housing price growth and the cost of equity capital · 2017-02-14 · we investigate whether and...
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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
Email: [email protected]
Tel.: 86-21-54030956
Samir Saadi1
Telfer School of Management
University of Ottawa
Ottawa, ON K1N 6N5, Canada
Email: [email protected]
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.
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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
3
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)).
4
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.
5
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
6
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.
8
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).
9
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.
10
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)).
11
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
12
(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.
13
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.
15
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).
18
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.
Insert Tables 6, 7, and 8 about here
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/
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.
Insert Tables 9, 10, and 11 about here
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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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
Implied cost of equity premium, defined as the cost of equity
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
Implied cost of equity premium, defined as the cost of equity
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
Authors’ calculations based
on Federal Housing Finance
Agency (FHFA) data
HPG2 Growth rate in housing prices in the state in which the firm is
located measured over the preceding two years
As above
45
HPG3 Growth rate in housing prices in the state in which the firm is
located measured over the preceding three years
As above
HPG4 Growth rate in housing prices in the state in which the firm is
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
Authors’ calculations based
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
Authors’ calculations based
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
Authors’ calculations based
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
Authors’ calculations based
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
Authors’ calculations based
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.
Authors’ calculations based
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
Authors’ calculations based
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
Authors’ calculations based
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
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and French (1997) industry classification. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.