put through
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
Ultimately, the remaining variables (percent of GDP from agriculture, inflation rate, unemployment rate, and literacy rate) were all tested in multiple functional forms to determine the positive or negative impact that the change in form would have on the model. After testing each variable in their level form as well as the natural log form the model’s R2, RESET test f-statistic, VIF, and White test results were compared to determine the best form function on a variable by variable basis. The results of these comparisons suggested that the variables associated with inflation rate, unemployment rate and percent of GDP from agriculture would all be better served in the log-log form instead of the semi-log form. It is important to note here though that when minimizing the F-statistic of the RESET test, versions of the model exist that were able to get the F-statistic as low as 1.50 (compared to the 4.11 produced by the final model) but this required dropping the R2 down as low as .66 compared to the .82 that the final model produced, and accepted heteroskedasticity, which can be corrected by using Robust standard errors. The results for this alternative model which reduces the RESET f-statistic are in appendix 1.
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literacy (hypothesized to have a positive impact on GDP per capita) and GDP from agriculture (hypothesized to have a negative impact on GDP per capita) were both significant, while other key variables such as inflation rate and unemployment were not significantly different from zero. To focus on the main point of the research though, it was necessary to test the significance of the religious variables as a whole. This entailed running an F-test on the five variables describing religious statistics. This produced an F-statistic of only .7639 which at the degrees of freedom provided by the data produced a P-value of 0.42 on the f-statistic10. This is interpreted as meaning that the inclusion religious indicators in a model explaining GDP per capita has an insignificant impact on the model’s statistical significance.
Model Results See Table 3.
Conclusions
With the model finally correctly specified, the correlation coefficients, robust standard errors, and t-statistics were calculated for the remaining variables as well as the F-statistic for the model as a whole. This final model accounted for a large amount of variation in the dependent variable as represented by the R2 of 0.82; a very high R2 for cross sectional data. This coupled with the F-statistic of 99.37 (significant even at the 0.0001 level) gave good indication to the strong explanatory power of the model.
This study and subsequent regression analysis shone a light on a real world issue that haunts all political systems, not just that of developing nations. Although the regression proved that the religious profile of a country does not have a significant impact on the country’s observed Gross Domestic Product, the statistical significance of the four religion ratio and Christian population of an observed country could be interpreted as evidence for the
Some other highlights of the regression results include the statistically significant effect that the four religion ratio has in a negative direction, which verifies the assumptions that diversity would have a positive effect of GDP per capita. Similarly,
10 Calculated by using the “p-Value Calculator for an F-Test” on Dr. Daniel Soper’s website. -Dr. Daniel Soper “Statistics Calculators” Statistics Calculators Index, Web. 2006. http:// www.danielsoper.com/statcalc3/calc.aspx?id=7
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ECONPress Semi-Log Model
Semi-Log Model w/ (Robust Std Err)
Percent of GDP from Agriculture Unemployment Rate Inflation Rate Literacy Percent of Population Christian Percent of Population Muslim Percent of Population Buddhist Percent of Population Hindi Four Religion Ratio
-.7113~ -.0475~ -.0017~ .0183 .0074 .0049 .0081 .0038 -.0738
-.7113~ -.0475~ -.0017~ .0183 .0074 .0049 .0081 .0038 -.0738
R Square Adjusted R Square F-statisticistic ( 9, 143) *-Significant at Alpha of .05
0.8231 0.8120 73.94* ~ - Log-Log Est.
(.0469)* (.0504) (.0573) (.0035)* (.0029)* (.003) (.0046)* (.0056) (.0494)
(.0584)* (.0716) (.0593) (.0037)* (.0030)* (.0031) (.0049) (.0049) (.0342)*
0.8231 -99.37*
Table 3. Regression results.
argument supporting government policy to control religious profiles in its country. It is observed that some other coefficients, specifically the percent of GDP from the agricultural sector, have much stronger impacts on the model and would make for more productive policy topics with respect to many of the developing nations around the world. This study is admittedly limited due to the lack of data for so many countries around the world and in the future, studies within economics of religion could be better served by a model similar to this one if panel data could be collected. This would prove substantially stronger since it would be implied (since it is one observation over time) that similar methodologies of data collection would be used in panel data, whereas the consistency of religious data available today, like that used in this model, is not nearly as accurate as it could be.
R
Appendix 1 (opposite top). Linear Regression. Appendix 2 (opposite bottom). Final Regression.
An Econometric Inquiry into the Effect of Religious Profiles on National Wealth
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ECONPress Works Cited
Brown, Timothy T. “A Monetary Valuation of Individual Religious Behavior: The Case of Prayer” (Working Paper), The Association of Religion Data Archives, Accessed Nov. 2011 http://www.thearda.com/workingpapers/download/Valuing%20 Religious%20Behavior.pdf Central Intelligence Agency, “The World Factbook”, cia.gov, Accessed Oct. 2011 https://www.cia.gov/library/ publications/the-world-factbook/ Fitzgerald, Michael , “Satan, the great motivator” Boston.com (Boston, MA) Nov.15.2009 http://www. boston.com/bostonglobe/ideas/ articles/2009/11/15/the_curious_economic_effects_of_religion/?page=full Franck, Raphaël and Iannaccone Laurence R., “Why did religiosity decrease in the Western World during the twentieth century?” From the April 1, 2010 Seminar, Bar-Ilan University, April 1, 2010. Accessed Oct 2010 http:// www.biu.ac.il/soc/ec/seminar/ data/4_01_2010/franck%20iannaccone%20religiosity%20biu.pdf Grier, Robin , “The Effect of Religion on Economic Development: A Cross National Study of 63 Former Colonies” Kyklos: International Review for Social Sciences, 50, (1997). Accessed Oct 2011. http://faculty-staff.ou.edu/G/ Robin.M.Grier-1/religion.pdf Iannaccone, Laurence R. , “Introduction to the Economics of Religion” Journal of Economic Literature, XXXVI (September 1998). Accessed Oct 2011. http://www.scribd.com/ doc/62863336/Iannaccone-Introduction-to-the-Economics-of-Religion
McCleary, Rachel M. , “Religion and Economic Development: The advantage of moderation”, Hoover Institution, Stanford University, 147 (March 28, 2008) Accessed Oct. 2011 http:// www.hoover.org/publications/ policy-review/article/5729 Noland, Marcus , “RELIGION, CULTURE, AND ECONOMIC PERFORMANCE” (Working Paper), The Peterson Institute for International Economics Accessed Oct. 2011 http://www. iie.com/publications/wp/03-8.pdf World Christian Database Vol.2 , “Excel Datafile” worldmapper.org, http://www.worldmapper.org/ data/nomap/religion_data.xls
Equity Volatility across Industries from IPO Day
Equity Volatility across Industries from IPO Day Andrew Nielsen Lewis Princeton University
Abstract While the volatility of any given stock changes over time, certain identifiable factors consistently contribute to increased stock price volatility. For example, stocks are typically more volatile immediately following their IPOs than they are after years of active trading. In addition, industries that are characterized by increased uncertainty typically include companies with more volatile stock prices. This study examines the trends of intraday stock volatility by industry over time from IPO date and determines which industries have the most volatile IPOs, which industries’ stocks take the longest amount of time to stabilize after IPO day, and which industries’ stocks stabilize the most over time. It uses a nonlinear model to estimate the trends of stock price volatility in various industries as well as the overall market.1
Section I: Introduction
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IPOs than they are after years of active trading. In addition, industries that are characterized by increased uncertainty typically include companies with more volatile stock prices. This study examines the trends of intraday stock volatility by industry over time from IPO date and determines which industries have the most volatile IPOs, which industries’ stocks take the longest amount of time to stabilize after IPO day, and which industries’ stocks stabilize the most over time. Although many studies have investigated returns following IPO date or general trends in equity volatility, they have not focused on modeling trends in volatility relative to IPO dates. The study of de facto IPO returns is more appealing in that it has quick and obvious applications – after discovering a way to predict abnormal stock returns around an IPO, traders or hedge fund managers can quickly apply their new knowledge to realize excess gains. The findings of this study regarding volatility trends from IPO, however, can also be used by investors to profit. The ability to predict volatility can lend insight into forecasting option prices by using the Black-Scholes options pricing model; being able to predict with some certainty the change in a stock’s volatility from its IPO day will also allow a trader to predict with more accuracy the motion of related option prices. With information about volatility trends in an industry, an investor can more accurately value a stock’s options.
While the volatility of any given stock changes over time, certain identifiable facAdditionally, the findings of this study tors consistently contribute to increased can help companies to make better choices volatility. For example, stocks are typically regarding their own IPOs – having an unmore volatile immediately following their derstanding of typical industry volatility will help to guide decisions on whether to go public and how to price IPOs. This 1 Acknowledgements: I greatly appreciate will not only benefit the few who stand to the guidance provided to me by Professor Yuliy make extraordinary profits from such busiSannikov (Princeton University Department ness deals but the entire stock market and of Economics), Wei Cui (Princeton University economy as the IPO market becomes more Department of Economics), and Oscar Torresefficient. The findings can also be used for Reyna (Princeton University Data and Statistical risk management purposes, in behavioral Services) during this study.
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ECONPress
finance studies, and other industry-based equity returns in â&#x20AC;&#x153;Stock Returns and Volastock studies. tilityâ&#x20AC;? (1990, p. 211). This study differs in that it only analyzes and models trends in price volatility instead of returns. Section II: Literature Review
Section III: Data
Existing literature has not focused on Data for all stocks used in this study trends in volatility from IPO date or indus- were retrieved from the Center for Research try-specific volatility trends. in Security Prices (CRSP) daily stock database via Wharton Research Data Services. Differences between volatility levels For each stock, all available trading data and IPO behavior across industries are was retrieved during the period ranging recognized phenomena. In â&#x20AC;&#x153;Stock volatil- from January 1, 1925 through December ity in the new millennium: how wacky is 31, 2009; data after December 31, 2009 Nasdaq?,â&#x20AC;? G. William Schwert notes that was not comprehensive or fully accurate technology stocks and recent IPO stocks in the CRSP database. The decision to use exhibit much higher trading volatility than trading data from before 2010 should not other stocks (2002, p. 3-4). A model con- have a significant impact on results. structed by Michelle Lowry, Micah Officer, and Schwert shows that technology stocks First, the stocks that were components see returns that are different from other of the S&P 500 on December 31, 2009 stocks on a statistically significant level were studied in aggregate to create a broad both including and excluding the technolo- market benchmark. Then a series of Dow gy bubble of the late 1990s and early 2000s Jones sector indexes (which were not lim(2010, p. 438). ited to S&P 500 stocks) were used to represent the ten sectors examined in this study. Existing literature is more concerned The components of these indexes were with IPO returns or IPO return volatility â&#x20AC;&#x201C; provided by MarketWatch.2 An inaccurate which can help to predict immediate returns intraday trading range assigned to one obfrom IPO investments â&#x20AC;&#x201C; than with absolute servation (IdeaRC on December 31, 2009) stock price volatility near IPO. Investiga- was removed from the Consumer Services tions of volatility trends focus more on pe- industry data set prior to regression. riod-specific trends or other general trends. For example, the Schwert 2002 study foFor each stock, the data retrieved from cuses on volatility trends in the NASDAQ CRSP to complete the study included comduring the dot-com period. In another ex- pany name, CRSP-assigned PERMNO, ample, Schwertâ&#x20AC;&#x2122;s â&#x20AC;&#x153;Why Does Stock Market trading date, dividend amount, daily low Volatility Change Over Time?â&#x20AC;? deals only price, daily high price, and daily closing with trends in overall market volatility price. All price values were automatically throughout modern market history (1989, adjusted by CRSP to reflect the impact of p. 1120). David Simon investigates market stock splits on real changes to equity value. volatility trends around the dot-com bub- A database error caused some daily closing ble period in â&#x20AC;&#x153;The Nasdaq Volatility Index prices to be returned as negative numbers; During and After the Bubble.â&#x20AC;? Just as with as a result, all negative closing prices were IPO inquiries and industry-based investigations, much volatility trend research relates 2 Components used for each index can to predicting security returns. For example, be found at http://bigcharts.marketwatch.com/ Baillie and DeGennaro search for (but do industry/bigcharts-com/default.asp (originally not find) correlation between volatility and accessed March 22, 2011)
regression  of   values  against  time  from  IPO  in  order  to  estimate  volatility  tr was  meant  to  reflect  the  real  effects  of  dividend  payments  on  shareholder  value.  Fo Equity  Volatility  across  Industries  from  IPO  Day  each  industry.  Equity Volatility across Industries from IPO Day -37each  industry.  issued  a  one-Ââ&#x20AC;?time  special  dividend  of  $3.00  on  November  15,  2004;  because  the  pri Equity  Volatility  across  Industries  from  IPO  Day  was  meant  to  reflect  the  real  effects  of  dividend  payments  on  shareholder  value.  For  example,  Micros  Methodology  Subsection  I:  Calculating  with  dividend  payouts  do  not  affect  shareholder  value,  3  was  added  to  the  closing  p replaced with their absolute values before Calculating  Methodology  Subsection  I:  Calculating  issued  a  one-Ââ&#x20AC;?time  special  dividend  of  $3.00  on  November  15,  2004;  because  the  price  drops  associate continuing. Since CRSP cannot automatifrom  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediatel The   calculation  process  was  run  individually  us cally adjust prices to reflect the impact of The calculation process was run inhigh  prices  for  all  Microsoft  observations  on  or  after  the  day  the  dividend  was  issue with  dividend  payouts  do  not  affect  shareholder  value,  3  was  added  to  the  closing  prices,  low  prices,  a dividend payments, a cumulative dividend across  Industries  from  IPO  Day  dividually using data sets that include the The   calculation  process  was  run  individually  using  data  sets  that  include  th Equity  Volatility  equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  on Equity  Volatility  across  Industries  from  IPO  Day  payment variableto  a  perfect  adjustment  for  dividend  payouts.  Since  no  stocks  paid  out  dividends  wi was generated and added trading history for the S&P 500 and each 500  and  each  of  the  ten  selected  industry  groups to all price variables; this adjustment was of the ten selected industry groups providhigh  prices  for  all  Microsoft  observations  on  or  after  the  day  the  dividend  was  issued.  This  does  not  le 500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch Equity  Volatility  across  Industries  from  IPO  Day  variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  d Equity  Volatility  across  Industries  from  IPO  Day  meant to reflect the real effects of dividend ed by MarketWatch. For all examined data from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  imme days  of  trading,  however,  no  observations  used  in  regression  were  affected;  as  a  res a  day  counter  variable  was  generated  for  each  o from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediatel payments on shareholder value. For ex- sets, a day counter variable was generated to  a  perfect  adjustment  for  dividend  payouts.  Since  no  stocks  paid  out  dividends  within  their  first  thirt a  day  counter  variable  was  generated  for  each  observation  to  mark  the  num ample, Microsoft issuedindustry  possible.  a one-time special for each observation to mark the number from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediately  following equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented did  not  affect  results.  equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  on from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediately  followin dividend of $3.00 on November 15, 2004; of days that had passed from IPO. On a days  of  trading,  however,  no  observations  used  in  regression  were  affected;  as  a  result,  this  inaccurac because the price drops associated with stockâ&#x20AC;&#x2122;s IPO day, the variable equals 1. On equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  cre variable  makes  comparison  of  the  chronologically  scattered  IPO  period dividend payouts do not affect shareholder the day immediately following IPO, the variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  d Actual  volatility  ( )  was  calculated  for  every  observation  using  int equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  cr did  not  affect  results.  The  data  is  subject  to  some  level  of  selection  bias.  All  of  the  companies  chosen  wer value, 3 was added to the closing prices, low variable equals 2. For each additional day variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  different  st prices, and high prices for allindustry  possible.  Microsoft ob- from IPO, the variable is incremented Hby industry  possible.  ),  low  price squared  relative  to  closing  price.  high  price  (P variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  different  servations on or December  31,  2009;  as  a  result,  companies  taken  private  for  reasons  including  bank after the day the dividend one. The creation of this variable makes The  data  is  subject  to  some  level  of  selection  bias.  All  of  the  companies  chosen  were  still  trading  as  of  was issued. This does not lead to a perfect comparison of the chronologically scattered industry  possible.  were  used  to  calculate  volatility   for  each  trading  day:  adjustment forindustry  possible.  dividend payouts. Since no IPO periods for different stocks in each inActual  volatility  ( )  was  calculated  for  every  observation  using  acquisition  may  be  underrepresented.  Furthermore,  the  accuracy  of  the  S&P  500  as Actual  volatility  ( )  was  calculated  for  every  observation  using  int stocks paid out dividends within their first dustry possible. December  31,  2009;  as  a  result,  companies  taken  private  for  reasons  including  bankruptcy  and  thirty days ofActual  volatility  ( )  was  calculated  for  every  observation  using  intraday  trad trading, however, no observasquared  relative  to  closing  price.  high  price  (P ' " ( H),  low benchmark  is  not  perfect  because  the  S&P  500  includes  only  large  companies  that  h squared  relative  to  closing  price.  high  price  (P H),  low  price Actual  volatility  ( )  was  calculated  for  every  observation  using  intraday  tra   were affected; as a tions used in regression Actual volatility ( )$was! calculated for acquisition  may  be  underrepresented.  Furthermore,  the  accuracy  of  the  S&P  500  as  a  true  market  result, this inaccuracy did not affect results. every observation using the stockâ&#x20AC;&#x2122;s intraday squared  relative  to  closing  price.  high  price  (P were  used  to  calculate  volatility   for  each  trading  day:  H),  low  price  (PL),  and  c consistent  profitability.  If  stock  resilience  or  company  sizes  are  correlated  with  IPO  were  used  to  calculate  volatility   for  each  trading  day:  squared  relative  to  closing  price.  high  price  (P trading range squared relative to closing L),  and H),  low  price  (P Equity  Volatility  across  Industries  from  IPO  Day  benchmark  is  not  perfect  because  the  S&P  500  includes  only  large  companies  that  have  maintained  The dataEquity  Volatility  is subject Microsoft  Corporation  had  its  initial  public  offering  on  March  13,  1986.  On  it to some level of se- price. Each observationâ&#x20AC;&#x2122;s high price (PH), across  Industries  from  IPO  Day  trends,  the  results  of  this  study  may  be  skewed  as  a  result.  lection bias. were  used  to  calculate  volatility   for  each  trading  day:  All of the companies chosen low price (PL), and closing price' (P ) were were  used  to  calculate  volatility   for  each  trading  day:  C " ( ' " (! consistent  profitability.  If  stock  resilience  or  company  sizes  are  correlated  with  IPO  period  volatility    were still trading as of December 31, 2009; used to calculate volatility for each trad   adjusted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  ad
$ !$ from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  va as a result, companies taken private for rea- ing day: from  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediately  following ' ! " ( trends,  the  results  of  this  study  may  be  skewed  as  a  result.  sons including bankruptcy and acquisition Â
$$ ' ! "  ( Section  IV:  Methodology  equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this   $28.00.   may be underrepresented. Furthermore, the (1) Microsoft  Corporation  had  its  initial  public  offering  on  March  13,  1986. equals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  crea Microsoft  Corporation  had  its  initial  public  offering  on  March  13,  1986.  On  it accuracy of the S&P 500 as a true market variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each benchmark is not perfect because the S&P Microsoft Corporation had its initial Section  IV:  Methodology  Microsoft  Corporation  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  o adjusted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  ' ( variable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  different  sto adjusted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  ad 500 includes only large on $ March 13, 1986. its Microsoft  Corporation  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  $ On   companies that public offering
have maintained consistent profitability. If first day of trading, its adjusted low price industry  possible.  adjusted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  clos $28.00.   stock resilience or company sizes are cor- was $25.50, its adjusted high price was industry  possible.  $28.00.   adjusted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  clo values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  th related with IPO period volatility trends, $29.25, and its adjusted closing price was The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation  of Â
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Volatility  to  a  perfect  adjustment  for  dividend  payouts.  Since  no  stocks  paid  out  dividends  within  their  first  thirty  Equity  Volatility  across  Industries  from  IPO  Day  acquisition  may  be  underrepresented.  Furthermore,  the  accuracy  of  the  S&P  500  as  a  true  market   values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  day  in   (8)   regression  of  did  not  affect  results.  trends,  the  results  of  this  study  may  be  skewed  as  a  result.  Equity Volatility across Industries from IPO Day ! " -38-39ECONPress The  results  of  the  regressions  for  each  industry  and  the  market  benchmark  are  as  follows  with  The  results  of  the  regressions  for  each  industry  and  the  market  benchmark  are  as  follows  with  The  results  of  the  regressions  for  each  industry  and  the  market  benchmark  are  as  follows  with Â
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,  where  N  defines  the  number  of  periods  sampled,  is:  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  days  of  trading,  however,  no  observations  used  in  regression  were  affected;  as  a  result,  this  inaccuracy  benchmark  is  not  perfect  because  the  S&P  500  includes  only  large  companies  that  have  maintained  each  industry.  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chosen  to  capture  corresponding  sample  sizes  and  t-Ââ&#x20AC;?statistics  in  parentheses:  corresponding  sample  sizes  and  t-Ââ&#x20AC;?statistics  in  parentheses:  corresponding  sample  sizes  and  t-Ââ&#x20AC;? statistics  in  parentheses:  The  data  is  subject  to  some  level  of  selection  bias.  All  of  the  companies  chosen  were  still  trading  a corresponding  sample  sizes  and  t-Ââ&#x20AC;? statistics  in  parentheses:  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  no The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  uity  Volatility  adid  not  affect  results.  cross  Industries  from  IPO  Day  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  Section  IV:  Methodology  consistent  profitability.  If  stock  resilience  or  company  sizes  are  correlated  with  IPO  period  volatility  Methodology  Subsection  I:  Calculating   The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  After calculating values for every day ' # the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? (3) Â
$$ & & IPO  events  on  the  data.  The  ' # ( (    Sector Methodology  Subsection  I:  Calculating  (3) from IPO in(3)  each industry (represented usDecember  31,  2009;  as  a  result,  companies  taken  private  for  reasons  including  bankruptcy  and  regressions  run  to  estimate  all  three   values  for  each  index  use ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  2  2  2   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  Sector  Sector  Sector  trends,  the  results  of  this  study  may  be  skewed  as  a  result.        Sector        R2  R R R ing a variable), a500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  nonlinear regression was m  IPO.  On  IPO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  variable  The  data  is  subject  to  some  level  of  selection  bias.  All  of  the  companies  chosen  were  still  trading  as  of  (Baseline Volatility) (IPO-Driven (Stabilization The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  For the purposes of thisregressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  study, N is used to model as a function of The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation  of  day from  acquisition  may  be  underrepresented.  Furthermore,  the  accuracy  of  the  S&P  500  as  a  true  market values  for   and  :   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  s  study,  N  is  equal  to  1  because  volatility  is  measured  on  a  day-Ââ&#x20AC;?by-Ââ&#x20AC;?day  basis:  (Baseline  Volatility)  (IPO-Ââ&#x20AC;?Driven  (Stabilization  Rate)  (Baseline  Volatility)  (IPO-Ââ&#x20AC;?Driven  (Stabilization  Rate)  (Baseline  Volatility)  (IPO-Ââ&#x20AC;?Driven  (Stabilization  Rate)  The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  equal to 1 because volatility is measured on IPO. No values besides one value for each (Baseline  Volatility)  (IPO-Ââ&#x20AC;?Driven  (Stabilization  Rate)  ss  Industries  from  IPO  Day  his  study,  N  is  equal  to  1  because  volatility  is  measured  on  a  day-Ââ&#x20AC;?by-Ââ&#x20AC;?day  basis:  a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  uals  2.  For  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this  Volatility) Rate) Equity  Volatility  across  Industries  from  IPO  Day  values  for   and  :  a day-by-day basis: value were required to run the reDecember  31,  2009;  as  a  result,  companies  taken  private  for  reasons  including  bankruptcy  and  500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  Industries  from  IPO  Day  values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  the  nonlinear  Section  IV:  Methodology  benchmark  is  not  perfect  because  the  S&P  500  includes  only  large  companies  that  have  maintaine ss  Industries  from  IPO  Day  Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  gression. To investigate the IPO period inapproaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  Equity  Volatility  across  Industries  from  IPO  Day  Volatility)  Volatility)  Volatility)  500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  Volatility)   (8.81) Equity  Volatility  a cross  Industries  from  IPO  Day  iable  makes  comparison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each  .9929 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 isolation, observations for any day past 30 6  ! " Equity  Volatility  a cross  Industries  from  IPO  Day  acquisition  may  be  underrepresented.  Furthermore,  the  accuracy  of  the  S&P  500  as  a  true  market  term  merely  represents  deviation  with  respect  to  an  average,  intraday  trading  range  Equity  Volatility  a cross  Industries  from  IPO  Day  ' # ( $ a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed Â
$$ & & # (   (4)  regression  of   values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  day  in   Industries  from  IPO  Day  consistent  profitability.  If  stock  resilience  or  company  sizes  are  correlated  with  IPO  period  volatilit ' # ( $%' Consumer 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 impact  of  significant  non-Ââ&#x20AC;? IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? dServices ay  period  was  chosen  to  capture  across  Industries  from  IPO  Day  %' (4)  from approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  were dropped the a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  regression in order Equity  Volatility  Basic  Materials  (548) Â
Basic  Materials  (548)   Basic  Materials  (548)  (8)  (798)  # ( (4)  1.496436  (7.88)  PO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  variable  ! "Basic  Materials  (548)  0.0303853  (47.53)  0.0632364  (27.65)  1.496436  (7.88)  .9675  .9675  0.0303853  (47.53)  0.0632364  (27.65)  1.496436  (7.88)  .9675  0.0303853  (47.53)  0.0632364  (27.65)  .9675  0.0303853  (47.53)  0.0632364  (27.65)  1.496436  (7.88)  erm  merely  represents  deviation  with  respect  to  an  average,  intraday  trading  range  to minimize the impact of significantdnonimpact  of  significant  non-Ââ&#x20AC;? IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? ay  period  was  chosen  to  capture  ustry  possible.  Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) related  volatility  and  1.769266 (11.59) .9860 The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation  of   This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? oss  Industries  from  IPO  Day  benchmark  is  not  perfect  because  the  S&P  500  includes  only  large  companies  that  have  maintained  age  of  closing  price  was  used  instead  to  normalize  differently  priced  stocks.  Since  the  each  industry.  trends,  the  results  of  this  study  may  be  skewed  as  a  result.  Equity  Volatility  across  Industries  from  IPO  Day   term  merely  represents  deviation  with  respect  to  an  average,  intraday  trading  range  Since the impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? term merely repre- IPO events on the regression results; the 6  (25.97) The  regression  estimates  average  industry  volatility  ( Healthcare (821) 0.0575546 (25.57) 0.2345721 2.959527 (5.58) .9619)  as  a  func the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? dConsumer  Goods  (653)  ay  period  was  chosen  to  capture  day  period  was  chosen  to  capture  tional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this  0.0390784  (31.01)  0.1378587  (30.74)  1.463953  (8.81)  .9929  .9929  Consumer  Goods  (653)  0.0390784  (31.01)  0.1378587  (30.74)  1.463953  (8.81)  .9929  Consumer  Goods  (653)  0.0390784  (31.01)  0.1378587  (30.74)  1.463953  (8.81)  .9929  rm  merely  represents  deviation  with  respect  to  an  average,  intraday  trading  range  Consumer  Goods  (653)  0.0390784  (31.01)  0.1378587  (30.74)  1.463953  (8.81)  age  of  closing  price  was  used  instead  to  normalize  differently  priced  stocks.  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  sents deviation the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? with respect to an average, 30-day period was chosen to capture the 6  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and   I PO  events  on  the  data.  The  Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  the  nonlinear  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  7  7  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  consistent  profitability.  If  stock  resilience  or  company  sizes  are  correlated  with  IPO  period  volatility  intraday trading range squared as a percentfull effect of the IPO event while minimizsquared  as  a  percentage  of  closing  price  was  used  instead  to  normalize  differently  priced  stocks.  tual  volatility  ( )  was  calculated  for  every  observation  using  intraday  trading  range   1.936521 IPO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  variable  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  t Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) (5.20) .9379 regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The    events the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The  ison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each  to norConsumer  Services  (798)  0.0598604  (24.60)  0.4793099  (47.82)  3.806189  (8.87)  .9884  Consumer  Services  (798)  0.0598604  (24.60)  0.4793099  (47.82)  3.806189  (8.87)  .9884  Consumer  Services  (798)  0.0598604  (24.60)  0.4793099  (47.82)  3.806189  (8.87)  .9884   0.0598604  (24.60)  Methodology  Subsection  I:  Calculating  used Equity  Volatility  across  Industries impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  ge  of  closing  price  was  used  instead  to  normalize  differently  priced  stocks.  age of closing price was instead ing the effects of non-IPO on the Consumer  Services  (798)  0.4793099  (47.82)  3.806189  (8.87)  .9884  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The   (5) Â
Equity  Volatility  a cross  Industries  from  IPO  Day  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  Section  IV:  Methodology  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142  captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility;  regression  of   values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  day  in  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  trends,  the  results  of  this  study  may  be  skewed  as  a  result.  malize differently priced stocks. data. HThe regressions run to estimate all across  Industries  from  IPO  Day  ),  low  price  (P uared  relative  to  closing  price.  high  price  (P L),  and  closing  price  (PC)  dditional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this   since  the  denominator  of  the  second  te is  estimated  by   Equity  Volatility  (5) Â
regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Technology (890) 0.1173751 (26.78) 0.7072644 2.997637 (8.57) .9837 values  for   and  :  (40.15) regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  index used the folthree values for each Financials  (2058)  0.0395426  (69.25)  0.0907731  (42.87)  1.769266  (11.59)  .9860  .9860  Financials  (2058)  0.0395426  (69.25)  0.0907731  (42.87)  1.769266  (11.59)  .9860  Financials  (2058)  0.0395426  (69.25)  0.0907731  (42.87)  1.769266  (11.59)  .9860  the  full  effect  of  the  IPO  event  while  minimizing  the  eff y  across  Industries  from  IPO  Day  Financials  (2058)  0.0395426  (69.25)  0.0907731  (42.87)  1.769266  (11.59)  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known   captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility;  model each  industry.   valuesThe  (5)  Â
values  for   and  :  Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  impact  of  significant  non-Ââ&#x20AC;?IPO  eve  calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  lowing given known for and  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? d ay  period  was  chosen  to  capture  re  used  to  calculate  volatility   for  each  trading  day:   and  :  Â
parison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each  he  calculated  percentage  was  not  taken.  The  final   calculation  measures  variance  following  IPO,  volatility  decays  as  the  ! "  term  grow values  for   and  :  : (5)  (5) values  for  The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chosen  to  capture  Healthcare  (821)  0.0575546  (25.57)  0.2345721  (25.97)  2.959527  (5.58)  .9619  .9619  Healthcare  (821)  0.0575546  (25.57)  0.2345721  (25.97)  2.959527  (5.58)  .9619  Healthcare  (821)  0.0575546  (25.57)  0.2345721  (25.97)  2.959527  (5.58)  .9619  (143) Section  IV:  Methodology  regressions  run  to  estimate  all  three   values  for  each  Healthcare  (821)  0.0575546  (25.57)  0.2345721  (25.97)  2.959527  (5.58)  values  for   and  :  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1. Â
 (8)   The   calculated  for  every  observation  using  intraday  trading  range  e  calculated  percentage  was  not  taken.  The  final   calculation  measures  variance  the  full  effect  of  the  IPO  event  wh 500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   IPO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  variable  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  ! " the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? I PO  events  on  the  data.  The  Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794   (8)  values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  the  nonlinear  Methodology  Subsection  I:  Calculating  square  root of the calculated' per (8) deviation:  The approaches  0.  The  model  effectively  represents  the  significant  im Equity  Volatility  a cross  Industries  from  IPO  Day  The  square  root  of  the  calculated  percentage  was  not  taken.  The  final   calculation  measures  variance  ! " the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The  ! " ( Industrials  (1141)  0.0412802  (47.95)  0.1061883  (31.54)  2.424831  (7.50)  .9740  .9740  Industrials  (1141)  0.0412802  (47.95)  0.1061883  (31.54)  2.424831  (7.50)  .9740  Industrials  (1141)  0.0412802  (47.95)  0.1061883  (31.54)  2.424831  (7.50)  .9740  values  for   and  :  Industrials  (1141)  0.0412802  (47.95)  0.1061883  (31.54)  2.424831  (7.50)  Equity  Volatility  a cross  Industries  from  IPO  Day   (1) Â
$ centage was not taken. The final calcula  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The Â
 (8)  Â
 (8)    calculated  percentage  was  not  taken.  The  final   calculation  measures  variance   is  an  indicator  of  the  average  level  of  Equity  Volatility  a cross  Industries  from  IPO  Day  increases  and  the  second  regression  term  approaches  zero;  )  ing  price.  high  price  (P eviation:  H),  low  price  (P L),  and  closing  price  (P C regressions  run  to  estimate  all  th a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  ach  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  ! " estimates ! " (8)  results. ! "  tion measures variance instead of standard The  regression  estimates  average  industry  volatility  ( Theregressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  regression average indus-  The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation  of   Table 1. Regression ty  across  Industries  from  IPO  Day  )  as  a  function  of  the  number  of  days  from  IPO  instead  of  standard  deviation:  regression  of   values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  da regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Market  (S&P  500)  0.0470464  (20.04)  0.1760342  (19.88)  1.936521  (5.20)  .9379  Market  (S&P  500)  0.0470464  (20.04)  0.1760342  (19.88)  1.936521  (5.20)  .9379  Market  (S&P  500)  0.0470464  (20.04)  0.1760342  (19.88)  1.936521  (5.20)  .9379  The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  deviation: tryimpact  of  significant  non-Ââ&#x20AC;? volatility(6)  ( ) as aincreases  and  the  second  regression  term  approaches  zero;  function of the num- Market  (S&P  500)  0.0470464  (20.04)  0.1760342  (19.88)  1.936521  (5.20)  .9379  was  calculated  for  every  observation  using  intraday  trading  range  This  model  was  chosen  for  its  ability  to  break  down  volatility  into IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO Â
 viation:   is  an  indicator  of  the  average  level  of   variable  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  volatility   for  each  trading  day:  values  for   and  :   comparison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each   impact  of  significant  non-Ââ&#x20AC;? I PO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  values  for   and  :  ber of days from IPO ( ). On IPO 6  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  re ! values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  the  nonlinear  crosoft  Corporation  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  of  trading,  its  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO   (6) Â
each  industry.  Equity  Volatility  a(cross  Industries  from  IPO  Day  values  for   and  :  (6) day,L),  and  closing  price  (P the - 1) term that stocks will 0.049487  (17.32)  exhibit after the effects of comes, see Appendix II. For graphs of the Oil  &  Gas  (578)  0.049487  (17.32)  0.1118282  (10.66)  1.686358  (2.93)  .8142  Oil  &  Gas  (578)  0.049487  (17.32)  0.1118282  (10.66)  1.686358  (2.93)  .8142  Oil  &  Gas  (578)  0.049487  (17.32)  0.1118282  (10.66)  1.686358  (2.93)  .8142   500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  Oil  &  Gas  (578)  0.1118282  (10.66)  1.686358  (2.93)  .8142  IPO  day,  the  variable  equals  1.  On  the  day  immediately  following  IPO,  the  variable  )  as  a  function  of  the  number  of  days  from  IPO  )  is equal to 0; The  regression  estimates  average  industry  volatility  ( closing  price.  high  price  (P baseline  volatility.  Since  the Â
second  term  rapidly  decays "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  H),  low  price  (P Cun  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The  long-Ââ&#x20AC;? r ( ).  On  IPO  day,  the  !  variable  represents  stabilization  rate   the  larger  the  value  of   (6)  Â
,  the  quicker  stock  volatility  converges  to  its  this means that average IPO day volatility the IPO period have ebbed. The variregression models with calculated values, le.  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? I PO  events  on  the  data.  The  " ( the  full  effect  of  the  IPO  event  while  minimizing  the  effe regression  of  values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  day  in  usted  low  price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  closing  price  was   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  ( ).  On  IPO  day,  the  !  (6)  ' !  calculated lated  for  stocks  in  the  ten  Dow  Jones  Sector  Indexes  provided  by  MarketWatch  in  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility    baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its Â
$ Volatility was for stocks in isis  estimated  by  estimated by "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  since the denomi- Technology  (890)  able represents rate â&#x20AC;&#x201C; the larger see Appendix V. 2.997637  (8.57)  stabilization (8)   (1)  The  regression  estimates  average  industry  volatility  (  0.1173751  (26.78)  Technology  (890)  0.1173751  (26.78)  0.7072644  (40.15)  2.997637  (8.57)  .9837  .9837  ) Technology  (890)  0.1173751  (26.78)  0.7072644  (40.15)  2.997637  (8.57)  .9837  0.1173751  (26.78)  0.7072644  (40.15)  .9837  a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  Technology  (890)  0.7072644  (40.15)  2.997637  (8.57)  each  additional  day  from  IPO,  the  variable  is  incremented  by  one.  The  creation  of  this  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  ate  volatility   for  each  trading  day:  value  represents  the  effect  of  IPO  on  stock  volatility;  ! " regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known   capture ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  Methodology  Subsection  I:  Calculating   impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  Equity  Volatility  a cross  Industries  from  IPO  Day  the ten Dow Jones Sector Indexes provided nator of the second term becomes equal to the value of , the quicker stock volatility  .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level Â
 (8)  lated  for  stocks  in  the  ten  Dow  Jones  Sector  Indexes  provided  by  MarketWatch  in  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  ! " each  industry.  8.00.   by MarketWatch in additionvalue  represents  the  effect  of  IPO  on  stock  volatility;  to the one. For each day following IPO, volatilconverges to its long-term volatility levelregressions  run  to  estimate  all  three   values  for  each  in In every regression, all three variables following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  y  ( )  was  calculated  for  every  observation  using  intraday  trading  range  is  estimated  by  500  which  serves  as  a  market  benchmark.  Volatility  ratings Â
 for  stocks  in  each  S&P is  estimated  by   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day   captures  the  expected  additional  volatility  on  an   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  Volatility Â
 was  calculated  for  stocks  in  the  ten  Dow  Jones  Sector  Indexes  provided  by  MarketWatch  in  ( ).  On  IPO  day,  the  ! .9137  "  term  is  equ Telecommunications  (143)  0.0297135  (12.20)  0.1283577  (16.27)  1.045903  (4.98)  .9137  Telecommunications  (143)  0.0297135  (12.20)  0.1283577  (16.27)  1.045903  (4.98)  .9137  Telecommunications  (143)  0.0297135  (12.20)  0.1283577  (16.27)  1.045903  (4.98)  .9137  Telecommunications  (143)  0.0297135  (12.20)  0.1283577  (16.27)  s  comparison  of  the  chronologically  scattered  IPO  periods  for  different  stocks  in  each  all  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  IPO  day  when  ! 1.045903  (4.98)  "  is  0  and Â
2 . values  for   and  :  500 which serves as a market benchmark. ity decays as the ( 1) term grows For industries, this model approxiwere statistically significant at the 1% level. .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  6  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? I PO  events  on  the  data.  The   values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R The  regression  estimates  average ted  for  stocks  in  the  ten  Dow  Jones  Sector  Indexes  provided  by  MarketWatch  in  ' ! " ( had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  of  trading,  its  500  which  serves  as  a  market  benchmark.  Volatility  ratings Â
 for  stocks  in  each  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  values  for  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chosen  to  capture   each indus(1)  regression
$ The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  t Volatility ratingsfollowing  IPO,  volatility  decays  as  the  ! for stocks in and the  and  :  second term mates values very well with all regressionvalues  for  Since all stock prices change regularly, base   and  :  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  following  IPO,  volatility  decays  as  the  ! approaches "  term  grows  and  the  second  regression  term  e  to  closing  price.  high  price  (P IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  then  divided  by  the  number  of  stocks  in  the  index  (N)  to  calculate  an  average  "  term  grows  and  the  second  regression  term  H),  low  price  (P L),  and  closing  price  (P C)  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  addition  to  the  S&P  500  which  serves  as  a  market  benchmark.  Volatility  ratings Â
 for  stocks  in  each  2 2.732502  (3.12)  is  estimated  by  ' ( Utilities  (206)  0.0276752  (33.32)  0.0460092  (13.93)  2.732502  (3.12)  .8794  Utilities  (206)  0.0276752  (33.32)  0.0460092  (13.93)  2.732502  (3.12)  .8794  Utilities  (206)  0.0276752  (33.32)  0.0460092  (13.93)  .8794  2 Methodology  Subsection  I:  Calculating   was  since  the  denominator  of  the  try group were then divided by the number 0. The model effectively represents the sigR values above 0.8100 and seven of eleven line volatility expected to be positive Utilities  (206)  0.0276752  (33.32)  0.0460092  (13.93)  2.732502  (3.12)  .8794  ble.  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term   term  is  the  value  of  the  horizontal  asymptote  above  whic The   values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  $  for  stocks  in  each   (2) Â
$ regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  coefficients  were  significant  at  the  1%  level.   ( ).  On  IPO  day,  the  ! 0  which  serves  as  a  market  benchmark.  Volatility  ratings   $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  closing  price  was  then  divided  by  the  number  of  stocks  in  the  index  (N)  to  calculate  an  average  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  of stocks in the index (N) to calculate an nificant impact of an IPO event on stock above all (8)  estimated co- and statistically significant from zero. The 0.950.  In addition,  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The  500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data ! " approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  alculate  volatility   for  each  trading  day:  The  of  industry  volatility Â
 for  each  day  relative  to  IPO.  Where  N  is  the  number  of  stocks  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   ( ).  On  IPO  day,  the  ! efficients  (8)  at the 1%increases  and  the  second  regression  term  approaches  zero;   "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  industry  group  were  then  divided  by  the  number  of  stocks  in  the  index  (N)  to  calculate  an  average  average composite measure of industry volatility. were significant level.  following  IPO,  volatility  decays  as  the  ! consistency of increased volatility "  t       on IPO   Equity  Volatility  a cross  Industries  from  IPO  Day  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  on  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  of  trading,  its  ! "  i coefficients  were  significant  at  the  1%  level.   ! values  for   and  :   since  th is  estimated  by  hen  divided  by  the  number  of  stocks  in  the  index  (N)  to  calculate  an  average  The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  volatility for each day relative to IPO. dates means that IPO-driven volatility of  industry  volatility   for  each  day  relative  to  IPO.  Where  N  is  the  number  of  stocks  is  estimated  by  ty  ( )  was  calculated  for  every  observation  using  intraday  trading  range   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  p a  result,  volatility  rating   for  IPO  day  was  0.5022321.  A  higher  calculated   represents  increases  and  the  second  regression  term  approaches  zero;  vailable   value:  Where N is the number of' stocks in an inThis model was chosen for its ability All calculations and regressions were was expected to be positive and nonzero, as  is  an  indicator  of  the  average  level  of   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  composite  measure  of  industry  volatility Â
 for  each  day  relative  to  IPO.  Where  N  is  the  number  of  stocks  approaches  0.  The  model  effectively  represents  the  sig long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  ! "( baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  closing  price  was  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? rFor  tables  ordered  by  regression  outcomes,  see  Appendix  II.  For  graphs  of  the  regression  models  with  elated  volatility  and   (1) Â
$ dex with an available value: to break down volatility into two types: run using Stata version 11.1. For a discuswell. Finally, since the levels of volatility obfollowing  IPO,  volatility  decays  as  industry  volatility Â
 for  each  day  relative  to  IPO.  Where  N  is  the  number  of  stocks  For  tables  ordered  by  regression  outcomes,  see  Appendix  II.  For  graphs  of  the  regression  models  with  For  tables  ordered  by  regression  outcomes,  see  Appendix  II.  For  graphs  of  the  regression  models  with  500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  impact  of  significant  non-Ââ&#x20AC;? I PO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? d ay  period  was  chosen  to  capture  vailable   value:  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  For  tables  ordered  by  regression  outcomes,  see  Appendix  II.  For  graphs  of  the  regression  models  with  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  )  ve  to  closing  price.  high  price  (P This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  H),  low  price  (PL),  and  closing  price  (P baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  )  a values  for   and  :  ' ( sion  (8)  methodology, see Ap-The  regression  estimates  average  industry  volatility  (  following  IPO,  volatility  decays  as  the  ! baseline C volatilreased  volatility.  IPO-related volatility and of Stata-specific served on IPO dates are typically expected  variable  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  "  term  grows  and  the  second  regression  term  ! " $ $  (2) Â
in  an  index  with  an  available   value:  represents  stabilization  rate   the  larger  the  value  of  value  represents  the  effect  of  IPO  on  stock  volatility;  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  (7) ity. Since the rapidly pendix I. to decline over time, stabilization rates ,  the  qui  captures  the  expected  additional  volatility  on  an  (7)  modelâ&#x20AC;&#x2122;s second term
baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  approaches  0.  The  model  effectiv ailable   value:   the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? This  model  was  chosen  for  its  ability  to  break  down  vol calculated  values,  see  Appendix  V.  calculated  values,  see  Appendix  V.  calculated  values,  see  Appendix  V.  IPO  events  on  the  data.  The  9  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  calculated  values,  see  Appendix  V.  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  calculate  volatility   for  each  trading  day:  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its   captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility;  ( ).  On  IPO  day,  the  ! "  term  is  equa decays as the counter variable increases, were also expected to be positive nonzero oration  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  of  trading,  its   represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  (7) Â
approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.   (8)  values. The regression  ! "  s  calculation  is  based  on Â
Volatility  For example, on Day 1 the S&PThe  regression  estimates  average  industry  volatility  ( 500 its value represents the of IPO on )  as  a  function  of  the  number  of  days  from  IPO  results confirmed .  For  all  industries,  this  model  approx long-Ââ&#x20AC;?term  volatility  level  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.   captures  the  expected  additional  volatility  on  an   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  value  represents  the  effect  of  IPO  on  stock  volatility;  value  represents  the  effect  of  IPO  on  stock  volatility;  9  effect  captures  the  expected  additional  volatility  on  an  baseline  volatility.  Since  the Â
second  term  rapid
 (7)  Â
volatility  rating Â
 for  IPO  day  was  0.5022321.  A  higher  calculated   represents  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  is  estimated  by  ' ( value  represents  the  effect  of  IPO  on  stock  volatility;   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  index contained 500 stocks with available stock volatility; captures the expected these expectations on all counts. Further  captures  the  expected  additional  volatility  on  an  6  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.   since  the  denominator  of  the  se is  estimated  by  $ $ (2) Â
This  model  was  chosen  for  its  abi  1  the  S&P  500  index  contained  500  stocks  with  available  data.  The  sum  of  all    .  For  all  industries,  this  model  approximates   values  very  well  with  all  " ( term  volatility  level Â
'  !long-Ââ&#x20AC;? This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  rice  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  closing  price  was  (7)  2 10   (1)  on an IPO day when
$ data. The sum of all values divided by "  is  0  and Â
becomes  equal  to  1.  additional volatility Section V: Results the high  R2 values associated with 10  10  10   ading  (2008,  p.  16). Â
,  where  N  defines  the  number  of  periods  sampled,  is:   values  above  0.8100  and  seven  of  eleven  above  0.9 regression  Rmore, The  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  IPO  day  when  !  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? r elated  volatility  and  value  represents  the  effect  of  IPO  on  stock  volatility;  1  the  S&P  500  index  contained  500  stocks  with  available  data.  The  sum  of  all   values  for   and  :  500 was 0.2221825 on  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   Day 1 and 0.114652 ( - 1) is 0 and the denominator of IPO  day  when  ! the regressions indicate that the model de-   "  te   following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  "  is  0  and Â
becomes  equal  to  1.  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  The  2 following  IPO,  volatility  decays  as  the  ! baseline  volatility.  Since  the Â
0  was  0.2221825  on  Day  1  and  0.114652  on  Day  2.  This  suggests  that  an  average   values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  For  example,  on  Day  1  the  S&P  500  index  contained  500  stocks  with  available  data.  The  sum  of  all   on Day 2. This suggests that an average the modelâ&#x20AC;&#x2122;s second term becomes equal to The results of the regressions for each scribed by Equation (8) captures the typical coefficients  were  significant  at  the  1%  level.   increases  and  the  second  regression  term  approaches  zero;  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  The  The Â
volatility  rating Â
stockâ&#x20AC;&#x2122;s  for  IPO  day  was  0.5022321.  A  higher  calculated   represents   is  an  indicator  of  the  average  level  of   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   is  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  the  S&P  500  index  contained  500  stocks  with  available  data.  The  sum  of  all   large-cap volatility decreases by 1. The term the value of the horizonindustry and the market benchmark are in IPO  day  when  ! trends in price volatility by stocks exhibited "  is  0  and Â
0  was  0.2221825  on  Day  1  and  0.114652  on  Day  2.  This  suggests  that  an  average  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  poration  had  its  initial  public  offering  on  March  13,  1986.  On  its  first  day  of  trading,  its  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility   is  an  indicator  of  the  average  level  of  increases  and  the  second  regression  term  approaches  zero;  approaches  0.  The  model  effectively  represents  the  signi value  represents  the  effect  of  IPO (asymptote  value  represents  the  effect  of  IPO  on  stock  volatility;  (3)  $ & ' #tal
decreases  by  about  50%  after  its  first  day  of  trading.  d  on Â
Volatility  about 50% after its first day ofcoefficients  were  significant  at  the  1%  level.  above which the regression Table 1 with corresponding sample sizes in each sector very accurately. At the 10%   captures  the  expected  additional  volatility  on  an Â
 (8)   trading. values  divided  by  500  was  0.2221825  on  Day  1  and  0.114652  on  Day  2.  This  suggests  that  an  average  ! " long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  ' ( increases  and  the  second  regression  term  approaches  zero;   is  an  indicator  of  the  average  level  of  increases  and  the  second  regression  term  approaches  zero;  Â
decreases  by  about  50%  after  its  first  day  of  trading.   variable  settles as increases and the second regresand t-statistics in parentheses. level, sample size had an insignificant effect  is  an  indicator  of  the  average  level  of  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term   captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility;  was  0.2221825  on  Day  1  and  0.114652  on  Day  2.  This  suggests  that  an  average   term  is  the  value  of  the  horizontal  asymptote  a The  $  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? (2) Â
$ increases  and  the  second  regression  term  approaches  zero;  related  volatility  and   is  an  indicator  of  the  average  level  of  2 price  was  $25.50,  its  adjusted  high  price  was  $29.25,  and  its  adjusted  closing  price  was  an indica  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  Regression Model sion term approaches zero; is on fit quality R (see Appendix III); this "  is  0  variable  IPO  day  when  !
,  where  N  defines  the  number  of  periods  sampled,  is:  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  large-Ââ&#x20AC;?
decreases  by  about  50%  after  its  first  day  of  trading.  This  model  was  chosen  for  its  ability  to  break  down  volat ction  II:  Regression  Model  tor of the average level of long-run volatility For tables ordered by regression outimplies that variations in sample size be,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of   variable  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The   variable  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1. Â
decreases  by  about  50%  after  its  first  day  of  trading.  r  the  purposes  of  this  study,  N  is  equal  to  1  because  volatility  is  measured  on  a  day-Ââ&#x20AC;?by-Ââ&#x20AC;?day  basis:  increases  and  the  second  regression  term  approaches  z The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its   variable  ased  on Â
Volatility  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of   term  is  the  value  of  the  h The  ction  II:  Regression  Model  The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  volatility  rating   for  IPO  day  was  0.5022321.  A  higher  calculated   represents  baseline  volatility.  Since  the Â
second  term  rapidly .  For  all  industries,  this  model  approximates   values  very  well  with  all  long-Ââ&#x20AC;? term  volatility  level  ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  Methodology  Subsection  II:  Regression  Model   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effec "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility   (3) Â
$ & ' # (( ).  On  IPO  day,  the  ! ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  alues  for  every  day  from  IPO  in  each  industry  (represented  using  a    captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility; Â
Volatility  Rating  v Â
the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The  ! "
 (8)   The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  ! " regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Equity  Volatility  across  Industries  from  IPO  Day  Equity Volatility across Industries from IPO Day -40-41ECONPress approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Equity  Volatility  across  Industries  from  IPO  Day  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  is  estimated  by   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  values  for   and  :  The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volat ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatili values  for   and  :  Equity  Volatility  across  Industries  from  IPO  Day  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chos Equity  Volatility  across  Industries  from  IPO  Day  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  A significant positive correlation ex- stockâ&#x20AC;&#x2122;s industry has on the way it behaves ( ).  On  IPO  day,  the  ! is  estimated  by  a  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  da  (8)   is  estimated  by  "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  ! " Volatility  Relative  to  IPO  (Regression  Models)  Equity  Volatility  a cross  Industries  from  IPO  Day  Equity  Volatility  cross  Industries  from  IPO  Day  .  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  d ists between and A linear regression in the market. the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data. baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its   since  the  denominator  of  the  second  term  becom is  estimated  by  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term Â
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becomes  equal  to  1.  impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chose impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  t Equity  Volatility  across  Industries  from  IPO  Day  volatility will also exhibit relatively high The results theDay study have a number 0.7  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? IPO  events  on  the  data.  The  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The  approaches  0.  The  model  effectively  represents  the  significant  impact  of  a Equity Volatility across Industries fromofIPO regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility Consumer  Goods  long-run volatility (See Appendix IV). True of applications. Most practical is the potenThis  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  Equity Volatility across Industries from IPO Day baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  ( ).  On  IPO  day,  the  ! Industries "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility Equity Volatility across from IPOcompare Day 0.6  Healthcare  to this observation, the top and bottom tial to industry volatility trends Equity Volatility across Industries from IPO Day The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? I PO  events  on  the  data.  T the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  kn regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  kno values  for  values  for   and  :  Equity  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  is  estimated  by  IPO Dayoption since  (8   and  :  with related Volatility across Industries from impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  by three sectors are the same as when prices; option Market  ! " volatility of their underlying stocks, the regression models generated in thi This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  type baseline  volatility.  Since  the Â
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second  term  rapidly  decays  as  the  counter  variable  increases,  its  risk-free  is  an  indicator  of  the  average  level  of  is  estimated  by   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day is  estimated  by  1  3  5  7  9  11  13  15  17  19  21  23  25  27  29   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  d the highest and values, of spot of the underlying isunderlyin security,the K isvalue the strike price,price r is the rate, andsecurity, Ď&#x192; is the volatility of t standard Black-Scholes model for the pricing of call options follows the equ  is  an  indica increases  and  the  second  regression  term  approaches  zero;   variable  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  of Ď&#x192; and represents  stabilization  rate   the  larger  the  value  of   captures  the  expected  additional  volatility  on  an value  represents  the  effect  of  IPO  on  stock  volatility;  security, the strike price, the risk-free rate, is the volatility the under Counter  Day  ,  the  quicker  stock  volatility  converges  to  its  does not appear to beK is significantly cor- r isthe price, r isand the Ď&#x192;risk-free rate, strike approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  s standard Black-Scholes model for the pricing of call options follows the equations: coefficients  were  significant  at  the  1%  level.    is  an  indicator  of  the  average  level  of  increases  and  the  second  regression  term  approaches  zero;  ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  da security, Black-Scholes K is the strike price, for r is risk-free and isfollows the volatility ofthe the  variabl underly model ofrate, callofoptions the equations: long-Ââ&#x20AC;? ris  estimated  by  un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  is  estimated  by   captures  the  expected  additional  volatility  on  an value  represents  the  effect  of  IPO  on  stock  volatility;   varia  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  related with standard either or ;  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For forBlack-Scholes example, is "  term  grows  and  the  second  regression  term  the volatility theĎ&#x192;ofunderlying asset, pricing following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  following  IPO,  volatility  decays  as  the  ! the standard model for the pricing call options follows the equa The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  long-Ââ&#x20AC;? r un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of    tween the industries studied are no reason Gaminglong-Ââ&#x20AC;?term  volatility  level  Corp, a casino operator. On some the Utilities sector has theBlack-Scholes fourth highest standard Black-Scholes model for the .  For  all  industries,  this  model  approximates   values  very  well  with  all  IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  standard model for the pricing of call options follows thepricequations: ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť á&#x2C6;ťÜľ ŕľ&#x2020; á&#x2C6;şÝ&#x20AC;ଶ á&#x2C6;ťequations: Ü°the â&#x20AC;ŤÝ Üâ&#x20AC;Ź â&#x20AC;ŤÜĽâ&#x20AC;Źofá&#x2C6;şÜľÇĄ â&#x20AC;ŤÝ?â&#x20AC;Źá&#x2C6;ť options ŕľ&#x152; Ü°á&#x2C6;şÝ&#x20AC;ଵfollows  variable  long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  is  estimated  by   since  the  denominator  of  the  second  term  becomes  equal  to  one.  Fo is  estimated  by  model theofpricing call  since  the  denominator  of  the  second  term  becomes  equal  to  one.  Black-Scholes for concern. level, however, their performances are all valuefollowing  IPO,  volatility  decays  as  the  ! but the standard lowest "  is  0  and Â
becomes  equal  to  1. and values. As foring call options follows the equations: represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  te "  term  grows  and  the  second  regression  te IPO  day  when  ! ,  the  quicker  stock  volatility  converges  to  its  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatil approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  vo ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş Üľ ŕľ&#x2020; Ü° Ý&#x20AC; â&#x20AC;ŤÝ Üâ&#x20AC;Ź â&#x20AC;ŤÜĽâ&#x20AC;Ź ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź ŕľ&#x152; Ü° Ý&#x20AC; ଵ ଶ á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş 2 Üľ ŕľ&#x2020; Ü° Ý&#x20AC; â&#x20AC;ŤÝ Üâ&#x20AC;Ź â&#x20AC;ŤÜĽâ&#x20AC;Ź ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź ŕľ&#x152; Ü° Ý&#x20AC; correlated with both  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  the availability of cona result, we can .  For  all  industries,  this  model  concluderepresents  stabilization  rate   the  larger  the  value  of  that IPO period approximates  ,  the  quicker  stock ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť long-Ââ&#x20AC;?term  volatility  level  regression  R  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  â&#x20AC;Ť ÜĽâ&#x20AC;Źá&#x2C6;şÜľÇĄŕŹľ  values  very  well  with  all  â&#x20AC;ŤÝ?â&#x20AC;Źá&#x2C6;ť ŕľ&#x152; Ü°á&#x2C6;şÝ&#x20AC;ଶଵ á&#x2C6;ťÜľ ŕľ&#x2020; Ü° á&#x2C6;şÝ&#x20AC; ଶ á&#x2C6;ťâ&#x20AC;ŤÝ Üâ&#x20AC;Ź In  every  regression,  all  three   variables  were  statistically  significant  at  the  1%  level.  Since  all  stock  ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť The sectors with the highest baseline sumersâ&#x20AC;&#x2122; disposable income in addition to stabilization rate and volatility magnitude ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regressio following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  t á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş Üľ ŕľ&#x2020; Ü° Ý&#x20AC; â&#x20AC;ŤÝ Üâ&#x20AC;Ź â&#x20AC;ŤÜĽâ&#x20AC;Ź ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź ŕľ&#x152; Ü° Ý&#x20AC; .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  v  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  ఎ ଵ ଶŕł&#x201E; ŕ´&#x2018; baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  in ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť is  estimated  by  2 not closely ŕŞŕŹá&#x2030;&#x20AC;á&#x2C6;ťâ&#x20AC;ŤÝ Üâ&#x20AC;Ź á&#x2030; ା൬௥ା ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť(9)  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  volatility are technology, consumer ser- consumersâ&#x20AC;&#x2122; constantly-shifting preferences; are linked when observing iná&#x2C6;ť á&#x2C6;ş á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş Üľ ŕľ&#x2020; Ü° Ý&#x20AC; â&#x20AC;ŤÜĽâ&#x20AC;Ź ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź ŕľ&#x152; Ü° Ý&#x20AC; ಟ ŕ°Ž .  For  all  industries,  this  model  a pproximates  long-Ââ&#x20AC;?term  volatility  level  ଵ ଶ  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R ŕ°Ž This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? related  volatility  and  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  coefficients  were  significant  at  the  1%  level.   prices  change  regularly,  baseline  volatility   was  expected  to  be  positive  and  statistically  significant  increases  and  the  second  regression  term  approaches  zero;  ఎ ŕ´&#x2018;  is  an  indicator  of  the  average  level  of  ŕł&#x201E; ŕł&#x201E;Ý&#x20AC; ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ା ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ଵ ŕ´&#x2018;ŕľ&#x152;ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť vices, and healthcare. Technology, the most the unpredictability of these factors adds to dustryapproaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock averages. ŕ°Ž 2 2 ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ା ŕ°&#x2122;ΞŕŻ?ି௧ ŕł&#x201E; ಟ ŕ°Ž .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  st ŕ°Ž ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ାŕ´&#x2018; ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R 9  increases  and  the  second  regression  term  approaches  zero;  ŕľ&#x152; ಟ  captures  the  expected  additional  v Ý&#x20AC;ŕľ&#x152; ଵ  is  an  indicator  of  the  average  level  of  value  represents  the  effect  of  IPO  on  stock  volatility;  ఎ Ý&#x20AC; volatile industry, exhibits volatility levels uncertainty for all Service companies. following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  ŕł&#x201E; ŕ°&#x2122;ΞŕŻ?ି௧ ŕ´&#x2018;ఎಟ 2 ଵ This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatil This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? r elated  volatili ŕ°&#x2122;ΞŕŻ?ି௧ ŕľ&#x152; ŕŞŕŹá&#x2030;&#x20AC;Ý&#x20AC; á&#x2030; ା൬௥ା ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  add regression  R from  zero.  The  consistency  of  increased  volatility  on  IPO  dates  means  that  IPO-Ââ&#x20AC;?driven  volatility   was  coefficients  were  significant  at  the  1%  level.   baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  ଵ  long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  ಟ ŕ°&#x2122;ΞŕŻ?ି௧ ŕ´&#x2018;ŕ°Ž ŕ°Ž  variable  that are equal to nearly double those seen (10) 2 ಟŕł&#x201E; á&#x2030; ା൬௥ା Ý&#x20AC;ଵ ŕľ&#x152;ŕŞŕŹá&#x2030;&#x20AC; ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R ŕ°Ž ŕ°&#x2122;ΞŕŻ?ି௧ coefficients  were  significant  at  the  1%  level.  coefficients  were  significant  at  the  1%  level.     variable  long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  ŕł&#x201E; ŕ´&#x2018;ŕ°Ž in the runner-up Consumer Services secThe three stocks exhibiting the lowest IPO  day  when  ! "  is  0  and Â
becom Ý&#x20AC;ଵ ŕľ&#x152; ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ି ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť r elated  vo approaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volati expected  to  be  positive  and  nonzero,  as  well.  Finally,  since  the  levels  of  volatility  observed  on  IPO  dates  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increas baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increas ŕ°Ž ŕ°&#x2122;ΞŕŻ?ି௧ ŕ°Ž ಟ coefficients  were  significant  at  the  1%  level.    captures  the  expected  additional  volatility  on value  represents  the  effect  of  IPO  on  stock  volatility;   captures  the  expected  additional  volatility  on  a value  represents  the  effect  of  IPO  on  stock  volatility;  ŕł&#x201E; ŕ´&#x2018; ŕ°Ž tor. For the Technology sector, this can be amount of baseline volatility â&#x20AC;&#x201C; basic materiSection VI: Conclusion ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  Ý&#x20AC; ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ŕł&#x201E; á&#x2030; ା൬௥ି ଶ ŕ´&#x2018;ŕľ&#x152;ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ŕŞŕŹá&#x2030;&#x20AC;ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ି ŕ°&#x2122;ΞŕŻ?ି௧ ŕ´&#x2018;ŕ°Ž ŕ°Ž ŕł&#x201E; coefficients  were  significant  at  the  1%  level.   ಟ ಟ ŕ°Ž ŕŞŕŹá&#x2030;&#x20AC; á&#x2030; ା൬௥ି ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť explained by the unpredictability of earnals, telecommunications, and utilities â&#x20AC;&#x201C; are (11) ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  Ý&#x20AC; ŕľ&#x152; ଶ  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as The  ఎ Ý&#x20AC;ଶ ŕľ&#x152; ŕł&#x201E; ŕ°&#x2122;ΞŕŻ?ି௧ ŕ´&#x2018;ఎಟ are  typically  expected  to  decline  over  time,  stabilization  rates   were  also  expected  to  be  positive  baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  inc baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increa ŕ°&#x2122;ΞŕŻ?ି௧ ŕľ&#x152; ŕ°Ž ŕ°Ž ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ŕŞŕŹá&#x2030;&#x20AC;Ý&#x20AC;  captures  the  expected  additional  volat value  represents  the  effect  of  IPO  on  stock  volatility;  value  represents  the  effect  of  IPO  on  stock  volatility;  ଶá&#x2030; ା൬௥ି ings linked to the dynamic, rapidly-evolvall characterized by relatively stable revenue The models used in this studyâ&#x20AC;&#x2122;s regres  captures  the  expected  additional  volati IPO  day  when  ! "  is  0  and Â
becomes  equal  to IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1 ಟ .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  ŕ°&#x2122;ΞŕŻ?ି௧ ŕł&#x201E; ŕ´&#x2018; This  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  9  Ý&#x20AC;ଶ greater ŕľ&#x152;ŕŞŕŹá&#x2030;&#x20AC; ಟá&#x2030; ା൬௥ି ŕľ°á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ing nature of the industry and the uncer- streams and predictable earnings. Responsions provide both the tools greater to predict Having into thegiven motion ŕ°Ž ŕ°&#x2122;ΞŕŻ?ି௧ approximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  .  For  all  industries,  this  model  Having insight into the motion of Ď&#x192;insight in this model a companyâ&#x20AC;&#x2122;s nonzero  values.  The  regression  results  confirmed  these  expectations  on  all  counts.  Furthermore,  the  Ý&#x20AC; ŕľ&#x152;  is  an  indicator  of  the  averag increases  and  the  second  regression  term  approaches  zero;   ଶ  captures  the  expected  additional  vo value  represents  the  effect  of  IPO  on  stock  volatility;   captures  the  expected  additional  vola value  represents  the  effect  of  IPO  on  stock  volatility;  ŕ°&#x2122;ΞŕŻ?ି௧ tainty surrounding the future profitability sible for functions earlier in the production trends in around the of Ď&#x192; in this model given a companyâ&#x20AC;&#x2122;s indusIPO  day  when  ! "  is  0  and Â
becomes  eq IPO  day  when  ! "  is  0  and Â
becomes  eq 2 stock price volatility  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  Having greater insight into the motion of Ď&#x192; in this model given a companyâ&#x20AC;&#x2122;s industry  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  insight the motion of Ď&#x192;allow in thisfor model given a companyâ&#x20AC;&#x2122;s industry of technological innovations. For similar line, companies in the Basic Materials in30-day IPO Having period greater as well as greater an into effective try will accurate of 9  wi Having insight into the motion of more Ď&#x192; in this model forecast given a companyâ&#x20AC;&#x2122;s high  R2  values  associated  with  the  regressions  indicate  that  the  model  described  by  Equation  (8)  regression  R2  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated   IPOâ&#x20AC;&#x2122;s call options. T accurate of dmotion long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  Th Having greater insight intoits the Ď&#x192; inasthis model a companyâ&#x20AC;&#x2122;s industry reasons, the healthcare industry ranks in dustry deal with a customer pool with less breakdown of IPO period volatility into d1 1and andd2dofand, and, asa aresult, result,agiven arecent recent IPOâ&#x20AC;&#x2122;s call IPO  day  when  ! forecast "  is  0  and Â
become IPO  day  when  ! "  is  0  and Â
becomes  e  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as  The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as  The  2  is  an  indicator  of  the  average  level  of  increases  and  the  second  regression  term  approaches  zero;   is  an  indicator  of  the  average  level  of  increases  and  the  second  regression  term  approaches  zero;  and d and, as a result, a recent IPOâ&#x20AC;&#x2122;s call options. This inform accurate forecast of d coefficients  were  significant  at  the  1%  level.   1 2  captures  the  expected  additional  volatility  on  an  value  represents  the  effect  of  IPO  on  stock  volatility;  Having greater insight into the motion of Ď&#x192; in this model given a companyâ&#x20AC;&#x2122;s industry w and d and, as a result, a recent IPOâ&#x20AC;&#x2122;s call options. This informati accurate forecast of d the top three most volatile industries. For elastic demand than those in other industwo main components: accurate IPO-fueled options. This can IPOâ&#x20AC;&#x2122;s also be 1 volatil2 and d2 and, as information a result, a recent callapoptions.9  Th forecast captures  the  typical  trends  in  price  volatility  exhibited  by  stocks  in  each  sector  very  accurately.  At  the  coefficients  were  significant  at  the  1%  level.   of d1 plied applied to put option pricing using the Black-Scholes model: pharmaceutical companies, profitability is tries. For Telecommunications businesses, ity andThe  baseline volatility. The results indito put option pricing using the Black,  the  quicker  stock  volatility  conver represents  stabilization  rate   the  larger  the  value  of  and d and, as a result, a recent IPOâ&#x20AC;&#x2122;s call options. This inform accurate forecast of d  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as  The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as  1 2  is  an  indicator  of  the  average  lev increases  and  the  second  regression  term  approaches  zero;   is  an  indicator  of  the  average  lev increases  and  the  second  regression  term  approaches  zero;  model: long-Ââ&#x20AC;? rwhich un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The   applied to put option pricing using the Black-Scholes  variab  variable determined by the approval (or rejection) client contract volume is not typified by cate industries have the most volatile Scholes model: 2 IPO  day  when  ! "  is  0  and Â
becomes  equal  to  1.  and d and, as a result, a recent IPOâ&#x20AC;&#x2122;s call options. This informa accurate forecast of d applied to put option pricing using the Black-Scholes model: 1 2 10%  level,  sample  size  had  an  insignificant  effect  on  fit  quality  R  (see  Appendix  III);  this  implies  that  applied to put option pricing using the Black-Scholes model: of drugs by the FDA; the future cash flows sharp drops or big spikes. Utilities, the secIPOs, which stabilize the fastest, andpricing about using the Black-Scholesapproximates   values  very  well  long-Ââ&#x20AC;?term  volatility  level  applied to put option .  For  all  industries,  this  model  model: increases  and  the  second  regression  term  approaches  zero;  increases  and  the  second  regression  term  approaches  zero;   is  an  indicator  of  the  averag  is  an  indicator  of  the  average  le ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť (12) long-Ââ&#x20AC;? un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  long-Ââ&#x20AC;? rrun  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  generated by a drug awaiting approval can tor with the lowest baseline volatility, is where each industry stabilizes; they provide á&#x2C6;ťŕľŻ á&#x2C6;ş á&#x2C6;ť á&#x2C6;ş ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  represents  stabilization  rate   the  larger  the  value  of  ྍͳ â&#x20AC;ŤÝ Üâ&#x20AC;Ź ŕľ&#x2020; ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;ଵ ܲ ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź ŕľ&#x152; ŕľ&#x2020; Ü° Ý&#x20AC; ଶ  term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   The  applied to put option pricing using the Black-Scholes model: variations  in  sample  size  between  the  industries  studied  are  no  reason  for  concern.  ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť be very large if the drug receives approval or perhaps characterized by the most predictboth ordinal and cardinal measures of volaá&#x2C6;ťŕľŻâ&#x20AC;ŤÝ Üâ&#x20AC;Ź ŕľ&#x2020; ྍͳ ŕľ&#x2020;á&#x2C6;şÜ° Ý&#x20AC;ଵܵá&#x2C6;ťŕľŻÜľ ŕľ&#x152; ྍͳ ŕľ&#x2020;á&#x2C6;şÜ° 2 á&#x2C6;ťŕľŻŕŹśâ&#x20AC;ŤÝ Üâ&#x20AC;Ź ྍͳ ŕľ&#x2020;Ü° Ý&#x20AC; á&#x2C6;şá&#x2C6;ťŕľŻ ܲ á&#x2C6;şÜ˛ ܾǥá&#x2C6;şâ&#x20AC;ŤÜľÝ?â&#x20AC;ŹÇĄá&#x2C6;ť â&#x20AC;ŤÝ?â&#x20AC;Źŕľ&#x152;á&#x2C6;ť ྍͳ ŕľ&#x2020;Ü° Ý&#x20AC;ଶá&#x2C6;şÝ&#x20AC;  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estima regression  R ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;ଶ á&#x2C6;ťŕľŻŕľ&#x2020; long-Ââ&#x20AC;? run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The long-Ââ&#x20AC;? rsectors un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  â&#x20AC;ŤŕŹż Ý Üâ&#x20AC;ŹŕŻĽá&#x2C6;şŕŻ?ି௧á&#x2C6;ť ŕľ&#x2020;ଵ ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;ଵ á&#x2C6;ťŕľŻ ܲ á&#x2C6;şÜľÇĄ â&#x20AC;ŤÝ?â&#x20AC;Źá&#x2C6;ť ŕľ&#x152; can be zero if the drug is ultimately reject- able future cash flows; profits seen in this tilityrepresents  stabilization  rate   the  larger  the  value  of  for all examined. While no two ,  the  quicker  stock  volatility  converges  t represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  t .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  .  For  all  industries,  this  model  a pproximates   values  very  well  with  all  long-Ââ&#x20AC;?term  volatility  level  ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť increases  and  the  second  regression  term  approaches  zero;  ŕľ&#x2020; ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;ଵ á&#x2C6;ťŕľŻÜľ ܲ á&#x2C6;şÜľÇĄ â&#x20AC;ŤÝ?â&#x20AC;Źá&#x2C6;ť ŕľ&#x152; ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;ଶ á&#x2C6;ťŕľŻâ&#x20AC;ŤÝ Üâ&#x20AC;Ź  is  an  indicator  of  the  average  level  of  9 ed. Consumer Services is a very broad sec- sector are usually stabilized by both steady stocks can be expected to Once behave exactly ି௥á&#x2C6;şŕŻ?ି௧á&#x2C6;ť again, if d1the and dá&#x2C6;ť2 ŕľ&#x152; canྍͳbeŕľ&#x2020;predicted with more accuracy á&#x2C6;ťŕľŻ á&#x2C6;ťŕľŻÜľ indust9 á&#x2C6;ş á&#x2C6;ş ྍͳ ŕľ&#x2020; Ü°á&#x2C6;şÝ&#x20AC;across â&#x20AC;ŤÝ Üâ&#x20AC;Ź ŕľ&#x2020; ܲ ܾǥ â&#x20AC;ŤÝ?â&#x20AC;Ź Ü° Ý&#x20AC; ଶ ଵ coefficients  were  significant  at  the  1%  level.   tor and includes companies ranging from 4 consumer demand and heavy regulation in samelong-Ââ&#x20AC;?term  volatility  level  regardless of again, their commonalities, thebe Once again, if accuracy d1 andacross dacross can be pre-putput ,  the  quicker  stock  volatility  converg represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges represents  stabilization  rate   the  larger  the  value  of  2 2 Once again, and predicted with industry, opt pproximates  more .  For  all  industries,  this  model  values  very  well  with long-Ââ&#x20AC;?term  volatility  level  aapproximates  1 .  For  all  industries,  this  model  2 can 2   values  very  well  with  Once if dif dand d dcan be predicted with more accuracy industry, option  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R long-Ââ&#x20AC;?rKids un  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  Once1found again,2here if d1 can and d2dicted can bewith predicted with moreacross accuracy across industry Entertainment, a childrenâ&#x20AC;&#x2122;s film and cases where monopolies are allowed.  variable  industry volatility forecasts more accuracy industry, 11  valued and their trends predicted more accurately. Most important, Once again, if dimpact canprice predicted with more accuracy acrossand industry, put oph 1 and d2that television production company, to Boyd help tolong-Ââ&#x20AC;?term  volatility  level  lend insight into the abepredicted put options can be better valued their 22 .  For  all  industries,  this  model  a pproximates   values  very  well  w long-Ââ&#x20AC;?term  volatility  level  .  For  all  industries,  this  model  a pproximates   values  very  well  with  valued and their price trends more accurately. Most important, however,  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R Once again, if d and d can be predicted with more accuracy across industry, put valued and their 1price trends predicted accurately. Most important, however,opti is si coefficients  were  significant  at  the  1%  level.   trendsmore coefficients  were  significant  at  the  1%  level.   price 2 represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  valued and their predicted more accurately. Most important, ho the regressions to identify typical volatility trends by industry and, as a resu valued 2 2 and their price trends predicted more accurately. Most important, however,  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimat regression  R  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  regression  R the regressions to identify typical trends industry and, a result, predic coefficients  were  significant  at  the  1%  level.   coefficients  were  significant  at  the  1%  level.   volatility valued and their trends predicted more accurately. Most important, however, is the regressions to price identify typical volatility trends by by industry and, as as a result, predicted
abnormal volatility spikes on long-run volatility, we can calculate: Equity  Volatility  across  Industries  from  IPO  Day Â
volatility spikes over the course of the trading year. Using some percentage Ď to represent the effect of
each  industry.  Equity Volatility across Industries from IPO Day -43 Methodology  Subsection  I:  Calculating   ଷ଴ ଶ abnormal volatility spikes on long-run calculate: á&#x2030;&#x20AC;ߎcan ŕľ&#x152; Ď&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵwe á&#x2030; ŕľ&#x2026; aá&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť (15) ߪ volatility, ଵ ŕľ&#x2026;Equity  Volatility  cross  Industries  from  IPO  Day  ଵା ŕ°?ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;? day  period  was  chosen  to  capture   Methodology  Subsection  I:  Calculating  ŕ°? ŕ°Ž ଷ଴ ଶ The   calculation  process  was  run  individually  using  data  sets  that  include  price trends predicted more accurately. rately predict the motion of values from tion sector exhibit total IPO-time volatility The  methodology  followed  throughout  this  study  consists  of  two  processes.  First  is  the  calculation  of   á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; IPO  events  on  the  data.  The  á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť (15) ߪ ŕľ&#x152; Ď&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵ the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;? ଵା ŕ°?ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť impact  of  significant  non-Ââ&#x20AC;?IPO  events  on  the  regression  results;  the  30-Ââ&#x20AC;?day  period  was  chosen  to  capture  Most important, however, is simply the use ŕ°?ŕ°Ž IPO day, it cannot be assumed that these of about 0.16 while their baseline volatilଷ଴ ߪ ŕľ&#x152; ටĎ&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026;The  É?á&#x2C6;ť  calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P (16) of the regressions to identify typical volatilଵା ŕ°?ŕ°Żâ&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť (16) trends can be used to 500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatc effectively predict ity levels are close to 0.03. If a portfolio values  that  represent  average  intraday  price  volatility  for  each  industry.  Second  is  the  nonlinear  regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  the  full  effect  of  the  IPO  event  while  minimizing  the  effects  of  non-Ââ&#x20AC;?IPO  events  on  the  data.  The  ity trends by industry and, as a result, pretrends in individual stocks without further manager wants to wait until the stock has ŕ°? ŕ°Ž ߪ ŕľ&#x152; ටĎ&#x192;ଷ଴ (16) ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; ଵା ŕ°? â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť dicted directional options price movement. analysis. stabilized and volatility has dropped below ŕ°Ż 500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  a  day  counter  variable  was  generated  for  each  observation  to  mark  the  nu regression  of   values  against  time  from  IPO  in  order  to  estimate  volatility  trends  following  IPO  day  in  values  for   and  :  being further scaled 0.05 to evaluate it, this studyâ&#x20AC;&#x2122;s regression After being further scaledAfter by price for compatibility withby theprice Black-Scholes model, ߪ ଶ and ߪ values can regressions  run  to  estimate  all  three   values  for  each  index  used  the  following  model  given  known  Determining the precise effects on for compatibility with the Black-Scholes ଶ Other Applications suggests that the manager should wait until a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  2 After being furtherby scaled by price for compatibility with the Black-Scholes model, ߪ and ߪ values can each  industry.  option price movement provided the model, Ď&#x192; and Ď&#x192; values can be used to after day 7. be used to estimate the fair value of options for IPO stocks; estimated prices can be compared with real values  for   and  :  across Industries from IPO Day fair  value (8)   scope of regression results exceeds the this estimate the of options for IPO Stock price volatility on and follow ! " be used to estimate the be fair value of options for IPO prices stocks; estimated prices can be compared with real study. Afrom starting point, however, would stocks; estimated can be compared ing IPO date is also relevant for companies It is surprising that the effects of induscross Industries IPO Day 6 prices to lend insight into pricing efficiency and, when studied using historical discrepancies, can be their used own IPOs and the tries and the IPO period on stock volatility Industries from IPO Day Day Methodology  Subsection  I:  Calculating  to from estimate annualized volatility using the with real  prices to lend insight into pricing trying to launch ility across Industries from IPO Day Industries IPO prices to lend intodays, pricing efficiency and, whenlevels using historical discrepancies, can be t variance, that any results given year includes 252insight trading and that volatility  (8)  not been studied previously. Although  studied used ! " regression â&#x20AC;&#x201C; the Black-Scholes modand, whenstudied using historiinvestment have banks helping them to do so. The  regression  estimates  average  industry  volatility  ( )efficiency  as  a  function  of  the  number  of  days  from  IPO  to develop an arbitrage-based options can trading strategy for IPO an stocks. usesanyvolatility onincludes an annualized basis. discrepancies, be used to develop Having access to a model that can help to volatility trends were successfully modeled variance,elthat given year 252 trading days,cal and that volatility levels to develop an arbitrage-based options tradinglevels strategy for IPO stocks. ଶ volatility nce, that any given year includes 252 trading days, and that ߎ after IPO, estimated annualized volatility as variance ߪ for any industry could be The   calculation  process  was  run  individually  using  data  sets  that  include  the  trading  history  for  the  S&P  Assuming that the ratings represent variarbitrage-based optionslevels trading strategy for predict a companyâ&#x20AC;&#x2122;s volatility after IPO during this study, much work is left to be esent variance, that year any given year includes 252 trading days, and thatlevels volatility ଵ that nce, any given includes 252 trading days, and that volatility ( ).  On  IPO  day,  the  ! "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  ଶ ance, that any given year includes 252 tradIPO stocks. can help to guide decisions on whether a done to fully understand the impact of The  regression  estimates  average  industry  volatility  ( )  as  a  function  of  the  number  of  days  from  IPO  after IPO, estimated annualized volatility as variance ߪ for any industry could be ଵ ଶ ଶ ing days, and that volatility levels remain company should sell equity in the public these factors on volatility and the applicaer IPO, estimated annualized volatility as variance ߪ for any industry could be ଶ 500  and  each  of  the  ten  selected  industry  groups  provided  by  MarketWatch.  For  all  examined  data  sets,  e to ߎ after IPO, estimated annualized volatility as variance ߪ for any industry could be s is  estimated  by  Industries from IPO Day er IPO,ଵ estimated annualized volatility as variance ߪ for any industry could be IPO,  since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  close to after estimated annualized Although such ( ).  On  IPO  day,  the  ! further investigation market in addition to how its shares should tions of a deeper understanding; further 15 "  term  is  equal  to  0;  this  means  that  average  IPO  day  volatility  2 15 volatility as variance Ď&#x192; for any industry exceeds the scope of this study, some highbe priced. These findings on volatility are study into these relationships will certainly a  day  counter  variable  was  generated  for  each  observation  to  mark  the  number  of  days  that  had  passed  sing: ŕ°?ŕ°Ž be calculated using: level hypotheses can be fairly formulated most relevant when value preservation is a provide valuable insight for both academics following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  ଷ଴ ଶ ance, thatcould any given year includes 252 trading days, and that volatility levels (13) is  estimated  by   since  the  denominator  of  the  second  term  becomes  equal  to  one.  For  each  day  ߪ ŕľ&#x152; Ď&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; ଵା ŕ°? â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť without further analysis. While options key objective for the IPO candidate; disand profit-seeking arbitrageurs. ŕ°Ż ŕ°?ŕ°Ž ŕľ&#x152; Ď&#x192;ଷ଴ á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (13) ߪ ଶ ଷ଴ ଶ (13) traders are probably forward-thinking covering that its share prices may be more ଵ ŕľ&#x2026;ŕ°?ଵା ŕ°? ଵ 6  ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;ߎvolatility ŕ°Ž erapproaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  IPO, estimated annualized as variance ߪ for any industry could be ଶ ŕ°? ŕ°Ž ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ŕ°?ŕ°Ž ଶ ଵŕľ&#x2026; Ď&#x192;ଷ଴ ŕľ&#x152; Ď&#x192; á&#x2030; ŕľ&#x2026; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ á&#x2C6;şÍ´Í´Í´ ߎ (13) ߪଶ ŕľ&#x152; ŕŻ&#x153;ŕ&#x20AC;ଵ following  IPO,  volatility  decays  as  the  ! "  term  grows  and  the  second  regression  term  ŕľ&#x152; Ď&#x192;ଷ଴ á&#x2030; ŕľ&#x2026;ଵଵ á&#x2C6;ťá&#x2C6;ťá&#x2C6;şÍ´Í´Í´enough â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť to(13) ߪá&#x2030;&#x20AC;ߎ recognize(13) that volatility will devolatile than ଵ ŕľ&#x2026; á&#x2030; â&#x20AC;ŤßŽ ×&#x203A;×&#x203A;â&#x20AC;Ź ߪ ଵା ŕ°?á&#x2030;&#x20AC;ߎ ŕŻ&#x153;ŕ&#x20AC;ଵ  expected in the public market ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; ଵା ŕ°? ଵା ŕ°? ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ng annualized standard deviation ߪ, which is also a component of the Black-Scholes cline following the IPO period, the drop may lead a more conservative company to corresponding standard in volatility expect may be under- or seek alternative sources of capital. For exapproaches  0.  The  model  effectively  represents  the  significant  impact  of  an  IPO  event  on  stock  volatility.  gThis  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;? annualizedThe standard deviation annualized ߪ, which is also a component of the they Black-Scholes related  volatility  and  deviation Ď&#x192;, whichߪ, iswhich also aisߪ, component of a component overestimated. For example, the studyâ&#x20AC;&#x2122;s ample, companies in the Technology and nualized standard deviation also a component of the Black-Scholes lculated using: onding annualized standard deviation which is also of the Black-Scholes ualized standard deviation ߪ, is also a component of the Black-Scholes ŕ°?ŕ°Ž whichcan ଶ the Black-Scholes model, be calculated results suggest that stocks in the TechnolConsumer Services sectors may decide not Ď&#x192;ଷ଴ á&#x2030;&#x20AC;ߎ ŕľ&#x152; ŕľ&#x2026; á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (13) ߪ ଵ ଵ ŕŻ&#x153;ŕ&#x20AC;ଵ culated using: baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  ଵା ŕ°?ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť using: ogy sector typically exhibit about 7.5 times to issue common stock to raise capital beThis  model  was  chosen  for  its  ability  to  break  down  volatility  into  two  types:  IPO-Ââ&#x20AC;?related  volatility  and  ed using: be using: ed calculated using: their long-term volatility levels on IPO day. cause their industries can be characterized ŕ°? ŕ°Ž value  represents  the  effect  of  IPO  on  stock  volatility;  á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹIn á&#x2C6;ťthe case of an(14) ߪ ŕľ&#x152; ට Ď&#x192;ଷ଴ (14) underestimated drop, the by above-market volatility during both the ଵ  captures  the  expected  additional  volatility  on  an  ଵ ŕľ&#x2026; ଵା ŕ°? ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;ߎ â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť nualized standard deviation ߪ, which is ŕ°?also a component of the Black-Scholes baseline  volatility.  Since  the Â
second  term  rapidly  decays  as  the  counter  variable  increases,  its  య ŕ°Ž market may forecast that IPO volatility for IPO period and the long run. á&#x2030;&#x20AC;ߎ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (14) ߪ ŕľ&#x152;ଷ଴ට Ď&#x192;ଷ଴ ଵ ŕ°?ଵା ŕ°? ଵ ŕŻ&#x153;ŕ&#x20AC;ଵ ŕ°? á&#x2C6;şÍ´Í´Í´ ŕ°Ž ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ŕ°?ŕ°Žŕ°Ž ଷ଴ "  is  0  and Â
becomes  equal  to  1.  Ď&#x192; á&#x2030;&#x20AC;ߎ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (14) ߪ ŕľ&#x152; ට Technology stocks is typically 4 times longIPO  day  when  ! ଷ଴ ଵ ଵ Ď&#x192; á&#x2030;&#x20AC;ߎ ŕŻ&#x153;ŕ&#x20AC;ଵ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (14) ߪ ŕľ&#x152; ට ted using: ଵ ଵ á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť (14) ߪ ŕľ&#x152; ට Ď&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026; ଵା ŕ°? ŕŻ&#x153;ŕ&#x20AC;ଵ â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť value  represents  the  effect  of  IPO  on  stock  volatility;   captures  the  expected  additional  volatility  on  an  ଵା ŕ°? ŕ°Żâ&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ଵା ŕ°?ŕ°Żâ&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť run volatility andfirst that volatility will ultiWhen attempting to manage any portvalue represents the sum of allŕ°Ż daily expected daily volatility ratings â&#x20AC;&#x201C; the term mately drop by 75% by the end of the IPO folio, minimizing risk is of utmost imporThe   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   IPO  day  when  ! value represents sum of ŕ°?Ď&#x192; allŕ°Ž2 daily dailythe volatility ratings â&#x20AC;&#x201C; the term we forecast that "  is  0  and Â
becomes  equal  to  1.  Theଷ଴the resulting valueexpected represents period; using ourfirst results, tance. In â&#x20AC;&#x153;How Relevant is Volatility Foreଶ IPO Ď&#x192;ŕŻ&#x153;ŕ&#x20AC;ଵ represents the sum of all daily expected daily volatility ratings â&#x20AC;&#x201C; the first term á&#x2030;&#x20AC;ߎ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť (14) ߪsum ŕľ&#x152;period ට as modeled by the regression results while the second term represents ଵ ଵ value represents the sum of all daily expected daily volatility ratings â&#x20AC;&#x201C; the term by about g0-day ߪ ofsum all daily expected daily volatility rat- ratings volatility willfirst actually be reduced casting for Financial Risk Management?â&#x20AC;? represents the of allଵା ŕ°? daily expected daily volatility â&#x20AC;&#x201C; the term first ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť increases  and  the  second  regression  term  approaches  zero;   is  an  indicator  of  the  average  level  of  â&#x20AC;&#x201C; the first termbyrepresents the 30-day 85%. a result, associated put or call opChristoffersen and Diebold observe that -day IPOings period as modeled the regression results while theAs second term represents The   term  is  the  value  of  the  horizontal  asymptote  above  which  the  regression  settles  as   IPO period as modeled modeled by the regression regression results while the second term represents 22 trading days in the 252-day trading year. Additional adjustments could be made tobecause of inacIPO period asby modeled theregression regression tions could be overpriced the ability to forecast volatility of a security he 30-day IPO period as modeled bybythe results while the second term represents IPO period as the results while the second term represents long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The  e represents the sum all expected daily volatilitythe ratingscurate â&#x20AC;&#x201C; the first term forecasting. Given market  variable  thedaily second termyear. represents volatility is incredibly useful for  is  an  indicator  of  the  average  level  of  risk management increases  and  the  second  regression  term  approaches  zero;  2 tradingresults days inwhile theof252-day trading Additional adjustments could be made to remaining 222 trading days in the 252-day nonrecognition of industry-based volatility purposes (2000, p. 12). The new insight ding days in the 252-day trading year. Additional adjustments could be made to or example, the long-run volatility term could be adjusted to account for unforeseen ng 222 trading days in the 252-day trading year. Additional adjustments could be made to ing days inas the 252-day trading year. Additional adjustments could be made to IPO period modeled the regression results while the second term represents trading year. by Additional adjustments could trends, industry-based arbitrage opportunithat this study provides into industry-based represents  stabilization  rate   the  larger  the  value  of  ,  the  quicker  stock  volatility  converges  to  its  or example, the long-run term could be adjusted account for long-Ââ&#x20AC;?run  volatility  that  stocks  will  exhibit  after  the  effects  of  the  IPO  period  have  ebbed.  The   variable  belong-run made tovolatility thisvolatility estimation; for example, tiestoĎ exist and canunforeseen be identified with further IPO volatility forecasting can advance risk ample, the term could be adjusted to account for unforeseen over the course of the trading year. Using some percentage to represent the effect of on; for example, the long-run volatility term could be adjusted to account for unforeseen mple, the volatility term could be adjusted unforeseen ding days inlong-run the 252-day trading year.term Additional adjustments could be for made to the long-run volatility could be ad-to account study. management proficiency. For example, the long-Ââ&#x20AC;? term  volatility  level  .  For  all  industries,  this  model  approximates   values  very  well  with  all  ver the course of the trading year. Using some percentage Ď to represent the effect of represents  stabilization  rate   the  larger  the  value  of  justed to account for unforeseen volatility values of the ,  the  quicker  stock  volatility  converges  to  its  variables lend insight into he course of the trading year. Using some percentage Ď to to represent represent the effect effect of of spikes on long-run volatility, we can calculate: kes over the course of the trading year. Using some percentage Ď to represent the effect of ample, the long-run volatility term could be adjusted to account for unforeseen etycourse of the trading year. Using some percentage Ď the spikes2 over the course of the trading year. Regardless of whether significant arbithe rate of regression from IPO volatility regression  R  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  somevolatility, percentage tocalculate: represent the trage opportunities do exist, it is important .  For  all  industries,  this  model  levels to baseline volatility. When  values  very  well  with  all  deciding approximates  long-Ââ&#x20AC;?term  volatility  level  ty spikes Using on long-run we Ď can kes on long-run long-run volatility, we cansome calculate: he course of theon trading year. Using percentage Ď to represent the effect offinal values and associated effect of abnormal volatility spikes on longto note that the whether to invest in the stock of a recent olatility spikes long-run volatility, we can calculate: kes on volatility, we can calculate: ŕ°?ŕ°Ž ଶ coefficients  were  significant  at  the  1%  level.   â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źregression 2 trends in ŕľ&#x152;volatility, Ď&#x192;ଷ଴ ŕľ&#x2026; can calculate: á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ á&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť coefficients (15) regression  R ߪ run reflect only IPO, the regression values can help portŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵwe  values  above  0.8100  and  seven  of  eleven  above  0.950.  In  addition,  all  estimated  ଵା ŕ°?ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ikes on long-run volatility, we canŕ°?calculate: ŕ°Ž average industry volatility; no regressions folio managers decide when prices have ଷ଴ ଶ Ď&#x192; ŕľ&#x152; ŕŻ&#x153;ŕ&#x20AC;ଵ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026;ŕ°?ଵା ŕ°? á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť (15) ߪ ଷ଴ ଶ ŕ°? á&#x2C6;şÍ´Í´Í´ ŕ°Ž ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ଷ଴ ŕ°?ŕ°Žŕ°Ž were run using values for individual stocks. stabilized enough to buy the stock safely. ଶ ଵ (15) Ď&#x192;ଷ଴ á&#x2030;&#x20AC;ߎ ŕľ&#x2026; á&#x2030; ŕľ&#x2026; â&#x20AC;Ť×&#x203A;â&#x20AC;Ź ߎ á&#x2C6;ť â&#x20AC;Ť×&#x203A;â&#x20AC;Ź á&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť (15) ߪ ଶ ŕľ&#x152; Ď&#x192; ଵ Ď&#x192; ŕŻ&#x153;ŕ&#x20AC;ଵ ŕľ&#x2026;ଵ á&#x2C6;ťá&#x2C6;şÍ´Í´Í´ (15) coefficients  were  significant  at  the  1%  level.   ଵ ŕľ&#x2026; á&#x2030; ଵ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť ŕľ&#x2026;ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť á&#x2C6;şÍ´Í´Í´ á&#x2030; â&#x20AC;ŤßŽ×&#x203A;â&#x20AC;Ź â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł â&#x20AC;Ť×&#x203A;â&#x20AC;Źŕľ&#x2026;ߎÉ?á&#x2C6;ť (15) ߪ ŕľ&#x152; ŕŻ&#x153;ŕ&#x20AC;ଵߪá&#x2030;&#x20AC;ߎŕľ&#x152;ଵ ŕľ&#x2026; ŕŻ&#x153;ŕ&#x20AC;ଵ ଵା ŕ°?á&#x2030;&#x20AC;ߎ ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ଵା ŕ°?
Section  IV:  Methodology Â
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ŕ°?ŕ°Ž
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ଵା ŕ°?ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť
Although the regression models do accu-
ŕ°? ŕ°Ž ଷ଴ á&#x2030;&#x20AC;ߎĎ&#x192;ଵଷ଴ ŕľ&#x2026; á&#x2030;&#x20AC;߮ଵâ&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ߮ଵ á&#x2C6;ťá&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ťŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026;(15) ߪ ଶ ŕľ&#x152; ߪĎ&#x192;ŕľ&#x152; ŕľ&#x2026; á&#x2030; ŕľ&#x2026;ŕ°Ž á&#x2C6;şÍ´Í´Í´ á&#x2030; â&#x20AC;Ť×&#x203A;â&#x20AC;Źŕľ&#x2026; â&#x20AC;ŤßŽ×&#x203A;â&#x20AC;Ź É?á&#x2C6;ť ŕŻ&#x153;ŕ&#x20AC;ଵ ට ŕŻ&#x153;ŕ&#x20AC;ଵଵା ŕ°? ŕ°? ŕ°Ż
ଵା ŕ°?ŕ°Żâ&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ŕ°?
ŕ°Ž ߪ ŕľ&#x152; ටĎ&#x192;ଷ଴ á&#x2030;&#x20AC;߮ଵ ŕľ&#x2026;ŕ°?ŕ°Ž á&#x2030; ŕľ&#x2026; á&#x2C6;şÍ´Í´Í´ â&#x20AC;ŤßŽ ×&#x203A;â&#x20AC;ŹŕŹľ á&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť ŕ°Ž ŕ°Ż â&#x20AC;Ť×&#x203A;â&#x20AC;Źá&#x2C6;şŕŻ&#x153;ିଵá&#x2C6;ť ߪ ŕľ&#x152; ටĎ&#x192;ଷ଴ á&#x2030;&#x20AC;ߎŕŻ&#x153;ŕ&#x20AC;ଵŕľ&#x2026; ଷ଴ ŕ°?ଵା ŕ°? á&#x2030; ŕľ&#x2026;ŕ°? á&#x2C6;şÍ´Í´Í´ â&#x20AC;Ť ߎ ×&#x203A;â&#x20AC;Źá&#x2C6;ť â&#x20AC;Ť ×&#x203A;â&#x20AC;Źá&#x2C6;şÍł ŕľ&#x2026; É?á&#x2C6;ť ŕ°Ž
(16)
(16)
(16)
For example, stocks in the Telecommunica-
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Equity Volatility across Industries from IPO Day The results of the regressions for each industry and the market benchmark are as follows with
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corresponding sample sizes and t-‐statistics in parentheses: corresponding sample sizes and t-‐ statistics in parentheses:
Variable Name counter total permno denominator vbar
Value Day from IPO Sum total of all values for a given counter value CRSP-assigned permanent identification number for company Number of companies for a given counter value Calculated value of industry volatility rating for a given counter value
Table 2. STATA variables.
Appendix I: Description Of Nonlinear Regression Process For Stata
sion, all other variables can be dropped.
Nonlinear regression models can be To calculate the values for a given in- specified using Stata’s nl command. Repredustry data set pulled from CRSP, the value senting using C1, using C2, and using of all volatility ratings were added into one C3, the regression is generally run using: total sum using: by counter:egen total=sum(v)
nl (vbar = {C1} + {C2}/ (1+{C3}*(counter-1)))
Sector
Sector
(Baseline Volatility) (Baseline
(IPO-Driven (IPO-‐Driven
(Stabilization (Stabilization Rate)
R2
R2
Equity Volatility across Industries from IPO Day
Volatility) Rate) Volatility) Volatility) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 Equity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific Equity Volatility across Industries from IPO Day Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 methodology, see Appendix I. All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐specific All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 methodology, see Appendix I. methodology, see Appendix I. methodology, see Appendix I. Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Section V: Results Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Section V: Results Section V: Results Section V: Results Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 The results of the regressions for each industry and the market benchmark are as follows with (143) Market (S&P 500)
0.0470464 (20.04)
0.1760342 (19.88)
1.936521 (5.20)
.9379
Oil & Gas (578)
0.049487 (17.32)
0.1118282 (10.66)
1.686358 (2.93)
.8142
corresponding sample sizes and t-‐statistics in parentheses: Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 The results of the regressions for each industry and the market benchmark are as follows with The results of the regressions for each industry and the market benchmark are as follows with The results of the regressions for each industry and the market benchmark are as follows with corresponding sample sizes and t-‐ statistics in parentheses: corresponding sample sizes and t-‐ statistics in parentheses: corresponding sample sizes and t-‐ statistics in parentheses: Table Sector 3. Regression results ordered by values. 0.7072644 (40.15) Technology (890) 0.1173751 (26.78) Telecommunications (143)
Sector Sector Sector
2.997637 (8.57) .9837
R2
0.0297135 (12.20) 0.1283577 (16.27) .9137 (Baseline Volatility) (IPO-‐Driven 1.045903 (4.98) (Stabilization Rate) 2 2
R R R2
Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) .8794 Because the regression requires the estiVolatility) 2.732502 (3.12) R2 Sector (Baseline Volatility) (IPO-Driven (Stabilization (Baseline (Baseline Volatility) (IPO-‐Driven (Stabilization Rate) (IPO-‐Driven (Stabilization Rate) (Baseline Volatility) (IPO-‐Driven (Stabilization Rate) mation of three coefficients with only two The number of individual companies in Equity Volatility across Industries from IPO Day given variables, however, initial value estithe industry was then determined using: Volatility) Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) Rate) 1.496436 (7.88) .967 Volatility) mates for all three variables must be passed Volatility) Volatility) Volatility) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 by permno counter:generate in order generate the desired results. After All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific For tables ordered by regression outcomes, see Appendix II. For graphs of the regression models with Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) .992 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.8061891.463953 (8.81) (8.87) .9884 denominator=_N experimentation, it was discovered that Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 0.05, 0.2, and 1.75 can be used methodology, see Appendix I. as initial calculated values, see Appendix V. Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) .988 To calculate the average volatility rat- values for C1, C2, and C3 respectively in Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.9365213.806189 (8.87) (5.20) .9379 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 every industry to produce the regression ings for the data, set, a simple average of Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 results with the best fit: these values was taken: Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .986 10 Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137
generate vbar = total/denominator
After using these commands, all stocks have the same “vbar” rating on any given counter day so duplicates can be dropped by counter: duplicates drop counter, force
Section V: Results Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 .9884 nl (vbar = {C1} + {C2}/ (143) Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .961 (1+{C3}*(counter-1))), initial Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Financials (2058) .9860 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Oil & Gas (578) 0.0395426 (69.25) 0.049487 (17.32)0.0907731 (42.87) 0.1118282 (10.66) 1.769266 (11.59) 1.686358 (2.93) .8142 (C1 0.05 C2 0.2 C3 1.75) Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.4248312.424831 (7.50) (7.50) .9740 The results of the regressions for each industry and the market benchmark are as follows with Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) .974 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Healthcare (821) 0.2345721 (25.97) .9619 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Financials (2058) 0.0575546 (25.57) 0.0395426 (69.25) 0.0907731 (42.87) 2.959527 (5.58) 1.769266 (11.59) .9860 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.4964361.936521 (5.20) (7.88) .9675 Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) .937 Appendix II: Ordered Regressioncorresponding sample sizes and t-‐statistics in parentheses: Results Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) .9740 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.424831 (7.50) 2.732502 (3.12) .8794
For all regression tables, relevant sample Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .814 0.0470464 (20.04) 1.936521 (5.20) R2 Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 Market (S&P 500) 0.1760342 (19.88) .9379 Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 sizes and t-statistics are listed parentheti- Sector Table 4. Regression results ordered by values. The leftover observations represent in- cally. Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .983 (Baseline Volatility) (IPO-‐Driven (Stabilization Rate) dustry volatility with vbar and use counter Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 .8142 to show how much time has passed from Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .913 IPO. Before running the nonlinear regresVolatility) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 .9837
Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .879 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137
The results of the regressions for each industry and the market benchmark are as follows with e results of the regressions for each industry and the market benchmark are as follows with The results of the regressions for each industry and the market benchmark are as follows with
-46corresponding sample sizes and t-‐ statistics in parentheses: responding sample sizes and t-‐ statistics in parentheses: corresponding sample sizes and t-‐ statistics in parentheses: Sector Sector Sector
PO Day
Sector
ECONPress
R2 R2 R2
R (IPO-Driven (Stabilization (Baseline (Baseline Volatility) (IPO-‐ Driven (Stabilization Rate) (Baseline Volatility) (IPO-‐ D(IPO-‐ riven (Baseline Volatility) Driven (Stabilization Rate) (Stabilization Rate) 2
Volatility) Rate) Volatility) Volatility) Volatility) Volatility) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 n using Stata version 11.1. For a discussion of Stata-‐ Equity Volatility across Industries from IPO Day uity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day specific Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 sic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12)specific .8794 All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ All calculations and regressions were run using Stata version 11.1. For a discussion of Stata-‐ specific Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 nsumer Goods (653) 0.1378587 (30.74) 1.463953 (8.81) Consumer Goods (653) 0.0390784 (31.01) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 .9929 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 methodology, see Appendix I. thodology, see Appendix I. Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 methodology, see Appendix I. Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 nsumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 .9884 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Oil & Gas (578) 0.0395426 (69.25) 0.049487 (17.32)0.0907731 (42.87) 0.1118282 (10.66) 1.769266 (11.59) 1.686358 (2.93) .8142 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 ancials (2058) .9860 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Section V: Results ection V: Results Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Section V: Results ndustry and the market benchmark are as follows with Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 2.959527 (5.58) 1.463953 (8.81) .9929 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 althcare (821) 0.0575546 (25.57) 0.2345721 (25.97) .9619 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137
ics in parentheses: The results of the regressions for each industry and the market benchmark are as follows with e results of the regressions for each industry and the market benchmark are as follows with Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 dustrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) The results of the regressions for each industry and the market benchmark are as follows with Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 .9740 (143)
corresponding sample sizes and t-‐ sordered tatistics in parentheses: statistics in parentheses: responding sample sizes and t-‐ 0.0470464 (20.04) R2 Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 arket (S&P 500) 0.1760342 (19.88) 1.936521 (5.20) statistics in parentheses: Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 .9379 corresponding sample sizes and t-‐ Table 5. Regression results by values.
Volatility) (IPO-‐Driven (Stabilization Rate) Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 .8142 Sector Sector R2 R2 R2 Sector Volatility) 0.1173751 (26.78) Technology (890) 0.7072644 (40.15) 2.997637 (8.57) chnology (890) 0.7072644 (40.15) 2.997637 (8.57) 2 .9837 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) R.9837 .9837 Sector 0.1173751 (26.78) (IPO-Driven (Stabilization (Baseline (Baseline Volatility) (IPO-‐ Driven (Stabilization Rate) (Baseline Volatility) (IPO-‐ D(IPO-‐ riven (Baseline Volatility) Driven (Stabilization Rate) (Stabilization Rate) 3 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 Volatility) Rate) Volatility) 0.1283577 (16.27) Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 ecommunications (143) 0.0297135 (12.20) 1.045903 (4.98) .9137 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 Volatility) Volatility) Volatility) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 4 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 (42.87) 2.732502 (3.12) Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 lities (206) 0.0460092 (13.93) .8794 Financials (2058) 0.0276752 (33.32) 0.0395426 (69.25) 0.0907731 1.769266 (11.59) .9860 Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 sic Materials (548) 0.0632364 (27.65) 1.496436 (7.88) Basic Materials (548) 0.0303853 (47.53) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 .9675 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 4 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 (31.54) 2.424831 (7.50) Industrials (1141) 0.0412802 (47.95) 0.1061883 .9740 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 nsumer Goods (653) 0.1378587 (30.74) 1.463953 (8.81) Consumer Goods (653) 0.0390784 (31.01) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 .9929 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 6 (69.25) Basic0.0907731 (42.87) 1.769266 (11.59) .9860 (27.65) 1.496436 (7.88) Materials (548) 0.0303853 (47.53) 0.0632364 .9675 .9884 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) nsumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 .9884 For tables ordered by regression outcomes, see Appendix II. For graphs of the regression models with tables ordered by regression outcomes, see Appendix II. For graphs of the regression models with For tables ordered by regression outcomes, see Appendix II. For graphs of the regression models with Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 6 (25.57) Market 0.2345721 (25.97) 2.959527 (5.58) 0.1760342 .9619 (19.88) 1.936521 (5.20) (S&P 500) 0.0395426 (69.25) 0.0470464 (20.04) .9379 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 ancials (2058) 0.0907731 (42.87) 1.769266 (11.59) .9860 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 calculated values, see Appendix V. culated values, see Appendix V. calculated values, see Appendix V. Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 2 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 althcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 .9619 (143) 4 (20.04) Utilities 0.1760342 (19.88) 1.936521 (5.20) .9379 (13.93) 2.732502 (3.12) (206) 0.0276752 (33.32) 0.0460092 .8794 10 10 10 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 dustrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 arket (S&P 500) 0.1760342 (19.88) 1.936521 (5.20) Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 .9379 Table 5. Regression 0.0470464 (20.04) results ordered by R2 values. 1 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 & Gas (578) 0.049487 (17.32) 1.686358 (2.93) Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 0.1118282 (10.66) 1.686358 (2.93) .8142 .8142 5 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 chnology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 .9837 2 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 ecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 .9137
Utilities (206) lities (206) Utilities (206)
0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 .8794
Equity Volatility across Industries from IPO Day
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Appendix III: Correlation Between R2 And Industry Sample Size
The results of a linear regression of sample sizes on R2 values show that sample size and quality of regression fit are not significantly correlated.
Appendix Iv: Correlation Between Long-Run Volatility And IPO Volatility
Appendix V: Calculated And Regression Results As A Function Of Day From IPO The following graphs were generated by Stata and show both observed values and estimated regression models as a function of day from IPO . Observed values are represented in red and are labeled “vbar” for each industry graph and “average” for the S&P 500 graph. Regression estimates are represented in blue and are labeled “Fitted values” for all graphs. All graphs were generated using Stata version 11.1. For all graphs, day relative to IPO is measured on the x-axis and average industry volatility is measured on the y-axis.
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ECONPress
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Equity Volatility across Industries from IPO Day
S&P 500
Consumer Services
Industrials
Telecommunications
Base Materials
Financial Services
Oil & Gas
Utilities
Consumer Goods
Healthcare
Technology
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ECONPress Works Cited
Baillie, Richard T. and Ramon P. DeGennaro. “Stock Returns and Volatility.” The Journal of Finance and Quantitative Analysis, Volume 25, Number 2, pages 203-214. Christoffersen, Peter F. and Francis X. Diebold. “How Relevant is Volatility Forecasting for Financial Risk Management?” The Review of Economics and Statistics, Volume 82, Number 1, February 2000, pages 12-22. Draho, Jason. The IPO Decision: Why and How Companies Go Public. Edward Elgar Publishing, Inc.: Northampton, MA (2004). Lowry, Michelle, Micah S. Officer, and G. William Schwert. “The Variability of Initial IPO Returns.” The Journal of Finance, Volume 65, Issue 2, April 2010, pages 425-465. Schwert, G. William. “Stock volatility in the new millennium: how wacky is Nasdaq?” Journal of Monetary Economics, Volume 49, Issue 1, January 2002, pages 3-26. Schwert, G. William. “Why Does Stock Market Volatility Change Over Time?” The Journal of Finance, Volume 44, Number 5, December 1989, pages 1115-1153. Simon, David P. “The Nasdaq Volatility Index During and After the Bubble.” The Journal of Derivatives, Volume 11, Number 2, Winter 2003, pages 9-24. Sinclair, Euan. Volatility Trading. John Wiley & Sons, Inc: Hoboken, NJ (2008).
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Should punitive damages be scaled to wealth?
Should Punitive Damages be Scaled to Wealth? Harrison A Seitz
Northeastern University
R Introduction In cases in which society, and by proxy, courts, want to deter future problematic behavior, punitive damages serve a fundamental role. As an additional source of damages that can be levied upon an injuring party, punitive damages can excise gains that were obtained through illegitimate or harmful means and also prevent future similar actions from being taken. However, there are many questions that must be resolved in order for punitive damages to have any merit in our justice system. How large do punitive damages need to be in order to provide a socially optimal level of deterrence? How large ought punitive damages be in relation to compensatory damages awarded in the same case? Should the injurer be liable for harms that may have occurred to a third party? The discussion of punitive damages, especially in their relation to tort reform, has been a popular topic in the public discourse in the past couple of years. There are many scholars, supported by legislation and decisions at the state and federal levels, who advocate strongly for restricting punitive damages or eliminating them entirely. On the other hand, there are those who would suggest that the extent of punitive damages ought to be modified or increased. This paper will discuss one proposed modification of punitive damages, which is the inclusion of the wealth of the injurer as a factor in considering the magnitude of the damages.
Literature Review There have been several opinions published in the literature regarding this issue. The first piece of relevant literature is a response paper by A. Mitchell Polinsky, titled, “Are Punitive Damages Really Insignificant, Predictable, and Rational? A Comment on Eisenberg et al.” (1997). In this paper, Polinsky rebuffs three assertions made by separate study of punitive damages. First, Polinsky demonstrates that punitive damages, although seemingly insignificant on a trial level because the amount awarded over a large number of cases is relatively small, still have significance in the pretrial settlement process and are therefore still a part of an injurer’s decision calculus. Second, Polinsky shows that punitive damages are typically unpredictable not only in when they are awarded, but also in determining their magnitude. For example, he notes that the injurer’s conduct as well as the type of misconduct may have varying impacts on whether or not punitive damages are awarded. Finally, Polinsky addresses the argument that there is a positive correlation between punitive and compensatory damages. He argues that there are cases in which there may be positive or negative correlations between the two values, thus assumptions about how punitive damages ought to be constrained based on proportionality are not rational. For example, he addresses cases in which the injurer may have zero chance of escaping liability. In accordance with theory that punitive damages are meant as a deterrent, in these cases there can be no meaningful deterrence from punitive damages, thus they ought to be lower even if the compensatory damages are high. The second piece of relevant literature on this topic is a paper titled, “A Theory of Wealth and Punitive Damages,” by Keith Hylton (2008). In this paper, Hylton argues that wealth should be a consideration in the calculation of punitive damages for some cases. In general, the conclusion that he reaches is, “Where the parameter of in-
-52terest in the determination of an optimal punitive award, external cost or internal gain, is unobservable and correlated with the defendant’s wealth, the optimal punitive award will be a function of the defendant’s wealth”. Put simply, this tells us that in some cases, an injurer’s valuation of committing a harmful act may increase according to their wealth, much like how a normal good’s value increases with a consumer’s wealth. In order to achieve an optimal amount of punishment, Hylton would argue that punitive damages should be scaled to wealth. The third piece of related literature that will be discussed is a paper from A. Mitchell Polinsky and Steven Shavell titled, “Punitive Damages: An Economic Analysis” (1998). This article is an extensive look at punitive damages with attempts to explain a formula-based approach to determining optimal awards. Additionally, this piece covers the issue of wealth in the determination of punitive damages. Polinsky and Shavell argue that wealth should never be a consideration in determining the scale of punitive damages for several reasons. First, they cite that it discourages corporations from expanding and taking any sort of risks because greater wealth actually increases their liability. Under this point, they also argue that the deciding factors in determining the amount of punitive awards ought to be limited to solely the amount of harm caused and the chance of escaping liability. In contention with these claims, they note some circumstances in which wealth could be a useful determinant of the magnitude of punitive damages. They first demonstrate that injurers who are poorer are more likely to be risk-averse since they cannot afford liability insurance and will take proper prevention measures. In this case, they ought to receive lower levels of punitive damages. The next argument they advance is that wealthier individuals tend to value money less, so in order to offset the utility that they gain from causing harm, they must be punished proportional to their wealth.
ECONPress The next piece of relevant literature is a paper by Robert Cooter titled, “Punitive Damages, Social Norms, and Economic Analysis” (1997). In this paper, Cooter describes the economic reasoning behind punitive damages and their purpose of either internalizing costs or deterring future behavior. In the discussion of how punitive damages ought to be determined, Cooter argues that the criteria for punishment to achieve deterrence should be determined on the basis of the actual harm caused and the expected liability. In cases in which the harm caused may be unclear, such as when the illicit gain may be satisfaction, Cooter argues that even though there is no clear standard for how to value that satisfaction, courts ought to use aggregate statistical data to form the amounts of punitive damages, much like fines for criminal acts.
damages that exceed the combined amount of the harm caused to the victim and gains that the injurer may have made from committing a malicious action. This suggests that the goal of punitive damages is not to internalize costs (as compensatory damages do this already, assuming they are set at the correct amount), but rather to deter future malicious behavior.
Analysis
A common theory of how punitive damages ought to be determined in order to achieve optimal deterrence is the simple calculation of the cost of the harm multiplied by “punitive damages multiplier”, or essentially the chances that the injuring party will actually be held liable for their action (Polinsky and Shavell, 1998). This method of deterrence seeks to reach an optimal level based on a valuation of the social costs of harmful behavior. Proponents of this calculation would argue that because this is the only way to achieve a specific, non-arbitrary level of punitive damages, wealth should not be a consideration. It can be said that any rational actor will only consider taking preventative action based on calculations of expected costs. In this case, only the direct value of the harm that an injuring party causes can be expected. For example, in a case of an automobile accident, the wealth of the driver is irrelevant since they will both presumably take the same measures to prevent an accident from happening and cause the same amount of harm. If the damages were instead scaled to wealth, it would actually cause inefficient over-deterrence since the punishment is based off a more arbitrary and far less contributory factor.
Before analyzing the effects of considering the injurer’s wealth, it would be useful to first define what situations should deserve punitive damages. According to Cooter, punitive damages are awarded when the injurer’s behavior is determined “bad enough”, or malicious enough to warrant additional punishment (1997). Punitive damages are considered to be any
On the other hand, there are situations in which the value of the harmful action committed by the injuring party may be relevant. As a person’s wealth increases, their valuation of nominal amounts of money decrease due to diminishing marginal returns. However, we can consider the utility that an injuring party gains from causing harm to be similar to a normal
The last piece of relevant literature that will be discussed is a study from Theodore Eisenberg, et. al, titled, “The Decision to Award Punitive Damages: An Empirical Study” (2009). Using cross-sectional data from 2005, this study determined a model to explain the relationship between how often punitive damages are requested in civil cases, how often they are awarded, and how proportional they are to compensatory damages. They found that punitive damages are very rarely pursued, were likely to be awarded if they were, and were often proportional with regards to the compensatory damages awarded in the case.
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Should punitive damages be scaled to wealth?
good (Hylton, 2008). As their wealth increases, they would be more willing to pay for that amount of utility. This would tell us, then, that the amount of punitive damages shouldn’t be based on the exact monetary harm caused by the injurer, but rather on how much they would value that harm. The justification behind this is because in order to achieve deterrence, the punitive measures must have some sort of impact in meaningfully changing the injurer’s behavior. If punitive damages were restricted to proportionality to the harm caused, then wealthier individuals would be able to internalize the punishments in many cases and would not be deterred from committing harmful actions in the future.
Conclusion Based on the goal of deterring future harmful behavior, it would seem as if considering wealth in punitive damages fulfills the philosophical intent as well as providing an optimal level of deterrence based on the injurer. However, this is problematic for determining legal consistency or a bright line in calculating the magnitude of punitive damages. In addition to muddling the standard for acceptable punishment, scaling punitive damages to the wealth of the injurer may discourage individual and firm behavior in ways that are unjustified. For example, increased liability because of wealth may disincentivize corporations from conducting research and development. In another case, wealthier people may be subject to a disproportionate amount of risk from punitive damages that they could not meaningfully be able to prevent in some cases, causing over-deterrence. Based on the context, it may be useful for wealth to be considered in determining the amounts of punishment, but it should be restricted to some reasonable standard in order to have solvency and to check abuse.
R
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ECONPress Works Cited
Cooter, R. (1997). Punitive damages, social norms, and economic analysis. Law and Contemporary Problems, 60(3), 73-91. Eisenberg, T., Heise, M., Waters, N., & Wells, M. (2009). The decision to award punitive damages: an empirical study. Cornell Law School Legal Studies Research Paper Series. Retrieved from http://ssrn.com/abstract=1397587. Hylton, K. (2008). A theory of wealth and punitive damages. Widener Law Journal, 17. Retrieved from http:// www.bu.edu/law/faculty/scholarship/workingpapers/documents/ HyltonKWealthPunitives2REV.pdf Polinsky, A.M. (1997). Are punitive damages really insignificant, predictable, and rational? a comment on eisenberg et al. The Journal of Legal Studies, 26(S2), 663-677. Polinsky, A.M., & Shavell, S. (1998). Punitive damages: an economic analysis. Harvard Law Review, 111(4), 869-962.
International Collective Action on Climate Change
International Collective Action on Climate Change
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Climate Change And Uncertainty
Over the last hundred years, the mean global temperature has risen by approximately .6 degrees Celsius. This change has coincided with a drastic increase in the concentration of greenhouse gases (primarily carbon dioxide) in the Earth’s atmosphere. Evan Richards Sankey Though there is a vocal minority of climaNortheastern University tologists who deny it, the vast mainstream opinion favors the proposition that the industrial revolution caused the increase in greenhouse gases (concentrations are thought to have risen by about 30% since 1750) which in turn is heating the Earth up Climate change is a negative externality (Barrett, 2007). The basic warming mechawhich afflicts humanity on a global scale. nism is that an excessive level of greenhouse If it is left unchecked, it is reasonable to gases in the upper atmosphere absorbs exexpect that warming will negatively affect cessive levels of infrared radiation from the the diversity of our biosphere, our economy sun and increases the overall temperature of and our way of life. Any remedy for global the Earth. climate change – one which slows or halts further increases in the global temperaUnfortunately, climatologists are far ture by curbing greenhouse gas emissions less certain of the future path of warm– would classify as a pure public good. ing and the consequences it will have. The That is, it would be both non-rival and most reliable climate models predict that non-excludable. On a global level, this has over the next century, the average global huge implications. A welfare improvement temperature will increase by a further 1.4 brought to the citizens of Bangladesh by to 5.8 degrees Celsius (Barrett, 2007). It is climate change mitigation could be equally widely believed in the scientific commuenjoyed by Americans and Europeans. Ad- nity that at some point, these temperature ditionally, no body anywhere could be pre- changes could cause catastrophic changes vented from enjoying these benefits. These in climate patterns. The shrinking of the ice characteristics, however, seem to present sheets in Greenland and Antarctica could policy-makers with a problem. The guar- lead to changes in the undersea currents anteed benefits of mitigation to all may in the Atlantic Ocean which might lead to generate a destructive incentive for some drastic cooling in Northern Europe. Meltto free-ride on its provision by others. This ing ice may also make life very difficult for paper will begin with a brief introduction countries at low elevations like the Malto the scientific community’s assessment of dives and Bangladesh. Average sea levels climate change. It will follow with an over- rose by about two tenths of a meter in the view of the literature on collective action last century. Some expect them to rise by and its application to the problem at hand. half a meter in this century. Another posThen there will be a critical examination sibility is that changes in rainfall patterns of current and past international efforts to could render large parts of the southwestaddress climate change. It will conclude by ern United States uninhabitable. Events suggesting possible alternatives to these ef- such as these could entail huge costs to the forts. global economy. William Nordhaus, an economist at Yale University, has made a widely publicized calculation that unabated
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-56climate change could potentially lower the gross domestic product of the world by 2% by 2100. An alternate estimate made the British Government that global GDP will take a hit of between 5.3% and 13.8% by 2200 (Barrett, 2007). Complicating this picture even further is the notion that the costs of climate change will not be evenly distributed. Countries at specific latitudes are expected to benefit from increased agricultural opportunities which warming will present. The key point here is that the benefits of climate change mitigation – the benefits of attempting to avoid a variety of disastrous possibilities – are highly uncertain. A similar pattern holds for the cost side of the equation. Policies which aim to limit greenhouse gas emissions will necessarily target the sources of those emissions: transportation, power generation and industrial machines. An otherwise unnecessary investment in a massive expansion of nuclear power and low emission vehicles seems in the cards. This will undoubtedly be costly, but again it is unclear exactly how costly. Drastic action on climate change such as a commitment to cut carbon dioxide emissions by 50% has been calculated to lower global output by between 1% and 3% with poorer countries incurring less cost than wealthy countries (because they use energy more inefficiently). Other estimates are much higher. The models used to generate these figures necessarily involve certain assumptions which may not hold in reality. There are always unintended consequences. A further consideration is that the costs of action will likely be front-loaded. That is, the pain will come early, and the benefits of mitigation will take possibly hundreds of years to become evident. This makes a direct comparison of costs and benefits inherently difficult. What should be clear from this overview is that there is room for reasonable international policymakers to disagree about the net payoffs and worthwhile goals associated climate change mitigation. Awareness of this capacity for disagreement
ECONPress is critical for understanding the prospects for effective collective action.
Olson And The Collective Action Problem The modern conception of collective action in the context of political economy is based on the work of Mancur Olson. In The Logic of Collective Action published in 1965 Olson mounted a massive critique of the prevailing wisdom at the time on group behavior. Groups had been conceived as perfect embodiments of the common wills of their individual members. Effective collective action was taken as given (Sandler, 2004). Olson’s model imagines groups as existing to provide their members with intra-group public goods – that is, goods which no group member can be prevented from benefitting equally from. A classic example is a labor union which wins a wage increase from management by striking. Obviously all union members, even those who did not strike will enjoy the wage increase. This tension is the crux of Olson’s contribution. There emerges within groups a gap between the level of a public good (in this case a strike) which is optimal for the group as a whole to provide, and the level which is optimal for an individual member of that group to provide. Since all union members benefit from a strike-induced wage hike, each member will try to “freeride” on every other member’s walkout. As a result, this particular public good is undersupplied. Though Olson considers this problem to be endemic to group behavior in general, he highlights some group characteristics which can variously aggravate or remedy the free-rider problem. Small groups are most likely to supply an optimal level of public goods. Their most important advantage stems from the fact that their members’ contributions to the provision of their goal are clear and large. If a member is contemplating free-riding,
International Collective Action on Climate Change
he will see that the venture will fall apart without his contribution. Contribution becomes a dominant strategy. Smaller groups also find it easier to coordinate solutions to the the problem of verification and enforcement and arbitrate conflicts of interest between its members. Finally, members of small groups will tend to engage with one another repeatedly over time. The prospect of repetition can be a powerful incentive to cooperate with your peers (Shepsle, 2010). Small groups’ tendency to achieve their stated goals makes them what Olson calls “privileged” groups. Large groups, on the other hand, are seen as being much less effective at providing an optimum level of public goods to their members. In general, as groups get larger each individual contribution will count for a smaller percentage of the collective outcome. Therefore, holding costs constant, the probability that the individual will find contribution worth his while declines. Then too, a large group will find it difficult to verify and enforce compliance and reconcile more frequent conflicts of interest between its members. Free riders in a large group are anonymous and probably only identified at a high cost. Furthermore, it is difficult to prevent them from using a good which is by definition non-excludable. Overall, large groups’ size makes them unlikely to be able to surmount these various coordination problems and therefore unlikely to supply the optimal level of public goods to their members. As a result, Olson labels them as “latent” groups. Another important determinant of the effectiveness of groups at supplying public goods is the nature of their membership. Some groups are highly homogenous. Their members are more likely to look alike, talk alike and think alike. They are less likely to get caught up in conflicts of interest because their members’ preferences are more homogenous. Unsurprisingly, small groups tend to be more homogenous (that is often why they form in the first place). This status
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further augments their capacity to provide public goods. Large groups, however, are usually highly heterogeneous. Their members have widely divergent priorities, beliefs and levels of knowledge. This variety massively increases the probability that the aforementioned problem of anonymity and enforcement as well as the scope for deep conflicts of interest will make cooperation impossible. Surprisingly, the heterogeneity of large groups may sometimes be a blessing in disguise. As heterogeneous groups grow, the probability that a small group of large and highly capable group members will choose to supply the public good grows. The reason for this is that large and capable members usually have more to gain overall from the provision of a public good than the small, less capable members. They may decide that their potential gains are so large that they will supply the entire public good themselves (thereby making the group privileged), despite the inevitability that smaller members will free-ride (Sandler, 2004). This notion will prove invaluable for understanding the role of rich countries in climate change mitigation. In the absence of a government which can force cooperation and public good provision through outright coercion, some groups (especially large ones) will remain perpetually latent with their members worse off as a result. Olson refuses to accept this sorry state of affairs and proposes a remedy. In large groups, the core impediment to optimal public good provision is, as already noted, the fact that individual members notice that their individual contributions seem to count for less while the costs they incur to contribute remain fixed. Therefore, as the group grows, members’ willingness to work for the group declines. Olson’s solution is to attach private benefits to contribution towards the public good. If those who contribute (and only those who contribute) are guaranteed a wholly private benefit like a cash payment, members’ overall willingness to contribute would be greatly enhanced (Shepsle, 2010). It would
-58be a challenge, of course, to determine the optimal level of private payments to confer on contributors. Too low and the public good will remain undersupplied, but too high and the group may exhaust its collective resources making excessive payments to its members. The payments must come from somewhere!
International Collective Action On Climate Change The first, most obvious observation to make about the international community is that it is mostly comprised of sovereign nation states which are fiercely protective of their rights to self-determination. There is no world government with unlimited coercive powers which can be expected to save the day simply by mandating global cuts in carbon emissions. There are (depending on the definition) about 193 sovereign states in the world. On their own, many of them have succeeded in providing public good solutions to various regional externalities like excessive water and air pollution. However, at a global level, the community of nations is not so different from a group of self-interested individuals. Since there is no known other civilization to compare it to, it is unclear exactly how large and heterogeneous we can consider our global community to be. However, in order to proceed, this analysis will consider it to be large and heterogeneous. This seems reasonable. There are many more countries now than there were at the close of World War II and their interests seem to be as divergent as ever. The weaknesses of large heterogeneous groups correspondingly apply. The countries of the Earth will attempt to free-ride on the provision of climate change mitigation by others and there will be little to keep them from doing so because global verification and enforcement is quite difficult (as evidenced by our nuclear proliferation problems). Furthermore, as already
ECONPress noted there is scope (even if just based on the uncertainty in the data) for reasonable countries to come to quite different conclusions about the costs and benefits of climate change mitigation and therefore about the emissions targets which will play a huge part in any mitigation agreement. At a glance then, it would seem that cooperation on supplying the public good of climate change mitigation is not forthcoming and that the world is not a privileged group. On closer examination, however, our prospects are not so terrible. The heterogeneity of the world is also a major strength. There are severe inequities in wealth, population size and carbon emissions amongst those 193 countries. The United States alone comprises approximately 20% of global output and 16% of global carbon dioxide emissions. Similarly, a relatively small number of countries have most of the Earth’s population and wealth and generate most of its carbon emissions. In fact, a formal organization of states which fits this description already exists. It is called the Group of Twenty or G20. It includes (among others) China, India, the United States, the United Kingdom, Russia, Germany, and Japan – countries which are all major players on the world stage. Precisely because of this, however, these nations have significantly more in common with each other than with the majority of small and relatively less influential states in the world. Each of these countries would sustain big loses to their economies (if only because they have more to lose) were some or all of the disastrous climate scenarios predicted by climate models to come true. None would gain from climate change, as some small agriculturally dependent countries would. This is not to say, however, that their interests are perfectly aligned. As we will see, there is considerable disagreement between the developed and developing wings within this group of major players over what to do about climate change. As a result, it is unclear whether these commonalities are enough to encourage them to provide cli-
International Collective Action on Climate Change
mate change mitigation for the world.
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of an international environmental agreement which achieved its stated intentions. There are two other factors working in It is therefore important to understand why favor for these major countries (like those it worked so well. in the G20) possibly supplying the public good of climate change mitigation. The first In the 1970s and 1980s a number of sciconcerns the nature of mitigation itself. This entific studies were published which made small, but weighty group of countries might it abundantly clear that emissions of CFCs be thought of as a “k-group” – a grouping of from industrial processes and aerosol cans actors whose full participation is necessary were drifting into the upper atmosphere, to supply the public good (Shepsle, 2010). interacting with sunlight and causing seriThe smaller countries’ free-ridership can be ous damage to the earth’s ozone layer. The tolerated because they do not matter very ozone layer is important because it protects much to mitigation. However, if even one the surface of the Earth from harmful ullarge country free-rides, the goal (the emis- traviolet rays from the sun. Ultraviolet rays sions target) cannot be reached (McGinnis are known to cause damage to plant life and & Somin). This fact serves as an incentive sea life and well as skin cancer in humans for each nation to contribute lest the pub- (Barrett, 2007). Like carbon dioxide, CFCs lic good not be provided at all. However, drift around in the atmosphere far from as noted by Kenneth Shepsle in Analyzing where they are emitted. As a result CFC Politics, this will be no consolation if even emissions by multiple emitters combine to some of the countries involved believe that make everyone worse off. Ozone damage the costs of contribution outweigh the ben- mitigation can therefore be considered a efits. The dominant strategy will turn to de- public good, suffering from the same ostenfection. Secondly, these major players, the sible problems of international collective G20 members, tend to interact frequently. action as climate change mitigation. Yet, This is not a one-shot game. Life will go the treaty was successful. on and there will be future issues (like this one) which many of these countries will The Montreal Protocol as well as the have to cooperate with each other on in dozen amendments which followed and order to solve. In contemplating torpedo- strengthened it has led to a sharp decline ing the provision of climate change mitiga- in the concentration of CFCs in the atmotion, a large country may find the prospect sphere and a recovery in the strength of the of future reprisals by its peers too costly to ozone layer which is expected to continue. be engaging in intransigence. Given all of How was the Montreal Protocol so fantastithese favorable factors, it seems odd that we cally successful at solving a problem which don’t already have an effective mitigation seems so similar to climate change? There is agreement. some disagreement on this question, but it seems the single biggest reason is that there was far less uncertainty in the cost-benefit analyses provided by the scientific commuMontreal nity at the time. In addition to being more certain, most studies confirmed that the Before considering the results of the benefits of acting to limit CFC emissions most important climate change mitigation outweighed the costs by very large martreaty, it is instructive to examine the Mon- gins (Sandler, 2004). Unlike with climate treal Protocol of 1987 which imposed lim- change, no countries benefited from the its on the consumption and production of deterioration of the ozone layer. As a result, chlorofluorocarbons (CFCs) internation- more countries’ preferences were aligned. ally. It is often held up as the prime example There were fewer conflicts of interest. Many
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countries (like the United States) had started limiting CFC emissions even before the treaty was signed. Another important factor which helped the Montreal Protocol succeed was the extreme concentration of CFC emissions amongst a relatively small number of countries. In 1987, it was estimated that 12 countries accounted for more than 78% of emissions (Sandler, 2004). This made the relevant “k-group” of major countries smaller and easier to coordinate. It also meant that those countries which had the most to lose from CFC emissions were also the ones who produced the most CFCs. This made it relatively easy for the major players to make the world a privileged group. Though most small nations did sign the treaty, their participation was not strictly necessary to achieve the favorable outcome we have today. Finally, some observers have drawn attention to the role that external incentives (not unlike Olson’s private benefit remedy idea) played in compliance with the Montreal Protocol. The treaty provided two types of incentives – one positive, one negative. First, developed countries agreed to make payments to developing countries to help defray the cost of compliance with the treaty. Second, punishments were imposed on countries which judged the optimal level of emissions reductions to be below what the treaty demanded. These punishments came in the form of trade restrictions. Compliant countries were permitted to impose severe restrictions on imports of products containing CFCs from noncompliant countries. Since participation in the treaty was so high, these restrictions proved to be highly costly to noncompliant countries (Barrett).
Kyoto And Copenhagen
ber states (under the auspices of the UN) in 1997. It entered force in 2005. It was intended to force binding cuts on carbon dioxide emissions sufficient to keep global temperature increases at or below 2 degrees Celsius. Though Kyoto only entered force recently, it has not yet had any noticeable effect on carbon dioxide emissions and it is not expected to. Earlier, it was noted that understandable disagreement over the costs and benefits of climate change mitigation may be enough to scuttle the whole enterprise (even within a smaller k-group). This is precisely what has happened (Sandler, 2004). In order to secure an agreement, the drafters of the treaty at Kyoto had to exempt a number of major developing countries (like China and India) from binding emissions cuts. These countries effectively concluded that the costs of the requisite massive cuts exceeded the benefits (especially in the context of rapid economic development). The problem is that those countries are massive and necessary members of any k-group coalition of major powers which might decide to provide climate change mitigation. China now generates more emissions overall than the United States. Since major developing polluter nations whose contributions are necessary to provide the public good of mitigation effectively defected, it became a dominant strategy for other otherwise cooperative nations to defect (McGinnis and Somin, 2007). As a result, the United States never ratified the treaty. Despite, the obvious disincentives, Europe did adopt it – perhaps because of some vague unifying notion of “European values.” A further problem is that compliance by countries which had agreed to binding cuts is not enforceable. As an example, Canada has missed its targets by considerable margins and will not face any sanction for doing so. What incentive does it now have to comply anyway?
The Kyoto Protocol is an international environmental agreement which was signed Similar problems plagued the more and ratified by many United Nations mem- recent 2009 Copenhagen Summit on Cli-
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International Collective Action on Climate Change
mate Change. At Copenhagen, imposition of binding targets wasn’t even attempted. Most developed countries made incredible promises of further emissions cuts and affirmed their general commitment to some kind of climate change mitigation. Developing nations, meanwhile, skated by with promises to reduce the “carbon intensity” of their economies – to lower the carbon emissions per dollar of output they produce. Even if they kept these promises, the speed of their economic growth means that their emissions would continue to rise. Most observers have concluded that Copenhagen was a bigger failure than Kyoto. What is to be done? One possibility would be an incentive mechanism analogous to the one proposed by Olson and similar in form to the one implemented in the Montreal Protocol. However, given the wide divergence of opinion on the costs and benefits of climate change mitigation (as opposed to in the Montreal Protocol) and already weak participation levels, it seems unlikely that rich countries would be willing to pay enough compensation to developing countries and that potentially noncompliant countries would find noncompliance too costly due to trade restrictions. Trade restrictions tend to be more effective when there is already high compliance (Barrett, 2007). An alternative solution would be to provide a decision making environment which excluded the interests of small countries. One problem with the United Nations decision-making apparatus is that it demands absolute unanimity for an agreement to enter force (Barrett, 2007). Given the large scope for conflicts of interest over climate change mitigation (especially amongst the smaller countries), the unanimity requirement tends to unnecessarily water-down treaties and prevent the big countries from cooperating more effectively with each other. The appropriate k-group of nations could assemble under the Group of Twenty (a ready-made k-group) frame-
work. As already noted, small groups suffer from fewer coordination problems and so are more likely to be privileged. More substantial cooperation from developing nations could potentially be secured in a small group and enforcement and verification would be easier. Ultimately, though, the cold reality boils down to the fact that the net benefits of climate change mitigation are not nearly as high as the net benefits of ozone layer protection were (Sandler, 2004). Additionally, there are more big carbon emitters than there were big CFC emitters at the time the Montreal Protocol entered effect (the relevant k-group is bigger). These differences may make the climate change compliance gap unbridgeable – at least until there is more certainty about its costs and benefits and the net benefits are shown to be unambiguously positive.
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ECONPress Works Cited
Barrett, Scott. Why Cooperate? The Incentive to Supply Global Public Goods. New York, New York: Oxford University Press, 2007. Print. McGinnis, John O. and Ilya Somin. “Should International Law be Part of our Law?” Stanford Law Review. 59.5 (2007): 1175-1247. Print. Olson, Mancur. The Logic of Collective Action: Public Goods and the Theory of Groups. 2nd ed. Cambridge, Massachusetts: Harvard University Press, 1971. Print. Sandler, Todd. Global Collective Action. Cambridge, the United Kingdom: Cambridge University Press, 2004. Print. Shepsle, Kenneth A. Analyzing Politics: Rationality, Behavior and Institutions. 2nd ed. New York, New York: W. W. Norton & Company Inc, 2010. Print
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