Real Estate and the Stock Market: A Meta-Regression Analysis

REAL ESTATE AND THE STOCK MARKET:

A META-REGRESSION ANALYSIS

Authors:

Deirdre Reilly, Brian Lucey and Constantin Gurdgiev

Institution:

Trinity College Dublin

ABSTRACT

The real estate finance literature provides diverse and contradictory findings regarding the

distribution of real estate returns and the linkage between these returns and stock market returns.

Despite the importance of this relationship to the economy in general relatively little is known of

what causes such differences. In this paper, through applying the technique of meta-regression

analysis to the empirical studies in the area a significant step is made towards objectively

integrating and synthesising the results and identifying systematic variations in the results of

studies.

1. INTRODUCTION

The distributional properties of the returns of common stocks have been the subject of numerous

empirical studies. Analysis of kurtosis in the equity market dates back as far as Mandelbrot (1963)

and Fama (1965). For real estate assets, there exists a substantial body of research investigating the

first two moments of returns (mean and variance), however analyses of the third and fourth

moments (skewness and kurtosis) is very limited. The overwhelming majority of studies that do

investigate these four properties find real estate returns to be non-normally distributed. There is

little, if any, concrete analysis of what are the factors affecting the degree of non-normality, or in

the case where returns are found to be normally distributed (Lizeri and Ward,1997; Seiler et al.,

1999; Brown and Matysiak, 2000), what are the features of such studies.

Despite the importance of real estate assets to the general economy, surprisingly little is known of

how such assets interact with other macroeconomic variables. There is much disagreement in

literature regarding the nature of the relationship between real estate prices and the stock market.

There is mixed evidence as to whether such a relationship actually exists, and where one is found

on the size and direction of the relationship. The lack of an extended period of analysis and the

omission of structural change periods in existing literature has led to confusion regarding the

nature of any relationship.

The purpose of this paper is to overcome many of these limitations by employing meta-regression

analysis to integrate and summarize in a statistically meaningful way disparate extant research

results. By combining studies, a longer period of analysis is achieved that will incorporate the

various cycles and shifts over time for which data was recorded and studied, leading to more

accurate and meaningful results. Seiler et al. (1999) argues that studies of REIT performance

should use as long a time period as possible as real estate has probably experienced the greatest

number of booms and busts of any investment asset and as such this has lead to conflicting results

in studies. Meta-regression analysis can improve the assessment of this important relationship by

merging all of the existing estimates and investigating the sensitivity of the overall estimate to

variations in the underlying studies. Furthermore, meta-regression analysis provides a method of

quantitatively reviewing the empirical literature in a systematic and objective framework.

In this paper, three related but independent issues will be analyzed by meta-regression analysis:

(1) The degree of normality in real estate returns distributions, (2) To what extent has the literature

confirmed that real estate returns and stock market returns are correlated, and (3) What is the

effect of stock market returns on real estate returns?

2. EMPIRICAL RESEARCH ON THE DISTRIBUTION OF REAL ESTATE RETURNS

AND THE RELATIONSHIP BETWEEN REAL ESTATE RETURNS AND STOCK

MARKET RETURNS

The assumption of normality of the return distribution for direct (private) real estate returns and

returns of real estate securities has been rejected in many studies (Myer and Webb, 1994, Byrne

and Lee, 1997; Liow and Chan, 2005, Liu et al., 1992). There is considerable disagreement as to

the direction of skewness of returns. Lizieri and Satchell (1997) and Brown and Matysiak (2000)

have found returns to be positively skewed, Myer and Webb (1991), Knight et al. (2005) and

Okunev (2000) found that they were negatively skewed, while within the one study Maurer et al.

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(2004) and Pagliari and Webb (1995) found some return series to be positively skewed and others

to be negatively skewed. The vast majority of studies concluded that real estate returns displayed

excess kurtosis, (Myer and Webb, 1994; Byrne and Lee, 1997; Liow and Chan, 2005; Young et al.,

2006).

Hutson and Stevenson (2008) examined the asymmetry in daily REIT returns and found skewness

to be inversely related to the index¡¯s relative performance. In contrast, Bond and Patel (2003)

found little evidence of time variation in the skewness parameters of REIT returns. Brounen et al.

(2008) find property shares to be non-normally distributed, with kurtosis decreasing in all markets

over time. Furthermore, kurtosis is found to be greatest among property stocks which have a high

volume traded, are geographically specialised and have a small market capitalisation.

There is much disagreement in literature regarding the nature of the relationship between real

estate prices and the stock market. As a starting point to many studies, the mostly commonly

reported variable is the correlation between real estate returns and stock market returns. There is

huge disparity in the size and direction of this variable ¨C ranging from a negative correlation of

0.32 (Miles and McCue, 1984) to a positive correlation of 0.89 (Gyourko and Keim, 1992). Very

high correlations are mostly reported for the US (Gyourko and Keim, 1992; Brown & Matysiak,

2000; Clayton and MacKinnon, 2001; Ghosh et al., 1996; Mei and Lee, 1994).

Standing out from these is Brown & Matysiak (2000) which reported a correlation of 0.86 for UK

commercial real estate returns. Apart from being based in the US, the majority of studies which

found high correlations looked at REIT returns or property share returns. Nevertheless even some

of those analyzing REIT returns in the US found negative to small positive correlations - Miles

and McCue, 1984 (-0.32), Goldstein and Nelling, 1999 (-0.04) and Ghosh et al., 1996 (0.07).

Differences in the time period of analysis may have a role to play in these results as both Miles

and McCue (1984) and Goldstein and Nelling (1999) began their analysis in the early 1970s, much

earlier than the vast majority of these studies. Small capitalization stock returns appear to have a

higher correlation with real estate returns than large capitalization stocks. Mei and Lee (1994) are

the only study looking at small capitalization stocks that reported a negative correlation (-0.04).

Below a positive correlation of 0.25 there are very few studies that look at small capitalization

stocks.

Similarly, significant disparity exists in the findings of studies which estimate the effect of real

estate returns on stock market returns. Tse (2001), Qikarinen (2006), Okunev et al. (2000) and

Aperergis and McGuire (2007) find a significant inter-relationship between the two markets, while

Quan and Titman (1997), Yunus (2008) and Beltratti and Morana (2010) find a relationship in

some countries but not in others. However, there is still considerable disagreement between the

studies relating to the size, direction and nature of the relationship.

Liow and Yang (2005) find the housing and stock markets to be cointegrated, Chen et al. (2009)

finds cointegration in some time periods, while Qkunev and Wilson (1995) believe the markets are

fractionally cointegrated. In some studies, the real estate market is found to have a strong granger

causality effect on the stock market, with Okunev et al. (2000) reporting a stock market coefficient

of 1.67. However, using a similar method the findings of Yunus (2008) suggest that the real estate

market does not have any granger causality effect on the stock market.

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While most of the literature is US based, some authors have examined the relationship in an

international context, either by analyzing other countries individually or through panel data

analysis. By examining a larger set of countries, panel data analysis attempts to increase the

number of observations and hence the reliability of the results. Mixed findings stem from such

methods of analysis. Quan and Titman (1997) find a stock coefficient of 0.53 when doing a panel

data analysis of 7 Asian countries between 1979 and 1984. However, in a later paper by the same

authors (1999) a panel data analysis of 6 European economies between 1983 and 1996 reveals a

stock coefficient of -0.5. Cross sectional studies also produce mixed results. Quan and Titman

(1997) utilize cross section data to allow for a longer holding period while still having sufficient

data to examine the relationship between real estate and stock returns. Over a 7 year holding

period, the stock coefficient found to be 0.53. However, in their later study (1999) of 14 different

countries, cross sectional results for the same length of holding period ranged from 0.2 to 0.47

depending on the period of the study and whether rental rates or capital values were analyzed.

As with the literature of the correlation between real estate returns and stock market returns,

analysis of the effect of the real estate market on the stock market generally found the largest

positive effects in the US (Okunev et al., 2000; Liang et al., 1995; Okunev and Wilson, 1997;

Clayton and MacKinnon, 2001). However, this is not always the case as an analysis of the US

market by Glascock et al. (2000) revealed that the real estate market had a negative effect on the

stock market of -2.06 between 1992 and 1996.

Studies examining the returns to REITs or property shares, as opposed to commercial property or

housing assets, generally found a higher positive effect of these real estate assets on the stock

market. Okunev et al. (2000) found a stock coefficient of 1.67 in a granger causality test of the

effect of Equity REITs on the S&P500 between 1989 and 1998. Using a two index market model,

Liang et al. (2005) revealed a stock coefficient of 1.08 in the relationship between Hybird REITs

and NYSE/ASE market return index between 1973 and early 1989. However, on the other end of

the scale, Glascock et al. (2000) based his strongly negative stock coefficient value on the

relationship between Mortgage REITs and the S&P500.

3. META REGRESSION ANALYSIS: APPROACH

Stated simply, ¡°meta-regression analysis is the regression analysis of regression analyses¡±, Stanley

and Jarrell (1989:299). It provides a means of removing the subjectivity in literature surveys and

objectifying the review process. Unlike a traditional literature review where the review chooses

which studies to include, what weight to give to each to the results of each study and how to

interpret the finding, with meta-regression analysis all relevant studies are included, the results are

weighted objectively based on their expected accuracy or reliability and the process of analysis

integrates and summarises the results to provide estimates of empirical magnitudes and to

determine what factors cause variations in the results.

Meta-regression analysis is becoming increasingly popular in the social sciences, including

economics and finance, as a means of examining and combining different research results on a

given issue. It is particularly useful where alternative specification and assumptions lead to

conflicting results. The advantages of using the technique of meta-regression analysis is best

explained in the seminal work of Stanley and Jarrell (1989:300): ¡°Meta-regression analysis not

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only recognises the specification problem but also attempts to estimate its effects by modeling

variations in selected econometric specifications. Meta-regression analysis provides us with the

means to analyze, estimate, and discount, when appropriate, the influence of alternative model

specification and specification searches. In this way, we can more accurately estimate the

empirical magnitudes of the underlying econometric phenomena and enhance our understanding of

why they vary across the published literature.¡±

Meta-regression analysis developed from a popular technique, particularly in medical research,

called meta-analysis. From each study, meta-analysis calculates the effect size, w = (ue ¨C uc)/¦Òc,

where ue is the mean of one group (generally the experimental group), uc is the mean of the control

group and ¦Òc is the standard deviation of the control group. The effect size w is used to compare

the parameter estimates from various studies. This standardised statistic provides a means of

consistently interpreting in a numerical fashion the results of highly individualised studies across

all variables and measures involved, (Lispey and Wilson, 2001). However, the applicability of this

technique to finance and economics is limited because it is rare to encounter studies with

experimental and control groups. Unlike effect size, in the context of a regression, there are units

of measurement attached to a regression coefficient. Analogous to the effect size would be the

reported t-statistic associated with the regression coefficient. A t-statistic does not have

dimensionality and therefore is a standardised measure of the critical parameter of interest,

(Stanley and Jarrell, 1989).

A further limitation of meta-analysis is that it fails to address the question of what are the key

differences that cause variation among the studies results. Meta-regression analysis attempts to

overcome these limitations by explaining the assumptions and specifications that systematically

affect the results of studies.

A typical meta-regression model takes the form:

bi = ¦Â + ¡ÆKk=1¦ÁkXik + ei

i = 1,2,...L.

where bi is the is the reported estimate of the statistic of ¦Â of the ith study in the literature totalling

L studies, ¦Â is the ¡°true¡± value of the parameter of interest, Xik is the meta-independent variable

which measures the relevant characteristics of an empirical study, ¦Ák the meta-regression

coefficient that indicates the effect of particular study characteristics and ei denotes the metaregression disturbance term.

Stanley (2001) outlines five steps for conducting a meta-regression analysis, as follows:

1.

2.

3.

4.

5.

Include all relevant studies from a standard database

Choose a summary statistic and reduce the evidence to a common metric

Choose moderator variables

Conduct a meta-regression analysis

Subject the meta-regression analysis to specification testing

Following these five steps the three meta-regression analyses of this paper serve the purpose of

assessing:

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