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The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF, the Federal Reserve Board, or anyone in the Federal Reserve System. We thank Gadi Barlevy, Javier Bianchi, Martin Bodestein, Bora Durdu, Raphael Espinoza, Jordi Galì, Gaston Gelos, Luca Guerrieri, Olamide Harrison, Narayana Kocherlakota, Thore Kockerols, Alberto Martin, Maria Soledad Martinez Peria, Enrique Mendoza, Toan Phan, Fabian Valencia, Jaume Ventura, Pengfei Wang, Ivan Werning, and seminar participants at the IMF, Federal Re-serve Board, 2019 Barcelona GSE Summer Forum, University of Toronto, 2nd Annual NuCamp Conference Oxford, 4th International Macro-Finance Conference Hong Kong, 2019 CEF Ottawa, 2019 SED St Louise, and 2019 IBEFA San Francisco for their comments and suggestions.
By credit imbalances we mean elevated levels of debt.
An additional factor seems to be timely and precise identification of overvaluations. Concerns about the quality of existing tests for asset overvaluations have made many policymakers reluctant to automatically react to rapid asset price growth. This issue is, arguably, less concerning in the aftermath of the GFC, as policymakers and academics have placed more effort on detecting “valuation pressures” in asset prices. Some examples include the Office of Financial Research’s Financial System Vulnerabilities Monitor and the Shiller’s CAPE index (Cyclically Adjusted Price Earnings).
We define asset price overvaluation as a positive deviation of the market price from its fundamental value. In the rest of the paper, we will use the terms asset price bubbles and price overvaluations interchangeably.
Guerrieri and Iacoviello (2017) emphasize the role of occasionally binding collateral constraints in generating asymmetric effects of house prices on economic activity, but abstract from asset price bubbles.
For low debt levels a policy intervention is not needed as collateral constraints do not bind in the present or in the future.
While the focus in our paper and in Miao and Wang (2018) is on a stock price bubble, many papers have focused on studying the existence of pure bubbles, like money, in production economies. Pure bubbles can also provide liquidity by raising borrowers net worth (Caballero and Krishnamurthy, 2006; Farhi and Tirole, 2012; Kiyotaki and Moore, 2012; Martin and Ventura, 2012; Aoki, Nakajima and Nikolov, 2014; Ikeda and Phan, forthcoming). However, the borrowing constraints in models of pure bubbles are different than ours and that in Miao and Wang (2018) because they do not depend on the stock market value of the firm.
The formulation of this composite commodity is defined by Greenwood, Hercowitz and Huffman (1988) and removes the wealth effect on labor supply inducing a countercyclical increase in the labor supply during crises.
A bubble on a productive asset would not be supported in equilibrium if the firm could only borrow against the liquidation value of physical capital. Instead, a typical collateral constraint akin to Kiyotaki and Moore (1997), where borrowing is limited up to the liquidation value of capital, can only ensure the existence of a pure bubble in equilibrium, i.e. a bubble on an intrinsically useless asset. See Miao-Wang for details. In our model, pure real estate bubbles cannot exist because the durable productive asset is part of the producing firm. However, we could easily introduce an additional intrinsically useless asset, akin to real estate in Miao, Wang and Zhou (2015), which can have a positive valuation as long as it serves as collateral. As a result, we would be able to study the differential liquidity properties of equity price bubbles and real estate bubbles.
More recently, Guerron-Quintana, Hirano and Jinnai (2019) develop a model of recurrent bubbles in an environment with endogenous growth and infinitely-lived households.
Alternative instruments that affect the inter-temporal margin can be used instead of the tax. The tax can also be imposed on the interest rate expenses.
Bianchi-Mendoza show that the optimal policy under commitment is time inconsistent since asset prices are determined by a dynamic condition linking the present and future (expected) marginal utilities of consumption. Instead, they follow the time-consistent approach under which a planner cannot commit at t to the whole path of future policy choices.
The household’s first-order condition with respect to consumption is the same regardless of whether there is a bubble or not.
This can easily be shown by substituting for ψt+1 from equation 32 and noting that Ucc,t +1 < 0.
In order to obtain the solution for the competitive economy, we iterate the (competitive) Euler equation for borrowing, which does not incorporate the effect of borrowing decisions on prices. Value function iteration internalizes the effect of pecuniary externalities on welfare and, hence, yields the planner’s solution. Given that we solve for time-consistent policies, we use a nested fixed point algorithm for the value function iteration. See Appendix A.6 for details on the numerical method.
We choose to simulate the economy for a shorter horizon, yet many times, because the bubble in our setting does not re-emerge after busting, generating an absorbing state. Thus, the distribution of outcomes would be biased towards the no-bubble outcomes if we simulated the economy for a longer horizon.
The Lagrange multipliers on the collateral constraint µt and