Asset bubbles, collateral, and policy analysis

Abstract

This paper provides a theory of credit-driven asset bubbles in an infinite-horizon production economy. Entrepreneurs face idiosyncratic investment distortions and credit constraints. An intrinsically useless asset such as land serves as collateral for borrowing. A land bubble can form because land commands a liquidity premium. The land bubble can provide liquidity and relax credit constraints, but can also generate inefficient overinvestment. Its net effect is to reduce welfare. Property taxes, Tobin's taxes, macroprudential policy, and credit policy can prevent the formation of a land bubble.

Introduction

Many countries have experienced asset bubbles. As evidence, Fig. 1 presents the real housing price indexes, the price–income ratios, and the price–rental ratios for the United States, Japan, Spain, and Greece. This figure reveals that the three series comove for each country, indicating that fluctuations in housing prices may not be driven entirely by fundamentals (i.e., incomes or rents). The collapse of housing bubbles is often accompanied by a financial crisis. It is widely believed that the credit crisis resulting from the bursting of the housing bubble is the primary cause of the 2007–2009 recession in the United States. The collapse of the Japanese housing bubble contributed to the so-called “Lost Decade”. The collapse of housing bubbles in European countries may be partly to blame for the European sovereign debt crisis.

What causes an asset bubble? What is its welfare effect? If an asset bubble reduces welfare, what policies can prevent a bubble from forming? The goal of this paper is to present a theoretical study to address these questions by providing a model of credit-driven asset bubbles in an infinite-horizon production economy. To be concrete, we focus on bubbles on an intrinsically useless asset such as land bubbles.¹ The model economy is populated by a continuum of identical households. Each household is an extended family consisting of a continuum of entrepreneurs and a continuum of workers. Each entrepreneur runs a firm and workers work for the firms. There is no aggregate uncertainty about fundamentals.

There are three key assumptions in our model. First, entrepreneurs face borrowing constraints because of financial market imperfections. In particular, they have limited commitment and contract enforcement is imperfect. They must pledge land as collateral and borrow against at most a fraction of the land value. That is, they must make down payments in order to purchase land. This kind of borrowing constraint is often called a leverage constraint or a margin constraint. It is related to the idea put forth by Kiyotaki and Moore (1997) and Brunnermeier and Pedersen (2009), among others.

Second, entrepreneurs face idiosyncratic distortions on the investment good price. For example, governments may offer different tax credits or subsidies to different firms financed by lump sum taxes on households. As Restuccia and Rogerson (2008) and Hsieh and Klenow (2009) argue, policy distortions can generate resource misallocations and are widespread in many developed and developing countries. In this paper we consider idiosyncratic investment subsidies, e.g., investment tax credit (ITC), which are an important policy tool to stimulate investment.²

Third, land trading is illiquid. Following Kiyotaki and Moore (2008), we assume that entrepreneurs face a resaleability constraint, which means that they can resell at most a fraction of their existing land. In addition, they cannot short sell land.

Land plays two important roles in the model. First, it is an asset that allows resources to be transferred intertemporally and generate capital gains or losses. Second, it is used as collateral to facilitate borrowing. In general, land may be productive and useful for producing agriculture products. In this paper we abstract away from this role of land and focus on its first two roles instead. In particular, we assume that land is intrinsically useless so that its fundamental value is zero. We will show that land can have a positive value in equilibrium, which represents a bubble.

In standard models with infinitely-lived agents, bubbles can typically be ruled out by transversality conditions. Why can a land bubble exist in our model? The reason is that in our model entrepreneurs face borrowing constraints and land can provide liquidity. Hence land commands a liquidity premium. Consider the special case where entrepreneurs cannot borrow. Since they face idiosyncratic ITC, those with high ITC are willing to invest more. Resources should be reallocated from entrepreneurs with low ITC to those with high ITC. In the absence of a credit market, land as an asset plays the role of transferring resources among entrepreneurs and also over time. As a result, land is valuable just like money. In the presence of a credit market, land also serves as collateral for borrowing and a high land value can relax the credit constraint. Hence land generates a collateral yield. The two benefits provided by land constitute the liquidity premium.

Since liquidity depends at least partly on beliefs, so does the existence of a land bubble. If no one believes that land is valuable, then no one will trade it or use it as collateral. Then land is indeed valueless in equilibrium. Thus our model features two types of equilibria: the bubbly equilibrium and the bubbleless equilibrium.³ Which type is more efficient? Having discussed the good side of a land bubble in terms of providing liquidity and relaxing credit constraints, we now turn to its bad side. Our model features idiosyncratic tax/subsidy distortions. The existence of a land bubble allows entrepreneurs with high ITC to make more investment. This creates inefficient overinvestment and resources misallocation, which reduces welfare. The overall welfare effect of a land bubble is ambiguous. We prove that a land bubble can reduce welfare in some special cases and provide numerical examples for more general cases.

Given that land bubbles can reduce welfare, what policies can prevent the formation of a bubble? In the standard models of rational bubbles (e.g., Tirole, 1985), the return on the bubble is equal to the capital gains only since the bubble does not deliver any payoffs. In a deterministic model, this implies that the interest rate is equal to the growth rate of the bubble. By contrast, in our model the return on the bubble is equal to capital gains plus the liquidity premium. This asset pricing equation has important policy implications. In particular, we focus on fiscal and macroprudential policies that can reduce the liquidity premium and hence the benefit of having a land bubble. If the benefit is sufficiently small, the bubbly steady state cannot exist and the economy reaches the unique bubbleless equilibrium. We study four types of policies: (i) limit the loan-to-value (LTV) ratio to a sufficiently low level or raise the down payment to a sufficiently high level; (ii) raise property taxes to a sufficiently high level and transfer the tax revenue to households; (iii) raise property transaction taxes (or Tobin's taxes) to a sufficiently high level and transfer the tax revenue to households; and (iv) the government purchases private bonds financed by lump sum taxes. These policies have been implemented in some countries, though empirical studies are needed to see whether they are effective in eliminating asset bubbles.

We show that the interest rate in the bubbleless steady state is lower than that in the bubbly steady state. The reason is that the land bubble crowds out the bond demand, thereby reducing the bond price and raising the interest rate. This implies that all four policies will reduce the interest rate in the long run after the bubble is eliminated. This seems to contradict the conventional wisdom that a low interest rate may cause a land bubble because a low interest rate encourages excessive mortgage borrowing.⁴ But this can be reconciled by noting that the conventional wisdom ignores the general equilibrium effect of the land bubble.

Related literature: Our paper is related to a growing literature on rational bubbles.⁵ Most models of rational bubbles adopt the overlapping generations framework (Tirole, 1985, Weil, 1987). Introducing rational bubbles into an infinite-horizon model is generally nontrivial due to the transversality conditions (Santos and Woodford, 1997). Kocherlakota (1992) shows that infinite-horizon models of endowment economies with trading frictions or borrowing constraints can generate bubbles. Recently, there has been a growing interest in introducing rational bubbles into production economies with borrowing constraints. Examples include Caballero and Krishnamurthy (2006), Farhi and Tirole (2012), and Martin and Ventura (2012) in the overlapping generations framework and Kocherlakota (2009), Wang and Wen (2012), Miao and Wang, 2012, Miao and Wang, 2013, Miao and Wang, 2014, Miao and Wang, 2015, Miao et al., 2015a, Miao et al., 2015b, and Hirano and Yanagawa (2013) in the infinite-horizon growth framework. In particular, Miao and Wang (2013) study how a variety of endogenous credit constraints derived from optimal contracts with limited commitment can generate stock price bubbles. They show that stock price bubbles can relax credit constraints and generate dividend/collateral yields, which also represent the liquidity premium. Unlike their study, this paper focuses on leverage constraints and pure bubbles attached to intrinsically useless assets.

Fiat money is a pure bubble. Kiyotaki and Moore (2008) provide a model in which money is valued due to its liquidity. Our idea is similar to theirs. But land is different from money because land is illiquid and serves as collateral and also because land is not produced by the government.

Our paper is more closely related to the literature on housing or land bubbles.⁶ Kocherlakota (2009) provides a model of land bubbles based on Kiyotaki and Moore (2008). In his model firms face idiosyncratic productivity shocks and collateral constraints. Land is intrinsically useless, but serves as collateral as in Kiyotaki and Moore (1997) Thus land bubbles improve welfare. He et al. (2013) build a model of housing bubbles in a monetary economics framework. Their model does not incorporate real investment and the credit constraint applies to households instead of firms. As in our paper, the existence of a housing bubble is due to the liquidity premium. Unlike our model with two steady states, their model delivers a unique steady state. Housing in their model can also provide direct utility. Arce and Lopez-Salido (2011) study housing bubbles in an overlapping generations framework with credit constraints. The interest rate is equal to the growth of the bubble in their model. In contrast to our result, they show that the interest rate in the bubbly steady state is lower than that in the bubbleless steady state. They also incorporate utility from housing and show that the housing price in the bubbly equilibrium is less than the discounted value of the utility flow (or dividends).

Bubbles must provide some benefits to economic agents, or else, they could not exist in the first place. However, policymakers and researchers are more concerned about the welfare costs of bubbles. Potential costs include volatility and fire sales after the collapse of bubbles (Caballero and Krishnamurthy, 2006, Miao and Wang, 2015) and misallocation of resources in the presence of market distortions such as externality (Grossman and Yanagawa (1993) and Miao and Wang (2014)). In this paper we focus on the cost generated by resource misallocation in the presence of idiosyncratic tax policy distortions. Most papers in the literature discuss the role of monetary policy in preventing bubbles. In an overlapping generations model, Galí (2014) studies how monetary policy can affect the fluctuations of bubbles. But monetary policy cannot eliminate bubbles.⁷ Because the asset pricing equation for the bubble includes the liquidity premium in our model, we argue that other policy tools can be used to lower this premium and eliminate bubbles.

Property tax policy and LTV policy are often discussed by the policymakers and the general public. For example, the Chinese government has implemented these policies to curb the growth of housing prices and to prevent housing bubbles.⁸ Our analysis provides a theoretical foundation for these policies. The asset purchase policy proposed in our paper is related to those in Kocherlakota (2009), Hirano et al. (2015) (current issue), and Miao and Wang (2013). Kocherlakota (2009) discusses credit policy to restore the bubbly equilibrium. Miao and Wang (2013) provide a credit policy to achieve the first-best allocation. Hirano et al. (2015) (current issue) study bailout policy and welfare implications for workers who are taxpayers.

The key difference between our paper and some of the aforementioned papers is that our model adopts the infinite-horizon growth framework, which is amenable to quantitative studies (see, e.g., Miao et al., 2014, Miao et al., 2015b). In addition, the borrowing constraint in our model differs from those often used in the literature on housing prices. Many papers adopt the Kiyotaki and Moore (1997) collateral constraint, which ensures that the debt repayment does not exceed the collateral value so that the borrower will never default. The borrowing constraint in this paper is a type of margin constraint, consistent with the institutional feature in the mortgage market. We show that given the margin constraint, the Kiyotaki-Moore collateral constraint is always satisfied so that default never occurs in our model. The margin constraint is also adopted in Arce and Lopez-Salido (2011) and some references therein.