In history, most bubbles are taught in exactly one way. There's an asset of dubious quality that suddenly rises in demand. This rise in demand causes a rise in price, which encourages speculation, which causes a further rise in prices, with each investor betting on the continued irrationality of the market. Then finally, the market remains irrational no more, and prices crash. Fortunes are lost, livelihoods are ruined, and the destructive capitalist machine marches on forward. Or we're told.
This basic outline is how the Dutch tulip bubble is taught, or how the South Sea bubble is taught, or how the Panic of 1873 is taught. This paper posits that this model is wrong. Glaeser instead makes the case that real estate bubbles are actually founded on rational expectations on the future prices of land, backed up by multiple models of land valuation. The reason bubbles 'pop', then, is not because of irrational speculation, but because investors fail to incorporate the effect that the elastic supply of crops and structures (i.e. the things that make land valuable) have on the future value of land.
Glaeser formalizes the above description by defining the terms ordinary error and limited cognition:
He then states that most markets are between these extremes, and speculators' downfall comes from not understanding global supply and demand chains. Namely, in a market with elastic supply, "the value of a thing tends in the long run to correspond to its cost of production." Rationality in Glaeser's definition means that an investor using 'reasonable' methods of valuation would find the market pricing land correctly.
How does an investor decide the value of a plot of land? This is the fundamental question that underlies real estate speculation. Glaeser frames this question by layering two major assumptions that determine the range of possible prices in a market.
The first assumption is the possibility of arbitrage. That is, can an investor in a given market make an outsized profit, relative to the amount of risk they've undertaken? By Glaeser's definition, to be a "rational" investor you cannot believe in arbitrage opportunities because most markets have been shown to follow a continuous random walk, and so investors "timing" the market tend on average to not perform better than random.
<aside> 💡 NOTE: A useful clarification we discussed here was that earning a standard return year-over-year is not considered an "outsized" return, because the amount of money earned correspond directly to the risk taken on.
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The second assumption is rationality, which as we defined earlier, is whether a reasonable model of asset valuation is consistent with the market. Glaeser goes on to then define the primary families of models that dominate real estate valuation: the Thunenites and the Gordonians.
The Thunenite model is based on the work of David Ricardo and Johann Heinrich Von Thunen, the originators of the foundational theory of land rent: that the value of land is defined by its utility compared to other, similar plots of land. In this model, the price of real estate is determined solely by evaluating against land with similar amenities in other areas. This model, for example, predicts the "concentric zone model" of urban development, where transport costs to the center predict density and thus price.
<aside> 💡 Glaeser has written extensively about this model. We've previously read the paper, "What is Different About Urbanization in Rich and Poor Countries? Cities in Brazil, China, India and the United States," which went into how this model of spatial equilibrium applies in different socioeconomic environments.
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The Gordonians, by contrast, use net-present value to determine the value of land, assuming a constant growth rate. Net-present value is defined as:
$$ P_t = \frac{x_t}{\rho + m + \tau - \alpha} $$
where P_t is the net-present value, x_t is the current rent, rho is the discount rate, m is maintenance costs, tau is property taxes, and alpha is the growth rate of rent (assumed constant). Then, what this formula is actually saying is that if you take the decay rate (which is the other terms subtracted from alpha), subtract that from 1, and then divide the current rent by that, you get the current value of the home factoring in all future rents.
This formula forms the base of the Gordonian model. Glaeser fleshes this out further, where he assumes geometric Brownian motion (essentially a random sequence that models asset prices well) models x_t, then incorporates uncertainty, and then compares the resultant valuation model with a perfect information buyer to find that the key downfall of this model is its inability to recognize the decay in price growth due to the elasticity of supply. Namely, because the Gordonian model assumes a constant growth rate, it overestimates the net-present value of real estate.
Naive Gordonian pricing will cause an overestimation of price growth and thus considerable overbuilding.
<aside> 💡 An important digression that Glaeser mentions here, and that is repeatedly mentioned throughout the paper, is the idea of a free default option. A default option is essentially the ability to exit a loan cheaply. This arises when low down payments and low interest rates make the cost of default—namely, surrendering the down payment and interest paid thus far—relatively cheap. This is often mentioned in the case of government subsidized mortgages, where entities like Fannie Mae and Freddie Mac push down mortgage rates. A free default option pushes up the value of real estate, as it makes buyers more willing to pay higher prices.
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