House price to income ratio and fundamentals: Evidence on long‐horizon forecastability

• Author: Han‐Liang Cheng,Nan‐Kuang Chen
• Date: 01 August 2017
• DOI: http://doi.org/10.1111/1468-0106.12231
• Published date: 01 August 2017

Received: 26 January 2017 Accepted: 20 April 2017

DOI: 10.1111/1468-0106.12231

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SPECIAL ISSUE ARTICLE

House price to income ratio and fundamentals:

Evidence on long-horizon forecastability

Nan-Kuang Chen1Han-Liang Cheng2

1Department of Economics, National

Taiwan University,Taipei, Taiwan

2Chung-Hua Institution for Economic

Research, 75 Chang-Hsing St. Taipei,

106, Taiwan

Correspondence

Nan-Kuang Chen, Department of

Economics, National Taiwan

University, No.1Section 4 Roosevelt

Road, Taipei, 106, Taiwan.

Email: nankuang@ntu.edu.tw

Abstract

This paper studies the relationship between the house

price-to-income ratio (PIR) and economic fundamentals,

and investigates the long-horizon forecastability of the PIR.

We first construct a small DSGE model to derive a dynamic

expression of PIR, linking PIR to macroeconomic fun-

damentals and the stance of monetary policy. Based on

the theoretically derived PIR, variance decomposition sug-

gests that interest rate and real income growth appear to

be the main sources for the deviations of PIR. Using the

difference between actual PIR and the estimated funda-

mental PIR as the predictor, we find that both in-sample

and out-of-sample forecastability of the PIR over the future

dynamics of PIR are significant.

1INTRODUCTION

The ratios of housing price to income (or rent) are often used as indicators of overvaluation of

housing prices. Economic commentators often express concerns over price-to-income (or rent)

ratios that deviate from the long-term trends. Forexample, price-to-income ratios (PIR) are closely

monitored by the IMF, being an indicator of possible housing bubble formation. Naturally, PIR

is also considered as a measure of the affordability of housing. The intuition is clear: increases in

housing prices cannot deviate indefinitely from growth in the incomes of potential house buyers.

If the appreciation of housing prices outpaces the growth of incomes for a considerable period

of time, households will no longer afford to buy houses, which brings housing prices back to the

long-term growth of incomes. Therefore, the forecasting of PIR should be of importance both for

academics and policy-makers.

In this paper, we focus on the forecastability of PIR for two reasons. First, even with the

importance of PIR being considered as an indicator of overvaluation of housing prices and a

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CHEN AND CHENG

measure of housing affordability, the formal formulation of PIR is rare (Leung, 2014; Leung

& Tang, 2015). Second, previous studies have extensively investigated the relationship between

house prices and income. For example, many empirical works have found that house prices and

income maintain a long-run equilibrium relationship; that is, house prices and income are coin-

tegrated (Black, Fraser,and Hoesli 2006; Gregoriou, Kontonikas, and Montagnoli 2013; Malpezzi,

1999; Meen, 2002; Renaud, 1989). Some others find no cointegration relationship between house

prices and income (Gallin, 2006; Mikhed and Zemˇ

cik, 2009a,2009b). However, the implications

of non-stationarity of the PIR and the forecastability of the PIR have not been fully explored.

The present paper attempts to fill these gaps by first constructing a small dynamic stochastic

general equilibrium (DSGE) model to derive a dynamic expression of PIR, which we label as the

fundamental PIR, linking PIR to the macroeconomic fundamentals and the stance of monetary

policy. Specifically, the fundamental PIR depends on the expected growth rate of real income,

interest rates, the expected inflation rate, and housing demand. This provides a theoretical foun-

dation of the PIR determination equation in a dynamic equilibrium model where all of these

variables are determined endogenously. Second, based on the theoretically-derived PIR, we then

conduct some preliminary examinations of the PIR, including evaluating the stationarity of the

PIR and the variance decomposition of the deviations of PIR. Finally,we examine the predictabil-

ity of PIR over long horizons, including in-sample and out-of-sample forecasts of the dynamics of

future PIR. Given the PIR derived from our model, we estimate the fundamental PIR using a gen-

eralized method of moments (GMM) estimation, with data covering the periods 1979Q1–2015Q3.

Then, similar to Rapach and Wohar (2005), who test predictability of stock prices, weuse the dif-

ference between the actual PIR and the estimated fundamental PIR to serve as the predictor to

examine the forecastability of future PIR. The intuition for using this measure as a predictor is

that if a stable long-run relationship exists between the actual PIR and the estimated fundamen-

tal PIR, then we can exploit this relationship by using its difference to predict future movements

in PIR.

The main findings of the paper are as follows. First, we test for the existence of a unit root in

PIR as in the published literature and find that the PIR is a non-stationary series. To understand

the sources of variations in PIR, we then estimate a five-variatevector autoregression (VAR) based

on the derived expression of PIR. Results from variancedecomposition show that interest rate and

real income growth appear to be the main shocks that account for the volatility of PIR, suggesting

that monetary policy maintains a major source of the variations of PIR. Finally, to examine the

forecastability of the PIR, we first test whether there exists a long-run relationship between the

actual PIR and estimated fundamental PIR. It turns out that the difference between the actual PIR

and the estimated fundamental PIR is stationary. Therefore, we use this measure as a predictor

for future dynamics of PIR. The estimation results show that both in-sample and out-of-sample

forecastability of the PIR over the future PIR are significant. In particular,the out-of- sample fore-

castability of the PIR is significant for all horizons. Because the fundamental PIR is estimated from

our model, this suggests that our theoretical model performs well in explaining and forecasting

the future movement of house prices.

This paper is related to the increasing literature which focuses on the theoretical and empiri-

cal investigation on the PIR. For example,Gregoriou et al. (2013), Taipalus (2006) and Leung and

Tang (2015) find that the house price-to-income (or rent, wages)ratios are non-stationary for var-

ious countries and time periods, which may suggest that besides incomes, other macroeconomic

aggregates or monetary policy can also significantly affect house prices.

A paper that is close to ours is Leung and Tang (2015),who also propose a simple DSGE model

and derive the equilibrium PIR. Their focus, however, is to show theoretically that the PIR is