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Who Runs the ECB?

Regional Influences in EMU Monetary Policy

Winter 2013

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Monetary and Fiscal Union in the EMU

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Who Runs the ECB? Regional Influences in EMU Monetary Policy

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Winter 2013

Better Together? Monetary and Fiscal Union in the EMU

Chris Belfield and Tom Lee Cambridge University

In 1961, Robert Mundell introduced the idea that it may be optimal for independent sovereign states to share a common currency. The European Union (EU) embraced this idea, first with the European Monetary System in 1979 and then with the introduction of the euro in 2002, creating a fully-fledged monetary union. Initially, the European Economic and Monetary Union (EMU) benefited from the economic efficiency and stability gains associated with a common currency. However the recent sovereign debt crisis has underlined the inherent problems in a monetary union operating without some degree of fiscal union. Spillover effects, fiscal indiscipline, and asymmetric shocks suggest some level of fiscal union is required. We explore these issues by considering three possible degrees of fiscal union. Under a monetary union we shall define three states of fiscal union that can exist as follows: · Fiscal independence – The fiscal stance of the individual nations is entirely and autonomously determined by the national fiscal authorities. · Rules and constraints – Each national government stipulates its own fiscal policy subject to predetermined constraints coupled with a supranational

institution that may have discretionary authority over member states and powers of enforcement. · Fiscal Union – The individual nations provide revenue to a supranational institution, which determines the fiscal policy across all nations, comprised of a communal budget and policy coordination.

The sovereign debt crisis has demonstrated the fiscal problems apparent in the EMU. The strength of a fiscal union depends on the amount of revenue apportioned to the communal budget and the extent of policy coordination. A fiscal union is likely to be coupled with rules and constraints on individual national budgets. The EMU lacks a communal budget, although there is a limited EU budget that performs some of the functions of a hypothetical EMU budget. However, the EU budget is capped at maximum 1.23 percent of EU GNP (Financial Programming and Budget, 2011) and does not serve the same collection of countries as the EMU. Columbia Economics Review

It therefore cannot fulfill the stabilizing functions of a communal budget under fiscal union. National autonomy is constrained by the Stability and Growth Pact (SGP), which stipulates that the national government deficit and debt levels cannot exceed 3 percent and 60 percent of GDP, respectively. Countries have, however, continuously violated these fiscal rules without being subject to sanctions. During the creation of the EMU only seven of 12 original members had public sector debt under 60 percent; Italy entered the EMU with public debt at 114 percent of GDP (Llewellyn and Westaway 2011). Over the period 2000 to 2003 only four of the original members met the conditions of the SGP (Ferrero 2005). Because countries have not adhered to the SGP, the EMU effectively functions as a monetary union with fiscal independence. The sovereign debt crisis has demonstrated the fiscal problems apparent in the EMU. Our analysis will explore the economic consequences of a monetary union under different states of fiscal union, seeing whether there are inherent problems with fiscal independence or with the design of the EMU. Fiscal Independence In line with the current body of literature, we make the following assump-

tions. National fiscal authorities are maximizing their own welfare and not coordinating in order to maximize aggregate welfare of the monetary union. The welfare function is increasing in income and decreasing in volatility of income. Given the fiscal policies of other nations and the monetary policy of the independent central bank, the fiscal policies that are optimal for individual nations may not be optimal for the union. Lambertini and Rovelli (2002) point out that because countries under a monetary union are closely integrated, there are spillover effects in terms of aggregate demand and inflation. Aggregate demand and inflation influence both the volatility and level of national income and thus impact the welfare function. Through its impact on domestic imports, exports, and exchange rates, the policy stance of one country can also potentially impact the aggregate demand and growth of all the other countries. Additionally, the existence of short-term nominal rigidities creates non-trivial interactions between monetary and fiscal policy: consumption and investment decisions, for example, depend on interest rates determined by the independent central bank to control inflation. As fiscal policies influence aggregate demand and therefore the inflation rate, they will also affect the interest rate. Fiscal policies often aim to reduce unemployment and therefore are typically expansionary. In the case of expansionary fiscal policy, monetary policy will then have to be contractionary to limit inflation. This conflict tends to cause fiscal policy to be over expansive compared to union-wide optimality, potentially causing public sector spending to crowd-out private investment. With national authorities acting independently, there is no cooperation and a sub-optimal Nash equilibrium emerges. Although Lambertini and Rovelli’s paper shows the negative externalities associated with independent fiscal policy, their choice to model fiscal and monetary policy as being chosen simultaneously constitutes a major limitation. In contrast, Nordhaus (1994) models a game in which fiscal authorities are represented as a leader who incorporates the central bank’s reaction into his decision-making. Nordhaus finds that the solution of the Stackelburg game dominates the Nash outcome. This is because national governments know that a more expansive fiscal policy will lead to tighter monetary policy that counteracts the perceived benefits of an overly expansive policy.

The authorities set less expansive fiscal policy and so optimal monetary policy is less contractionary. This model more effectively captures the EMU’s institutional structure; the mandate of the ECB clearly states it shall target under a 2 percent year-on-year increase in the Harmonised Index of Consumer Prices (ECB Monthly Bulletin 1999). Given the constraint of fiscal independence, this model leads to a superior outcome with less volatility. However, the individual nations are still in conflict rather than a state of cooperation. As we explore later, once we allow for some degree of fiscal union, superior social welfare outcomes can be found. Ferrero (2005) reaches a drastically different conclusion. He compares the benevolent central planner’s optimal plan, in which the central authority chooses monetary and fiscal policy to maximize the present discounted value of the welfare objective for the entire union, to fiscal independence. Ferrero concludes that the welfare difference is minimal and thus fiscal independence is viable. However, this paper has little relevance to practical applications due to the social welfare function chosen, which models national fiscal authorities maximizing union-wide welfare rather than individual national welfare. There is little reason to believe governments would want to maximize union-wide welfare while maintaining fiscal independence. This assumption inColumbia Economics Review

ternalized the spillover externalities outlined in this section, making this result not only irrelevant but also expected. In addition to allowing conflict between fiscal and monetary objectives, fiscal independence permits individual countries to run large fiscal deficits. In 2010 Greece’s public sector debt GDP ratio reached 142.7 percent and Italy’s 119.1 percent (CIA World Factbook, 2011). As 10-year bond yields rose to above 7 percent in Italy, there were calls for the ECB to underwrite Italian debt, because default threatened the stability of the common currency. The current crisis has demonstrated that “indisciplined fiscal policy, possibly unsustainable in the long run, forces the central bank to give up its independence and monetize the fiscal debt” (Sargent and Wallace 1981). This deviation from the central banks’ inflation targeting mandate creates uncertainty about credibility and risks, resulting in large discrepancies in expected and actual inflation rates. Unexpected inflation lowers social welfare because it increases uncertainty about present and future states of the economy, reducing investment and altering consumption decisions. Rules and Constraints Evidence overwhelmingly shows that in Europe the SGP was not followed and stringent penalties were not imposed. However, to continue our analysis, we shall examine the effects of such con-

straints if they were in place and enforced. The major benefit of such a rule stems from the problem of undisciplined and unsustainable fiscal policy outlined in the previous section. The Stability and Growth Pact states that the government debt to GDP ratio cannot exceed 60 percent. At this level there is little or no risk of default, a prospect that would destabilize the common currency. Lambertini and Rovelli (2002) argue that the spillover effects of independent fiscal policies persist under the SGP, as they did under fiscal independence. Expansive fiscal policy, even within the 3 percent of GDP deficit limit prescribed by the SGP, can increase aggregate demand and thus create inflation. Fear of such an outcome was evident in 2001 when the European Commission made a formal recommendation against Ireland’s expansionary fiscal policy. Despite Ireland’s compliance with SGP requirements, with a fiscal surplus of 4 percent of GDP and a debt level of only 40 percent, Ireland’s policies were rejected because they would increase aggregate demand and generate inflation across the EMU. It is clear many of the same problems outlined for fiscal independence are still applicable, if constrained by an upper bound.

Winter 2013 Hishow (2007) argues the SGP can be detrimental as it restricts the individual countries’ ability to use fiscal policy to boost aggregate demand in times of recession or slow growth. The independence of the central bank means it would refuse to monetize individual fiscal expansions. However, these expansions are sometimes required to boost aggregate demand and stabilize the business cycle. Yet without a loosening of monetary policy, there can be large crowding out effects and a country can fail to return to trend growth. This effect is greater for larger economies, as they require greater fiscal stimuli for recovery. This is not to say that small countries are free from constraints. The SGP requires long term balanced budgets; to fund a fiscal stimulus the country must raise taxation once trend growth has been reached again. The resultant taxation will increase the labor supply by reducing the level of private consumption and thus raising the marginal utility of consumption. As a result, people work more in order to consume more. However, both income and consumption taxes lower the real wage and so have negative distortionary effects on the labor supply. As the tax burden increases, the negative effect dominates: it is likely that the expansionary power of fiscal stimulus will be negated. Thus fiscal rules, if followed, stop the risk of irresponsible and excessive government debt, but they fail to correct for spillover effects and constrain the individual countries’ ability to recover from shocks. Therefore in a monetary union, a set of central policies that consists only of the SGP is not optimal. Fiscal Union: Communal Budget There is a general consensus in the literature that the EMU is not an Optimal Currency Area (OCA). Severely limited labor mobility due to language barriers and disparate cultural and historical backgrounds inhibits the EMU ability to function as a OCA. Limited mobility means that labor markets are less able to absorb shocks. There are also large structural differences between the member states, which mean the shocks are asymmetric. This partially explains the divergence in outcomes of the economies within the EMU and why some governments have had to increase spending to maintain growth. For example, recovery from the 2008 recession was strong in Germany, which resulted in less expansionary policy in the following years than would have been optimal for other nations. This, at least to some extent, hindered recovery in many EMU countries. Columbia Economics Review

Winter 2013 A communal budget could help to create business cycle convergence that would reduce these asymmetries. An OCA without perfect labor mobility requires an automatic fiscal transfer mechanism to redistribute money between countries suffering asymmetric shocks (Mundell 1961). As previously discussed, there is limited labor mobility in the EMU, implying the need for a fiscal transfer system. It is important that these stabilizing transfers are automatic; otherwise, the self-interests of national governments will lead to frequent demands for transfers. In addition countries may delay or refuse to transfer money in times of need due to domestic political considerations. Moreover if union-wide fiscal policy were discretionary, it is likely that public expectations would anticipate policies to be more volatile due to the lack of accountability of foreign politicians to the home population. Additionally, the non-instantaneous relationship between spending and growth means that,

However, the individual nations are still in conflict rather than a state of cooperation. to avoid destabilizing effects, an EMU budget should be restricted to solely stabilizing functions. Although an automatic transfer system may be theoretically desirable, it is unlikely that countries with strong stable economies would agree to it in practice. The recent EMU crisis has shown that countries are predominantly self-interested and in general do not like new policies that reduce national sovereignty. Although the EU does have a small budget designed for redistribution among its members, it does not act as a communal budget to facilitate redistribution or to smooth asymmetric shocks within those countries that share the euro. In contrast, when one of the nine main regions in the USA suffers a negative shock, revenue provided to the federal budget falls by up to one third, smoothing the business cycle by 40 percent. If applied to the EMU, this could greatly improve its ability to recover from shocks. (Sala-iMartin et al 1992). A direct comparison to the USA cannot be made because, for reasons outlined earlier, a communal EMU budget would have to be limited to automatic stabiliz-

ers. Hishow (2007) attempts to estimate the size of such a budget assuming the worst-case scenario of the EMU’s three largest economies – Germany, France, and Italy - falling into recession. With these parameters, he concludes a budget of around 3-4 percent of total EMU output would be needed to ensure stability. This solution is not without its caveats. The EMU budget would provide insurance for countries that pursue reckless fiscal policy and bail these countries out in times of need. In order to counteract the resultant free-rider problem, fiscal constraints need to be implemented with enforced sanctions for breaking them. There is also a terms-of-trade problem. If transfers are made to any of the large economies, their received benefits are effectively doubled due to price effects caused by their size (Hishow 2007). Expenditure in the recipient country increases, whereas expenditure falls elsewhere. Relative demand shifts along with relative prices, giving the transfer-receiving countries an additional competitive boost. A smaller economy would not benefit from this secondary effect. In addition, the 3-4 percent budget estimate is based on a worst-case scenario, in which the three largest EMU economies fall into recession. However, during the current crisis every single member of the EMU was in recession in 2009 (Eurostat 2011). A communal EMU budget would not have prevented an EMU recession, due to the unprecedented scale of the global financial crisis. It is likely, however, that the recovery would have been stronger and more uniform than in the absence of such a budget. Nevertheless, more integrated global markets, especially in the financial sector, have led to greater interdependence between countries. This increases the transmissibility of shocks, allowing a shock to an individual country to have a wider global impact, and thus a larger budget may be required. Despite the benefits of a communal budget, it is clear that only having a budget is not sufficient to restoring union-wide optimality. To this end, we shall analyze and evaluate policy coordination. Fiscal Union: Policy Coordination In the first two sections we outlined the set of externalities and free-rider problems that make a monetary union ill-suited for co-operative fiscal policies. We then demonstrated that the SGP alone fails to correct these misaligned incentives. The Excessive Deficit Procedure (EDP) complements the SGP and aims to

avoid disproportionate fiscal expansion. It is designed to impose political costs on deficits; higher debt-to-GDP ratios require greater debt reduction efforts (Von Hagen and Mundschenk 2002). However, like the SGP, the EDP is largely ignored and sanctions are not imposed. Beyond explicit rules and sanction mechanisms, policy coordination relies on soft measures such as peer pressure and persuasion (Von Hagen and Mundschenk 2002). Larger countries will not tolerate the reprimands and public warnings required for a more open approach. Countries are currently required to submit annual stability and convergence programs; however, these run on loosely connected calendars and rarely involve the relevant politicians. This method of coordination is weak, and worse, inequitable. Newer and smaller economies are influenced by peer pressure whereas the larger economies are more independent: 50 percent of initiatives in Belgium are influenced by the EU compared to only 15-20 percent in Germany (Von Hagen and Mundschenk 2002). This limits the scope of negotiation. It is assumed that balanced fiscal budgets are optimal for macroeconomic stability across the entire EMU. While this may be true in the long run, there is no mechanism for addressing short-term fiscal conflicts. EMU policy coordination entirely consists of requesting that countries adhere to the SGP, which when broken, imposes no sanctions. To solve these problems, fiscal policy must be coordinated not only across countries but also with monetary policy. A framework in which EMU aggregate preferences over inflation, growth, trade and fiscal policy are decided is required. These preferences must

To maximize social welfare within a monetary union generally – and the EMU specifically – there must be some form of fiscal union comprised of a communal budget and coordinated policies. be reconciled with centralized monetary policy and complemented by binding commitments to ensure fiscal cooperation at the national level. Monetary union with an independent central bank targeting inflation and naColumbia Economics Review

7 tional fiscal authorities concerned with national stability and growth causes conflict and results in a sub-optimal equilibrium. Overly expansive fiscal policies are counteracted by contractionary monetary policies. Spillover effects and externalities result from the narrow focus of fiscal policy. To overcome this, the EMU has imposed the Stability and Growth Pact, an attempt to ensure fiscal prudence that focuses on long-term balanced budgets for all members. It is continually broken without the imposition of penalties. However, even if enforced, the SGP aims to treat the symptoms of an ill-functioning system rather than the causes. It assumes balanced budgets are desirable and restricts the fiscal flexibility of individual nations, which is important for smoothing business cycle fluctuations. Currently the main method of ensuring policy coordination is through peer pressure, which benefits larger economies to the detriment of small ones. A communal budget providing supranational automatic transfers would reduce regional discrepancies in recovering from shocks, both symmetric and asymmetric. However, this may have inequitable term-of-trade effects and reduce national fiscal discipline as it creates misguided incentives, while not addressing the inherent conflict between monetary and fiscal policy. Policy coordination would help address these problems. Successfully coordinated policies would internalize the spillover effects, as well as reduce the conflict between monetary and fiscal policies, by collectively ensuring individual fiscal policies are not overly expansive. Although policy coordination would reduce fiscal flexibility, the communal budget would provide sufficient fiscal stimulus in times of need. In order for this regime to be effective, sanctions need to be implemented to disincentivize countries from breaking the stipulations of the coordinated policies. To maximize social welfare within monetary unions generally– and the EMU specifically – there must be some form of fiscal union comprised of a communal budget and coordinated policies. We acknowledge the difficulties of implementing such proposals given the unwillingness of individual nations to relinquish fiscal independence. Nevertheless, we believe that a communal budget of around 3-4 percent, as Hishow estimates, would be highly beneficial, if coupled with the coordination of nationally determined fiscal policies, without significantly reducing national sovereignty.

Winter 2013

Figure 1: EONIA rate (quarterly) and quarterly nominal interest rate as predicted by estimatedbased on the “Twin Sister Taylor rule (with estimated r = 2.5, α = .32, β = .35) Hypothesis” (TSH), which

Who Runs The ECB? Regional Influences in EMU Monetary Policy

Julian Richers Columbia University

On January 1st, 2012, the Euro completed its first decade as the sole official currency in the European Monetary Union (EMU). But member countries share more than bills and coins. The exchange of each country’s own currencies for a common one was preceded by a consolidation of monetary authority from the individual national central banks into the hands of the European Central Bank in Frankfurt. After over a decade of unified monetary policy in the EMU, it is time for some evaluation. While the new common currency facilitated the exchange of goods and services across member countries’ borders, each state surrendered monetary sovereignty to a centralized authority and therefore lost the ability to react unilaterally to domestic economic developments by monetary means. Under the Euro, one interest rate has had to balance the demands of the business cycle in Ireland with inflation concerns in Italy. In the aftermath of the 2008 Financial Crisis, the role of monetary policy in the developed world has garnered much public attention and has subsequently come under intense scrutiny. While most backward-looking criticism, both in academic and popular literature, focuses on overly loose monetary policy implemented by the Federal Reserve (Taylor 2010),

the past behavior of the European Central Bank (ECB) is also in need of further examination. Already prior to the bursting of the credit and housing bubbles in Ireland and Spain, Hayo (2006), Kool (2006) as well as Moons and Van Poeck (2008) show that ECB monetary policy, as demonstrated by its focus on short term

Columbia Economics Review

interest rates, does not fit all EMU member countries equally well. Most importantly, the authors find that interest rates are generally too low for most countries compared to traditional monetary policy benchmarks, with the sole exception of Germany. As all authors estimate the individual country preferences based on pre-EMU era data, these findings could simply be the result of a lower real interest rate during the EMU period, but Hayo (2006) shows that the observation still holds when changes in real rates are accounted for. In light of both recent events as well as observations about ECB policy in the past, this paper attempts to identify factors that might cause the ECB to diverge from optimal policy. While the term “optimal policy” deserves much discussion in itself, here I am mainly concerned with policy fairness. Policy can be misguided because of inaccurate data, faulty theories or personal ideology of policy makers, but in regard to the relative youth of the EMU, I am particularly concerned with the appropriate weight given to each member state in the decision process. In this paper, I explore whether policy has been exercised according to the guidelines set forth in the Maastricht Treaty establishing the ECB in 1992 and in the

following amendments. In practice, this paper is concerned with the existence of influences or biases, which could distort ECB policy away from its intended focus on the whole Eurozone and towards some specific objective, namely the individual needs and preferences of some – or one – specific member state(s). In accord with the Maastricht Treaty of 1992 and its subsequent amendments, monetary policy decisions are made in the Governing Council, which consists of all individual national central bank presidents and governors, as well as the six members of the Executive Council, which are appointed by the European Council. While the monetary policy committee features a large number of representatives selected at the national level, and a relatively small number of those selected at the EMU federalist level, ECB press releases consistently claim that all monetary decisions are made solely with an EMU-wide perspective, and only take Euro zone aggregate data into account. This is consistent with the ECB’s mandate, which only states that “[t]he primary objective of the ESCB shall be to maintain price stability [… and to] support the general economic policies in the [European] Community” (Maastricht Treaty Article 105.1). This primarily federalist perspective is what I will consider “optimal policy” in the following. While this setup should theoretically lead to a balanced and reasonably appropriate monetary policy for all members, its specific institutional design has been the target of much scrutiny as the impact of regional influences on monetary policy has been widely discussed in the academic literature.

In this paper, I examine the existence of a regional bias by empirically estimating an EMU Taylor rule-type reaction function, which takes into account possible regional influences. I conclude that diverging output developments, possibly in France but more certainly in the small Northern EMU member countries, have influenced ECB interest rate setting in a significant way, therefore violating the mandate and possibly causing adverse consequences for other EMU member countries. Literature While ECB officials steadfastly declare the unbiased nature of the bank’s monetary policy decisions, full adherence to the mandate can be seriously questioned based on a number of studies of other federal central banking systems. For the U.S. Federal Reserve, Meade and Sheets (2002) find that the occurrence of regional economic divergences can skew the voting behavior on monetary policy committees (MPCs), which, if it applied to the ECB, would clearly be in violation of the stated procedure. Through the analysis of voting records, Meade and Sheets show that the probability for a member of the MPC to dissent in the vote is closely tied to divergent economic developments, particularly unemployment trends, in their region of origin. Interestingly, this behavior is not only visible in the records of regional central bank governors but also in the voting pattern of members of the Board of Governors, who, most of all, are expected to represent federal interests (Meade and Sheets 2005). Berger and De Haan (2002) show similar findings for the Governing Council of the former Bundesbank for the pre-euro period. Therefore, Columbia Economics Review

emphasizes the similar institutional design of the former German and the European Central Bank, it seems very likely that these findings also hold for the ECB. Additionally, given that the EMU encompasses a more diverse economic landscape, it gives reason to assume that these impacts should be even more pronounced in ECB policy as interests diverge much more widely among the individual national central banks than within the Bundesbank alone. While sufficient grounds for the expectation of regional influences exist, demonstrating these empirically is not a straightforward task. In order to supposedly protect its members from nationalistic pressures and preserve their independence, the ECB provides neither meeting minutes nor voting records, while also publicly claiming that all decisions are made by consensus and without a formal vote. Due to the lack of observational data, the literature has looked to develop alternative approaches in order to identify the ECB decision process and the existence of regional influences. One approach emphasizes the distribution of legal, although not officially exercised, voting power. Using a median-voter approach, Heinemann and Huefner (2002) as well as Ullrich (2006) test ECB interest rate decisions for the existence of regional influences. If each country would solely take national data instead of the EMU averages into account (or some combination of the two), policy would be biased away from GDP-weighted averages to vote-weighted averages, meaning that the ECB would set the interest rate to a rate preferred by a simple majority of all countries. This “democratic bias” would advantage the smaller economies like Ireland and Slovenia, and disadvantage the larger ones like France, Italy and Germany. Heinemann and Huefner find only weak evidence of such a bias, while Ulrich argues that there is no evidence for such bias whatsoever. Following these results, and based on the influence of regional divergences as outlined by Meade and Sheets (2002), this paper explores ECB interest rate setting by taking into account both average values for the EMU as a whole as well as

10 measures of economic divergence for the four main regions or voting blocs of the Eurozone which, according to Hayo and Moné (2011) should drive decision making given their large aggregate economic weight and respective bargaining power. In contrast to the general literature, this paper does not attempt to generate models for ECB decision-making, which can then be compared to observed policy. Rather, it analyzes the actual interest path and tests for the existence of biases. The empirical application is discussed in the following section. The Model In the literature, it is common to identify (conventional) monetary policy as the short-term interest rate, which can then be used in a “Taylor rule,” a monetary reaction function. Following Taylor (1993), a central bank sets the short-term interest rate in response to deviations of inflation and output from its targets. Subsequently, this can be displayed in an equation as follows: it = r + πt + α (πt – π*) + β (yt GAP) with it denoting the nominal interest rate, r the long-run real interest rate, yt GAP the output gap, π the inflation rate, and π* the target inflation rate. α stands for the weight on inflation deviations and β for the output gap weight. As Taylor (1993) shows, this simple rule is effective in approximating historical interest rate setting by the Fed, and this structure has been used in many other studies of monetary policy. As visible in Figure 1, for describing the ECB interest rate path (here represented by EONIA, the Eurozone OverNight Index Rate), the rule does fairly well, although with coefficient values different from Taylor’s original estimates for the U.S. However, the predicted ECB interest rate path shows much less volatility than the observed rate. This holds true in particular for the period before the 2008 crisis.Following the findings in the literature discussed above, this lack of fit could be attributed to regional influences not accounted for in the original Taylor rule specification, which, consistent with the ECB mandate, only considers EMU average data. Subsequently, I extend the Taylor rule in order to make it more applicable to the ECB, which are consistent with the findings in Meade and Sheets (2002) and Hayo and Moné (2011). In order to account for the importance of regional divergences, I include additional output gap variables in the equation, which measure the diver-

Winter 2013

Figure 2: EONIA Target Interest Rate set by the ECB, Harmonized Index of Consumer Prices, Average Expected Level of Inflation One Year Ahead from ECB Survey of Professional Forecasters (all quarterly).

gence between the EMU average and the relevant national output gap. However, in order to account for the vast variation in negotiation power between the countries, I only use national output gap differences for the two largest and supposedly most influential member countries, France and Germany, and use aggregate measures for two additional voting blocs, which one can reasonably expect to have a significant voice in the Governing Council. To this end, I generate aggregate output gap measures for two country groups: South, which includes Italy, Portugal, and Spain, and Core, which includes the small northern EMU members Austria, Belgium, Denmark, Finland, and the Netherlands. The role of inflation (or lack thereof) will be discussed in the next section. It follows: it = r + πt + α (πt – π*) + βEMU (yt GAP EMU) + βGer (yt Diff Germany) + βFra (ytDiff France) + βSouth (yt Diff South) + βCore (ytDiff Core) where, in addition to the original Taylor rule equation from above, each yt includes the divergence of the national or group output gap from the EMU average and each β stands for the weighting of this divergence in the decision process. Findings Under the perfectly federalist mandate, Columbia Economics Review

every regional development should already be included in the EMU-wide values for inflation and output gap, weighted according to each country’s share of EMU GDP. Also, if, following Hayo and Moné (2011), all countries are solely influencing decisions with negotiation weights based on their GDP share, individual divergences from the average should not have much of an impact or significance, because these would already be captured in the average EMU values. Table 1 displays the summary statistics for the Taylor rule specifications. Starting from these specifications, fit visibly improves with the inclusion of regional divergences, although the effects are not the same for all countries or groups. While the coefficients on the output gap difference measures for France and for the Core countries are significant and sizeable throughout all specifications, the coefficient for Germany, surprisingly, is only significant when the Core countries are not included independently. Similarly, the Southern group’s coefficient is small and insignificant in the regression. Both the German and Southern coefficients are not just insignificant but also very small, further bolstering the conclusion that their output divergences do not enter the reaction function independently. Under

the extended specification, the addition of French and Core output gap differentials increases fit by almost 15 percent to about 0.95, while at the same time rendering inflation (both contemporaneous and expected) insignificant, so that ECB interest rates can be explained solely by variations in output; this is a surprising finding given the central bank’s “hawkish” reputation. Excluding inflation from the regressions (3), (4), and (5) changes the respective R2 values by less than one percentage point. Particularly in regard to inflation, this first look is likely not comprehensive. Although other authors (Kool 2006) have made the claim that the ECB has not been nearly as hawkish as its reputation and its “Germanic” institutional structure would suggest, a look at the data indicates something else. For the period under consideration, 1999 – 2011, inflation in the Eurozone has not been very volatile at all. For most of the period, up until 2008, observed inflation fluctuates between 2 and 2.5 percent, and expected inflation is almost flat slightly below or at 2 percent, the ECB inflation target (Figure 2). Given that the observed inflation rate (HICP) is a backward-looking measure, expected inflation as collected in the ECB survey of Professional Forecasters is likely to be closest to the indicators ECB policy makers use in order to make their decisions. The stability shown by this indicator, as well as its closeness to the

ECB target rate, indicates that the ECB is highly successful in its inflation targeting – but it also indicates that a standard OLS regression will fail to generate a meaningful coefficient, simply because there is not enough variation to be related to movements in the dependent variables. If we make the simplifying assumption that ECB policy makers target an inflation rate of 2 percent, and assume them to be so successful that the rate they consider for their decision exactly hits this mark, then the value for the inflation gap (but not necessarily the coefficient) would be equal to zero and therefore drop out of the regression. Instead, the target would enter the regression’s constant term, which in the relevant regression results is almost equal to 3 or higher. This then suggests that real rates in the EMU for the covered period were about 1 percent, mirroring both Taylor’s general criticism of excessively low real inter-

The empirical results indicate that within the closed doors of the Governing Council, some countries hold additional sway... est rates in the mid-2000s in Europe and the United States (Taylor 2011) as well as the findings in Hayo (2006), which esti-

Columbia Economics Review

mates real interest rates for the Eurozone during the ECB period from 1999 to 2006 to be 1.28 percent. In consequence, the empirical results that all variation in interest rates can be related back to output gap developments appear sensible. Interpretation The empirical results tell an interesting story. With inflation relatively stable around the target rate, ECB monetary policy can focus on stabilizing economic output, and while the average output gap already has a relatively high weight at 0.57 in regressions (4) and (5), the differences between the EMU output gap and those of France and the Core group are weighted with 0.25 and 0.41 respectively. Once the South group is included in the regression, the coefficient on France is only significant at the 10 percent level, but the Core coefficient remains significant even at the 1 percent threshold. A plausible explanation for this can be seen in Figure 3, which displays the difference between the region or country’s output gap and the EMU average. For the period from 1999 to 2008, the French output gap fluctuates around the EMU average, while the Core countries and the South countries, show a relatively stable trend; this trend is also partially visible in the German data. Interestingly, while not a perfect relationship, the Core and the South output gap differentials appear to be at least weakly inversely correlated, indicating that the importance of additional influence of the Core countries

Winter 2013

Figure 3: Output Gap difference measures of Germany, France,nounced than what the Core and the South group vs. the EMU average, from 1999,is visible in the Core data, the timing is difQ1 to 2008, Q2 (calculated by author). ferent. The difference only turns significantly negative in the middle of 2004, at which point in time interest rates were already at 2 percent (or 0 percent in real terms). Additionally, interest rates begin to rise in the third quarter of 2005, a time in which the difference between the EMU average and the German output gap is still strongly negative. These observations, in combination with the lack of many consistent trends in the German output gap difference, help to explain the surprising empirical insignificance for divergent economic developments in Germany. Trends visible in the aftermath of the 2008 crisis, displayed in Figure 4, are similar to those of the earlier data. While these data points have to be considered carefully and with the caveat that monetary policy has used a number of other tools in and after 2008, they hold valuacomes at the expense of diverging policy ble information. If anaway from the Southern group’s preferything, the ECB’s decisions in 2011, when ences in particular. the bank raised interest rates from 1 perFor the period between 2002 and 2006, cent to 1.5 percent, only to subsequently Spain, Italy and Portugal, in the aggrereverse course within a few months, give gate, performed much better economian indication that the ECB has not fully cally than the rest of the EMU, while the discarded the short-term interest rate as a Core performed worse, especially for the tool with which to achieve its objectives. period from 2003 to 2005. This difference Most importantly, the mechanisms guidcoincides with an extended period of exing interest rates in the past have not been tremely low interest rates from the first suspended indefinitely, although this quarter in 2003 until the second quarter claim can certainly be considered valid in 2005, during which nominal interest for the immediate aftermath of the crisis. rates were just as high, or even lower, Visibly, Germany is the most impressive than inflation, and flat at 2 percent. While post-crisis recovery story, and performs the Eurozone did go through a period significantly better than the rest of the Euof weak economic activity, the Southern rozone beginning in 2009, while continueconomies were much less affected than ing to do so through 2011. In comparison, the Core and, interestingly, Germany. France also performs slightly better than While the negative German output gap average, but does not follow a continudifference appears much more proous trend upwards like Germany or the Columbia Economics Review

Winter 2013 Core countries. Like Germany, the Core outpaces the EMU average by an increasing margin. In contrast, the Core only starts its upward ascent in the second quarter of 2010, which coincides with the onset of an upward trend in the EONIA rate as visible in Figure 1. At this stage however, this cannot be considered much more than a hint given that the ECB’s target rate remains unchanged for another two quarters, and that inflationary fears gained importance in the political as well as the academic discussion during this period. Still, the trend remains that the existence of regional influences, in particular from the Core countries does not bode well for the Southern group. For them, after monetary policy being too loose during a (relatively) expansionary phase in the middle of the decade, policy is arguably too tight in the post-financial crisis period. What do these observations mean for our understanding of the ECB policy making process? The empirical results indicate that within the closed doors of the Governing Council, some countries hold additional sway, influencing the decision process in a way that biases policy towards their own regional preferences and needs. As the public has no access to information on voting patterns or to the meeting minutes, one can only speculate about the mechanisms through which this imbalance of power could be achieved. Another possible explanation would be a return to the “democratic bias” scenario as described in Ullrich (2006) and Heinemann and Huefner (2002). Although the assumption of a linear one-country onevote distribution is very likely an overly strong one, a modified version might help to explain the empirically observed bias towards the Core countries. In regard to the still incomplete degree of economic integration in the Eurozone, as well as the sizeable differences in economic strength or even accession date of the member countries, the one-country one-vote power distribution might not encompass all members but only the historically more integrated and economically powerful countries. In such an artificially reduced voting distribution, an alliance of the five Core countries could hold substantial sway, although they only account for a combined 16 percent of EMU output. The countries might function as “swing voters,” coming down on either side of the debate at a particular point in time. Furthermore, given the historical and political similarities between the economic structures of the Core, France, and Ger-

Figure 4: Output Gap difference measures of Germaber of ways, one of course beny, France, the Core and the South group, from 2008, ing that no bias exists. Another Q3 to 2011, Q2 (own calculations). possibility might be that German influence does bias the ECB’s reaction function but that German interests might = target inflationary concerns rather than output. The high level of inflation aversion in German monetary policy is visible both in history as well as in academic research on the Bundesbank (Cuikermann 1992; Hayo 1998), and an extension of this trend into the ECB period seems likely. This factor has certainly motivated recent discussions on direct sovereign debt purchases by the ECB in the European debt crisis, and can also be suspected to have been a main driver in the ECB’s 2011, short-lived experiment of raising target rates. However, this remains a topic beyond the scope of this paper, particularly in the light of the earlier discussion of the role of inflation. Conclusion In this paper, I have attempted to empirically identify possible biases in the ECB decision process. To this end, I use a monetary reaction function in order to gather information on the weights policy makers place on the two generally used variables, inflation and output. Subsequently, this reaction function is expanded to include the divergences of regional values from the EMU average, which is then used in many, they might also find it easier to a regression analysis. As such, gain support of the two most influential two conclusions can be reached through countries in the Council in order to push the estimation results. for their preferred policy. Additionally, First, the coefficients on the regional one might speculate further about the role output gap difference for the Core group, of power dynamics resulting from the deand to a lesser extent also for France, are mographic composition of the ECB’s persizeable and significant. This indicates sonnel at the sub-executive level. that these countries are able to exert adThe empirically suggested lack of a Gerditional influence on the ECB decision man regional influence may strike the obprocess in excess of what their influence server as odd, given its status as the bigshould be given their share of EMU GDP. gest European economy, the high number Subsequently, this suggests that the ECB, of German executives at the bank, as well during its first decade of existence, has as the ECB’s “Germanic” institutional not performed according to its mandate, design and its location in Frankfurt. Of which prescribes a solely federalist percourse, this analysis cannot conclude spective, unbiased by regional preferwith certainty that no bias in this direcences. tion exists, but only that under the used Second, testing for regional influences specifications, no systematic influence is exerted by Germany or the South group visible. This can be explained in a numdoes not generate significant results, at Columbia Economics Review

13 least when focusing on output gap differences. While one has to be cautious with overly forward interpretations given the relatively short data set as well as other possible limitations on the data, the results suggest that Germany as well as Italy, Spain and Portugal (and possibly also a number of smaller countries, which have been excluded from the analysis so far) have not visibly or consistently influenced the ECB’s policy decision according to their national interests. Apart from the apparent conclusion that Germany and the South behaved like “good Europeans” in the sense of putting federalist objectives before national ones, the observer can also suspect that in the German case, this has been a conscious decision, possibly due to a different prioritization of policy goals. Meanwhile in the case of the Southern countries, it appears likely that their preferences have been disregarded due to the distribution of political and/ or economic bargaining power within the ECB decision mechanism. Finally, previous research can be extended in order to demonstrate the effects that unbalanced regional biases on ECB policy-making have had on some of the member countries. Spain stands as one example of how a downward bias on interest rates as exerted by the Core countries in the 2003 to 2005 period has likely contributed significantly to the fueling of a property bubble, which has created serious problems for the country in the recent past, and continues to do so today. This demonstrates some of the costs related to biases in ECB monetary policy as outlined here. This paper identifies possible distorting factors in ECB policymaking based on the possible existence of regional biases. While some indication has been found that regional interests have influenced policy in the past, more work is needed in order to give further substance to this indication as well as to convincingly identify the possible channels through which these biases could have entered policy. With Mario Draghi taking the helm of the ECB presidency in the Fall of 2011, a representative of the Southern economies is now in charge of the institution. In combination with increasing divergence between the European economies, the next few years will provide an insightful testing ground for the results presented here. I hope that my findings can contribute to our growing understanding of ECB monetary policy and provide some fruitful directions for further exploration of the topic of regional biases in monetary unions.

Winter 2013

Les Mariables Women’s Income Prospects and Age-at-first-marriage

Shirley Lee Princeton University

Introduction Men have historically married at a later point in life than women, and this age differential remains customary across nations. A study of 90 countries conducted by the United Nations found the average age of marriage for males to exceed that of females in all the countries investigated. Over time, this age differential has declined in most industrialized nations,

...a study conducted by the Pew Research Center found evidence of a reversal of the longstanding college marriage gap, reporting collegeeducated young adults to be more likely than their peers who lacked a bachelor’s degree to marry by the age of 30 but it continues to be high in traditional societies (United Nations 1990). Several competing theoretical models have been proposed to explain this

strikingly universal difference between the marriage ages of men and women. One particularly resonant model, the Bagnoli-Bergstrom (1993) model, posits that in marriage males are most valued for their earning capacity, while females are valued for their ability to perform traditional marital tasks such as caring for children. Because information on professional success becomes available later in life than information on the capacity to manage a household, males with bright prospects tend to postpone marriage until they complete their education and in general marry later than females (Bagnoli and Bergstrom 1993). However, beginning in 1994, women’s labor force participation began to grow again after briefly slowing down in the 1980s (Hayghe 1997), while the labor participation gap between men and women has been closing since 1970 (Mather 2007). More recent statistics show that educated women are now more likely to marry than their less-educated counterparts (Fry 2010). Men are becoming increasingly likely to marry wealthier partners, while the reverse is true for women (Cohn and Fry 2010). Given these considerable changes in the trends and composition of the marriage and labor markets since the development Columbia Economics Review

of the Bagnoli-Bergstrom model, it may be necessary to modify the original model to accommodate them. Most studies on the age differentials in marriage were conducted in the 1990s or even earlier. However, understanding the impact of recent trends in the marriage and labor markets is crucial, and the effects of these new trends in labor participation and selection into marriage may have significant implications for gender income disparity and the gender wage gap. In this study, I evaluate the BagnoliBergstrom model by exploring the relationship between women’s income prospects and age-at-first-marriage, using current data. Prior research found support for the Bagnoli-Bergstrom model using older data. The purpose of this study is to incorporate the effects of recent changes in the marriage and labor markets into the existing literature on marriage age differentials using updated data. Literature Review: Bagnoli Bergstrom The Bagnoli-Bergstrom (1993) model holds that a man’s desirability as a prospective spouse is determined by his earning capacity, while a woman’s desirability depends on her fertility and ability to manage a household. Bagnoli and Bergstrom suggest that because in-

formation on professional and economic achievements become accessible later in life than information on the ability to perform domestic roles, men who expect to be successful are more likely to delay marriage until their prosperity is definite and apparent. Meanwhile, females tend to marry earlier. More specifically, in equilibrium, the more desirable women typically marry the highly valued and successful, but older, men, while the less desirable women are matched with the younger, less prosperous men. Males’ incomes should be positively correlated with their age-at-first-marriage, but no relationship should hold for females. A study performed by Ted Bergstrom and Robert F. Schoeni (1996) offers an empirical analysis of the Bagnoli-Bergstrom model. Bergstrom and Schoeni examined data obtained from the 1980 United States Census, and ran regressions of household income and annual earnings on current age (in cubic form), the cohort-specific mean age-at-first-marriage, and age-at-first marriage as dummy variables, by race and gender. Consistent with the Bagnoli-Bergstrom model, Bergstrom and Schoeni found personal income and family income to be strongly correlated with age-at-first-marriage

for males. However, because women’s family income included their husbands’ earnings, Bergstrom and Schoeni found

that while family income for females is strongly correlated with age-at-first-marriage, personal income is not. Most interestingly, they found that personal earnColumbia Economics Review

15 ings and age-at-first-marriage are more strongly correlated for black than white women. Because black women have traditionally been more likely to enter the labor market than their white counterparts, potential marriage partners seem to value the labor potential of black women more highly (Bergstrom and Shoeni 1996). Bagnoli and Bergstrom create a model that explicitly incorporates the information available to each participant at each point in time. This equilibrium model explains individuals’ decisions about time of marriage. This detail is important because in an environment with perfect information, there is no apparent reason for an individual to postpone marriage until after acquiring human capital. However, if a male’s professional and economic successes only become evident after he is prosperous, then there is a motive for him to postpone marriage as long as he believes that he will be successful in the future (Bergstrom and Schoeni 1996). While the Bagnoli-Bergstrom model is currently the most persuasive of the theories proposed to explain age differentials in marriage, it does not account for a number of relatively recent changes in the labor and marriage market for females. Support for the Bagnoli-Bergstrom model comes primarily from Bergstrom and Schoeni’s study. Although this study was conducted in 1995, Bergstrom and Schoeni analyzed data obtained from the 1980 United States Census. Following a decline in the 1980s, women’s labor force participation picked up again in 1994 (Hayghe 1997). Data shows that the gap in labor participation between men and women has significantly diminished since 1970. In fact, while women’s participation has jumped from 43 percent to 60 percent, men’s labor participation has decreased from 80 percent to 74 percent (Mather 2007). Recently, a study conducted by the Pew Research Center found evidence of a reversal of the longstanding college marriage gap, reporting collegeeducated young adults to be more likely than their peers who lacked a bachelor’s degree to marry by the age of 30 (Fry 2010). This indicates that a woman’s education levels and ability to make money are becoming more important determinants of her value, and women who have higher education are now considered more desirable for marriage. More surprisingly, statistics from another recent study by the Pew Research Center show that men are becoming more likely to marry wealthier

Winter 2013

Winter 2013 fect on income. The strength of the correlation between age-at-first-marriage and income is also determined. Similar to Schoeni and Bergstrom, I regress personal annual earnings and household income on current age (in cubic form). To control for generational changes in the norms for marital age, I also include cohort-specific mean age-atfirst-marriage into the regression. Age-atfirst-marriage enters into the regression as single year dummy variables. Due to the small number of cases, those who married at ages 15 to 17 and 31 to 32 are grouped together. Mathematically, the regression equations are expressed as: đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 +

cantly since the majority of the sample is between 24 and 32 years old, and most will have already entered the labor force if they intend to do so. For this reason, I do not correct for selection into the workforce in my study. Selection into marriage It is crucial to correct for bias due to selection into marriage, however, especially if the dataset surveys a population of an age range during which marriage is likely and during which it is probable that some, but not all of those young adults who have the intention to marry have already done so. Since Wave IV of Add Health surveyed individuals aged 24 to 32, it is likely that a number of the

đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ??´đ??´đ??´đ??´đ??´đ??´ + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 +đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ??´đ??´đ??´đ??´đ??´đ??´ + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; . đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

women. The reverse is true for women, however, suggesting that the trends described by the Bagnoli-Bergstrom model may even have begun slowly to reverse (Cohn and Fry 2010). My study aims to reexamine the empirical validity of the Bagnoli-Bergstrom model, taking these considerations into account. More specifically, I attempt to replicate Bergstrom and Schoeniâ&#x20AC;&#x2122;s study, using current data that will implicitly include these changes in the composition of the labor and marriage markets. In particular, this paper empirically investigates the relationship between personal income prospects and age-at-first-marriage for both black and white females. Data The data analyzed in this study was obtained from the National Longitudinal Study of Adolescent Health (Add Health), a school-based longitudinal survey on adolescent health and respondentsâ&#x20AC;&#x2122; outcomes in young adulthood. Add Health follows the development into adolescence of seventh through twelfth graders in the 1994 to 1995 school year and as a large, nationally-representative study, can be generalized to the American adolescent population. I examine the results of 15,701 adult in-home interviews, of which 5,114 of the original respondents remained until Wave IV, and obtain supplemental information on the respondentsâ&#x20AC;&#x2122; race from Wave III of the study.

Wave IV was conducted in 2008 when the majority of respondents were 24 to 32 years of age. Data for men, unmarried women, and women of other races are not considered in my analyses, so the final sample includes 982 observations for white women and 207 observations for black women. Methodology This paper utilizes a regression model resembling that used by Schoeni and Bergstrom (1996) to analyze the relationship between income and age-at-firstmarriage. I run separate regressions for black and white females to test whether age-at-first-marriage has a significant ef-

However, due to the sample selection bias in my study, which I discuss in the next sections, it is possible that the cohort-specific mean age-at-first-marriage variable is also biased, since it is determined from the age-at-first-marriage for the respondents participating in the Add Health survey. For more accurate results, I rerun the two previous regressions, but without cohort-specific mean AFM, and compare the findings. Accordingly, the regression equations are:

there is a weaker relationship than anticipated even between age-at-first-marriage and family income people included had not been married at the time of the survey but did get married as they grew older. If this selection bias is not corrected, it will bias the results by

cially problematic in my study and must be corrected. In order to account for selection into marriage, I use the Heckman (1979) model. First, I run a probit regression based on the one done by Madalozzo (2008) to determine the probability that an individual will select into marriage. The probability model of marriage can be expressed as: đ?&#x2018;&#x192;đ?&#x2018;&#x192;đ?&#x2018;&#x192;đ?&#x2018;&#x192;(đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;) =

đ?&#x203A;ˇđ?&#x203A;ˇ ďż˝đ?&#x203A;žđ?&#x203A;ž1 + đ?&#x203A;žđ?&#x203A;ž2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;žđ?&#x203A;ž3 đ?&#x2018;?đ?&#x2018;?â&#x201E;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x203A;žđ?&#x203A;ž4 â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; + ďż˝ đ?&#x203A;żđ?&#x203A;żđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x153;&#x20AC;đ?&#x153;&#x20AC;ďż˝. đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

Age is included because it is an important factor in determining selection into marriage, as older women are more likely to be married, and women with more education are less likely to enter into marriage at an early age. Additionally, having children can both increase and decrease the likelihood that a woman will enter into marriage. According to Madalozzo (2008), having young children can motivate single mothers to marry by allowing them to split the responsibilities of providing for their children with their spouses. However, single mothers may also choose not to marry because they can lose a significant part of their income, such as child support receipts, if they opt to marry. While Madalozzo uses individuals under the age of six as an indicator for children, I

đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

Selection into the labor force Although labor market selection may exist, it is unlikely to be a large issue and will not affect my results signifi-

not taking into the account the possibility that those who have not already gotten married will get married later on. Bergstrom and Schoeni (1996) avoid selection bias by restricting their analysis to include only individuals who are both 40 and older and have been or are currently married. Unfortunately, even in Wave IV of the Add Health study, the majority of the sample is between 24 and 32 years old. For this reason, selection bias is espeColumbia Economics Review

choose to use the number of children living with the respondent simply because having a child at home is more likely to influence a womanâ&#x20AC;&#x2122;s decisions than just having a child under six. For instance, if a woman has a child under the age of six, but this child lives with the father or another legal guardian, it is unlikely that having this child will have much effect on the womanâ&#x20AC;&#x2122;s decision to marry. Finally,

Columbia Economics Review

Madalozzo (2008) contends that willingness to buy a house may indicate that an individual is ready for stability, implying that home ownership can predict the likelihood of selecting into marriage. The adjustment for selection bias into marriage is accomplished by incorporating the Inverse Mills Ratio (IMR) into the regression. The IMR is expressed as: , Where Zâ&#x20AC;&#x2122; denotes the independent vari-

ables and đ?&#x203A;žđ?&#x203A;ž represents the coefficients in the probit regression (Heckman 1979). I perform the Heckman correction for selection into marriage on each of the four regressions I previously ran and compare the results. In this model correcting for sample selection bias, the equations I use are the following:

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; đ??´đ??´đ??´đ??´đ??´đ??´ + đ?&#x203A;˝đ?&#x203A;˝5 đ?&#x153;&#x2020;đ?&#x153;&#x2020; + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x153;&#x2020;đ?&#x153;&#x2020; + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x153;&#x2020;đ?&#x153;&#x2020; + ďż˝ đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ??´đ??´đ??´đ??´đ??´đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; . đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

The last two regressions are expected to be the most accurate because they account for sample selection bias and do not include the cohort mean AFM variable, which may also be biased as a result of selection into marriage. Because of this, they will be the results on which I base my analysis and conclusions. Finally, I run two additional regressions based on these last two regressions in order to determine if there is a statistically significant difference between marrying â&#x20AC;&#x153;youngâ&#x20AC;? and marrying â&#x20AC;&#x153;old.â&#x20AC;? Instead of including a dummy variable for each age-at-first-marriage, I include one dummy variable, young, where 0 is â&#x20AC;&#x153;oldâ&#x20AC;? (age-at-first-marriage is over 25 years old) and 1 is â&#x20AC;&#x153;youngâ&#x20AC;? (age-at-first-marriage is 25 years or younger). These equations are expressed as: đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x153;&#x2020;đ?&#x153;&#x2020; + đ?&#x203A;˝đ?&#x203A;˝5 đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = đ?&#x203A;˝đ?&#x203A;˝0 + đ?&#x203A;˝đ?&#x203A;˝1 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x203A;˝đ?&#x203A;˝2 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 2 + đ?&#x203A;˝đ?&#x203A;˝3 đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; 3 + đ?&#x203A;˝đ?&#x203A;˝4 đ?&#x153;&#x2020;đ?&#x153;&#x2020; + đ?&#x203A;˝đ?&#x203A;˝5 đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś + đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; . Results Outliers for the household income and personal annual earnings variables are dropped to prevent bias; this does not affect the mean and standard devia-

Winter 2013

Figure 1. Graph showing relationship between age-at-first-marriage and income for white women without cohort-specific mean AFM, using Heckman correction for selection bias.

tions for these variables for either black or white women. Sampling weights are taken into account when running regressions. I estimate the relationship between family income and age-at-first-marriage. Then, I estimate the relationship between respondents’ annual earnings and age-atfirst-marriage for white and black women without correcting for selection into marriage, but controlling for generational changes in the norms for marital age. I do so by including cohort-specific mean ageat-first-marriage into the regression. I then repeat these initial regressions without controlling for generational changes. A comparison of these results reveals that there are very small differences between controlling and not controlling for generational changes of norms for marriage. In general, the same relationship holds regardless of whether cohort-specific mean AFM is included into the regression, which indicates that including this variable neither significantly improves nor biases the results. There are large differences between the results for black and white women. The relationship between age-at-first-marriage and income (family income and annual earnings) without cohort mean AFM and selection correction reveals a generally positive correlation between family or respondents’ income and ageat-first-marriage for white women. By contrast, the relationship between age-atfirst-marriage and income without cohort mean AFM and the Heckman correction

for black women is ambiguous, although there does appear to be a weak positive trend. For each of these regressions, the hypothesis that all the age-at-first-marriage dummies are equal to 0 is rejected at the 0.01 significance level. I account for this problem of selection bias by performing a Heckman correction. In the first step, I determine the likelihood that black and white women will select into marriage based on several characteristics, such as age, education, and the number of children living with the respondent, through positing a probit model. The hypothesis that all regressors included in the probit model are jointly equal to 0 is rejected at a 0.01 level of significance. This is then used to complete the Heckman correction both with and without a control for generational changes. Results of the Heckman correction regression excluding cohort-specific mean age-at-first-marriage are reported in Tables 1 and 2, while the graphs are displayed in Figures 1 and 2. similar, but I found a significant racial difference. Based on Figure 1, there is a positive correlation between income and age-at-first-marriage for white women. This relationship is ambiguous for black women, although there might be a weak positive trend, as illustrated in Figure 2. Moreover, the results of the uncorrected and corrected regressions for both black and white women are not greatly different. This implies that the sample selection bias due to marriage is not very large, but it should still be accounted for. However, Columbia Economics Review

Winter 2013 in the models with the Heckman correction, the hypothesis that all the age-atfirst-marriage indicators are jointly equal to 0 is rejected for the family income and annual earnings of white women at the 0.01 significance level, but not for bblack women. Still, this hypothesis is rejected at the 0.05 level of significance for the family income of black women. The results of this test are reported in Tables 1 and 2. Finally, to determine definitively whether there is a difference between marrying “young” and marrying “old,” I perform a regression using a single dummy variable for young (in place of the AFM dummy variables), where those who married at or below the age of 25 are considered “young,” and those who married after 25 years of age are considered “old.” The results of this regression for white women are reported in Table 3, and those for black women are shown in Table 4. The outcomes for the test that young is equal to 0 are also reported in these tables. This hypothesis is rejected for white women, but fails to be rejected for black women at a 0.01 level of significance for annual earnings and family income. However, it is rejected for the family income of black women at the 0.05

for men only, I observed a positive relationship for white women, without an inverted-U shape. This may be because my data included only between ages 15 to 32, while in Bergstrom and Schoeni’s study the relationship between age-at-firstmarriage and annual earnings peak in their late 20s and began to visibly decline around 34 to 35 years of age for men. Interestingly, I did not find any relationship between income and age-atfirst-marriage for black women. Moreover, my analysis indicates that there is no statistically significant difference between being married before or after 25 years of age for black women. However, these results can be explained by the fact

inverted-U-shaped relationship between family income and age-at-first-marriage to be equally strong for both men and women. Additionally, Bergstrom and Schoeni (1996) did observe a weak correlation between black women’s annual income and age-at-first-marriage but none for white women, since black women were traditionally more likely to participate in the labor force than white women. Finally, according to a study conducted in 2003 by the U.S. Equal Employment Opportunity Commission (EEOC), the employment of black women increased 43% between 1990 and 2001 (United States 2003). Because of this, the relationship between black women’s annual income

Figure 2. Graph showing relationship between age-at-first-marriage and income for black women without cohort-specific mean AFM, using Heckman correction for selection bias.

Therefore, it now seems that the Bagnoli-Bergstrom model can no longer explain, even in part, why men continue to marry later than women. significance level. Discussion These results provide empirical evidence of a relationship between women’s age-at-first-marriage and their annual earnings that directly contradicts the Bagnoli-Bergstrom model. As predicted, white women who married before the age of 25 earn a substantially lower annual income than those who married in their late 20’s. Because white women now have a higher labor force participation rate, potential mates may place a higher value on their earnings potential. For this reason, white women now also have a greater incentive to delay marriage until their success in the labor market is evident. (1996) study found an inverted-Ushaped relationship between age-at-firstmarriage and the respondent’s income

that there are only 207 observations for black women, so it is likely that the ageat-first-marriage indicators have greatly reduced power, which obscures this relationship between respondents’ income and age-at-first-marriage. This is confirmed by the fact that there is a weaker relationship than anticipated even between age-at-first-marriage and family income; the hypothesis that young is equal to 0 is rejected at a 0.05 significance level rather than 0.01, the significance level at which this same hypothesis is rejected for white women’s personal and family earnings. However, the relationship between age-at-first marriage and family income is expected to be especially robust since a woman’s household income is directly related to her husband’s annual earnings. In fact, Bergstrom and Schoeni (1996) found the

and age-at-first-marriage today should be stronger, not weaker, than the one found in Bergstrom and Schoeni’s study based on 1980 United States Census data. Therefore, the failure to find this relationship in this current study is likely due to a lack of available data. Conclusion The purpose of this study was to determine whether the Bagnoli-Bergstrom (1993) hypothesis, which states that men (but not women) who have greater labor market potential are more likely to delay marriage until their earnings capacity is revealed, still holds now that women are becoming increasingly likely to participate in the labor force. In contrast, my analyses based on data from the National Longitudinal Study of Adolescent Health in 2008, find personal earnings to be higher in white who marry later. Al-

Columbia Economics Review

19 though no correlation between annual income and age-at-first-marriage was observed for black women, it is likely that the relationship exists, but was masked by the small dataset. Bergstrom and Schoeni (1996) found, using U.S census data from 1980, that men who married in their late 20’s have the highest incomes later in their lives, providing support for the Bagnoli-Bergstrom model. More interestingly, Bagnoli and Bergstrom (1993) posit that women typically marry earlier than men partly because marrying later does not reveal more about their ability to perform household roles. While Bergstrom and Schoeni (1996) found that women who married in their late teens or early 20’s did not have significantly different future incomes than those who married in their late 20’s, I did observe such a difference, especially for white women. This observed positive relationship between women’s personal earnings and age-at-first-marriage contradicts the prediction of the Bagnoli-Bergstrom model. As more women enter the workforce, women are no longer valued only for their ability to perform traditional marriage roles. In fact, both men and women’s ability to perform economically is important to potential mates and information about this earnings capacity becomes available later in life. This can explain why both men and women are waiting longer to marry in the United States. However, even today men are marrying at a later age than women are: in 2011, the median age-at-first-marriage was 28.7 for men and 26.5 for women. Interestingly, between 1960 and 2011, this age differential in first marriage has remained consistently around two to three years (Cohn et al. 2011). Therefore, it now seems that the Bagnoli-Bergstrom model can no longer explain, even in part, why men continue to marry later than women. One possible future direction for this research is to replicate this study using a different dataset that can confirm that a positive correlation between income and age-at-first-marriage exists for black women. It would also be interesting to see if this relationship has changed in any way for black and white males. Finally, another possible development would be a new theoretical model or even an improvement of the current Bagnoli-Bergstrom model, as the existing models can no longer explain the enduring age differences in marriage between males and females as women’s earnings capacity becomes more important to potential mates.

Winter 2013

Citing Success Patent Valuation Through Indicators

Benjamin Chan Princton University

In today’s knowledge-based economy, the patent has a central role. As a form of intellectual property, it grants its inventor “the right to exclude others from making, using, offering for sale, or selling the invention” (35 USC § 154, ) and traditionally has been a central legal tool in the enforcement of property lights. In recent years, however, patents have not been treated solely as legal rights; instead they have gained popularity as financial assets. As early as 2005 it was estimated that patents and other intangibles such as trade secrets, copyrights, and trademarks contributed up to 75 percent of the value of publicly traded American companies, a significant jump from decades past (“A Market for Ideas”. 2005). In light of this newfound importance, a patent market has emerged in which patents can be disconnected from their inventor and assigned to another owner. As Figure 1 shows, there has been a stunning increase in the number of patent transactions over the past three decades. The growth of this market has outpaced improvements in the valuation of patents, a crucial part of the patent transactions process. Studies have considered the possibility of predicting patent value through patent indicators, such as citations and claims, and research over the

past two decades has shown some of these to be significantly correlated with value. Given that the indicators needed to estimate the value of a patent are public and easily accessible, this valuation approach has clear advantages over the traditional methods, requiring less time and incurring minimal costs (Omland 2011).

A patent market has emerged in which patents can be disconnected from their inventor and assigned to another owner.

However, these relationships have not been clearly quantified, due to the lack of publicly available patent price data. Instead, the majority of findings have been based in theory, as research has resorted to indirect measures, such as a firm’s market value, responses from inventors’ surveys, and patent renewal data to estimate patent value (Munari and Oriani 2011). Columbia Economics Review

The following studies provide a good foundation, but their results as a whole are not cohesive, even though all three studies use the same dataset. Sneed and Johnson (2009) establish technological scope, international filings, references, backward citations, claims, age, owner, and lot size for sale to be statistically significant predictors of price, but Odasso and Ughetto (2010) find only the lot size for sale, forward citations, and age to be statistically significant. Furthermore, Nair et al. (2011) show only forward citations, age, and international filings to be significantly correlated with price. Perhaps most alarming, their research does not agree on the direction of the relationships, as one study finds international filings to be inversely correlated to price, while the others suggest a positive correlation. One reason for this inconsistency may be the differing choices of instruments the studies use to account for the sample selection problem caused by a form of omitted variable bias. In this specific case, a valid instrument would be correlated with the probability of sale but have no influence on the price of the patent. It seems that no such instrument has been credibly established. This is a troubling result, as it is known that using an invalid instrument may exacerbate the bias and incon-

sistency of the estimates (Achen 1986). In contrast, this study establishes an alternative model for valuation, the censored regression model, which does not require instrumentation and will provide more precise estimates of the coefficients on each indicator. Data This study used the latest version of the Ocean Tomo dataset of U.S. patents, which details patents offered for sale in live auctions from 2006 to 2009. Each patent corresponds to a unique identification number, which I use to combine patent prices and indicators. From this dataset I select my measures of patent value to be the price of the patent (price) and the seller’s reserve value (open). Of the 1,628 patents I was able to acquire complete data for, 515 were sold and therefore had observations for their price. For the remaining unsold patents, the seller’s reserve value was available. Both price and open are right skewed, and there are a wide range of dollar values, so in the following analysis, I work with the logarithms of variables measured in dollar values . The patents offered for sale in the

Ocean Tomo auctions seem to provide a relatively good representation of patents as a whole; as Figures 2 and 3 in the Appendix, they were diverse in technology and numerous in all nine auctions. As for my indicators, I select the same indicators used by the previous authors, provided two criteria. First, the data must be easily accessible on the US Patent and Trademark Office (USPTO) website. Variations of indicators have been examined in theory, but I restrict my analysis to only those that are not derived from the bibliographic indicators. Second, the indicators must be pertinent to the patent value. That is, in considering that patents are most often traded to break market barriers to entry or to guard against lawsuits, the indicators should reflect some measure of the specificity and relevance of the coverage technology or the legal coverage of the patent. From the USPTO I found data on the number of references (the citations received: ref), the number of citations (the citations made: cit), the number of claims (claims), the number of included International Patent Classification (IPC) categoColumbia Economics Review

ries (scope), the number of foreign patent documents (inter), and whether the patent was invented by an individual or not (individ). The majority of these pat-

The growth of this market has outpaced improvements in the valuation of patents, a crucial part of the patent transactions process.

ent indicators were previously quantified in the National Bureau of Economic Research’s (NBER) U.S. Patent Citations Data File (Hall et al. 2001), which has been updated up to 2006. Because some patents in the Ocean Tomo dataset were granted following 2006, the missing data for several patents were found on the USPTO website. I construct a final term

inspired by the previous studies, the age of the patent (age), by subtracting the application date from the sale date. I chose not to construct age based on the grant date because a patent’s 20-year lifespan begins upon application, and there is often a lag period between the application and grant date. Summary statistics are included in the Appendix as Table 3. The following table describes what the specific indicators represent, based on theory. I also decided that I would augment my regressions with the following control variables: the number of patents within the lot (lotsize), technology class (techclass) and an auction tag corresponding to the auction at which the patent was offered for sale (auction). Although Odasso and Ughetto (2010) were the first to use measures for year and technology type, they do so only as instruments in the selection stage of their model. I chose to include those in the valuation stage because it seems likely that the state of the market over time and whether or not the patent is in an industry requiring patent protection would influence price. For the technology classification, I used the NBER’s classification system, which categorizes the technologies into six main groups: Chemical (excluding Drugs), Computers and Communications, Drugs and Medical, Electrical and Electronics, Mechanical, and Others. Methodology At first glance, the Ocean Tomo dataset seemed quite large, but a closer look revealed a possibly confounding issue: the

Winter 2013

1,628 patents were offered in 634 lots, so not all patents were offered singularly; in fact, only 377 lots correspond to the offering of a singular patent. As a result, the specific price for most patents is uncertain, since the price of a lot corresponds to the combined value of all the patents within a lot. Previous studies that have used the Ocean Tomo dataset have considered two methods to deal with this concern. Sneed and Johnson (2009) and Odasso and Ughetto (2010) study the patent indicators at the lot level, taking the average of all indicators, while Nair et al. (2011) restrict their analysis to only those patents sold singularly. In order to understand the differences between the results found from the models without introducing other variables, I test both of these two approaches of lot-level averaging and restricting to only singular patents. While the previous papers have treated the Ocean Tomo dataset as having a sample selection bias problem resulting from unobservable patent prices, I argue that the price data are not entirely unobserved but rather censored. Ocean Tomo auctions were “conducted according to an ascending bid model, and a contract for the sale of the patent is formed by the highest bid made above the seller’s reserve and before the fall of the auctioneer’s hammer” (Odasso and Ughetto 2010). This means that if a patent was sold, the price must have been higher than the reserve, and if unsold, then the reserve was not met, suggesting that the Columbia Economics Review

Winter 2013 price of the patent was lower than the reserve price. Mechanically, by combining these two variables into one variable and accounting for the observations that are censored, we have a left-censored dependent variable. This results in 515 uncensored observations and 1013 censored observations in this dataset. To account for the censored data, I use the Tobit model, which establishes a set upper or lower censoring points. Having elucidated the estimation method, I now propose the following base model, which I estimate first with OLS and then with this censored model, subsequently adding in controls: (1) logpricei = refi*β1 + agei*β2 + citi*β4 + claimsi*β5 + scopei*β6 + interi*β7 + individi*β8 + controls*β + εi where i indexes each individual patent or lot, β are the coefficients, and εi is the error term. The terms are explained in Table 1. Hypotheses In terms of the coefficients, I hypothesize that references will have a positive coefficient, as the previous studies have shown. An additional reference should suggest relevance, and thus interest in that specific patent. Age will have a negative correlation with price, given that the older a patent, the less time it has before expiration, and thus less time to generate value for the owner. I expect citations to have a positive coefficient, since a patent that cites many other patents is demonstrating its relevance. It is possible, however, that this measure is highly subjective, due to the fact that patent examiners often add new citations to an application. The relationship between technological scope and price seems less obvious. Because of the number of IPC categories in which a patent provides no legal power, I surmise there will no be strong correlation with price. Although a study has suggested otherwise, I expect claims and international filings to have substantial, positive coefficients, given that they represent the legal power of the patent. It is true that international filings require additional upkeep, but it seems reasonable to think that only patents that are worthwhile will be filed in other countries. It is hard to say how having an individual inventor affects price. Omland (2011) suggests that multiple inventors are linked with higher amounts of R&D investment, so I posit that individual inventor has a negative coefficient. Results The results from the censored regres-

sions are reported in Table 2 and 3. In both cases, I first estimate a base model of the indicators, before adding additional auction and technology class controls. In the lot-level averaged data, I was also able to include the term lotsize to estimate the impact of being sold in a group. For the lot-level averaged data (Table 2), the base regression in column 1 shows that the number of references and having an individual inventor are positive, significant predictors of patent value. Surprisingly, having an individual inventor initially seems to represent a 42.2% increase in value over having an organization or group inventor. However, once the controls are added, all indicators except for references are insignificant (age was significant and negative, as predicted, but only at the 10% level). Additionally, the two terms representing legal power, claims and international filings are insignificant. The results of the singular patent regressions (Table 3) are very similar. The coefficient on references is significant at the 1 percent level, while the rest of the indicators are insignificant. The magnitude of the references coefficient matches that of the lotlevel regressions (.008), suggesting that for each additional reference, a patent is worth 0.8 percent more in value. Analysis of the controls yields more interesting results, as the auction, technology class, and lot size controls are strongly significant at the 1 percent level. The continuous auction term, as seen in column 2 of Table 2, has a coefficient of 0.131, representing a 13.1 percent in-

crease in value per auction from Spring 2006 to Spring 2009. A closer look at this trend with the significant auction dummies, however, suggests that this trend Columbia Economics Review

was more nuanced. Fall 2006 is only significant at the 10 percent level, showing little difference in the price level from Spring 2006. Additionally, there are sub-

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Winter 2013 stantial, highly significant declines in Fall 2008 and Spring 2009 from the previous auctions. It is of note that in Spring 2009, only 21 patent lots were sold. This may explain the difference in the coefficient as estimated by the censored regression and the OLS regression, which is unable to take into consideration the sellerâ&#x20AC;&#x2122;s reserve. As for the technology class, the results show that coefficients for Computers and Communications, Electronics, and Mechanical are positive and significant at the 1 percent level, while Drugs and Medical and Others were not. This suggests that patents in the classes of Computers and Communications, Electronics, and Mechanical were positively correlated with prices and worth more than the base dummy, Chemical. Again, the singular patent regressions show similar results. Lastly, the term lotsize is significant and negative, representing around a 20 percent decrease in price per additional patent within a group. Previous literature claimed that several indicators are indeed good predictors of patent price, but the results of this study suggest a murkier picture, since all of the indicators except for references show insignificant coefficients. This study confirms the previous findings that references have a positive, significant correlation with patent price. This study finds a marginal effect of 0.8 percent, whereas the results of Sneed and Johnson (2009) show a less positive relationship, estimating it to be 0.2 percent. It also confirms that

More than ever, patents indeed are treated as financial assets that are closely tied to the status of the current economy. patent transactions play a big part in the hightech industries but are not as important in the medical field

patents sold in groups seem to be of less value than those sold singularly because the term lotsize has a negative coefficient. While this study hoped to contribute to the understanding of the relationship between international filings and price, international filings is shown to be an Columbia Economics Review

insignificant indicator in this study. Although the base regressions in this study show that some indicators were significant, the controlled regressions indicate otherwise. Thus, based on this analysis, I conclude that these other indicators are not suitable predictors of price. There are several reasons why the results of this study differ from previous literature, namely the use of the censored regression model as previously described. Additionally, previous researchers did not use the same control variables for their models, and this might explain the differences. From our regressions, however, the auction and technology class controls are valid and are significantly correlated with price. When added to the regressions, they account for significant jumps in the Wald chi-squared statistic of the maximum likelihood model, which is essentially the F-statistic used in OLS regressions; this suggests an improvement on the model. Although the results are inconclusive with regards to the power of indicators to predict patent prices, this study improves the current understanding of the patent market, specifically through the control variables. From the time period of this

analysis, 2006 to 2009, it seems the patent price level was increasing. The coefficient from the lot-level regression does not represent a yearâ&#x20AC;&#x2122;s difference but only several months, suggesting that the growth was extremely rapid. One possible explanation for this would be that the patent market was gaining popularity. Â At the same time, the auction dummy variables showed that the Fall 2008 and Spring 2009 auctions resulted in much lower prices, canceling out much of the increase in patent price level. It is possible this decline was the result of the recent global financial crisis, which significantly worsened in late 2008 and early 2009. It seems that more than ever, patents indeed are treated as financial assets that are closely tied to the status of the current economy. Additionally, the differing significance among the technology class dummies suggest that patents may play a bigger role in some industries than others. As Figure 1 at the beginning of this paper showed, patent transactions have not grown at the same pace in all industries. Based on the regression results, it seems that patent transactions play a big part in the high-tech industries but are not as important in the medical field. One explanaColumbia Economics Review

tion for this requires understanding the standard business model of each industry. While companies in computers and electronics often go through incremental improvements, thus generating a large number of patents, companies in biotechnology or pharmaceuticals have the majority of their value tied up with single novel drugs and treatments. If these types of companies were to trade their patents, their business could be significantly damaged. Conclusion Research on patent valuation through indicators suffers from the lack of publicly available pricing data. Although this paper is unable to make significant conclusions about the nature of the relationships between indicators and patent value, it still contributes a key insight: the use of a censored regression, which maximizes the information from the limited existing data. Even with the current confusion in this area of research, the growth in the patent transactions market makes continued study particularly intriguing.

Winter 2013

The Inventor’s Walk Optimal Patent Protection in Trial-and-Error Search

Ryan T. Lee Princeton University

perspective. Patent length is not considered under the model. I operationalize the strength of patent protection as the cost of imitation under a patent. This cost includes the fees an entrepreneur must pay to license a patented product (Shapiro 1985) in addition to any other implicit costs of replication, such as the probability-adjusted cost of potential litigation. The breadth of protection can be thought of as the number of potential products that are covered by the patent; a patent with a large breadth of protection will prevent the entry of more products than the same patent with a smaller breadth of protection. Summary of the Callander Model From a countable set of entrepreneurs, each chooses products sequentially in periods t = 1,2,3,... . The set of potential products is the entire real line, R . This set might represent a simple p r o d u c t with one dimension, or a single dimension of a more complicated product. On the market, a product yields an outcome

Figure 1: One possible Brownian mapping, ψ ( p ) . Modified from Figure 1 in Callander (2011). Outcome

ψ(p 0 * )

Product p0 * Slope = μ ψ( p)

ψ(p)

according to the function, ψ , where the set of outcomes is also the real line: ψ :R → R .

Introduction Product development is a process that relies heavily on learning by trial and error. Uncertainty in the potential outcome of experimentation leads agents to estimate the returns of experimentation by observing the outcomes of previous products. This trial and error search for ideal outcomes is easily described algorithmically. Under this framework, Callander (2011) models the uncertainty in trial-and-error search by mapping each potential product to an outcome of the realized path of a Brownian motion. Agents are aware of both the drift and the variance of the Brownian motion in this search model. The variance serves as the source of the uncertainty in the search, while the agents’ knowledge of the drift allows them to predict outcomes. In addition, agents are aware of all previous products and their outcomes, allowing the search to evolve over time through accumulated knowledge. Each agent’s knowledge of previous products implies that knowledge in the Callander model is both non-rival and non-excludable. The production of new goods is, therefore, a public good per se in this search model. The model is solved constructively, resulting in two distinct phases in the product development cycle. The first is

the monotonic phase, in which search occurs in one direction. The second phase is the triangulating phase, in which the search straddles the ideal product and then zeroes in on the best outcome. The end result is an equilibrium where no experimentation occurs and the most recent

Patents are typically designed with two main intentions in mind. The first is to encourage innovation by rewarding experimentation directly. The second is to encourage the disclosure of inventions so that others can build upon past inventions. product is replicated into perpetuity. Section 2 provides a summary of this model. In this paper, I consider the impact of introducing patent protection on the Callander model. This paper models the breadth and strength of protection, and describes their implications on the search Columbia Economics Review

for outcomes. Motivation Patents are typically designed with two main intentions in mind. The first is to encourage innovation by rewarding experimentation directly (Gallini 1992). The second is to encourage the disclosure of inventions so that others can build upon past inventions (Mazzoleni and Nelson 1998). Both of these goals aim to encourage economic growth through the development of new products and ideas (Porter 1990). The enforcement of intellectual property rights , however, is also restrictive in nature; by preventing market entry and the consequent competition, patents inherently restrict experimentation to some extent. Therefore, a social planner who seeks to maximize the quantity and the quality of products developed in an economy with patent protection needs to balance the economic benefits associated with the increase in incentives to the individual entrepreneur, and the economic costs associated with the decrease in market entry. Patent protection policy can be described by several dimensions: the breadth, length, and strength. The length, or duration, of a patent has been studied as the subject of several influential papers in the context of optimizing from a social

The true function ψ is determined and set as the realized path of a Brownian motion before experimentation begins. The Brownian motion has the following parameters: drift µ and variance σ . However, each entrepreneur knows these two parameters of the Brownian motion in addition to the set of all the products and their outcomes chosen by previous entrepreneurs. Each entrepreneur’s utility is quadratic 2

in the outcome of the product ψ ( p ) , taking the following form for utility u of j entrepreneur

u j ( p ) = −(ψ ( p )

From this equation, we have that each entrepreneur has a maximum utility of 0; the closer the outcome of a product is to zero, the better off he is. Play begins with common knowledge * * of one product p0 and its outcome ψ ( p0 ) . This initial, or status-quo, product can be thought of as any product that opens up a new space. Callander notes that this product may be a new, groundbreaking product or an old product that is ripe for innovation. Figure 1 shows one possible realization of a Brownian path. The dashed line represents the first entrepreneur’s best estimate of the mapping.

Let t

h =

{( p

* 0

)(

) }

,ψ ( p ) , p ,ψ ( p ) ,  * 0

* 1

be the set of known points to entrepreneur t . This set contains all products produced over the duration of the search up to and including time t − 1 . Let the left-most product in

and

denote

r t de-

note the right-most product in h t . By the Markov property of Brownian motion, beliefs about product p are determined only by the nearest points. Therefore, for any product to the right of

we have

Expected outcome :

(

)

E ψ ( p) | h t = ψ (r t ) + µ ( p − r t )

Variance :

(

)

var ψ ( p ) | h t = | p − rt |σ 2 t

All points to the left of l are analogous. For any product in b e t w e e n two known products in

h t , let q1 denote

q2 the left neighbor and denote the right neighbor. Then for any product

p ∈ [q1 , q2 ] , we have

Columbia Economics Review

Expected outcome :

(

)

E ψ ( p ) | h t = ψ (q1 ) +

ψ (q 2 ) − ψ (q1 ) q 2 − q1

Variance : var (ψ ( p ) | h t ) =

( p − q1 )

( p − q1 ) (q2 − p )σ 2 q2 − q1

Additionally, entrepreneurs face meanvariance expected utility in the Callander model:

(

)

(

E u t ( p | h) = E ψ ( p ) | h t var ψ ( p ) | h t

)

which is simply the utility of the expected product, less the variance of the outcome. Callander notes that this Brownian motion representation of uncertainty captures several key features of experimentation and learning in product markets that are consistent with empirical findings. Most importantly, it successfully describes the segmentation of product development into two distinct phases. It also incorporates many micro features of the product development cycle, such as path dependence of search and proportional invertibility. Each of these properties makes this dynamic decision-making model ideal for studying the role of patent protection in the product development cycle. Basic Extension

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28 Let

but also any implicit costs of replication.

denote the breadth of patent pro-

As these costs increase, entrepreneur j is worse-off, as his lower bound on utility is now smaller: his utility is the same

t e c - tion. Every product p is protected on both sides such that no new product may be developed on the inter-

as before in the case that | ψ ( p ) |≤| ψ (τ ) | , but his utility is less than before if * t

val [ p − δ , p + δ ] . Figure 2 depicts one possible realization of a Brownian path such that the status-quo product is cov-

| ψ ( p ) |>| ψ (τ t* ) | . The imitation cost in this model can vary by the underlying market of the search but not over the span of a single search.

ered by patent protection of breadth δ . Under this extension, patent protection is restrictive in that it limits the number of potential products that are available to be produced through experimentation in future periods. In addition, I impose a utility function bounded by the best outcome to date. De-

Although φ is a cost by definition, it also serves as an implicit incentive to the individual entrepreneur. To see this, note that each entrepreneur must either imitate an old product or produce a new, experimental product. Increasing the cost

fine φ as the price any entrepreneur must pay to reproduce a product, and

of product imitation, φ , makes the alternative to imitation– namely experi-

τ *j = arg min j′< j | ψ ( p *j′ ) |

define as the product with the most attractive outcome that has been tried up to period p and outcome ψ ( p ) , uct

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mentation– more desirable. Therefore, φ represents the incentive to experiment imposed by the patent system. Utility of this form implies that the market will support only the best product. If experimentation is successful, then

j . For prodthe utility

of entrepreneur j under this extension is:  − (ψ ( p ) 2 ) if | ψ ( p ) |≤| ψ (τ *j ) | U j ( p) =  * 2 * − (ψ (τ j ) − φ if | ψ ( p ) |>| ψ (τ j ) |

| ψ ( p ) |≤| ψ (τ t* ) | , and the experimenter

will receive the utility according to his product. If, however, the experimentation is unsuccessful, then | ψ ( p ) |>| ψ (τ t ) | , and the entrepreneur must produce *

In this model of patent protection, φ captures not only the cost of licensing, Outcome

Covered by patent Free for experimentation

ψ(p 0 * )

Product p0 * Slope = μ ψ( p)

ψ(p)

by paying the utility-penalty

An interpretation of this utility structure is that a single consumer finds the zero-outcome product to be ideal; as a result, this consumer is willing to pay more for a product closer to the ideal. Furthermore, the bounds on the entrepreneur’s utility indicate that our consumer buys only the best product in the market. This type of behavior is characteristic of monopsony in product markets, including the markets for military equipment, coal, and beef (Schroeter 1988; Atkinson and Kerkvliet 1989). Let

θt

Define as half of the adjusted search complexity in the underlying industry, and λ = δ | µ | as the outcome-breadth of a patent, or the range of outcomes the patent covers. 1 The equilibrium strategy of entrepreneur 1 is: λ 1. Stable at

denote the perceived probability

E u t(p | h ) =

− θE [ψ ( p )] − (1 − θ )(ψ (τ ) + φ ) − var (ψ ( p ) | h * 2 t

Combined, the first two terms in Equation 7 capture the tradeoff between expected gains in outcome from experimentation and the cost of defaulting to the best-so-far product. The last term imposes an uncertainty-penalty on entrepreneur t from increasing uncertainty in product outcomes.

For the sake of tractability, I take θ to be constant in the experimental product This constant probability of suc-

cess is denoted θ . By holding θ constant within a search, I allow equilibrium behavior to be described analytically without significant loss in detail. This might be a reasonable assumption in relatively complex markets, when an entrepreneur’s predictions might be based only on the successes of his predecessors. Such markets would be characterized either by limited information or simple irrationality. Searches based on underlying markets with more optimistic outlooks, for example, would have a greater θ than those based on more pessimistic markets. Equilibrium Behavior Equilibrium is solved for by construction, starting with the first entrepreneur at t = 1 . From the Callander paper, we

)

space surrounding threshold for stabil-

p0*

are fewer opportunities for future entreincreases the ity through the

term λ ; the greater the breadth

is,

the greater λ will be, and the wid- e r the outcome-interval for stability will be. Additionally, the cause of stability can be attributed to patent protection if

0 ≤ ψ ( p0* ) − α ≤ λ o r i f λ ≤ ψ ( p0* ) + α ≤ 0 In this case, which I call patent-induced stability, the entrepreneur is discouraged from experimentation by the presence of patent protection. In the absence of patents, the entrepreneur would have chosen to experiment such that his product would have been within λ units of the status-quo product in the outcome space. These equations imply that the threshold

2. Experimental if

p1* = p0*

ψ ( p0* ) ∈ [−α − λ , α +. λ ]

of a successful product at time t . The mean-variance expected utility of experimentation under this extension is:

have that product pt* is stable if pt*′ = pt* for any time t ′ > t . Therefore, once an entrepreneur chooses not to experiment, that product will be produced forever, as all future entrepreneurs will face the same Columbia Economics Review

decision and will therefore also optimize their outcome with the same knowledge passed on by the previous entrepreneur, thus leading to them making the same choice. The First Period

φ.

Figure 2: One possible Brownian mapping, ψ ( p ), with patent protection.

product

* t

ψ ( p0* ) ∈/ [− α − λ , α + λ ]

preneurs to experiment. Similarly, λ is strictly increasing in the absolute value of the drift parameter, | µ | . This is because a larger drift parameter implies that a patent of a given breadth will cover more potential outcomes, and is more likely to cover outcomes which future entrepreneurs would otherwise attempt to achieve through experimentation. Since α is decreasing in | µ | , a larger magnitude of drift parameter implies that patent-induced stability increases at the expense of decreasing good-enough stability, thus showing that it is more likely an entrepreneur will not experiment and will rather revert to the previous best outcome.

where

α E (ψ ( p1* | h1 ) ) = ψ ( p0* ) + µ ( p1* − p0* ) =  − α

if if

ψ ( p*0 ) > α + λ ψ ( p*0 ) < −α − λ

The first condition states that the initial, status-quo product will be stable and no experimentation will occur if its outcome is within the range

[−α − λ , α + λ ] . The second condition states that if the status-quo product is not stable, then entrepreneur 1 will choose product c o m e

p1*

such that his expected outis either

− α . Here,

E (ψ ( p1* | h1 ))

denotes t h e expected outcome of that first experimental product. There are several unique features of this strategy. Firstly, the stability is easier to achieve than in the Callander mod-

α′ = σ 2 | µ | . 2

el. To see this, let The stable interval in the Callander model is

[−α ′, α ′] , which is smaller than this extension’s

stable

interval,

[−α − λ , α + λ ] , for nontrivial breadth

of protection. The first reason for a wider interval in this extension is the change to the underlying utility structure; as the probability of successful experimentations decreases, the term α = α ′/θ increases, which widens the interval for stability in this model. Secondly, the restriction in the product

for patent-induced stability is greater for larger λ , and show exactly how– according to this model– patents discourage experimentation. This form of stability allows a systematic analysis of the cases where experimentation would occur in the absence of patents and thus hones in on the main issue with patent policy. Two factors determine the size of λ . Firstly, λ is strictly increasing in the breadth of protection, δ . When the breadth of protection is greater, the patent covers more products so that there Columbia Economics Review

If the entrepreneur chooses to experiment, however, he still seeks the same product as he would with no breadth of protection, optimizing his expected utility by choosing the product that yields

the expected result of either α or − α . Put another way, if patent protection does not force the entrepreneur to stability, then it does not impact his experimentation choices. 4.2 The Second and Subsequent Periods Assume, without loss of generality, that µ ≤ 0 for the following results. Re-

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time

if it has not yet stabilized,

p0* < p1* <,  < pt*−1

and ψ ( p ), ψ ( p ),  ,ψ ( p ) ≥ 0 . The following proposition describes equilibrium behavior in the monotonic phase: * 0

* 1

* t −1

2 In the monotonic phase at period the equilibrium strategy is: 1. Stable at

t ≥ 2,

ψ ( p ) = 0 line, then the search enters the triangulating phase. Using Definition 2 from the Callander paper, we have that a search is in the triangulating phase at period t ≥ t ∆ if it has not yet stabilized, p0* < p1* <  < p *∆

pt* = τ t* = pt*−1 i f ψ ( pt*−1 ) ∈ [0,α + λ ]

ψ ( p ), ψ ( p ), ,ψ ( p

(2θ − 1)α 2 + ψ (τ t* ) 2 2α

ψ ( p ) ∈ [α + λ , γ t ] ,where

* t

* t −1 ,

* t −1

* t

* t −1

In the monotonic phase there are two conditions for stability. Callander refers to the first condition as “good-enough stability,” since this stability occurs when the most recent product is “good enough” for stability to ensue. Again, stability is caused by patent protection if

0 ≤ ψ ( p0* ) − α ≤ λ . Condition 1 here is analogous to the first condition of Proposition 1 in logic and in results. The second condition results from an unexpected outcome from the most re* * * cent product pt −1 , such that ψ ( pt −1 ) > ψ (τ t ) . The decision to experiment occurs only if the expected utility of experimentation exceeds that of the given utility of that best-so-far product; if the utility of the best-so-far product exceeds the expected utility of experimentation, then the product search enters “bad-enough stability.” Intuitively, the threshold for a search getting stuck in this type of stability is de-

creasing in the probability of success, θ . As with good-enough stability, the greater θ is, the more attractive experimentation is, and the more is required to deter an entrepreneur from experimentation. If neither of the two stability conditions hold in the monotonic phase, then it must be the case that the outcome of the previ-

* t ∆ −2

and ) > 0 >ψ ( p ) * t ∆ −1

� (ψ ( z ) − ψ ( w) 2 − θ σ 2 (.z − w) λ (w ⋅ z) = δ θ (ψ ( z ) − ψ ( w))( z − w)

p >p

and E (ψ ( p | h ) ) = ψ ( p ) + µ ( p − p ) = α * t

* 1

. 2 z−w Define α ( w�⋅ z ) = σ and 2θ ψ ( z ) −ψ ( w)

3. Experimental if * t −1

t −1

* 0

2. Stable at pt* = τ t* =/ pt*−1 i f ψ ( pt*−1 ) > γ t =

ous product falls in the range The current entrepreneur will continue to experiment to the right, in the same direction as his predecessors. The entrepreneur will again optimize his expected utility such that the expected outcome is equal to α . If an experimental product from the monotonic phase of search crosses the

� Formally, α ( w⋅ z ) generalizes α by re-

placing µ bridge,

with the slope of

while

�

λ ( w⋅ z )

t h e

generalizes λ

by replacing µ with the probabilityadjusted slope of the bridge less the variance as a fraction of the outcome-span of the bridge. ∆

3 At period t in the triangulating phase, the equilibrium strategy is: 1.

Stable at

p *∆ = p *∆ t

t −1

    � � | ψ ( p *∆ ) |≤ α  p *∆ ⋅ p *∆  + λ  p *∆ ⋅ p *∆  t −1  t − 2 t −1   t − 2 t −1     

greater when λ ( p

* t ∆ −2

Reducing δ ψ ( p *∆ ) −ψ ( p *∆ )

(

t −1 * t ∆ −1

θ p

)

t −2 * t ∆ −2

−p

)−



we see that

t −2

t −1

)

δσ ψ(p

* t ∆ −1

) −ψ ( p

* t ∆ −2

)



�

  is strictly in-

 

creasing in δ . As with the monotonic phase, a greater breadth of patent protection in the triangulating phase pushes the entrepreneur towards earlier stability. The threshold for patent-induced stability is similarly increasing in θ ; when θ increases, both     � � λ  pt*∆ −2 ⋅ pt*∆ −1  α  pt*∆ − 2 ⋅ pt*∆ −1       de  and  crease, driving the search towards experimentation. Another interesting feature of this mod  � λ  pt*∆ − 2 ⋅ pt*∆ −1     is decreasing in el is that 

| p *∆ − p *∆ t −1

t −2

and

increasing

| ψ ( p *∆ ) −ψ ( p *∆ ) |

t −1 t −2 . A bridge that spans a wide range of outcomes will be more likely to result in patent-induced stability in the triangulating phase, as will a bridge that spans a smaller interval on the product space. This relationship implies that a steeper bridge span increases the chance of patent-induced stability at the expense of good-enough patent stability in the trian-



�



α  pt*∆ − 2 ⋅ pt*∆ −1  

 

 is degulating phase, as creasing in the slope of the bridge.

solves

   p −p �  E ψ ( p *∆ | h t ) = α  p *∆ ⋅ p *∆  1 − 2 * * t  t − 2 t −1   p∆ − p∆  t −1 t −2   

(

� λ ( pt*∆ −2 ⋅ pt*∆ −1 )

λ  pt*∆ − 2 ⋅ pt*∆ −1 

2. Experimental otherwise, where p *∆ ∈ ( p *∆ , p *∆ )

� * ⋅ p ∆ ) is larger. t −1

* t∆

* t ∆ −2

The first condition represents goodenough stability of the first period in the ∆ triangulating phase, t . As with the monotonic phase, the threshold for goodenough stability in the triangulating phase is increasing in the breadth of patent protection. The cause is patent protection when     � � 0 ≤| ψ ( p *∆ ) | −α  p *∆ ⋅ p *∆  ≤ λ  p *∆ ⋅ p *∆  t −1 t − t − t − t − 2 1 2 1        

From this equation, it is clear that the threshold for patent-induced stability is

Columbia Economics Review

∆ For period t > t , let pl denote the left

point of the spanning bridge, and let p * r denote the right point of the spanning bridge. Proposition 4 characterizes equilibrium behavior after the first period of the triangulating phase. ∆

4 At period t > t in the triangulating phase, the equilibrium strategy is: 1.

Stable at pt* = pt*−1 ∈ { pl* , pr*} if  �   �  ψ ( pt*−1 ) ≤ α  pl* , pr*  + λ  pl* , pr*          2.

Stable at

* * pt* = τ t* ∈ / { pl , pr }

ing time spent in the triangulating phase. Furthermore, this push towards early staσ ψ (τ t* ) < | pr* − pl* |andψ ( pl* ) ≈ −ψ ( pr* ) bility increases with the breadth of patent 2 protection for each search stage. According to this extension, then, the breadth of 3. Experimental otherwise, where coverage offered by a patent policy is a deterrent of innovation, and will typical* * * pt ∈ ( pl , pr ) solves ly lead to outcomes further from the ideal zero-outcome. As patent policy loosens, * *  �  innovation tends to continue for longer  − p p * * * t l E ψ ( pt | h ) = α  pl , pr  1 − 2 t*  durations, resulting in superior products. *   pr − pl    To the extent that the Callander model accurately describes product markets, Conditions 1 and 3 are analogous to patent policy may have significant ef∆ ∆ fects on economic growth. To see this, period t . As with period t , the breadth note that in this model each successive of protection increases the threshold for entrepreneur builds upon the knowledge good-enough stability for all periods of his predecessors’ products and their ∆ t > t , and the condition for patent-inresults, consistent with the fact that exduced stability is also perimentation has positive spillover effects onto future experimenters. Furthermore, the extent of the spillover effects

(

)

Figure 3: Average Utility Loss as a Function of

(a)

growth rate by increasing these spillover effects through an increase in the duration of experimentation. If research and

To the extent that the Callander model accurately describes product markets, patent policy may have signifcant effects on economic growth. development are the source of economic growth, as the Romer model suggests, then political-economic systems that encourage innovation and experimentation through looser breadth of protection should see higher growth rates than those with a large breadth of protection in place. Simulations The effect of patent protection on product outcomes in this search model can be better seen computationally, through Monte Carlo simulations. For the following simulations, each data point represents the average of 10,000 iterations of searches, and can be thought of as describing the average market characterized by a specific set of exogenous variables.

(b)

100

0.8

Monotonic Phase Triangulating Phase

0.7

80 70 60 50 40 30

0.6 0.5 0.4 0.3 0.2

µ = −1, σ = 2, and p0* = 0

20 0.1

10 0

5 10 15 Breadth of patent protection (!)

 �   �  0 ≤| ψ ( pt*−1 ) | −α  pl* , pr*  ≤ λ  pl* , pr*       .    Condition 2, however, is unique to peri∆

ods t > t ; it states that a search can get stuck if an outcome is moderately bad. The reasoning behind it is similar to the bad-enough stability of Proposition 2, even if the conditions for stability are different.Interestingly, a search that reaches the triangulating phase is more likely to achieve a better final outcome than a search that stabilizes in the monotonic phase. This is implied by Corollary 4 in the Callander model, which states that the boundary on good-enough stability is strictly converging in the triangulating phase. Therefore, the breadth of protection encourages worse outcomes by loosening the conditions for good-enough stability in all time periods. This push towards good-enough stability pushes a search to converge prematurely, reduc-

nously 0

5 10 15 Breadth of patent protection (!)

in this extension can be thought of as the duration of experimentation. Applied to the Romer endogenous growth model (Romer 1987), a looser patent policy may contribute to an increase in the economic

given

for

are exogeeach search.

δ = 1, φ = 3, andψ ( p0* ) = 10

unless otherwise noted. The results of the simulations performed under the assumption of a constant probability of success can be seen online, while the more realistic, variable-probability-of-success simulations are discussed below. 20

Figure 4: The effects of increasing cost of product imitation (b)

(a) 4.5

1.6

1.4

Monotonic Phase Triangulating Phase

Number of unique products

that has been tried up to period t . Definition 1 from the Callander paper s t a t e s that a search is in the monotonic phase at

[α + λ , γ t ].

Number of unique products

* t′

Average Final Utility Loss

call that τ = arg mint ′<t | ψ ( p ) | is the product with the most attractive outcome * t

Winter 2013

Average Final Utility Loss

3.5

2.5

1.5

1.2

0.8

0.6

0.4

10 15 Cost of Product Replication (!)

Columbia Economics Review

0.2

10 15 Cost of Product Replication (!)

Winter 2013

Figure 5: Utility loss as a function of the status-quo outcome 10 δ=1 δ=2 δ=3

Average Final Utility Loss

8 7 6 5 4 3

δ implies a restriction in the product space; as δ increases, the fewer definition,

products can possibly enter the search. Since fewer products implies worse outcomes, other things equal, we see that increases in the breadth of protection negatively impact final product outcomes through the reduction in the number of experiments in the triangulating phase. Another influence on triangulating time can be seen in Figure 4, which displays the result of varying the cost of

product replication, φ . Figure 4.a displays the average utility loss in stability, while Figure 4.b displays the num1 0 5 10 15 20 25 30 ber of unique products produced in each phase. The effect of imitation costs on the Status−quo outcome (ψ(p*0)) stable product is unique to the variablethe first term in the equation for expected probability model, and is unambiguously 5.1 Probability of success is a function utility increases with z until some negative. Other things equal, an increase of the experimental product in the cost of replication will push the z > p0* . This increasing weight on the exsearch towards a superior final product. Figure 3 shows the average result of repected outcome of an experiment across This result stems from the fact that stabilz intuitively causes the entrepreneur to ity requires an entrepreneur to produce a peated searches for δ ∈ [1,20] . Each point value experimentation to a greater extent, on Figure 3.a represents the average product that has already been developed, implying that the variable probability of squared final outcome of 10,000 searches, success is a driver of the aggressiveness with the additional cost φ . As a result, and establishes that a greater breadth of in experimentation. the cost of stability is greater, and patent protection leads to outcomes furFigure 3.b shows that the number of each entrepreneur is more inclined to exther from the ideal. Intuitively, this deterunique products produced in both the periment, resulting in longer searches on rent of experimentation is the result of monotonic phase and the triangulating average. Therefore, greater patent the restrictive nature of the patentstrength pushes a search towards better breadth. The larger an interval that a sinphase are decreasing in δ . The intuition results by changing individual incentives gle product commands in the product behind this reduction is the same as in favor of experimentation. Again, this space, the fewer products can possibly be with the constant-probability model. By positive relationship between the quantideveloped, according to the definition of 2

ty of experimental products and stable outcomes can be seen in Figure 4.b. The relationship between the breadth of patent protection and the final outcome also depends on the complexity relative to the starting outcome, described mathematically by Callander as

ψ ( p0* ) − α . Figure 5 shows the results of

varying this relative complexity through the status-quo outcome. The average utility loss of a search is largely decreasing in the status-quo outcome ψ ( p0 ) . One cause of this can be seen in Table 1, where we find that the time spent in the triangulating phase increases with the initial *

starting complexity. The logic behind this shift towards the triangulating phase is again straightforward. With more complex status-quo products, a more aggressive first-period follows, frequently resulting in overshooting with triangulation to follow. A striking feature of this variable-probability model can be seen in Table 1. It shows that better stable results are found under variable-probability than under constant-probability in spite of fewer experimental products produced before stability; not only does search stabilize to superior products in the variable-probability model, but it also takes less time to do so. This is because under accurate per-

δ established in Section 3. From the

viewpoint of a social planner, a higher breadth of protection leads to generally inferior stable product outcomes, resulting in loss of utility to the consumer and future entrepreneurs. It is interesting that the discontinuous

jump in stable outcomes seen at δ ≥ 1 5 in Figure 3.a occurs at a greater breadth of protection than the same cutoff in the constant-probability equilibrium. This jump signifies the level of δ after which no experimentation occurs, and the status-quo product is reproduced in stability. The deferred jump implies that entrepreneurs under accurate perceptions of successful experimentation have a greater tolerance for experimentation than those under the constant-probability model. The logic behind this difference can be found in quasi-concavity of θ in the experimental product z under the variable-probability model. Furthermore, θ is immediately increasing in z in the first period, implying that Columbia Economics Review

Columbia Economics Review

ceptions of success, searches spend drastically less time in the monotonic phase, and slightly more time in the triangulating phase, which implies better results. Entrepreneurs who fully understand the complexities of the market tend to act more aggressively, driving the search towards triangulation and better results. Empirical Implications Many studies have attempted to estimate the effects of patent protection on innovation. The results of these studies, however, are mixed; several studies suggest that overall patent strength is responsible for higher rates of innovation, while other studies suggest that the effect on innovation is negligible or even nega-

Winter 2013

34 tive (Allred and Park 2007). This model contributes to the literature through its specification of the level of patent protection, yielding unique results; while the breadth of protection is restrictive in its impact on innovation, the imita-

Other things equal, an increase in the cost of replication will push the search towards a superior final product. tion costs imposed by patent protection are positive in their impact. This finding corresponds well with the conflicting empirical studies on the economic impact of patent protection, as the overall index of patent protection has been defined differently across studies. Studies that define the overall strength of protection with a larger weight on the cost of imitation should find that patent protection has a positive effect on innovation, while studies that place a heavier emphasis on the breadth of protection should find that patent protection has a negative effect on innovation. One theme that can be seen throughout this paper is that better search outcomes result from increased experimentation. More specifically, better product outcomes can be explained largely through the number of unique products produced in the triangulating phase. Put another way, experimentation quantity acts as a proxy for product quality in this model. This relationship is cited frequently in empirical studies examining innovative activity, where innovative activity is operationalized as the quantity of patents cited. Economists, however, note that the mapping from experimentation quantity to innovative activity may not be exact, as this model suggests. Because this mapping is so frequently cited, it is important to verify empirically that experimentation quantity corresponds with product outcomes. Lastly, empirical studies suggest that optimal patent policy varies with the characteristics of the underlying market (Grossman and Lai 2004). In the model developed in this paper, this variation across markets is represented by a change in the parameters of the underlying Brownian motion. The results in Section 4 show that changes in these parameters significantly affect search outcomes under the constant-probability extension.

Conclusion This paper has introduced a discrete time model of sequential experimentation with explicit imitation costs and breadth of protection. It does so by extending the Callander model of search by trial and error, using Brownian motion as the specification of uncertainty in experimental product outcomes. This model assumes an infinite duration of protection, but features robust predictions about the trade-off between the static incentives and dynamic restrictions imposed by patents: experimental outcomes increase with cost of product imitation and decrease with the breadth of patent protection. In addition, this model predicts that a higher quantity of experimental products and a better outcome for the entrepreneur generally go hand in hand. The equilibrium results in Section 4 show that the constant-probability-ofsuccess extension is a generalization of the Callander model. Although the underlying utility structure in Section 3 is different, the results of the Callander model can be derived from Section 4 by setting

δ =0

and

this extension is unambiguously negative; the incentives imposed by imitation costs do not factor into equilibrium under constant-probability, while the breadth of protection acts to push the search towards earlier stability, deterring experimentation and reducing product outcomes in stability. In the variable-probability-of-success extension, the overall effect of patent protection on experimentation is mixed. The effect of the breadth of protection is similarly negative in this extension; however, under variable-probability, searches yield superior results following increases in cost of product imitation. Therefore, this variable-probability model successfully captures both the economic benefits and costs of patent protection. Table 2 shows that increasing the cost of product imitation and decreasing the breadth of protection will positively contribute to both the quantity and the quality of experimentation. It suggests that innovation-oriented policy should push patent protection in the northeast direction: larger imitation costs but smaller breadth of protection.

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