Bursting Bubbles: Consequences and Cures; Narayana Kocherlakota (Federal Reserve Bank of Minneapolis); Paper presented at the Macroeconomic and Policy Challenges Following Financial Meltdowns Conference, Hosted by the IMF; Washington, DC, April 3, 2009

I construct a model in which infinitely-lived entrepreneurs cannot borrowmore than the value of their landholdings. I show how this constraint leads naturally to an equilibrium in which the land’s price has a bubble. I demonstrate that bursting bubbles in land prices may have dramatic and persistent distributional and aggregate effects. I discuss appropriate and inappropriate policy interventions in the wake of a bubble collapse. ∗First version: October 23, 2008. This paper was originally titled, "Exploding Bubbles in a Simple Macroeconomic Model." The current version is a considerable simplification of the 1/31/09 version. The paper grew out of a discussion of Kiyotaki-Moore (2008), prepared for the 10/31/08-11/01/08 "Monetary Policy and Financial Frictions" conference at the Federal Reserve Bank of Minneapolis. I thank Katya Kartashova for valuable research assistance, and I thank Costas Azariadis, Marco Bassetto, Gadi Barlevy, Harold Cole, Robert E. Lucas, Jr., Nancy Stokey, and participants in bag lunches at FRB-Philadelphia and FRB-Chicago for their comments. I especially thank Barbara McCutcheon for many interesting conversations about bubbles. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Housing and housing price derivatives are important sources of collateral for loans in the United States. From July 2006 to October 2008, the twenty-city Case-Shiller house price index fell by just under 25%. This price decline is often interpreted as representing the bursting of a bubble. The decline is blamed for significant changes in credit markets that began in the second half of 2007, and to a recession that is now dated as having begun in December 2007. There has been a massive and varied government response to these events. Motivated by these observations, in this paper I construct a model in which collateralized borrowing plays an essential role in re-allocating capital to its efficient uses. I show that collateral scarcity can generate a stochastic bubble in the price of collateral. I discuss the implications of this bubble’s bursting for aggregates and for welfare. Using the model, I assess several ongoing policy initiatives and propose a specific superior intervention. The structure of my model closely resembles models described in Angeletos (2007), Kartashova (2008), and Kiyotaki-Moore (2008). A fraction of entrepreneurs have productive investment opportunities, while others do not. The arrival of the desirable projects is i.i.d. over entrepreneurs and over time. Efficient production requires the re-allocation of physical capital from entrepreneurs without good projects to those with good projects. This reallocation is accomplished via loans. Markets are incomplete in the sense that these loans cannot be made contingent on whether a given entrepreneur gets a good project. The novel feature of my model relative to theirs is that all entrepreneurs are each endowed with one unit of land.1 If the borrower defaults, a lender can seize a borrower’s land 1Heathcote and Davis (2007) document that the 2000-06 run-up in home prices was largely driven by a contemporaneous increase in land prices. Hence, I re-interpret the bubble in home prices as reflecting one in land prices. In an earlier version of this paper, I assumed that entrepreneurs could augment the stock of collateral (through home construction, for example). As long as there is a resource cost of adjusting the collateral but no other borrower resources. Hence, a borrower’s repayment is bounded from above by the value of his land. I assume that land is an asset that pays no dividend. (I discuss the role of this assumption later in the introduction.) Given this set of assumptions, it is not surprising that there is an initial value of capital consistent with an equilibrium in which capital is constant over time and land has zero value. In this equilibrium, no borrowing and lending takes place. However, there is also a specification of initial capital that induces an equilibrium in which capital is constant over time and the land price is a positive constant. I interpret this positive price as being a bubble in land prices. The intuition behind the existence of the bubble is simple, robust, but often ignored. In the model, all entrepreneurs face occasionally binding borrowing constraints. Land, even though it is intrinsically worthless, may have value because it serves to relax this constraint (see Kocherlakota (1992)). In this way, the bubble allows entrepreneurs to re-allocate physical capital more efficiently, which leads to higher wages, output, and consumption for the economy. Remarkably, this re-allocation is so useful that, as long as capital share is sufficiently low, the economy generates these higher aggregates in the bubbly steady-state equilibrium using less physical capital. I use these two equilibria to construct another one with a stochastic bubble. (Such equilibria can be quite complicated; I deliberately focus on one that is simple.) In this third kind of equilibrium, there is some small probability of the bubble’s bursting at each date. Before the bubble bursts, the land price is positive and constant. After the bubble bursts, the land price reverts to zero forever. Entrepreneurs can exchange any kind of financial contract stock, this augmentation possibility may be consistent with a price bubble.