Housing Price Growth and the Cost of Equity Capital · 2017-02-14 · We investigate whether and how past growth in housing prices influences a firm’s cost of equity capital. A

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Housing Price Growth and the Cost of Equity Capital

Sara Xiaoya Ding

School of Management

University of San Francisco

San Francisco, CA 94117, USA

Email: [email protected]

Tel.: 415-422-4558

Yang Ni

Antai College of Economics & Management

Shanghai Jiao Tong University

Shanghai, 200052, China


Tel.: 86-21-54030956

Samir Saadi1

Telfer School of Management

University of Ottawa

Ottawa, ON K1N 6N5, Canada


Tel.: 613-985-6476

1 Corresponding author.

We thank Frederick Bereskin, Alfred Davis, Denis Gromp, Jin Jeon, Lewis Johnson, Henock Louis, Alberto

Manconi, Massimo Massa, Adolfo de Motta, Edward Neave, Abdul Rahman, Enrichetta Ravina, Albert

Saiz, Selim Topaloglu, Theo Vermaelen, Ligang Zhong and seminar participants at Queen’s University,

University of Ottawa, University of San Francisco, University of Ontario Institute of Technology,

EMLYON Business School, Vlerick Leuven Gent Management School, 2012 FMA Asian Conference, 2012

Asian Finance Association Meetings, 2012 China International Conference in Finance, 2011 International

Paris Finance Meeting, and 2011 Financial Policies, Economic Growth, and Integration Conference for

their useful comments. We remain responsible for all errors and omissions. Part of this research was

conducted while Samir Saadi was visiting Stern School of Business, New York University.

mailto:[email protected]

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Housing Price Growth and the Cost of Equity Capital

Abstract

Building on recent research linking changes in housing prices to demand for stocks, we

find strong evidence that firms located in state with positive growth in housing prices

exhibit lower costs of equity. The association is economically significant. Specifically, a

one standard deviation increase in state housing prices leads to 14 basis points decrease

in the cost of equity. Our results are robust across different implied cost of capital

models, to various measures of growth in housing prices and to a variety of alternative

specifications. This study is the first to find a link between housing prices and cost of

equity.

JEL classification: G10, G11, G39

Key words: Housing price growth, cost of equity capital, local bias

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I. Introduction

We investigate whether and how past growth in housing prices influences a firm’s

cost of equity capital. A growing body of theoretical and empirical research documents

that growth in housing prices sways household consumption, portfolio choice and stock

prices (e.g., Campbell and Cocco (2007), Piazzesi, Schneider, and Tuzel (2007), Chu

(2010), Gan (2010), Sousa (2010), Anderson and Beracha (2012), and Louis and Sun

(2013)). We conjecture that change in housing prices influences cost of capital through

its effect on investors’ risk aversion. When housing prices experience a growth,

household’s wealth increases leading to lower degree of risk aversion (e.g., Paravisini,

Rappoport, and Ravina (2013)). Consequently, households would demand a lower

premium for bearing the risk associated with the stocks they hold (e.g., Cochrane

(2008)).

In conjunction with strong evidence of local bias,2 the heterogeneity in regional

housing prices within the U.S. (Beracha and Hirschey (2009)) provide an excellent

setting to investigate the potential effect of growth in housing prices on cost of equity

capital. To test our main prediction, we require a measure of growth in local housing

prices and a measure of cost of equity capital. We gauge the growth in housing prices at

state level, and this for at least three reasons. First, we adopt the same convention as in

relevant literature on local bias (e.g., Coval and Moskowitz (2001), Loughran and

Schultz (2005), Pirinsky and Wang (2006), Hong, Kubik, and Stein (2008)). Second, the

housing wealth effect at the state-level is economically significant as it is shown by

Calomiris, Longhofer, and Miles (2012). Third, state-level housing data are readily

available for a long time period.

2 Several papers show that investors tend to invest a disproportionate share of their stock portfolios in

local firms (e.g., Coval and Moskowitz (1999), (2001), Ivkovic and Weisbenner (2005), Loughran and

Schultz (2005), Pirinsky and Wang (2006), Hong, Kubik, and Stein (2008)).

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For cost of equity, we follow, among others, Hail and Leuz (2009), Chen, Chen, and

Wei (2011), Chen, Kacperczyk, and Ortiz-Molina (2011), Chen, Huang, and Wei (2013),

and Ortiz-Molina, and Gordon (2013) by considering firm’s ex-ante cost of equity

premium implied by current stock prices and analysts’ earnings forecasts. The use of

ex-ante cost of equity capital is motivated by extensive evidence implying that realized

returns are exceedingly noisy.3 Elton (1999, p. 1199), for instance, concludes that

‘‘realized returns are a very poor measure of expected returns’’ even over a long period.

Fama and French (1997) further stress that the uncertainty in the factor premiums and

the imprecision in the factor loading estimates lead to inaccurate estimation of expected

returns by ex-post returns and asset pricing models. More recently, Lee, Ng, and

Swaminathan (2009) add that the use of implied cost of equity capital offers clear

evidence of economic relations that would otherwise be concealed by the noise in

realized returns.

Consistent with our conjecture, we find strong and robust evidence that growth in

housing prices influences firms’ cost of equity. In particular, we document that a firm’s

cost of equity is negatively related to past growth in housing prices in the state where

the firm is located. This housing effect is also economically significant. Specifically,

firms located in a state experiencing a one standard deviation increase in housing prices

enjoy lower equity financing costs by about 14 basis points. Our results are robust

across different cost of capital models, to various measures of growth in housing prices,

and to a variety of alternative specifications.

3 See, among others, Elton (1999), Gebhardt, Lee, and Swaminathan (2001), Hail and Leuz (2006),

Lundblad (2007), Pástor, Sinha, and Swaminathan (2008), and Lee, Ng, and Swaminathan (2009). See also

Chava and Purnanandam (2010), Chen, Chen, and Wei (2011) and Kacperczyk and Ortiz-Molina (2013)

for more recent discussions motivating the use of implied cost of equity instead of realized returns.

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Our conceptual framework is based on the well supported housing wealth effect,

and how it lowers households’ risk aversion, and hence the premium on households’

stock holding. Yet, there are other potential explanations to our findings that we

carefully examined to see whether the housing effect explanation holds. First, our

results could be due to our measure of growth in housing prices capturing rather an

increase in real asset liquidity. In fact, a recent study by Ortiz-Molina and Philips (2013)

shows that real (or physical) asset illiquidity has a positive effect on implied cost of

equity capital. Following Ortiz-Molina and Philips, we control for asset illiquidity at the

firm and industry levels, and find that our results remain qualitatively unchanged.

Second, it is plausible that our measure of growth in housing prices reflects an

increase in firm’s collateral following an overall increase in real estate prices. Several

studies have shown that collaterals impacts firm’s capital structure by increasing firm’s

debt capacity (e.g., Bernanke and Gertler (1989), Campello and Giambona (2013),

Cvijanovic (2013), Rampini and Viswanathan (2013)). Though equity holders are

residual claimants, an increase in firm’s collaterals could induce a lower cost of equity.

Indeed, we find that implied cost of equity capital is negatively related to different

proxies of firm’s collaterals, yet the coefficient on growth in housing prices remains

highly statistically and economically significant.

A third concern is that the decrease in firm’s cost of equity could be due to growth

in state business activities which is typically positively correlated with increase in

housing prices. We address this concern by controlling for several proxies of state

economic activities, and find that our results remain qualitatively the same.

A fourth related concern is that housing prices might be related to unobservable

determinants of cost of equity. To deal with this potential endogeneity problem, we

follow, among others, Mian and Sufi (2011) and instrument for house price growth

using the land-topology based measure of housing supply elasticity introduced by Saiz

(2010). Similar to Engel, Hayes, and Wang (2007), we interact housing supply elasticity

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with 10-year borrowing costs to create time variation in housing price growth. In

addition, we introduce change in education as a second instrument for housing price

growth. We reproduce our results using a two-stage least squares approach, and find

that the coefficient on housing price growth continues to be significantly different from

zero.

This paper contributes to the growing body of studies on the implications of

changes in housing prices. Extant literature looks at the effects of housing prices on

households’ consumption, households’ asset allocation, and asset pricing. To the best of

our knowledge, this study is the first study to examine the association between growth

in housing prices and firm’s cost of capital. We also contribute to the emerging

literature on the economic importance of geographic proximity. Previous studies on

firm’s location emphasize the information advantage associated with geographic

proximity.4. Finally, we contribute to literature on the factors affecting a firm’s cost of

capital by introducing geography as a determinant of cost of equity.

The rest of this paper is organized as follows. Section 2 develops the hypothesis. In

Section 3, we describe the data and report summary statistics on our regression

variables. Section 4 presents our main evidence on the association between growth on

housing price and cost of equity. Section 5 provides sensitivity analyses. Section 6

concludes.

4 Previous studies report that the information advantage associated with geographic proximity explains

the local bias documented in both mutual fund investments (Coval and Moskowitz (1999, 2001)) and

individual investors’ portfolio decisions (e.g., Ivkovich and Weisbenner (2005), Pirinsky and Wang

(2006)). And, it affects analysts forecasting accuracy (Malloy (2005)), information resolution for bank

lending (Agarwal and Hauswald (2010)), and corporate decisions (e.g. John, Knyazeva, and Knyazeva

(2011)).

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II. Hypothesis Development

We derive our key hypothesis on the association between growth in housing prices

and cost of equity from the traditional economic theory together with the recent

evidence of local bias. To build our arguments, we first proceed by presenting the two

main channels through which growth in housing prices could influence investors’

investment behavior, putting more emphasis on the most empirically supported

channel: the wealth effect.

Housing wealth is the main source of private wealth around the world. In the U.S.,

for instance, where the residential real estate market is over $20 trillion in capital value,

more than two-thirds of households are homeowners (Tracy and Schneider (2001),

Bertaut and Starr-McCluer (2002), Anderson and Beracha (2012)). The implication of an

increase in household wealth for equity pricing is twofold. First, because the degree of

risk aversion is negatively related to agents’ wealth (e.g., Arrow (1971), Holt and Laury

(2002), Paravisini, Rappoport, and Ravina (2013)), as housing prices increase,

households’ risk aversion decreases (Paravisini, Rappoport and Ravina (2013)). The

decreasing risk aversion subsequently reduces the conditional market price of risk,

resulting in a lower required rate of return on stocks (e.g., Campbell and Cochran

(1999), Lettau and Ludvigson (2001), Cochrane (2008)). Second, an increase in

households’ wealth following growth in housing prices leads to higher participation in

the stock market, hence higher demand for stocks which in turn leads to higher stock

prices, and hence lower require rate of returns (Kraus and Stoll (1972), Shleifer (1986),

Anderson and Beracha (2012), Louis and Sun (2013)).5

The wealth argument has received much support especially from the empirical

literature examining the low stock market participation puzzle. Bertaut and

5 It is noteworthy that the second implication (i.e. higher market participation) could also be the result of

a decreasing risk aversion following an increase in housing prices.

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Starr-McCluer (2002), for example, report that doubling household wealth increases the

likelihood of owning stocks by 26%. Theoretical papers by Merton (1987) and Abel

(2001) suggest that the existence of fixed entry and ongoing participation costs cause

households with insufficient wealth to shy away from the stock market.6 Merton (1987)

and Abel (2001) theoretical prediction is widely supported empirically (e.g., Marshall

Parekh (2000), Vissing-Jørgensen (2002), Grinblatt, Keloharju, and Linnainmaa (2012)).

Flavin and Yamashita (2002), Cocco (2005), Vestman (2012), Anderson and Beracha

(2012), and Louis and Sun (2013) also document evidence of wealth effect. For example,

using detailed ownership data from Thomson Reuters Institutional Holding database,

Louis and Sun (2013) show that stock holdings of individual investors located in states

with high annual housing price growth are significantly higher than of those located in

states with low annual housing price growth.

Besides the wealth effect, there is an alternative channel through which growth in

housing price could influence cost of equity capital, namely the borrowing effect. It

suggests that an increase in housing prices lessens homeowners’ borrowing constraints,

facilitating their abilities to leverage their investments (Guiso, Jappelli, and Terlizzese

(1996), Lustig and Nieuwerburgh (2005)). 7 Lustig and Nieuwerburgh (2005), for

instance, show that an appreciation in house market increases the collateral value of

6 Such costs include trading costs, management fees, and money and time spent to monitor portfolio

investment, as well as keep up with stock market developments.

7 According to US census, during the two decades ending in 2001, the national median home price ranged

from 2.9 to 3.1 times median household income. This ratio rose to 4.0 in 2004 and 4.6 in 2006 (see Z.1

Historical Tables (1974) and current Z.1 release (2008), Table B.100, lines 31, 48). The housing bubble

resulted in many homeowners refinancing their homes at lower interest rates or financing consumer

spending by taking out second mortgages secured by the price appreciation. For instance, household debt

grew from $705 billion at year-end 1974, 60% of disposable personal income, to $7.4 trillion at year-end

2000, and finally to $14.5 trillion in mid-year 2008, 134% of disposable personal income (U.S. Census).

http://en.wikipedia.org/wiki/Disposable_personal_income

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housing, reduces household exposure to idiosyncratic risk, and reduces the conditional

market price of risk. In short, both channels, wealth effect and borrowing effect, predict

a negative association between change in housing prices and cost of equity capital.8

Local stocks are most likely to be affected by the fluctuation in local housing price.

The local bias studies find strong preference of investors holding more local stocks. For

example, Coval and Moskowitz (1999, 2001) find that mutual fund managers in the U.S.

have a strong bias toward nearby companies. Ivkovic and Weisbenner (2005) detect that

the local holding bias is even larger for retail investors. Coval and Moskowitz (2001)

argue that investors strongly prefer local stocks because they enjoy significant

information advantage in evaluating them, which reconciles with the evidence that local

investors earn abnormal returns on their local holdings, outperforming distant investors

(e.g., Huberman (2001), Grinblatt and Keloharju (2001), and Massa and Simonov (2006)).

Because state investors would hold more stocks located in the same state, the impact of

state housing prices on investors’ risk aversion/sharing ability and their demand for

stocks should exert a stronger effect on stocks of local firms.

A number of asset pricing studies show that state-level income shocks are

undiversifiable (e.g., Asdruball, Sorensen, and Yoshi (1996), Athanasoulis and van

Wincoop (2001)), and that returns on local stocks held by state investors are affected by

time-varying risk aversion of state investors and by changes in these investors ability to

engage in risk sharing (Korniotis (2008), Korniotis and Kumar (2013)). Hence, we argue

that change in housing prices at state level induces cross-state variation in the cost of

equity capital. In particular, in states where housing price growth is high, cost of equity

should be low; in states where housing price growth is low, cost of equity should be

high. Formally, our main testable hypothesis is as follow:

8 It is out of the scope of this paper to seek whether the housing effect in our study is due to a wealth effect

or to a borrowing effect.

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H1: A firm’s cost of equity is negatively related to past growth in housing prices in the state

where the firm is located.

III. Data and Variables

A. Sample Construction

Our primary data sources are the Center for Research in Security Prices (CRSP),

which provides stock return data; Compustat, provides financial statement data and

each firms’ headquarters’ state code; the I/B/E/S, provides data on analyst forecasts;

and Federal Housing Finance Agency (FHFA), provides housing data. Our sample

covers all U.S. public firms over the period from 1985 to 2008. As specified in Appendix

A, the computation of the cost of equity capital requires firms to have (i) positive one-

and two-year-ahead consensus analyst earnings forecasts, a consensus long-term

growth forecast, a share price, and shares outstanding in I/B/E/S; and (ii) earnings,

dividends, and book value of equity in Compustat.9 We follow Gebhardt, Lee, and

Swaminathan (2001) and Dhaliwal, Heitzman, and Zhen (2006) by estimating the cost of

capital as of the end of June in each year t. Finally, to construct firm-specific controls for

our regressions, we require firms to have market capitalization, shareholder equity,

total assets, and total debt in Compustat and at least 24 monthly stock returns during

the previous five years in CRSP.

9 The data screening leads to the exclusion of lesser-known firms with no, or hardly any, analyst

coverage. However, any selection bias that this restriction introduces would almost certainly work

against our tests, rejecting the null hypothesis that the housing price affects the firm’s cost of equity

capital. In fact, the extant literature documents that the location effects are much more pronounced in

firms with high information asymmetry, which tend to be small firms with weak, if any, analyst

following (Coval and Moskowitz (1999), Ivković and Weisbenner (2005), Malloy (2005), Bae, Kim, and Ni

(2011)).

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B. Housing Data

We obtain data on housing prices from the Federal Housing Finance Agency

(FHFA) website.10 The FHFA estimates and publishes house price indexes for the

nation, the nine U.S. Census divisions, and the 50 states plus the District of Columbia,

using data on mortgage transactions from the Federal Home Loan Mortgage

Corporation (Freddie Mac) and the Federal National Mortgage Association (Fannie

Mae). We use the one-year growth rate in housing prices of each state in our main

specification. In robustness checks, we conduct analysis using alternate measures of

housing price growth.

C. Cost of Equity Capital

The majority of models estimating the ex-ante cost of equity capital are rooted in

Williams (1938) dividend discount model in which the cost of equity is the internal rate

of return that connects current share price to the present value of the expected series of

dividends per share:

∑

( )

(

1)

(

1)

where is current share price, is expected dividends per share at time ,

and is the cost of equity capital.

We follow emerging cost of equity capital research (e.g., Dhaliwal, Heitzman, and

Zhen (2006), Barth, Hodder, and Stubben (2008), Hail and Leuz (2009), Chen, Chen and

Wei (2011)) by relying on the mean, labeled rAVG, of four practical implementations of

Equation (1) to estimate firms’ ex-ante cost of equity premium implied by current stock

prices and analysts’ earnings forecasts: Ohlson and Juettner-Nauroth (2005), Easton

10 Available at http://www.fhfa.gov

http://www.fhfa.gov/

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(2004), Claus and Thomas (2001), and Gebhardt, Lee, and Swaminathan (2001), denoted

rOJN, rMPEG, rCT, and rGLS, respectively. Although all models share Equation (1)’s starting

point, they diverge on their sets of assumptions for the imputation of expected

dividends from earnings forecasts, the choice of the explicit forecasting horizon, and the

selection of the long-term growth rate. Although a comprehensive discussion of these

issues is beyond our scope, we outline these models, along with their underlying

assumptions, in Appendix A. The cost of equity obtains directly in Ohlson and

Juettner-Nauroth (2005). For the remaining three models, we employ numerical methods

to extract the cost of equity from the corresponding valuation equation, restricting the

solution to lie between 0% and 100%. Then, we subtract the ten-year Treasury bond yield

(as of June in year t) from each cost of equity estimate to obtain the implied equity

premium.11 Prior research stresses that this ex-ante approach has superior construct

validity, than do realized returns, for gauging investors’ required rate of return (e.g.,

Stulz (1999), Hail and Leuz (2006), Lundblad (2007), Pastor, Sinha, and Swaminathan

(2008), Lee, Ng and, Swaminathan (2009), Chava and Purnanandam (2010), Chen, Chen,

and Wei (2011)).12

11 Throughout the paper, we use the terms cost of equity capital, implied cost of equity, and equity risk

premium synonymously.

12 Although averaging across the four models in our primary analysis ensures that the distinctive

characteristics of any single model are not spuriously behind our evidence, our core results are robust to

re-estimating our regressions using each individual cost of equity metric, the median, or the first

principal component of the four. Indeed, recent evidence reinforces the importance of avoiding specifying

a single implied cost of capital estimate when examining the determinants of equity pricing, (e.g., Botosan

and Plumlee (2005), Dhaliwal, Heitzman, and Zhen (2006), Guay, Kothari, and Shu (20011)). Nonetheless,

we concede that some measurement error may afflict our cost of capital estimates, stemming from

deviations between analysts’ and investors’ earnings expectations, an issue we consider in our sensitivity

analysis.

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D. Control Variables

To isolate the incremental impact of growth in housing prices on firms’ cost of

equity, we closely follow extant research in choosing and specifying controls for other

potential determinants (e.g., Gebhardt, Lee, and Swaminathan (2001), Gode and

Mohanram (2003), Hail and Leuz (2006)). These controls, which are summarized in

Table 3, are:

Beta (BETA): The capital asset pricing model purports a positive relation

between a firm’s beta and its expected stock returns. We control for beta, BETA, which

we obtain from regressing 60 monthly stock returns ending in June in year t on the

corresponding monthly CRSP value-weighted index returns.13 We require at least 24

monthly available observations for the beta estimations.

Book-to-market (BTM): We follow recent equity pricing research by controlling

for the book-to-market ratio (e.g., Hail and Leuz (2006)). Previous literature (e.g., Fama

and French (1992)) builds on empirical asset pricing research which documents higher

ex post returns for firms with high book-to-market ratios. We measure BE/ME as the

ratio of the book value of shareholders’ equity plus deferred taxes and investment tax

credits (if available) minus the book value of preferred stock to the market value of

equity.

Size (market capitalization: SIZE): Gode and Partha (2003) argue that firm

size proxies for the information environment in that larger firms disclose more and

13 We are grateful to Professor Kenneth French for making the one-month Treasury bill rate on his Web

site. Available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

14

attract more information intermediaries. This in turn should narrow informational

asymmetry between managers and stockholders, reducing the cost of equity capital.14

Leverage (LEV): In their seminal paper, Modigliani and Miller (1958)

propose that the firm’s cost of equity incorporates a risk premium that increases linearly

with leverage. Consistent with this theory, Fama and French (1992) find that more

levered firms earn higher subsequent stock returns. We use the debt-to-equity ratio

defined as total debt divided by total assets to proxy for leverage, LEV.

Long-term growth (LTG): La Porta (1996) reports that firms receiving high

I/B/E/S long-term earnings growth forecasts (LTG) earn lower ex post returns,

implying that analysts are overly optimistic about the prospects of these firms. In

contrast, Gebhardt, Lee, and Swaminathan (2001) find that investors in high LTG firms

require higher returns. Gode and Partha (2003) argue that firms with high LTG are

inherently more risky as small errors in LTG may materially affect current stock prices.

We include LTG measured at June in year t to control for the potential impact of forecast

bias on equity pricing.

Dispersion of analyst forecasts (DISP): Botosan, Plumlee, and Xie (2004) report

that firms with high analyst forecast dispersion exhibit higher cost of equity on average.

Gebhardt, Lee, and Swaminathan (2001) contend that earnings variability captures

fundamental cash flow risk. Consistent with this argument, Rountree, Weston, and

Allayannis (2008) find that future earnings volatility is negatively correlated with

contemporaneous firm value. We control for earnings variability using the dispersion of

analyst forecasts, DISP, measured as the coefficient of variation of one-year-ahead

earnings forecasts as of June in year t.

14 The empirical asset pricing literature provides another justification for controlling for size: Fama and

French (1992) find that large firms command higher ex post returns.

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Industry membership (Industry effects): Gebhardt, Lee, and Swaminathan

(2001) find that investors consistently demand higher discount rates in some industries

(e.g., sports and leisure, banks, and automotive). Accordingly, we control for industry

membership with dummies variables representing the Fama and French (1997) 48

industries.

Time (Year effects): Macroeconomic conditions affect stock prices and cash

flow expectations, which in turn influence equity financing costs. We use year dummies

to control for changing macroeconomic conditions over the sample period. Appendix B

provides definitions and data sources for all regression variables used in the hypotheses

tests.

E. Descriptive Statistics

After excluding firms with headquarters located outside the U.S., the intersection of

the four data sets leaves an unbalanced panel of 44,678 firm-year observations

comprised of 6,862 unique firms over the period 1985-2008.

Table 1 reports the sample’s industry (in accordance with the Fama and French 48

industry classification) and year distributions. Some clustering is evident in the sample

for firms belonging to the banking, business services, and retail industries, each

accounting for more than 6% of the firm-year observations.15 The observations are quite

evenly dispersed over the sample period with a maximum of 2,490 in 1998 and a

minimum of 1,377 in 1988.

Our Table 2 reports descriptive statistics on cost of equityfor each model, together

with the Pearson correlations between these estimates. In Panel A, the overall mean

15 Our core evidence is however robust to the exclusion of financial and utilities firms from the analysis.

More generally, none of our inferences are materially sensitive to recursively removing firms from each of

the 48 Fama and French (1997) industries from the samples.

16

(median) of rAVG is 5.05% (4.53%). Annual mean rAVG estimates range from a 4.02% (low)

in 1987 to a 6.54% (high) in 2003. The rCT and rGLS estimates are lower than those for rOJN

and rMPEG, which reconciles with recent rankings of the individual equity premium

estimates (e.g., Guay, Kothari, and Shu (20011)). It is comforting to observe that the

correlation coefficients between the four individual equity premium estimates in Panel B

are positive and generally very high, supporting that they share the same underlying

construct. However, there are some exceptions (e.g., the correlation of rCT with rMPEG is

only 0.46), implying that measurement error likely plays some role as well, which

reinforces the importance of triangulating our evidence to analyze whether our core

results depend on how we measure equity pricing. The correlations between the

estimates from the four individual models and rAVG vary from a low of 0.72 for rGLS to a

high of 0.93 for rOJN. Overall, these descriptive statistics fairly closely resemble those

reported in, for example, Hail and Leuz (2006) and Dhaliwal, Heitzman, and Zhen

(2006).

Table 3 reports summary statistics of the main variables used in our paper. Panel A

reports that the typical one-year growth rate in housing prices, HPG1, is 5%. The

magnitude of the standard deviations of HPG1 suggests a fair amount of variation in our

measure of housing price growth rate across states. Panel B presents the summary

statistics of HPG1 by state in our sample. We observe note-worthy heterogeneity in

housing price fluctuation across states. For example, California witnesses the highest

mean (6%) and standard deviation (10%) among all states. The negative correlation of

our measure of growth rate in housing prices HPG1 with rAVG in Panel C provides some

initial evidence supporting that firms located in states with high growth rate in housing

prices experience a lower cost of equity capital. Next, given the major role that other

determinants play in equity pricing, we evaluate whether this preliminary evidence

supporting the prediction remains in a multivariate framework.

Insert Tables 1, 2, and 3 about here

17

IV. Growth Rate in Housing Prices and the Cost of Equity Capital: Multivariate

Evidence

Table 4 tabulates the results of our main regressions. Following recent research (e.g.,

Dhaliwal, Heitzman, and Zhen (2006), Barth, Hodder, and Stubben (2008), Hail and

Leuz (2009), Chen, Chen and Wei (2011)), we first measure the firm’s cost of equity

capital with the average estimate derived from four models (rAVG). In our baseline Model

(1), our estimates are based on consistent robust standard errors clustered at firm level.

Our results strongly support our prediction that the growth rate in state’s housing

prices influences local firm’s cost of equity capital, even after controlling for time,

industry, and other firm-specific determinants. The coefficient on variable HPG1 is

negative and statically significant (t-statistic = -4.599). The interpretation of the effect of

housing price growth on cost of equity capital is that a one standard deviation increase

in housing price reduces equity financing costs by 13.51 basis points, which is

economically important. The other control variables enter significantly in the main

specification with their expected signs. The result from Model (1) confirms our

hypothesis that firm’s cost of equity capital, ceteris paribus, decreases with the growth

rate in housing prices in the state in which a firm is headquartered.

In Columns (2)–(6) of Table 4, we report the results using alternate estimation

approaches. In Model (2), we compute standard errors in our baseline model using the

Fama and MacBeth (1973) procedure in order to mitigate concerns about cross-sectional

dependence in the data. The results include that the impact of housing price growth on

the cost of equity capital is persistently strong economically (coefficient = -1.845) and

statistically (t-statistic = -2.962). Our equity pricing evidence on the role of housing

prices continues to hold when we take care of serial correlation of standard errors under

Newey-West specification in Model (3) and Prais-Winsten in Model (4). Our results also

hold when we exploit the panel structure of the data by estimating a fixed effects

regression in Model (5) and a random effects regression in Model (6).

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V. Robustness Tests

In this section, we extend our sensitivity analysis to confront concerns raised in

extant research on both equity pricing and housing price growth. This involves relying

on other proxies for the dependent and test variables, adding controls, and addressing

potential endogeneity issues. For the sake of conserving space, we focus on the baseline

Model (1) in Table 4, in which robust-cluster method is used. However, all of our

conclusions hold for the alternate specifications.

A. Alternate Measures of Growth in Housing Prices

To examine the sensitivity of our results in Table 4 to the use of one-year housing

price growth, we reproduce the main results of Table 4 using other alternative measures

of housing price growth: two-year housing price growth, three-year housing price

growth, four-year housing price growth, level of housing price, and housing/DPI ratio

over the previous year in dollar. Housing/DPI ratio is defined as the ratio of housing

prices to disposable personal income16 in the state in which the firm is located. We

introduce Housing/DPI ratio to capture the potential effect of individual income

dispersion across states. We expect that the alternate measures of housing price growth

to be negatively related to firms’ cost of equity.

Table 5 presents the results of the robustness checks using alternate measures of

housing price growth. The coefficients on all measures of housing price growth are

negative and highly significant. The coefficients on two-, three-, and four-year housing

price growth are -0.782, -0.562, and -0.403, respectively, all statistically significant at the

1% level or higher. Housing price and housing price scaled by personal disposable

income (housing/DPI ratio) are negatively and significantly related to cost of equity.

The evidence in Table 5 confirms our findings obtained in Table 4.

16 Available from U.S. Department of Commerce Bureau of Economic Analysis.

19

Insert Tables 4 and 5 about here

B. Alternate Cost of Equity Capital Measures

Results from Table 4 are based on a firms’ cost of equity capital measured as the

average estimate derived from four models, rAVG. To see whether our findings are

sensitive to the choice of cost of equity metric, we re-estimate the baseline regression

after replacing rAVG with alternate proxies for the cost of equity. Results are tabulated in

Table 6. The first four columns are devoted to the elements of rAVG. The coefficients on

HPG1 are negative and statistically significant for all four cost of equity estimates rOJN,

rMPEG, rCT, and rGLS.

For the remaining of Table 6, we consider other proxies that have been used in

empirical studies (e.g., Francis, LaFond, Olsson, and Schipper (2005), Botosan and

Plumlee (2005), Guay, Kothari, and Shu (20011)). In Model (5), we focus on the equity

premium estimated according to the finite horizon Gordon model (Gordon and Gordon

(1997)). We also consider the risk premium implied by the price-earnings-growth (PEG)

ratio based on short-term earnings forecasts in Model (6) and longer-term forecasts in

Model (7), as well as the dividend yield in Model (8). In line with our prediction, the

coefficient on HPG1 is statistically and economically significant for each of those cost of

equity estimates. The other control variables enter significantly in the main specification

with their expected signs.

C. Noise in Analyst Forecasts

Recent research documents an upward bias in analyst forecasts, which would

translate into inflated implied cost of equity capital estimates (e.g., Easton and Sommers

(2007)). Accordingly, we evaluate whether our core evidence is sensitive to distortions in

implied equity premiums stemming from analysts’ optimism. This involves measuring

optimism using the signed forecast error defined as the difference between the

one-year-ahead consensus earnings forecast and realized earnings deflated by June-end

20

stock price (FERROR). In Table 7, we mitigate this concern in several ways. In an initial

pass at tackling this issue, we include in Model (1) the forecast error as another

explanatory variable in our baseline model. We find that FBIAS loads positively,

corroborating that analyst optimism inflates the equity premium estimates. However,

more relevant for our purposes, the coefficient on HPG1 remains negative and

statistically significant at the 1% level when we control for forecast bias. In Models (2) to

(5), we continue to observe that HPG1 loads highly negatively when we exclude the top

5, 10, 25, and 50% of firm-year observations with extremely optimistic earnings forecasts,

despite the major sacrifice in power in these smaller samples. Finally, we repeat this

exercise for the long-term growth forecast (LTG) by discarding firm-year observations

with extreme values in Models (6) to (9) and still find that HPG1 exhibits a negative and

statistically significant (at the 1% level) relation with the cost of equity capital.

Additionally, prior studies identify another source of noise in analysts’ forecasts that

relates to their sluggishness, that is, their tendency to react gradually to publicly

available information (e.g., Ali, Klein, and Rosenfeld (1992)). We address this concern in

two ways. First, after Chen, Chen, and Wei (2009) and Guay, Kothari, and Shu (20011),

we control for price momentum estimated as compounded stock returns over the past

six months (Model (10)). In this regression, we continue to obtain a negative and highly

significant coefficient on HPG1, suggesting that firms’ equity financing costs are

decreasing in the growth rate in housing prices of the state in which the firm is located.17

Second, we re-estimate the implied cost for equity capital using January-end, instead of

June-end, prices to allow analysts to incorporate into their forecasts the recent price

movements (Hail and Leuz (2006), Guay Kothari, and Shu (20011)). The results reported

in Model (11) strongly corroborate our earlier evidence.

17 We obtain qualitatively similar evidence when we control for compounded stock returns over the past

three and twelve months, respectively.

21

D. Other potential explanations

The main hypothesis in this paper is based on the evidence that housing wealth

effect reduces households risk aversion, and henceforth lowers the premium on

households’ stock holding (e.g., Cochrane (2008), Paravisini, Rappoport and Ravina

(2013)). Nevertheless, the negative association between growth in housing prices and

cost of equity capital could be spurious as growth in housing prices can capture other

effects. In particular, there are two effects that could potentially be the results of a

growth in housing prices and have a negative impact on a firm’s cost of capital: (1) an

increase in a firm’s real asset liquidity and (2) a surge in a firm’s collateral value. In this

sub-section, we show that the housing effect continues to hold after accounting for these

two potential effects.

Recently, Ortiz-Molina and Phillips (2013) document a positive relation between

real asset illiquidity and cost of equity capital. To address the concern that our results

are driven by an increase in asset liquidity subsequent to a boom in housing market, we

control for the liquidity of real (fixed) assets and for the overall asset liquidity. Similar

to Benmelech and Bergman (2008; 2009), Gavazza (2011), and Ortiz-Molina and Phillips

(2013), we define liquidity of real (fixed) assets as the number of potential buyers, and

measure it using the number of rival firms in the industry with debt ratings (i.e.

NoPotBuyer). Results, reported in Model (1) of Table 8, suggest that the higher the

liquidity of real assets the lower is the cost of capital, yet the coefficient on growth in

housing prices remains statistically different from zero.

To further address the liquidity concern, we follow Ortiz-Molina and Phillips (2013)

and Gopalan, Kadan, and Pevzner (2012) and introduce four proxies of firm overall

asset liquidity: OALiq1, OALiq2, OALiq3, OALiq4. Defined in Appendix B, each of these

proxies is constructed as a weighted average liquidity measure where each of the major

asset classes is assigned a liquidity score. In Model (2) to (5), after replacing the measure

22

of liquidity of real assets by the four proxies that capture the firm’s overall asset

liquidity, respectively, we find that the housing effect still holds (p-value <0.001).

Recent papers by Campello and Giambona (2012), Cvijanovic (2013), Rampini and

Viswanathan (2013) argue that collaterals increase a firm’s borrowing capacity. For

instance, Cvijanovic (2013) examines how growth in real estate prices affects a firm

capital structure, and find that a one standard deviation increase in collateral value

leads to an increase of leverage by 2.6 percent, and a decrease in the cost of debt. To

address the concern that our results could reflect an increase in firm’s collateral

following a growth in housing prices, we augment our main regression model with

several proxies of firm collaterals, which we define in Appendix B (see Cvijanovic

(2013)). Model (6) of Table 8 controls for firm collateral in year t. Model (7) controls for

firm collateral in reference year multiplied by housing price in year t. Our results show

that growth in housing priced continues to negatively affect cost of equity capital after

controlling for collaterals.


Another related concern is the possibility that our results are driven by an

unspecified omitted variable. For this to be true, however, that omitted variable would

have to be correlated with housing price growth, but uncorrelated with the factors

known to explain housing price growth, at the individual level. It would also have to be

correlated with the dependent variable in a way consistent with our findings.

Nevertheless, we perform several tests to further mitigate this concern.

D.1. Controlling for state economic activities

To address the endogeneity issue, we first control for the local economic variables.

For example, a booming housing price is often accompanied by a growing local

economy. Investors in states with growing local economy may demand lower risk

premium. If our housing effect is driven by local economic variables, we would observe

23

the significance of housing variables to disappear after controlling for local economic

variables. In particular, we include two local economic variables: GDP growth rate and

DPI growth rate. GDP growth rate is the growth rate in GDP per capita, and DPI

growth rate is the growth rate in disposable personal income of the state in which the

firm is located in the preceding years. We obtain data on GDP and DPI from the U.S.

Department of Commerce Bureau of Economic Analysis.18 In addition, we include

another measure of housing price growth, DIFF_HPG_DPI, defined as the difference

between one-year housing price growth and DPI growth rate. This measure has been

adjusted for local economic growth and should be able to better capture the pure

housing effect.

Models (1)–(3) of Table 9 tabulate the results. We find that, the housing effect is

persistent after controlling for local economic growth. In all regressions, our main

independent variable of housing price growth remains highly economically and

statistically significant. Consistent with our prediction that local economic growth

reduces cost of equity, GDP growth rate (GDPG1), DPI growth rate (DPIG1), and the

adjusted housing price growth (DIFF_HPG_DPI), are negative and highly significant.

To control for other possible omitted economic variables at the state level, we

re-estimate our main specification by using state fixed effect (Model (4)). HPG1 remains

highly significant both in economics and statistics terms. Our results in Table 8 indicate

that the housing effect we find in the baseline regression is not driven by local economic

growth.

D.2. Instrumental variables

To further address the likely endogeneity of house prices, we instrument for house

prices using an exogenous geographic determinant of housing supply. Saiz (2010)

identified urban land geography as a major factor in residential development and

18 Available at http://www.bea.gov/

http://www.bea.gov/

24

introduced a land-topology based measure of housing supply elasticity. Areas with

elastic (inelastic) housing supply should experience modest (large) increase in house

prices in response to large shifts in the demand for housing (Faccio, Lang, and Young

(2001)). Mian and Sufi (2011) employ Saiz (2010)’s housing supply elasticity as an

instrument for house price growth to estimate borrowing against the increase in home

equity by homeowners. In order to create time variation in housing price growth, we

follow Engel, Hayes, and Wang (2007), and interact Siaz (2010)’s housing supply

elasticity with 10-year borrowing costs by taking advantage of the fact housing prices in

areas with geographic constraints on housing supply are likely to be more responsive to

national changes in borrowing costs. In addition, we introduce change in education as a

second instrument for housing price growth.

We reproduce our results using a two-stage least square approach. The F-statistics

in the first-stage regression are very high (p-value = 0.000 in all cases), and the Hansen

J-test fails to reject the orthogonality condition (for example, the p-values are between

0.11 and 0.61 for all cost of equity measures), which suggests that the instruments are

both valid and adequate. We tabulate the results in Table 10. To save space, we only

tabulate the key statistics, although the regression specifications include our usual

control variables. The results are similar to those reported in Table 4 that housing price

growth holds statistically and economically significant.

D.3. Additional controls

In Table 11 we control for additional variables that potentially relate to the cost of

equity, including state-level demographics and religiosity, and firm-level institutional

ownership, analyst coverage, and illiquidity.

Demographics: In a recent study, Calomiris, Longhofer and Miles (2012) show that

demographic and wealth characteristics of the population influence housing wealth

effects. We collect demographic data on population, education, senior, male-to-female

25

ratios, income, minority ratios, and marriage ratios at the state level from the 1980, 1990,

and 2000 U.S. Census. Population is the total population of that state where the firm is

located. Education is defined as the population finishing a bachelor's degree or higher in

a state divided by the total population of that state in which the firm is located. The

male-to-female ratio is defined as the population of males living in a state divided by the

population of females of that state in which the firm is located. Income is defined as the

median of household income of that state in which the firm is located. The minority ratio

is defined as the population of minorities living in a state divided by the population of

that state in which the firm is located. The marriage ratio is defined as the population of

marriage people living in a state divided by the population of that state in which the firm

is located. We use linear interpolations of Census data in off-Census years between 1980

and 2000 and use extrapolations for years after 2000. Model (1) in Table 10 presents the

results after controlling for various state-level demographic variables and shows that

the housing effect we find in Table 4 is not due to other state-level demographic

characteristics.

Religion: An emerging literature examines the effect of religion on corporate and

investor behavior. Prior research suggests a link between individual religiosity and risk

aversion (Miller and Hoffmann, 1995; Osoba 2004). Hilary and Hui (2009) find that

firms located in counties with higher levels of religiosity display lower degrees of risk

exposure, as measured by variances in equity returns or returns on assets. Fang and Lai

(1997) use religious background as a proxy for gambling propensity. Religion is also

documented to have an impact on financial reporting (Campbell and Hentschel (1992))

and corporate misbehavior (Jaffe and Westerfield (1985)). Specifically, El Ghoul,

Guedhami, Ni, Pittman, and Saadi (2012) finds that firms located in more religious

counties exhibit lower costs of equity. It is possible that the religiosity of local investors

is related to both housing price growth and cost of equity; thus, our housing price

growth variable is capturing the effect of religion on cost of equity. To explore this

26

possibility, we control for religion, as measured by the number of churches in the state,

CHU, which has been commonly used in earlier studies on religion. Church is defined

as the number of churches in the state to the total population in that state in which the

firm is located. Information on religiosity at the state level is obtained from the

American Religion Data Archive (ARDA) and is available for 1971, 1980, 1990, and 2000.

We linearly interpolate the data to obtain the values in the missing years. We predict

that religiosity have a negative impact on local firms’ cost of equity. We find strong

results to support this prediction (Model (2) in Table 10). The coefficient on CHU is

negative and highly significant. Consistent with El Ghoul et al. (2012), the result

indicates that firms located in areas in which investors have strong religious

background have lower cost of equity. After controlling for religion, our housing price

growth measure remains negative and significant.

Collectively, our conclusion holds in various endogeneity tests. The evidence from

Tables 8-10 supports our prediction that growth in housing price has a positive effect on

cost of equity capital.

Institutional Ownership: Institutional ownership is associated with less information

asymmetry and better monitoring (e.g., Bushee (1998), Yan and Zhang (2009)). In

contrast to dispersed shareholders, large institutional investors have the incentives,

resources, and ability to closely monitor managers, reducing the agency costs that all

shareholders experience (e.g., McConnell and Servaes (1990), Cremers and Nair (2005)).

Gaspar and Massa (2007) find that local institutional ownership translates into better

monitoring, although firms’ stock liquidity suffers. We control for this form of

monitoring by including the percentage ownership of institutions investing in the firm,

which we label IO, according to the Thomson Financial 13F database.19 In Table 10

19 All of our core evidence is very similar when we replace IO with the equity stake held by public pension

funds that tend to be more active shareholders (Cremers and Nair (2005)).

27

Model (3), institutional ownership loads negatively, consistent with prior research

without qualitatively affecting our primary evidence on HPG1 that U.S. public firms

have lower equity financing costs when the states in which they are located experience

high housing price appreciation.

Long-term Institutional Ownership: Investment horizons of institutional investors

influence firm’s agency costs. Attig, Cleary, El Ghoul, and Guedhami (2013) show that

long-term institutional investors are associated with smaller firm’s cost of equity than

short-term institutional investors as long-term investors exert better corporate

governance. We include long-term institutional ownership as robustness checks. 20

Consistent with Attig et al. (2013), we find firms held by long-term institutional

investors have lower cost of equity in Model (4). After controlling for investment

horizon, firms located in states with high housing price growth show significantly

lower levels of cost of equity.

Illiquidity: Several papers document a positive relation between illiquidity and

average stock returns (e.g., Amihud (2002), Acharya and Pedersen (2005), Sadka (2006)).

In Table 10, we investigate this issue in Model (5) by introducing a widely used

measure of illiquidity proposed by Amihud (2002), and construct it as the average over

the fiscal year of the square root of the ratio of daily absolute stock return to the

corresponding daily dollar volume.21 The results reinforce that our earlier evidence

20 Following Gaspar, Massa, and Matos (2005), we classify institutional investors into short-term and long-

term investors on the basis of their portfolio turnover over the past four quarters. Long-term institutional

ownership is computed as the number of shares held by long-term institutional investors divided by total

shares outstanding.

21 In untabulated results, we find that our conclusions hold when we replace Amihud’s illiquidity

measure with Lesmond, Ogden, and Trzcinka, (1999) measure of transaction costs, defined as the

28

linking housing price appreciation to their cost of equity capital does not reflect

illiquidity. More specifically, the coefficient on HPG1 remains negative and highly

significant (t-statistic = 4.714) after controlling for illiquidity which is statistically

significant in our case. Relative to our basic regression in Table 4, the magnitude and

statistical significance of distance remains quite stable after controlling for illiquidity.

Analyst Coverage: Similar to institutional ownership, analyst coverage can influence

corporate governance by improving external monitoring. Extant research finds that

financial analysts produce and transmit valuable information to investors (e.g., Chung

and Jo (1996)), strengthening the monitoring of managers (Jensen and Meckling (1976),

Healy and Palepu (2001)). We predict that equity financing costs will be decreasing in

ANA, which is the number of analysts providing earnings forecasts for the firm in

I/B/E/S. Results from Model (6) indicate that, whereas lower equity financing costs

ensue with more analyst coverage, the addition of this variable fails to overturn the role

of housing prices being negative and statistically significant at the 1% level.


VI. Conclusion

Building on recent research documenting that changes in housing prices influence

demand for stocks, we examine whether growth housing prices influences a firm’s cost

of capital. We hypothesize that growth in local housing prices leads to lower risk

premium on local stocks, thereby leading to lower cost of equity capital. We test our

prediction by analyzing the cross-regional association between growth in housing

prices and the cost of equity in the U.S. market over the period 1985-2008. Consistent

with our prediction, we document that firms located in states with high growth rates of

percentage of trading days with zero returns during the fiscal year, and Roll’s (1984) illiquidity measure

computed as the average bid-ask spread over the previous year.

29

housing prices exhibit significantly lower cost of equity capital. Our findings are robust

across different implied cost of capital models, to various measures of growth in

housing prices, and to a variety of alternate specifications. Our conclusion also holds

after accounting for potential endogeneity of housing prices, and after controlling for

liquidity of firm's real assets, overall asset liquidity, and state economic activities.

This study has several implications. First, there should be a negative impact of

growth housing prices on cost of equity capital. Second, there should be a positive

spread of cost of equity capital between firms located in areas with high growth in

housing prices and firms located in areas with low (or negative) growth in housing

prices. A third broad implication is that firm location is a determinant of a firm’s cost of

capital. Finally, this study adds a new dimension (i.e. cost of financing) to the growing

literature examining the implications of growth in housing prices on household

consumption, portfolio choice and stock prices.

30

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40

Appendix A. Models of Cost of Equity Capital

In this appendix, we describe the cost of equity models used in this paper. We start by defining variables

and specifying assumptions common to all models. We then successively cover each model and

its assumptions.

Common Variables and Assumptions

= stock price in June in year t

= actual dividend per share in year t - 1

= actual earnings per share in year t - 1

= long-term growth forecast in June in year t

= forecasted earnings per share for year t + τ recorded in June in year t

= book value per share at the beginning in year t

= yield on a ten-year Treasury note in June in year t

As explained in the text, we require firms to have positive one-year-ahead ( ) and

two-year-ahead ( ) earnings forecasts, as well as a long-term growth forecast ( ).

However, two models call for the use of earnings forecasts beyond year two. If a forecast is not

available in I/B/E/S, we impute it from the previous year’s forecast and the long-term growth

forecast, ( ).

Model (1): Ohlson and Juettner-Nauroth (2005)

The model is a generalization of the Gordon constant growth model. It allows share price to be

expressed in terms of the one-year-ahead earnings forecast and the near-term and perpetual

growth forecasts. The explicit forecast horizon is set to one year, after which forecasted earnings

grow at a near-term rate that decays to a perpetual rate. We follow Gode and Mohanram’s

(2003) implementation of the model. The near-term earnings growth rate is the average of i) the

percentage difference between two-year-ahead and one-year-ahead earnings forecasts; and ii)

the I/B/E/S long-term growth forecast. The perpetual growth rate is the expected inflation rate.

41

Dividend per share is assumed to be constant. The model requires positive one- and

two-year-ahead earnings forecasts. The valuation equation is given by

√

( ( )),

(A1)

where:

(( )

),

,

,

, and

( ) .

Model (2): Easton (2004)

This model is a generalization of the price-earnings-growth (PEG) model and based on Ohlson

and Juettner-Nauroth (2005). It allows share price to be expressed in terms of one-year-ahead

expected dividend per share, plus one- and two-year-ahead earnings forecasts. The explicit

forecast horizon is set to two years, after which forecasted abnormal earnings grow in

perpetuity at a constant rate. The model requires positive one- and two-year-ahead earnings

forecasts, as well as positive change in earnings forecast. The valuation equation is given by

, (A2)

Where .

Model (3): Claus and Thomas (2001)

This model assumes clean surplus accounting (Ohlson, 1995), allowing share price to be

expressed in terms of forecasted residual earnings and book values. The explicit forecast

horizon is set to five years, beyond which forecasted residual earnings grow at the expected

inflation rate, and dividend payout is assumed to be constant at 50%. The valuation equation is

given by

42

∑

( )

( )

( )( ) ,

(A3)

where

,

( ),

, and

.

Model (4): Gebhardt, Lee, and Swaminathan (2001)

This model also assumes clean surplus accounting, allowing share price to be expressed in

terms of forecasted returns on equity (ROE) and book values. The explicit forecast horizon is set

to three years, beyond which forecasted ROE decays to the median industry ROE by the twelfth

year and remains constant thereafter. Dividend payout is again assumed to be constant. The

valuation equation is given by

∑ ( )

( ) , (A4)

where

= forecasted return on equity for year t+τ,

( ), and

= expected dividend payout ratio in year t+τ.

For the first three years, is set equal to ⁄ . Beyond the third year,

fades linearly to the industry median by the twelfth year. Industries are defined according

to the Fama and French (1997) classification, and the median industry is calculated over

the past ten years, excluding loss firms.

The expected dividend payout ratio is set equal to ⁄ . If is negative, it is

replaced by the value implied by a 6% return on assets (the long-run return on assets in the

U.S.). We winsorize payout ratios at zero and one.

43

Alternate models

We also consider alternate models of the cost of equity.

Gordon Finite Horizon model

This model assumes that dividends grow over an explicit forecasting horizon set to four years,

beyond which the firm’s return on equity reverts to the expected cost of equity capital. The

valuation equation is given by

∑

( )

( )

( ) ,

(A5)

where

( ) , and

( )

.

Price-Earnings-Growth (PEG) ratio

This is a special case of the Easton (2004) model, which assumes no dividend payments. There

are two versions of the model. One is based on short-term earnings forecasts and the other on

long-term earnings forecasts. The valuation equations are given by

,

and

(A6)

.

(A7)

Earnings-Price (EP) ratio

This is a special case of the Easton (2004) model, which assumes that abnormal earnings growth

is set to zero. The EP ratio is given by

. (A8)

44

Appendix B. Regression Variable Definitions and Data Sources

Variable Definition Source

Panel A: Dependent variables

rOJN

Implied equity premium, defined as the cost of equity derived

from the Ohlson and Juttner-Nauroth (2005) model and

estimated in June of each year minus the rate on a ten-year

treasury note

Authors’ calculations based

on I/B/E/S and Compustat

data

rMPEG

Implied cost of equity premium, defined as the cost of equity

derived from the Easton (2004) model and estimated in June of

each year minus the rate on a ten-year treasury note

As above

rCT


derived from the Claus and Thomas (2001) model and estimated

in June of each year minus the rate on a ten-year treasury note

As above

rGLS


derived from the Gebhardt, Lee and Swaminathan (2001) model

and estimated in June of each year minus the rate on a ten-year

treasury note

As above

rAVG Average of rOJN, rMPEG, rCT, and rGLS As above

Panel B: Independent variables

HPG1 Growth rate in housing prices in the state in which the firm is

located measured over current year


on Federal Housing Finance

Agency (FHFA) data


located measured over the preceding two years

As above

45


located measured over the preceding three years

As above


located measured over the preceding four years

As above

HPRICE Level of housing prices in the state in which the firm is located

measured over current year

As above

HDPI Housing/DPI Ratio, defined as the ratio of housing prices to

disposable personal income in the state in which the firm is

located


on U.S. Department of

Commerce, Bureau of

Economic Analysis, and

FHFA data

Lag(HPRICE) One-year lagged housing prices in the state in which the firm is

located


on FHFA data

∆HPRICE Change in housing prices in the state in which the firm is located

measured over the previous years

As above

BETA Market beta obtained from regressions of firms’ monthly excess

stock returns on the corresponding CRSP value-weighted index

excess returns, using at least 24, and up to 60, months and

ending in June of each year. Excess returns are monthly returns

minus the one-month Treasury bill rate


on CRSP data

BTM Book value to the market value of equity. Book value is defined

as the book value of shareholders’ equity plus deferred taxes

and investment tax credits (if available) minus the book value of

preferred stock. Depending on data availability, the book value

of preferred stock is defined, in the following order, as the


on Compustat data

46

redemption, liquidation, or par value

SIZE Natural logarithm of total assets in $ million As above

LEV Leverage ratio defined as the ratio of long-term debt to total

assets

As above

LTG Average long-term growth forecast reported in June in year t I/B/E/S

DISP Dispersion of analyst forecasts defined as the coefficient of

variation of one-year-ahead analyst forecasts of earnings per

share in June in year t


on I/B/E/S data

FBIAS Signed forecast error defined as the difference between the

one-year-ahead consensus earnings forecast and realized

earnings deflated by June-end stock price

As above

RET6 Compound stock returns over the past six months Authors’ calculations based

on CRSP data

NoPotBuyer Number of potential buyers measured as the number of rival

firms in the industry with debt ratings.


on Compustat

ALiq1 (Cash & Eq./Total Assets)*1+(other Assets/Total Assets)*0 Compustat

ALiq2 (Cash & Eq./Total Assets)*1+(Non-Cash CA Assets/Total

Assets)*0.5+(other Assets/Total Assets)*0

Compustat

ALiq3 (Cash & Eq./Total Assets)*1+(Non-Cash CA Assets/Total

Assets)*0.75+(Tangible Fixed Assets/Total Assets)*0.5+(other

Assets/Total Assets)*0

Compustat

ALiq4 (Cash & Eq./Market Assets)*1+(Non-Cash CA Assets/Market

Assets)*0.75+(Tangible Fixed Assets/Market Assets)*0.5+(other

Assets/Market Assets)*0

Compustat

47

PPENT Property, Plant, and Equipment Net Total Compustat

PPENT0 Property, Plant, and Equipment Net Total in the reference year

t=0

Compustat

HPRICE_PPENT0 Interaction of level of housing prices and Property, Plant, and

Equipment Net Total in the reference year t=0

Compustat

GDPG1 Growth rate in GDP per capita in the state in which the firm is

located in the preceding one year


on U.S. Department of

Commerce and Bureau of

Economic Analysis data

DPIG1 Growth rate in disposable personal income in the state in which

the firm is located in the preceding one year

As above

DIFF_HPG_DPI Difference between HPG1 and DPIG1 Federal Housing Finance

Agency (FHFA), as above

Elasticity ×

Borrowing Cost

Saiz (2010)’s land-topology based measure of housing supply

elasticity interacted 10-year interest rate.

Saiz (2010)

Change in

Education

Change in Education is defined as the change in the ratio of the

population finishing a bachelor's degree or higher in a state to

the total population of that state where the firm is located

(Becker, Ivkovich, and Weisbenner (2011)).

POPU Total population of the state in which the firm is located U.S. Census

EDUC Ratio of the population finishing a bachelor’s degree or higher

divided by the total population of the state in which the firm is

located

As above

MFR Ratio of male population to female population of the state in

which the firm is located

As above

48

INC INC is the median income in the state in which the firm is located As above

MINO MINO is the ratio of the minority population to the total

population in the state in which the firm is located

MARR Ratio of the population that are married to the total population

of the state in which the firm is located

As above

CHU Ratio of the number of churches to the total population in the

country in which the firm is located

American Religion Data

Archive (ARDA)

IO Percentage ownership of institutional investors Authors’ calculations based

on Thomson 13-F data

LTIO Percentage ownership of long-term institutional investors As above

ILLIQ Average over the fiscal year of the square root of the ratio of

daily absolute stock return to the corresponding daily dollar

volume


on CRSP data

ANA Number of analysts who follow the firm I/B/E/S

49

Table 1. Sample Breakdown by Industry and Year

Industry N % Industry N %

Agriculture 116 0.26 Shipping Containers 196 0.44

Food Products 734 1.64 Transportation 1,269 2.84

Candy and Soda 73 0.16 Wholesale 1,342 3.00

Beer and Liquor 154 0.34 Retail 3,038 6.80

Tobacco Products 31 0.07 Restaurants, Hotels, and Motels 817 1.83

Recreation 253 0.57 Banking 5,303 11.87

Entertainment 536 1.20 Insurance 2,051 4.59

Printing and Publishing 491 1.10 Real Estate 66 0.15

Consumer Goods 873 1.95 Trading 1,089 2.44

Apparel 588 1.32 Almost Nothing 352 0.79

Healthcare 782 1.75 Total 44,678 100

Medical Equipment 1,153 2.58

Pharmaceutical Products 1,133 2.54 Year N %

Chemicals 1,008 2.26 1985 1,401 3.14

Rubber and Plastic Products 323 0.72 1986 1,437 3.22

Textiles 319 0.71 1987 1,431 3.20

Construction Materials 854 1.91 1988 1,377 3.08

Construction 463 1.04 1989 1,481 3.31

Steel Works Etc 607 1.36 1990 1,584 3.55

Fabricated Products 118 0.26 1991 1,535 3.44

Machinery 1,507 3.37 1992 1,562 3.50

Electrical Equipment 559 1.25 1993 1,639 3.67

Automobiles and Trucks 778 1.74 1994 1,964 4.40

Aircraft 260 0.58 1995 2,119 4.74

Shipbuilding and Railroad Equipment 140 0.31 1996 2,375 5.32

Defense 102 0.23 1997 2,387 5.34

Precious Metals 81 0.18 1998 2,490 5.57

Nonmetallic and Industrial Metal Mining 127 0.28 1999 2,402 5.38

Coal 59 0.13 2000 2,136 4.78

Petroleum and Natural Gas 1,388 3.11 2001 1,767 3.95

Utilities 2,512 5.62 2002 1,794 4.02

Communication 851 1.90 2003 1,782 3.99

Personal Services 485 1.09 2004 2,025 4.53

Business Services 3,925 8.79 2005 2,028 4.54

Computers 1,759 3.94 2006 2,045 4.58

Electronic Equipment 2,440 5.46 2007 2,033 4.55

Measuring & Control Equipment 874 1.96 2008 1,884 4.22

Business Supplies 699 1.56 Total 44,678 100

This table presents the industry (according to the Fama and French 48 industry group affiliations) and calendar year

distributions for the 44,678 firm-year observations comprising the sample between 1985 and 2008.

50

Table 2. Descriptive Statistics and Correlation Coefficients for Implied Equity Premium Estimates

Panel A. Descriptive Statistics

Variable Mean Q1 Median Q3 St. Dev.

rOJN 6.23 4.18 5.59 7.56 3.32

rMPEG 6.22 3.35 5.19 7.85 4.72

rCT 4.08 2.44 3.62 5.12 3.18

rGLS 3.66 2.01 3.58 5.19 2.66

rAVG 5.05 3.20 4.53 6.25 2.90

1985 4.31 2.20 3.47 5.57 3.30

1986 4.55 2.59 3.92 5.69 3.04

1987 4.02 2.27 3.54 5.13 2.64

1988 4.20 2.35 3.59 5.27 2.95

1989 4.27 2.58 3.75 5.36 2.70

1990 4.70 2.47 3.87 5.96 3.40

1991 4.57 2.44 3.80 5.91 3.17

1992 5.36 3.34 4.67 6.69 3.09

1993 5.56 3.75 5.09 6.66 2.66

1994 4.82 3.09 4.27 5.87 2.63

1995 5.40 3.75 4.94 6.51 2.56

1996 4.31 2.70 3.92 5.52 2.43

1997 4.46 2.87 3.93 5.50 2.55

1998 5.20 3.31 4.60 6.43 2.84

1999 5.28 3.15 4.76 6.71 3.23

2000 5.81 3.41 5.33 7.44 4.01

2001 5.32 3.41 4.78 6.51 3.10

2002 5.66 3.92 5.05 6.67 2.75

2003 6.54 4.92 6.09 7.59 2.52

2004 5.01 3.68 4.62 5.96 2.17

2005 5.39 4.13 5.04 6.26 2.04

2006 4.81 3.47 4.41 5.62 2.21

2007 4.38 3.07 4.05 5.21 2.10

2008 6.53 4.49 5.80 7.68 3.30

Panel B. Correlation Coefficients

rOJN rMPEG rCT rGLS rAVG

rOJN 1.00

rMPEG 0.87 1.00

rCT 0.62 0.46 1.00

rGLS 0.52 0.49 0.52 1.00

rAVG 0.93 0.89 0.76 0.72 1.00

This table presents the cost of equity premium estimates’ distribution statistics and correlation coefficients

for the 44,678 firm-year observations comprising the sample between 1985 and 2008. Panel A provides the

mean, first quartile, median, third quartile, and standard deviation. Panel B shows Pearson pair-wise

51

correlations. rAVG is the average implied cost of equity premium obtained from four models developed by

Ohlson and Juettner-Nauroth (2005), Easton (2004), Claus and Thomas (2001), and Gebhardt, Lee, and

Swaminathan (2001), which we denote as rOJ, and rES, rCT, and rGLS, respectively. Appendix A provides details

on the implementation of the four models. All correlation coefficients are significant at the 1% level.

52

Table 3. Descriptive Statistics and Correlation Coefficients for Regression Variables

Panel A: Descriptive Statistics

Mean Q1 Median Q3 St. Dev.

HPG1 0.05 0.02 0.04 0.07 0.06

BETA 1.09 0.61 1.01 1.43 0.67

BTM 0.57 0.32 0.50 0.75 0.35

SIZE 6.70 5.34 6.60 7.90 1.87

LEV 0.21 0.06 0.19 0.33 0.17

LTG 16.44 10.67 14.43 20.00 9.10

DISP 0.09 0.02 0.04 0.09 0.18

Panel B: HPG1 by State

State Mean Q1 Median Q3 St. Dev. State Mean Q1 Median Q3 St. Dev.

AK 0.04 0.02 0.04 0.09 0.08 MT 0.05 0.02 0.05 0.08 0.04

AL 0.04 0.03 0.04 0.05 0.02 NC 0.04 0.03 0.04 0.05 0.02

AR 0.03 0.03 0.04 0.05 0.02 ND 0.04 0.03 0.04 0.05 0.03

AZ 0.05 0.04 0.05 0.06 0.08 NE 0.04 0.03 0.04 0.05 0.02

CA 0.06 -0.01 0.07 0.13 0.10 NH 0.05 0.01 0.05 0.09 0.07

CO 0.05 0.02 0.05 0.08 0.04 NJ 0.06 0.00 0.05 0.11 0.07

CT 0.04 -0.01 0.03 0.09 0.07 NM 0.04 0.01 0.04 0.06 0.04

DE 0.05 0.01 0.04 0.08 0.05 NV 0.03 0.01 0.03 0.05 0.09

FL 0.05 0.03 0.04 0.10 0.09 NY 0.05 0.01 0.05 0.11 0.06

GA 0.04 0.03 0.05 0.06 0.02 OH 0.04 0.03 0.04 0.05 0.02

HI 0.05 -0.02 0.05 0.09 0.09 OK 0.03 0.02 0.04 0.05 0.03

IA 0.04 0.03 0.05 0.05 0.02 OR 0.06 0.04 0.06 0.09 0.05

ID 0.05 0.02 0.05 0.07 0.05 PA 0.05 0.02 0.04 0.07 0.04

IL 0.05 0.03 0.04 0.06 0.03 RI 0.06 -0.01 0.04 0.11 0.08

IN 0.04 0.03 0.04 0.05 0.01 SC 0.04 0.03 0.04 0.05 0.02

KS 0.04 0.02 0.04 0.04 0.02 SD 0.04 0.03 0.04 0.06 0.02

KY 0.04 0.03 0.04 0.05 0.01 TN 0.04 0.03 0.05 0.05 0.02

LA 0.04 0.03 0.05 0.06 0.03 TX 0.03 0.01 0.03 0.05 0.03

MA 0.05 -0.01 0.05 0.11 0.07 UT 0.05 0.03 0.05 0.07 0.05

MD 0.06 0.01 0.03 0.10 0.07 VA 0.06 0.01 0.06 0.09 0.06

ME 0.05 0.01 0.04 0.09 0.06 VT 0.05 0.01 0.03 0.08 0.04

MI 0.04 0.04 0.06 0.07 0.04 WA 0.06 0.04 0.05 0.06 0.05

MN 0.05 0.03 0.04 0.07 0.03 WI 0.05 0.04 0.05 0.05 0.02

MO 0.04 0.02 0.04 0.05 0.02 WV 0.04 0.02 0.04 0.05 0.02

MS 0.04 0.03 0.04 0.05 0.02 WY -0.04 -0.04 -0.04 -0.04 .

Panel C: Correlation Coefficients

rAVG HPG1 BETA BTM SIZE LEV LTG DISP

rAVG 1.00

HPG1 -0.03 1.00

BETA 0.09 -0.03 1.00

53

BTM 0.26 -0.04 -0.15 1.00

SIZE -0.11 -0.01 -0.21 0.13 1.00

LEV 0.12 -0.02 -0.15 0.17 0.24 1.00

LTG 0.21 0.05 0.35 -0.30 -0.45 -0.19 1.00

DISP 0.29 -0.03 0.14 0.15 -0.13 0.06 0.11 1.00

This table presents summary statistics and correlation coefficients between control variables for the 44,678

firm-year observations comprising the sample between 1985 and 2008. Appendix B outlines definitions and

data sources for the regression variables. Panel A provides mean, first quartile, median, third quartile, and

standard deviation of independent variables in baseline specification. Panel B presents mean, first quartile,

median, third quartile, and standard deviation of HPG1 by state. Panel C shows pair-wise correlations. All

correlation coefficients are significant at the 1% level.

54

Table 4. Results of Regressing the Implied Equity Premium on Housing Price Growth

Variable

Prediction Clustering

by Firm Fama-MacBeth Newey-West Prais-Winsten

Firm Fixed Effects

Firm Random Effects

(1) (2) (3) (4) (5) (6)

HPG1 - -1.351*** -1.845*** -1.351*** -1.397*** -1.556*** -1.535***

(-4.599) (-2.962) (-4.528) (-4.822) (-6.652) (-6.818)

BETA + 0.068** 0.160*** 0.068** 0.051** 0.000 0.013

(2.340) (3.935) (2.566) (2.128) (0.017) (0.567)

BTM + 2.651*** 2.388*** 2.651*** 2.139*** 2.202*** 2.330***

(40.070) (20.937) (44.453) (48.814) (48.738) (56.065)

SIZE - -0.159*** -0.149*** -0.159*** -0.156*** 0.083*** -0.117***

(-10.834) (-5.196) (-13.489) (-14.336) (3.472) (-7.731)

LEV + 3.084*** 2.967*** 3.084*** 3.031*** 2.793*** 3.082***

(23.247) (21.300) (26.731) (31.934) (24.524) (31.502)

LTG + 0.085*** 0.083*** 0.085*** 0.093*** 0.090*** 0.089***

(27.457) (16.714) (29.432) (56.143) (50.773) (55.298)

DISP + 3.371*** 3.429*** 3.371*** 3.130*** 3.034*** 3.067***

(24.476) (17.256) (26.137) (49.944) (45.037) (48.969)

INTERCEPT ? 3.073*** 1.413*** 3.073*** 3.333*** 2.508*** 3.254***

(12.123) (3.087) (13.808) (15.743) (12.699) (10.030) Industry effects

Yes Yes Yes Yes No Yes

Year effects Yes No Yes Yes Yes Yes N 44,678 44,678 44,678 44,678 44,678 44,678 Adj. R2 0.337 0.373 0.337 0.370 0.258

This table reports results from regressing the implied equity premium (rAVG) on the one-year housing

price growth (HPG1) and controls over the period 1985-2008. rAVG is the average implied cost of equity

premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004),

Claus and Thomas (2001), and Gebhardt, Lee, and Swaminathan (2001). Appendix A provides details on

the implementation of the four models. Appendix B outlines definitions and data sources for the

regression variables. Unreported industry controls are based on the Fama and French (1997) industry

classification. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

55

Table 5. Results of Regressing the Implied Equity Premium on Alternative Proxies of Housing Price Growth

Variable Prediction HPG4 HPG3 HPG2 HPRICE HDPI

(1) (2) (3) (4) (5)

HPG4 - -0.403*** (-3.960) HPG3 - -0.562*** (-4.596) HPG2 - -0.782*** (-4.758) HPRICE - -0.740*** (-3.744) HDPI - -18.375** (-2.495) BETA + 0.070** 0.070** 0.069** 0.076*** 0.072** (2.386) (2.392) (2.375) (2.585) (2.459) BTM + 2.653*** 2.651*** 2.651*** 2.655*** 2.656*** (40.038) (40.028) (40.038) (40.090) (40.098) SIZE - -0.159*** -0.159*** -0.159*** -0.157*** -0.158*** (-10.823) (-10.826) (-10.832) (-10.690) (-10.737) LEV + 3.082*** 3.082*** 3.083*** 3.076*** 3.079*** (23.244) (23.239) (23.241) (23.235) (23.237) LTG + 0.084*** 0.085*** 0.085*** 0.084*** 0.084*** (27.386) (27.422) (27.447) (27.372) (27.353) DISP + 3.375*** 3.373*** 3.372*** 3.384*** 3.381*** (24.505) (24.495) (24.483) (24.586) (24.541) INTERCEPT ? 3.189*** 3.140*** 3.100*** 3.427*** 3.339*** (12.566) (12.390) (12.237) (13.088) (12.824) Industry effects Yes Yes Yes Yes Yes Year effects Yes Yes Yes Yes Yes N 44,678 44,678 44,678 44,678 44,678 Adj. R2 0.337 0.337 0.337 0.337 0.337

This table reports results from regressing the implied equity premium (rAVG) on the alternative proxies of

housing price growth and controls over the period 1985-2008. rAVG is the average implied cost of equity

premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004),

Claus and Thomas (2001), and Gebhardt, Lee, and Swaminathan (2001). Appendix A provides details on

the implementation of the four models. Appendix B outlines definitions and data sources for the regression

variables. Unreported industry controls are based on the Fama and French (1997) industry classification.

Robust t-statistics adjusted for clustering by firm are reported inside the parentheses. ***, **, and * denote

statistical significance at the 1%, 5%, and 10% levels, respectively.

56

Table 6. Results of Regressing Individual and Alternative Implied Equity Premium Estimates on Housing Price Growth

Variable Prediction

Individual Implied Equity Premium

Estimates

Finite Horizon Gordon Model

Price-Earnings-Growth

(PEG)-Short-Term

Price-Earnings-Growth

(PEG)-Long-Term

Dividend

Yield

rOJN rMPEG rCT rGLS

(1) (2) (3) (4) (5) (6) (7) (8)

HPG1 - -1.410*** -1.941*** -1.539*** -0.513** -1.703*** -1.588*** -1.542*** -0.520*

(-4.208) (-3.937) (-4.649) (-2.092) (-4.379) (-3.525) (-3.732) (-1.684)

BETA + 0.016 0.269*** -0.253*** 0.242*** -0.277*** 0.540*** -0.248*** -0.454***

(0.481) (6.047) (-7.512) (9.816) (-7.768) (12.387) (-5.538) (-17.670)

BTM + 2.242*** 3.052*** 1.251*** 4.061*** 2.754*** 2.860*** 2.581*** 0.334***

(31.028) (29.370) (14.727) (67.714) (32.394) (29.935) (30.638) (4.840)

SIZE - -0.153*** -0.249*** -0.073*** -0.162*** -0.066*** -0.345*** -0.188*** 0.182***

(-9.302) (-10.983) (-4.394) (-11.614) (-3.482) (-18.095) (-10.597) (9.846)

LEV + 3.292*** 4.401*** 2.866*** 1.777*** 3.248*** 4.161*** 3.418*** 0.245

(22.770) (22.012) (17.741) (14.545) (19.798) (22.591) (20.696) (1.638)

LTG + 0.119*** 0.068*** 0.134*** 0.018*** 0.142*** 0.093*** 0.469*** -0.042***

(35.284) (16.461) (31.575) (7.675) (30.745) (23.770) (65.962) (-16.737)

DISP + 4.523*** 9.533*** -0.826*** 0.255*** -0.604*** 9.219*** -0.744*** 0.539***

(28.385) (39.175) (-5.155) (2.879) (-4.110) (40.451) (-4.651) (4.618) INTERCEPT ? 3.428*** 3.958*** 1.482*** 3.424*** 0.132 3.744*** -0.440 0.254 (11.802) (10.502) (5.182) (13.285) (0.423) (10.437) (-1.294) (0.985) Industry effects

Yes Yes Yes Yes Yes Yes Yes Yes

Year effects Yes Yes Yes Yes Yes Yes Yes Yes N 44,678 44,678 44,678 44,678 44,678 44,678 44,678 44,678 Adj. R2 0.324 0.335 0.186 0.464 0.266 0.419 0.632 0.312

This table reports results from regressing individual implied equity premium estimates (Models (1)–(4)) and alternate implied equity premium

estimates (Models (5)–(8)) on the one-year housing price growth (HPG1) and controls over the period 1985-2008. We estimate the cost of equity

capital from applications developed by Claus and Thomas (2001) in Model (1), Gebhardt, Lee, and Swaminathan (2001) in Model (2), Ohlson

and Juettner-Nauroth (2005) in Model (3), Easton (2004) in Model (4), the finite horizon Gordon model in Model (5), the risk premium implied

by the price-earnings-growth (PEG) ratio based on one- and two-year-ahead earnings forecasts in Model (6) and four- and five-year-ahead

earnings forecasts in Model (7), and the dividend yield in Model (8). Appendix A provides details on the implementation of the implied equity

57

premium models. Appendix B outlines definitions and data sources for the regression variables. Unreported industry controls are based on the

Fama and French (1997) industry classification. Robust t-statistics adjusted for clustering by firm are reported inside the parentheses, and ***,

**, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

58

Table 7. Robustness to Noise in Analyst Forecasts

FBIAS less than jth percentile LTG less than jth percentile January Stock Price Variable

Prediction

FBIAS j=95% j=90% j=75% j=50% j=95% j=90% j=75% j=50% RET6

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

HPG1 + -0.865*** -0.896*** -0.892*** -0.986*** -1.296*** -1.277*** -1.344*** -1.370*** -1.644*** -1.095*** -0.634** (-3.067) (-3.271) (-3.311) (-3.647) (-3.903) (-4.502) (-4.646) (-4.334) (-4.042) (-3.818) (-2.135) BETA + 0.061** 0.078*** 0.075*** 0.064** 0.069** 0.164*** 0.200*** 0.216*** 0.214*** 0.092*** -0.000 (2.170) (2.747) (2.695) (2.261) (2.142) (5.797) (6.804) (6.325) (4.531) (3.132) (-0.001) BTM + 2.332*** 2.544*** 2.533*** 2.523*** 2.560*** 2.498*** 2.432*** 2.299*** 2.211*** 2.814*** 3.214*** (36.982) (40.200) (40.125) (38.266) (34.347) (37.167) (35.757) (31.427) (24.840) (42.329) (44.862) SIZE - -0.132*** -0.148*** -0.136*** -0.111*** -0.117*** -0.150*** -0.136*** -0.097*** -0.014 -0.175*** -0.173*** (-9.435) (-10.722) (-10.502) (-8.920) (-8.532) (-10.334) (-9.315) (-6.238) (-0.785) (-11.747) (-10.694) LEV + 2.633*** 2.708*** 2.472*** 2.226*** 2.310*** 2.994*** 2.975*** 2.803*** 2.739*** 3.251*** 3.298*** (20.852) (21.119) (19.840) (17.738) (15.847) (22.795) (22.258) (19.336) (14.942) (24.383) (24.386) LTG ? 0.080*** 0.075*** 0.072*** 0.063*** 0.060*** 0.073*** 0.075*** 0.071*** 0.071*** 0.092*** 0.098*** (26.745) (24.590) (23.223) (19.887) (16.614) (20.139) (18.036) (12.307) (7.596) (30.931) (29.217) DISP + 2.305*** 2.735*** 2.521*** 2.403*** 2.720*** 3.601*** 3.698*** 4.017*** 4.257*** 2.811*** 2.018*** (17.479) (18.373) (15.177) (11.775) (11.243) (25.707) (26.069) (25.305) (21.095) (20.925) (15.779) FBIAS + 20.600*** (33.614) RET6 - -2.626*** (-52.097) INTERCEPT ? 2.845*** 2.915*** 2.907*** 2.762*** 2.607*** 3.156*** 2.969*** 2.862*** 2.222*** 2.918*** 2.612*** (13.080) (13.603) (13.892) (13.454) (11.271) (12.421) (11.343) (10.173) (5.254) (11.503) (9.608) Industry effects Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Year effects Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes N 42,828 40,686 38,546 32,121 21,414 42,432 40,178 32,994 22,332 44,678 44,447 Adj. R2 0.403 0.329 0.326 0.329 0.340 0.329 0.335 0.355 0.364 0.397 0.356

This table examines the robustness of the results of Model (1), Table 4 to noise in analyst forecasts. The dependent variable, rAVG, is the average implied cost of

equity premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004), Claus and Thomas (2001), and Gebhardt, Lee, and

Swaminathan (2001). Model (1) controls for the signed one-year-ahead forecast error (FBIAS). Models (2) to (5) exclude observations in the top 5%, 10%, 25%, and

50% of the FBIAS distribution, respectively. Models (6) to (9) exclude observations in the top 5%, 10%, 25%, and 50% of the long-term growth forecast (LTG)

distribution, respectively. Model (10) controls for price momentum computed as the compound stock returns over the past six months. Model (11) re-estimates

the implied cost of equity using January-end prices, instead of June-end prices. Appendix A provides details on the implementation of the models. Appendix B

outlines definitions and data sources for the regression variables. Unreported industry controls are based on the Fama and French (1997) industry classification.

59

Robust t-statistics, adjusted for clustering by firm, are reported inside the parentheses. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels,

respectively.

60

Table 8. Controlling for Real Asset Liquidity and Collaterals

Prediction

(1) (2) (3) (4) (5) (6) (7)

HPG1 - -1.349*** -1.342*** -1.377*** -1.405*** -1.387*** -1.395*** -1.265*** (-4.547) (-4.546) (-4.385) (-4.468) (-4.393) (-4.696) (-4.120) BETA + 0.065** 0.132*** 0.046 0.022 0.046 0.029 0.032 (2.181) (4.367) (1.459) (0.696) (1.414) (0.963) (1.052) BTM + 2.630*** 2.567*** 2.543*** 2.574*** 2.585*** 2.626*** 2.636*** (39.060) (37.868) (35.272) (35.708) (35.729) (38.813) (38.619) SIZE - -0.158*** -0.167*** -0.262*** -0.246*** -0.258*** -0.166*** -0.167*** (-10.683) (-11.109) (-16.242) (-15.271) (-16.488) (-11.046) (-11.132) LEV + 3.031*** 2.777*** 3.174*** 3.417*** 3.136*** 3.226*** 3.190*** (21.973) (20.068) (20.603) (22.528) (20.656) (23.963) (23.721) LTG + 0.084*** 0.086*** 0.077*** 0.077*** 0.078*** 0.084*** 0.083*** (26.853) (27.541) (23.145) (23.000) (22.969) (26.408) (26.024) DISP + 3.443*** 3.478*** 3.262*** 3.239*** 3.221*** 3.411*** 3.352*** (24.439) (24.686) (24.163) (23.981) (23.779) (24.457) (23.927) NoPotBuyer - -0.001*** (-3.136) ALiq1 - -1.424*** (-10.084) ALiql2 - -0.540*** (-3.159) ALiq3 - 0.284 (1.614) ALiq4 - -0.106*** (-4.762) PPENT - -0.444*** (-3.008)

HPRICE - -0.464** (-2.217) HPRICE_PPENT0 - -1.202*** (-2.727)

INTERCEPT ? 3.073*** 3.271*** 3.869*** 3.497*** 3.855*** 3.301*** 3.480***

(12.393) (13.059) (14.179) (11.951) (14.505) (13.029) (13.292)

Industry effects Yes Yes Yes Yes Yes Yes Yes Year effects Yes Yes Yes Yes Yes Yes Yes N 43,133 43,032 34,777 34,759 33,988 42,345 41,078

Adj. R2 0.341 0.344 0.353 0.353 0.353 0.343 0.343

61

This table examines the robustness of the results of Model (1), Table 4 to asset liquidity and collateral. rAVG is the average implied cost of equity

premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004), Claus and Thomas (2001), and Gebhardt, Lee,

and Swaminathan (2001). Models (1)-(4) control for total asset liquidity from Gapalan et al. (2012) and Ortiz-Molna and Philips (2013). Model (5)

controls for total asset liquidity from Benmelech and Berman(2008; 2009), Gavazza (2011) and Ortiz-Molna and Philips (2013). Models (6)-(8) control for

value of firm collateral from Dvijanovic (2013). Model (6) controls for firm collateral in year t. Model (7) controls for firm collateral in reference year

multiplied by housing price in year t. Appendix A provides details on the implementation of the four models. Appendix B outlines definitions and data

sources for the regression variables. Unreported industry controls are based on the Fama and French (1997) industry classification. ***, **, and * denote

statistical significance at the 1%, 5%, and 10% levels, respectively.

62

Table 9. Controlling for State Economic Activities

Prediction GDPG1 DPIG1 HPGM DPIG1

State effects

(1) (2) (3) (4) HPG1 - -0.662** -1.019*** -1.338*** (-2.171) (-3.400) (-4.559) BETA + 0.067** 0.068** 0.068** 0.060** (2.281) (2.324) (2.326) (2.052) BTM + 2.648*** 2.650*** 2.653*** 2.653*** (40.039) (40.082) (40.097) (40.179) SIZE - -0.159*** -0.159*** -0.159*** -0.162*** (-10.830) (-10.840) (-10.836) (-11.090) LEV + 3.085*** 3.083*** 3.085*** 3.091*** (23.266) (23.248) (23.250) (23.392) LTG + 0.085*** 0.085*** 0.085*** 0.085*** (27.516) (27.475) (27.431) (27.313) DISP + 3.358*** 3.369*** 3.374*** 3.371*** (24.389) (24.470) (24.487) (24.691) GDPG1 - -4.743*** (-6.146) DPIG1 - -4.621*** (-4.113) DIFF_HPG_DPI - -1.082*** (-3.598) INTERCEPT ? 3.230*** 3.229*** 3.059*** 2.904*** (12.615) (12.514) (12.034) (10.698) Industry effects Yes Yes Yes Yes Year effects Yes Yes Yes Yes N 44,678 44,678 44,678 44,665 Adj. R2 0.338 0.337 0.337 0.337

This table examines the robustness of the results of Model (1), Table 4 to various additional control variables. rAVG is the

average implied cost of equity premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005),

Easton (2004), Claus and Thomas (2001), and Gebhardt, Lee, and Swaminathan (2001). Models (1) to (3) control for

state-level growth in GDP, growth in disposable personal income (DPI), and difference in growth rates of housing

prices and DPI, respectively. Model (4) controls for state effects, and Model (5) controls for county effects. Appendix A

provides details on the implementation of the four models. Appendix B outlines definitions and data sources for the

regression variables. Unreported industry controls are based on the Fama and French (1997) industry classification. ***,

**, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

63

Table 10. Two-Stage Least Squares Estimation

Stage 1 Stage 2

HPG1 -1.203

(-1.775)

BETA 0.001 BETA 0.061

(1.101) (2.039)

BTM -0.004 BTM 2.669

(-5.135) (39.161)

SIZE -0.000 SIZE -0.159

(-1.546) (-10.800)

LEV -0.000 LEV 3.100

(-0.256) (23.286)

LTG 0.000 LTG 0.084

(3.529) (26.898)

DISP -0.006 DISP 3.391

(-4.314) (24.328)

Elasticity*Borrowing Cost -0.001

(-22.711)

Change in Education 0.324

(8.492)

N 44,360 N 44,360

F statistics 86.88 Hansen J statistics

2.641

F statistics p-value 0 Hansen J p-value

0.165

Adj. R2 0.024 Adj. R2 0.252

This table presents 2SLS regression results for the implied equity premium (rAVG) using instrumented housing

price growth and controls over the period 1985-2008. rAVG is the average implied cost of equity premium obtained

from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004), Claus and Thomas (2001),

and Gebhardt, Lee, and Swaminathan (2001). Stage 1 reports the results from regressing HPG1 on the

instrumental variables. Stage 2 reports the results from regressing the dependent variable (rAVG) on the predicted

value of HPG1 from stage 1 and the control variables. Appendix A provides details on the implementation of the

four models. Appendix B outlines definitions and data sources for the regression variables. Unreported industry

controls are based on the Fama and French (1997) industry classification. ***, **, and * denote statistical

significance at the 1%, 5%, and 10% levels, respectively.

64

Table 11. Additional State- and Firm-level Controls

Prediction State controls CHU IO LTIO BAS ANA

(1) (2) (3) (4) (5) (6)

HPG1 - -1.447*** -1.425*** -1.340*** -1.369*** -1.336*** -1.367*** (-4.930) (-4.856) (-4.567) (-4.666) (-4.553) (-4.676) BETA + 0.062** 0.059** 0.086*** 0.062** 0.081*** 0.094*** (2.100) (2.025) (2.950) (2.116) (2.778) (3.252) BTM + 2.652*** 2.655*** 2.636*** 2.647*** 2.620*** 2.541*** (40.080) (40.159) (39.883) (40.241) (39.645) (37.346) SIZE - -0.161*** -0.163*** -0.131*** -0.131*** -0.144*** -0.062*** (-10.794) (-11.172) (-8.316) (-8.490) (-9.607) (-3.058) LEV + 3.096*** 3.081*** 3.023*** 3.009*** 3.038*** 2.896*** (23.371) (23.210) (22.991) (22.902) (22.943) (21.697) LTG + 0.084*** 0.084*** 0.085*** 0.083*** 0.084*** 0.086*** (27.266) (27.234) (27.549) (26.982) (27.346) (27.906) DISP + 3.357*** 3.362*** 3.335*** 3.361*** 3.361*** 3.360*** (24.419) (24.420) (24.283) (24.468) (24.432) (24.419) Log(POPU) ? 0.041* (1.757)

Log(EDUC) ? -0.191** (-2.081)

Log(MFR) ? 0.813 (1.615)

Log(INC) ? 0.202 (1.257)

Log(MINO) ? -0.064* (-1.709)

Log(MARR) ? -0.539** (-2.562) Log(CHU) - -0.147*** (-2.845) IO - -0.520*** (-6.330) LTIO - -1.561*** (-7.402) ILLIQ + 8.114*** (4.276) ANA - -0.028*** (-7.243) INTERCEPT ? -0.575 3.033*** 3.151*** 3.140*** 2.980*** 2.646*** (-0.284) (11.813) (12.443) (12.388) (11.829) (10.056) Industry effects Yes Yes Yes Yes Yes Yes Year effects Yes Yes Yes Yes Yes Yes N 44,678 44,678 44,678 44,678 44,678 44,678 Adj. R2 0.337 0.337 0.338 0.339 0.338 0.337 This table examines the robustness of the results of Model (1), Table 4 to various additional control variables. rAVG is the average

implied cost of equity premium obtained from four models developed by Ohlson and Juettner-Nauroth (2005), Easton (2004), Claus

and Thomas (2001), and Gebhardt, Lee, and Swaminathan (2001). Model (1) controls for state-level demographics, including

population, education, male-to-female ratio, income, minority, and marital status. Model (2) controls for county-level religiosity.

Model (3) controls for institutional ownership. Model (4) controls for long-term institutional ownership. Model (5) controls for

bid-ask spread. Model (6) controls for analyst coverage. Appendix A provides details on the implementation of the four models.

Appendix B outlines definitions and data sources for the regression variables. Unreported industry controls are based on the Fama

65

and French (1997) industry classification. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

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