3.2 Theory of Rational Bubbles

from the linear trend) was also larger in the 2000s. Indeed, the average bubble was almost three times larger in the bubble episodes of the late 2000s than during the 1990s (109 over 39).6 Therefore, it seems that both the likelihood of having a global housing bubble and the size of the bubble were increasing over time. These results are consistent with the fndings of Pavlidis et al. (2016), which use time-series techniques to identify housing bubble episodes in a panel of 22 countries between 1975 and 2013. They also document an exceptional emergence and synchronization of housing bubble episodes in the late 2000s.7 In the next chapters, we will offer a possible explanation for this increasing trend.

references

Brunnermeier, M. K. (2009). Bubbles. In L. Blume & S. Durlauf (Eds.), New

Palgrave Dictionary of Economics. Basingstoke: Palgrave Macmillan. Giglio, S., Maggiori, M., & Stroebel, J. (2016). No-Bubble Condition: Model-

Free Tests in Housing Markets. Econometrica, 84, 1047–1091. Jordà, Ò., Schularick, M., & Taylor, A. M. (2015). Leveraged Bubbles. Journal of Monetary Economics, 76, S1–S20. Kindleberger, C. P., & Aliber, R. (2005). Manias, Panics, and Crashes: A History of Financial Crises (5th ed.). Hoboken: Wiley. ISBN 0-471-46714-6. Knoll, K., Schularick, M., & Steger, T. (2017). No Price Like Home: Global

House Prices, 1870–2012. American Economic Review, 107(2), 331–353.

6 The size of the bubble is computed as a simple average of the deviation from the trend for the countries with the housing bubble indicator equal to one. 7 Other economists have attempted to identify housing bubbles. In an important empirical contribution, Giglio et al. (2016) analyze the housing boom in London in the late 2000s. As we will see in the next chapter, classical rational bubbles can only emerge in infnite time horizon models. The authors take advantage of a peculiar feature of the London housing market to compare the price of an “identical” house under two types of ownership: (i) leaseholds (ownership expires in fnite time, often more than 700 years) and (ii) freeholds (there is no expiration date). Thus, theoretically, rational bubbles could only emerge in houses under freehold ownership. Since they do not fnd a statistically signifcant difference between the prices of houses under the two types of ownership, they conclude that rational bubbles alone cannot explain the recent housing boom in London. The frst thing to remark is that the authors do not rule out the presence of a housing bubble in London. Moreover, although they perform a very interesting exercise, we do not think that their fndings rule out rational bubbles as drivers of housing booms. In other words, as we describe in the rest of the book, features of both rational and irrational bubbles seem relevant to describe the recent housing booms.

Mackay, C. (1841). Memoirs of Extraordinary Popular Delusions and the Madness of Crowds. London: Richard Bentley. Pavlidis, E., Yusupova, A., Paya, I., Peel, D., Martínez-García, E., Mack, A., et al. (2016). Episodes of Exuberance in Housing Markets: In Search of the

Smoking Gun. Journal of Real Estate Finance and Economics, 53, 419–444. Shiller, R. J. (2003). From Effcient Markets Theory to Behavioral Finance.

Journal of Economic Perspectives, 17(1), 83–104. Temin, P., & Voth, H.-J. (2004). Riding the South Sea Bubble. American

Economic Review, 94(5), 1654–1668.

CHAPTER 3

Origin of Asset Price Bubbles

Abstract The recurrence of asset price bubbles throughout history has stimulated the interest of economists in different generations. We divide theories on the origin of bubbles in two: (i) behavioral and (ii) rational. First, we explain how differences in the beliefs of agents may result in bubbles (behavioral explanation). Second, we discuss how asset price bubbles may emerge because the economy has a shortage of assets (rational explanation). Finally, we develop a simple model to explain how rational housing bubbles may appear in fnancially underdeveloped economies.

Keywords Behavioral · Rational bubbles · Shortage of assets · Financial constraint

Asset price bubbles have triggered the interest of distinguished economists across generations. This list includes several Nobel Prize winners. Starting with the late Paul Samuelson, who was awarded in the second edition (1970) and ending with the most recent Nobel Prize winner, Richard Thaler (2017). In between, Robert Shiller (2013) and Jean Tirole (2014) have also been awarded with the Nobel Prize. This (incomplete) list of economists help us to distinguish between two very different views on the origin of asset price bubble episodes. The frst group, which includes Samuelson and Tirole, developed models to explain how asset price bubbles can be the rational market response

© The Author(s) 2018 S. Basco, Housing Bubbles, https://doi.org/10.1007/978-3-030-00587-0_3 17

to a market imperfection. The second group, which includes Shiller and Thaler, resorts to behavioral (or irrational) models to explain how boombust asset price episodes occur in equilibrium.1 It is outside the scope of this book to make a formal literature review of these two big strands of the literature. Instead, we discuss a toy model version of each of these two groups to illustrate how these theories explain the emergence of asset price bubbles in equilibrium.

3.1 BeHAviorAl explAnAtion

As we saw in the review of famous asset price bubbles, there seems to be an element of irrationality behind these episodes. How could that investor from Amsterdam think that a tulip could be worth “4600 forins, a new carriage, two grey horses, and a complete suit of harness” (Mackay 1841)? In order to understand why people may be willing to make this seemingly irrational investment, it is useful to describe how information is transmitted and how it may shape the beliefs of agents.

The next quote, taken from Shiller (2003), reproduces a fctional conversation written by an anonymous observer in 1637 (the year of the peak of the Tulipmania).

Gaergoedt: You can hardly make a return of 10% with the money that you invest in your occupation [as a weaver], but with the tulip trade, you can make returns of 10%, 100%, yes, even 1000%. Waermondt: …But tell me, should I believe you? Gaergoedt: I will tell you again, what I just said. Waermondt: But I fear that, since I would only start now, it’s too late.

Because now the tulips are very expensive, and I fear that I’ll be hit with the split rod, before tasting the roast. Gaergoedt: It’s never too late to make a proft, you make money while sleeping. I’ve been away from home for four or fve days, and I came home just last night, but now I know that tulips I have have increased in value by three or four thousand guilder; where do you have profts like that from other goods?

1 Brunnermeier (2009) considers a thinner classifcation of models. His classifcation contains two additional groups with elements of both rational and behavioral group. For the purpose of this book, we will focus on the most extreme versions. The interested reader is referred to the references in Brunnermeier (2009).

Waermondt: I am perplexed when I hear you talking like that, I don’t know what to do, has anybody become rich with this trade? Gaergoedt: What kind of question is this? Look at all the gardeners that used to wear white-gray outfts, and now they’re wearing new clothes.

Many weavers, that used to wear patched up clothes, that they had a hard time putting on, now wear the glitteriest clothes. Yes, many who trade in tulips are riding a horse, have a carriage or a wagon, and during winter, an ice carriage,…

From this informal conversation, we want to highlight three things. First, this conversation takes place in a moment when buying a tulip is considered an investment. That is, Waermondt is looking for an investment opportunity and knows that Gaergoedt is in the tulip trade and he has already been making profts. Second, neither the potential investor (Waermondt) nor the actual investor (Gaergoedt) seems to care about the fundamental value of their investment. Indeed, note how their only concern is on the price-appreciation of the asset. Third, and related to the last point, the decision of Waermondt to enter into the tulip trade depends on his expectation about the future price of the asset. Note also that the way in which he forms the price expectations does not seem very rational. On the one hand, he seems to recognize that he would be entering into an overheated asset price market. He argues: “I fear that, since I would only start now, it’s too late.” However, since he is eager to participate in the tulip trade, he is happy to change his mind and let Gaergoedt convince him that purchasing a tulip is a good investment. In addition, he bases his expectations on the past evolution of prices. That is, he seems to believe that since people have become rich in the past purchasing the asset, this trend can be extrapolated into the future and he can also become rich. Formally, this process of forming expectations is known as feedback theory (see, e.g., Shiller 2003). The reader may have heard (or even participated in) conversations similar to the one between Gaergoedt and Waermondt. For example, it was not unusual to hear taxi drivers in Spain in the late-2000s to talk about purchasing houses. The sentence “you have to invest in brick, which never falls” was heard everywhere even from professional economists. This narrative not only applies to houses or the Tulipmania. From casual observation, it can be argued that the same was happening during the Dot-Com Bubble. There was an excitement about Dot-Com frms and investors were eager to participate

in this trade. Something similar may also be happening around the cryptocurrencies.

There exist different models based on this behavioral explanation. These models generally make two assumptions: (i) people have different expectations on the value of an asset and (ii) there exist short-selling constraints. Miller (1977) is the seminal paper in this literature. There are different versions of assumption (i). For example, there may be two groups of investors: irrational and rational. Another possibility is that some agents become more optimistic than others. The interested reader is referred to Barberis and Thaler (2003) for a survey on different behavioral models. We now consider a toy model to emphasize the role of behavioral agents.

Imagine that in our economy there are two assets. One storage technology, with a net return equal to π and a risky asset with unknown return and supply equal to one. There are two periods: today and tomorrow. There is a continuum of investors of mass one indexed by i. Each investor has an endowment equal to e. We make the assumption that this endowment is large enough. We also assume that there is no short-selling and agents cannot borrow. The short-selling assumption is important and it is generally made in this literature to limit arbitrage.2 Consumers only consume in the second period. Therefore, they just need to choose in which asset they want to invest today to maximize expected future consumption. We consider that a mass 1 − µ of rational investors belief (with certainty) that the payoff of the asset will be σ. The rest of investors receive a signal about the payoff, si, which they assume to be the true payoff. That is, they think that the price will be si with probability one. This signal follows a uniform distribution between 0 and 2σ. The intuition behind these assumptions is that rational investors know the fundamental value of the asset, whereas the opinion of behavioral

2 The importance of the “no short-selling” assumption is better understood with an example. In these behavioral models, agents have different beliefs on the future return on the asset. With the short-selling constraint, the marginal buyer of the asset will be an optimistic investor, who thinks that the return on the asset will be high. That is, the investor who hopes to proft from trading the asset is the one with “high expectations”. In contrast, if short-selling is possible, the marginal investor may be a pessimistic investor, who thinks that the return on the asset will be very low. An empirical justifcation for this assumption is that, in practice, it is costly to short sell a stock. The investor needs to borrow a stock and sell it. Then, she needs to repurchase the stock (at a hopefully lower price) to return it to the lender.