DISCOUNT SHOCK, PRICE–RENT DYNAMICS, AND THE BUSINESS CYCLE

• DOI: http://doi.org/10.1111/iere.12455
• Author: Tao Zha,Jianjun Miao,Pengfei Wang
• Published date: 01 August 2020
• Date: 01 August 2020

INTERNATIONAL ECONOMIC REVIEW

Vol. 61, No. 3, August 2020 DOI: 10.1111/iere.12455

DISCOUNT SHOCK, PRICE–RENT DYNAMICS, AND THE BUSINESS CYCLE∗

BYJIANJUN MIAO,PENGFEI WANG,AND TAO ZHA1

Boston University, U.S.A.; Hong Kong University of Science and Technology,Hong Kong,

Peking University HSBC Business School, China; Federal Reserve Bank of Atlanta, Emory

University, and NBER, U.S.A.

The price-rent ratio in commercial real estate is highly volatile and its variation comoves with the business

cycle. To account for these facts, we develop a dynamic general equilibrium model that introduces a rental

market and incorporates the liquidity constraint on an individual firm’s production as a key ingredient. Our

estimation identifies the discount shock as the most important factor in driving price-rent dynamics and linking

the dynamics in the real estate market to those in the real economy. We illustrate the importance of the liquidity

premium and endogenous TFP in the nexus of the financial and real sectors.

1. INTRODUCTION

The rise and fall of real estate prices in the past decades and the 2008 financial crisis triggered

by the collapse of real estate prices have generated a great deal of research on the impact of

real estate prices on the macroeconomy. Most research has focused on consumers’ behavior

and the residential real estate market. When we study firms’ investment dynamics, it is often the

commercial real estate market that becomes relevant. In a recent paper, Chaney et al. (2012)

provide micro evidence that links the commercial real estate price to investment. They estimate

that a $1 increase in a representative U.S. firm’s value of real estate raises its investment by

$0.06. At the aggregate level, however, the link between commercial real estate prices and

investment dynamics has been largely unexplored.

In this article, we develop a medium-size dynamic stochastic general equilibrium (DSGE)

model and show that this model is capable of reproducing quantitatively key stylized facts about

the commercial real estate price and the business cycle if one incorporates two key ingredients:

shocks to households’ subjective discount rate and the liquidity constraint on an individual firm’s

production. We call these shocks “discount shocks.” We confront our model with financial and

real time series and estimate it using the Bayesian method of Fern´

andez-Villaverde and Rubio-

Ram´

ırez (2007) and Herbst and Schorfheide (2015) to account for the following two salient

facts:

∗Manuscript received May 2018; revised January 2020.

1We are grateful to the editor and two anonymous referees for constructive comments, which help improve the

article significantly. We also thank Mark Bils, Larry Christiano, Marty Eichenbaum, Jordi Gal´

ı, Lars Hansen, Simon

Gilchrist, Pat Higgins, Lee Ohanian, Sergio Rebelo, Richard Rogerson, Giorgio Valente, Gianluca Violante, Wei Xiong,

and seminar participants at University of Pennsylvania, University of North Carolina, the NBER Summer Institute,

the AFR Summer Institute of Economics and Finance, the PBC Finance School of Tsinghua University, Hong Kong

Monetary Authority, University of Toronto, Vanderbilt University, and University of Rochester for helpful discussions.

The research is supported in part by the National Science Foundation Grant SES 1558486 through the NBER and by

the National Natural Science Foundation of China Research Grants (71473168, 71473169, and 71633003). The views

expressed herein are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of

Atlanta or the Federal Reserve System or the National Bureau of Economic Research. Please address correspondence

to: Tao Zha, Research Department, Federal Reserve Bank of Atlanta, 1080 Peachtree, Atlanta, GA 30309. Phone:

+404 723 3254. E-mail: zmail@tzha.net.

1229

C

(2020) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1230 MIAO,WANG,AND ZHA

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

Log price – log rent

15.4

15.45

15.5

15.55

15.6

15.65

15.7

Log output

Price–rent

Output

FIGURE 1

THETIMESERIESOFTHELOGPRICE-RENTRATIO IN THE U.S.COMMERCIAL REAL ESTATE SECTOR (THE LEFT SCALE)AND THE

TIME SERIES OF LOG OUTPUT IN THE U.S.ECONOMY (THE RIGHT SCALE)[COLOR FIGURE CAN BE VIEWED AT

WILEYONLINELIBRARY.COM]

i. Volatility: Commercial real estate price fluctuates much more than rent. Over the past

20 years, while the volatility (measured by the standard deviation of quarterly changes) is

about 1% for real estate rent, the volatility of real estate prices is 4%.

ii. Comovements: The price–rent ratio comoves with output as demonstrated by Figure 1.

Since consumption and investment comove with output, the price–rent ratio tends to also

move together with consumption and investment.

How to account for these facts within one structural framework has been a challenging task in

the macro-finance literature. The existing general equilibrium models with real estate markets

typically fail to generate large price–rent variations.1Our model builds on the DSGE literature

with a combination of two distinctive features: we introduce a rental market of commercial

real estate and assume that an individual firm faces a liquidity constraint when financing its

working capital. Without modeling the rental market explicitly, the existing macroeconomic

models (Iacoviello, 2005; Iacoviello and Neri, 2010; Liu et al., 2013, 2016, for example) reveal

that the real estate price and rent move in comparable magnitude so that there is little price–

rent variation, which is inconsistent with what is observed in the data (Figure 1). As a result,

1See Campbell et al. (2009), Piazzesi and Schneider (2009), Kiyotaki et al. (2011), Caplin and Leahy (2011), Burnside

et al. (2011), Pintus and Wen (2013), Head et al. (2014), and Kaplan et al. (Forthcoming) for models of housing. This

literature does not address the commercial housing market nor does it reproduce facts (i) and (ii) simultaneously in

one dynamic general equilibrium framework.