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Understanding Housing Market Volatility
Joseph Fairchild∗ Jun Ma† Shu Wu‡
January 7, 2014
∗Bank of America, 600 Peachtree Street, Atlanta, GA 30308, phone: 949-422-0968,email: [email protected].†Department of Economics, Finance and Legal Studies, Culverhouse College of Com-
merce and Business Administration, University of Alabama, Auscalosa, AL 35487, phone:205-348-8985, email: jma@cba,ua.edu.‡Department of Economics, University of Kansas, Lawrence, KS 66045, phone: 785-
864-2868, email: [email protected].
Abstract
The Campbell-Shiller present value formula implies a factor structure
for the price-rent ratio of the housing market. Using a dynamic factor
model, we decompose the price-rent ratios of 17 major housing markets
into a national factor and independent local factors, and we link these
factors to the economic fundamentals of the housing markets. We find
that a large fraction of housing market volatility is local. And the local
volatilities mostly are due to time-variations of idiosyncratic housing
market risk premiums, not local growth. At the aggregate level, the
growth and interest rate factors jointly account for up to 47% of the
total variations in the price-rent ratio. The rest is due to the aggregate
housing market risk premium and a pricing error. We find evidence
that the pricing error is related to money illusion, especially at the
onset of the recent housing market bubble. The rapid rise in housing
prices prior to the 2008 financial crisis was accompanied by both a
large increase in the pricing error and a large decrease in the housing
market risk premium.
Key words: housing market, dynamic factor model, price-rent ratio,
risk premium, money illusion.
JEL Classifications: G10, R31, C32
1
1 Introduction
Housing markets are segmented. There does not exist a centralized market
for housing assets. Demographic changes, household preferences for geo-
graphic locations and climate plus inelastic land supply can lead to hetero-
geneous regional price dynamics. Some existing studies, such as Gyourko,
Mayer and Sinai (2006) and Del Negro and Otrok (2007), have already ob-
served the price level and growth rate vary drastically across major U.S.
housing markets in the past few decades. As we can see in Table 1, for
example, the average annual nominal price change was 6.8% in New York
City but was only 3.5% in Kansas City during the period between 1979 to
2009. Moreover, the volatility of house price also varies greatly across dif-
ferent cities. Table 1 shows the standard deviation of annual nominal price
changes for the same period. It was 7.5% in New York City but was 2.7% in
Kansas City. Table 2 reports similar statistics for the log price-rent ratios
of the same cities. For example, in New York City the log price-rent ratio
had an annual standard deviation of 22% while in Kansas City it was only
8.7% between 1979 to 2009.
On the other hand, all housing markets are obviously affected by a few
aggregate variables such as the monetary policy, mortgage market innova-
tions and national income. When the central bank lowers the key interest
rate, it could stimulate the demand for houses in all markets and have a
positive effect on housing prices. In fact Table 1 and Table 2 show that the
correlation among some housing markets can be very high (e.g. New York
City and Boston, Los Angles and Philadelphia).
In this study we use a dynamic factor model to decompose housing prices
into a common national factor and idiosyncratic local factors in order to
better understand the sources of housing market volatility. We treat a resi-
dential house as a dividend-paying asset and base our dynamic factor model
on the Campbell-Shiller log-linear approximate present value formula for
the price-dividend ratio (Campbell and Shiller, 1988). Such an approach
allows us to link the unobservable factors to the economic fundamentals of
2
the housing markets such as interest rates and expected rent growth.
Quantitatively distinguishing the national factor from local factors in the
housing markets is important. From the perspective of policy makers, for
instance, it is crucial to know if monetary policy was responsible for creating
a national housing market bubble by keeping the short-term interest rate
too low for too long, or if the increase in housing prices prior to the 2008
financial crisis instead reflected a collection of local bubbles. On the other
hand, identifying a market “bubble” is intrinsically difficult. An increase in
asset prices could be due to improved economic fundamentals as perceived by
investors or due to purely speculative activities. By linking the unobserved
price factors to economic fundamentals, our paper also seeks to distinguish
between the part of housing market volatility attributable to changes in
expected rent growth and the discount rate and the part that could be due
to speculations or pricing errors.
Given the importance of the housing sector in the aggregate economy,
there have been many studies on housing markets in recent years. For ex-
ample, Fratantoni and Schuh (2003) uses a heterogeneous-agent VAR to
examine the effect of monetary policy on regional housing markets. Davis
and Heathcote (2005) points out that residential investment is more than
twice as volatile as business investment and leads the business cycle. Ia-
coviello (2005) develops and estimates a monetary business cycle model
with housing sector. Brunnermeier and Julliard (2007) finds evidence that
money illusion can play an important role in fueling run-ups in housing
prices. Stock and Watson (2009) estimated a dynamic factor model with
stochastic volatility for the building permits of the U.S. states from 1969-
2007. Mian and Sufi (2009) uses detailed zip-code level data to examine
the role of subprime mortgage credit expansion in fueling the house price
appreciation prior to the recent financial crisis. Kishor and Morley (2010)
uses an unobserved component model to estimate the expectations of the
housing market fundamentals and investigate the sources of the aggregate
housing market volatility. Ng and Moench (2011) estimates a hierarchical
factor model of the housing market and examines the dynamic effects of
3
housing market shocks on consumption. Favilukis et al (2011) argues that
international capital flow had played a small role in driving the last house
market bubble, and the key causal factor was instead the cheap supply of
credits due to financial market liberalization. Our paper contributes to this
growing literature that seeks to understand the fundamental driving forces
of the housing market and its relationship to the aggregate economy.
Perhaps the closest studies to ours are Del Negro and Otrok (2007) and
Campbell et al (2009). Del Negro and Otrok (2007) was among the first to
apply dynamic factor models to housing markets.1 In their study state-level
house price movements are decomposed into a common national component
and local shocks via Bayesian methods. They find that historically the lo-
cal factors have played a dominating role in driving the movement in house
prices in different states. But a substantial fraction of the recent increases in
house prices is due to the national factor. They further use a VAR to inves-
tigate the effect of monetary policy on housing markets. The key difference
between our study and Del Negro and Otrok (2007) is that we treat a house
as a dividend-paying asset and infer a factor structure for the price-rent ratio
based on the Campbell-Shiller log-linear present value formula. As a result,
we can explicitly link the unobserved factors to economic fundamentals of
the housing markets. The Campbell-Shiller formula has been widely used
to analyze the volatility of bond and equity markets. In an intriguing study,
Campbell et al (2009) applied the same method to price-rent ratio in housing
markets.2 The ratio is split into the expected present values of rent growth,
the real interest rate and a housing risk premium. The study found that
the housing risk premium accounts for a significant fraction of the price-
rent volatility. An important difference between our paper and Campbell et
al (2009) is that we are able to disentangle the relative importance of the
common component in the price-rent ratios across individual markets from
1Recent applications of dynamic factor models include Cicarelli and Mojon (2010) onglobal inflation, Ludvigson and Ng (2009) on bond risk premiums and Kose et al. (2003,2008) on global business cycles among many others. Forni et al. (2000) provides a thoroughanalysis of the identification and estimation of generalized dynamic factor models.
2 Brunnermeier and Julliard (2007) also uses the same approach to isolate the pricingerror in the aggregate housing market due to money illusion.
4
idiosyncratic local factors using a dynamic factor model. We show that this
factor structure is an implication of the Campbell-Shiller present formula
and both factors have similar Campbell-Shiller representations. Moreover,
we show that a pricing error associated with money illusion is also important
in driving the housing market dynamics.
To implement the Campbell-Shiller formula, we need to estimate the
expected future rent growth and real interest rate. Another innovation of
our paper is that the forecasting vector auto-regression model (VAR) for
future rent growth and real interest rate is embedded in a dynamic factor
model, and the two models are estimated jointly. The macro variables in the
VAR are correlated with the national factor of rent growth but are indepen-
dent of the local factors. Such a specification is important for appropriate
identifications of the national and the local factors.
The rest of the paper is organized as follows. Section 2 describes our
model. Section 3 discusses the data and estimation strategy. Section 4
presents the main empirical results. Section 5 concludes.
2 Model
We treat a house as a dividend-paying asset and equate the house price
to the present value of the expected future rental income under rational
expectations.3 Following Campbell and Shiller (1988), we can write the
price-rent ratio as the sum of expected growth rate of rental income minus
the expected rate of return on the housing asset.
In particular, if Pi,t denotes the ex-dividend price of a housing asset in
market i at time t, Di,t+1 the rental income of the housing asset between t
and t+1, let xi,t = log(Pi,t
Di,t
), di,t = logDi,t and ri,t+1 = log
(Pi,t+1+Di,t+1
Pi,t
).
3Using rent as an approximation of the dividend income of a housing asset, we implicitlyassume that individuals are indifferent between owning and renting. Glaeser and Gyourko(2007) points out that the rental units in the housing markets tend to be very differentfrom owner-occupied units.
5
Under log-linear approximation, we have (ignoring constant terms):
xi,t = Et
∞∑τ=0
ρτ [∆di,t+1+τ − ri,t+1+τ ] (1)
where ρ = 1/(1+e−x), and x is the steady state price/rent ratio. The house
price today should equal the present value of expected future rent growth
minus the weighted average of expected future rates of return.
We assume in this study that the growth rate of rent in one market
consists of two components, a national factor that is common to all markets
and an independent local factor that is specific to market i. We can now
rewrite the standard Campbell-Shiller decomposition as
xi,t = Et
∞∑τ=0
ρτ∆dt+1+τ+Et
∞∑τ=0
ρτ∆di,t+1+τ−Et∞∑τ=0
ρτrf,t+1+τ−Et∞∑τ=0
ρτeri,t+1+τ
(2)
where ∆dt is the national factor of rent growth rate,4 ∆di,t is the idiosyn-
cratic rent growth rate in market i, rf,t is the real interest rate and eri,t is
the excess rate of return in market i, eri,t = ri,t − rf,t.
The last term in Equation (2) corresponds to the risk premium for in-
vesting in the housing market, which also can be written as the sum of two
components
Et
∞∑τ=0
ρτeri,t+1+τ = Et
∞∑τ=0
ρτ ert+1+τ + Et
∞∑τ=0
ρτ eri,t+1+τ (3)
The first part on the right side of the equation above can be thought of as the
national housing market risk premium and the second part an idiosyncratic
risk premium component that is specific to market i. This decomposition
can be justified as follows: if housing markets were fully integrated without
4For the purpose of exposition we have assumed that the factor loading is 1 for allmarkets. We also estimate a more general case where the factor loadings vary acrossdifferent markets. The results under the two specifications are very similar. See morediscussions below.
6
transaction cost and other frictions, it would follow from the standard asset
pricing theory that Et(eri,t+1) = βiEt(ert+1), where ert+1 is the excess
return on a portfolio of housing assets that is perfectly negatively correlated
with the pricing kernel (or the stochastic discount factor).5 Of course much
evidence shows that housing markets are far from integrated and there are
many kinds of frictions within each market as well such as transaction costs,
liquidity constraints and etc. The second part on the right side of Equation
(3) therefore captures the expected excess rate return that is orthogonal to
the aggregate housing market risk premium. Notice that we again assume
in Equation (3) the factor loading is 1 for all i. Relaxing this assumption
doesn’t change our main empirical results.6
In summary, the log-linear Campbell-Shiller present value formula im-
plies a factor structure for the price-rent ratios of the housing markets as
follows:
xi,t = xt + xi,t, i = 1, 2, ..., N (4)
where
xt = Et
∞∑τ=0
ρτ∆dt+1+τ − Et∞∑τ=0
ρτrf,t+1+τ − Et∞∑τ=0
ρτ ert+1+τ = yt − lt − ηt
(5)
and
xi,t = Et
∞∑τ=0
ρτ∆di,t+1+τ − Et∞∑τ=0
ρτ eri,t+1+τ = µi,t − εi,t (6)
As we will further show in Section 4.3, there could be an additional
pricing error term in Equation (5) if investors are not able to form rational
expectations of future real rent growth or the real interest rate. For example,
they may suffer from money illusion and mistaken a decline in the nominal
interest rate due to a change in inflation for a decrease in the real interest
5Since we will estimate the risk premium as the residual term in the Campbell-Shilleridentity, the coefficient βi is not important as long as it is constant. If βi is time-varying,our decomposition in (3) will not be valid because βi can depend on local state variables.
6Another implicit assumption is that investors in different housing markets share thesame information set.
7
rate (or equivalently they extrapolate the historical nominal rent growth rate
without taking into account changes in inflation). Under money illusion, the
observed price-rent ratio, xt, will include an extra term (a pricing error) as
follows,
xt =Et
∞∑τ=0
ρτ∆dt+1+τ − Et∞∑τ=0
ρτrf,t+1+τ − Et∞∑τ=0
ρτ ert+1+τ
+ (Et − Et)∞∑τ=0
ρτrf,t+1+τ
(7)
where Et denotes people’s subjective expectation under money illusion, Et
denotes the rational expectation. Investors perceive the real interest rate to
be Et∑∞
τ=0 ρτrf,t+1+τ , while the actual real interest rate is Et
∑∞τ=0 ρ
τrf,t+1+τ .
The first part of Equation (7) corresponds to the “correct” or “true” house
value under rational expectations. If households underestimate the real in-
terest rate, for example, the observed house price xt will exceed its true
value by (Et − Et)∑∞
τ=0 ρτrf,t+1+τ . This pricing error will disappear if in-
vestors are able to correctly form rational expectations of future interest
rates (Et = Et). In our decomposition exercise, we will need to distinguish
empirically the pricing error from the risk premium term in the Campbell-
Shiller formula.7
3 Data and Estimation
In our model specification there are two types of unobserved factors: the
unobserved national and local factors for both rent growth and price-rent
ratio, and the unobserved agent’s expectations of future rent growth, future
interest rates and future excess returns or risk premiums. Typically the un-
observed national and local factors can be extracted from the observed series
by applying the type of Dynamic Factor Model (DFM) proposed in Stock
7We treat money illusion as a national factor because there is no appealing reason toassume only households in one or some particular markets make this mistake while othersdon’t.
8
and Watson (1991), and the unobserved expected future variables can be es-
timated by a VAR model that was first implemented in Campbell and Shiller
(1988) to study sources of price-dividend variations. We combine these two
lines of work and propose a novel VAR augmented DFM that allows us to
simultaneously decompose the observed series into the national and local
factors and obtain estimates of these expectations of future variables. Using
these estimated expectations along with the Campbell-Shiller present-value
accounting identity, we can further decompose the housing price variations
into movements in different economic fundamentals including time-varying
risk premiums.
Our data are the annual real rent growth and price-rent ratio of 17
metropolitan areas. The data on rent growth cover a long span, from 1936 to
2009. The real rent growth are obtained through deflating the nominal rent
by the CPI. When applying the DFM to the real rent growth we augment the
DFM with a multivariate VAR that includes several important macroeco-
nomic variables (such as the interest rate) to allow for potential interactions
between the national factor of real rent growth and observed macroeconomic
activities. This is very important for several reasons. First it ensures the
appropriate identification of the local factor of real rent growth in (6) which
is supposed to be independent of the national factor of rent growth and the
real interest rate in (5). Second, as pointed out by Engsted et al. (2012),
a critical requirement for proper Campbell-Shiller VAR decompositions is
that the forecasting state variables should include the current asset price.
We address this issue by including the Case-Shiller home price index as one
of the macro variables in our model. Third, the extra information contained
in the macro variables can in principle improve the forecasts of the national
real rent growth as well as the future interest rate. More information on the
data used in this paper can be found in the appendix.
Denote the annual real rent growth in the 17 metropolitan areas by ∆di,t.
Assume a common national factor represented by ∆dt and the idiosyncratic
local factors denoted by ∆di,t. We use 2 lags for all dynamic factors since all
data are annual and 2 lags appear sufficient to capture potential dynamics.
9
Notice that all variables are demeaned before being used to estimate the
model. Specifically, the DFM part is set up as below:
∆di,t = βd,i∆dt + ∆di,t, i = 1, 2, ..., 17 (8)
∆dt = φ1∆dt−1 + φ2∆dt−2 + ωt (9)
∆di,t = ψ1∆di,t−1 + ψ2∆di,t−2 + νi,t, i = 1, 2, ..., 17 (10)
where ωt and νi,t are independent Gaussian shocks.
We augment the above DFM with a VAR to allow the latent national
factor ∆dt to interact with four macroeconomic variables that include the
real interest rate, rf,t, real GDP growth, gt, log changes in the Case-Shiller
home price index, st, and CPI inflation rate, πt:
Zt = Φ(L)Zt−1 + ξt (11)
where Zt = (∆dt, rf,t, gt, st, πt)′ and ξt = (ωt, εr,t, εg,t, εs,t, επ,t)
′. The vari-
ance matrix of the innovations to the VAR is given by Σ. We also use 2 lags
in the VAR specification.
To estimate this VAR-DFM model we cast it in a state-space framework.
The Kalman filter then can be conveniently employed to estimate such state-
space model. The resulting state-space model consists of the measurement
and transition equations as detailed below.
Measurement equation:
Ut = MYt (12)
10
where
Ut =
∆d1,t
...
∆d17,t
rf,t
gt
st
πt
, M =
1 0 · · · 0 0 βd,1 0 0 0 0 0 0 0 0 0...
......
...
0 0 · · · 1 0 βd,17 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 · · · 0 0 0 0 0 0 1 0 0 0 0 0
0 0 · · · 0 0 0 0 0 0 0 0 1 0 0 0
0 0 · · · 0 0 0 0 0 0 0 0 0 0 1 0
Transition equation:
Yt = ΛYt−1 + Θt (13)
where
Yt =
∆d1,t
∆d1,t−1
...
∆d17,t
∆d17,t−1
∆dt
∆dt−1
rf,t
rf,t−1
gt
gt−1
st
st−1
πt
πt−1
, Θt =
ν1,t
0...
ν17,t
0
ωt
0
εr,t
0
εg,t
0
εs,t
0
επ,t
0
11
and
Λ =
ψ1,1 ψ1,2
1 0...
· · · ψ17,1 ψ17,2
1 0
φ1,1 · · · φ1,10
1 0 0
φ2,1 · · · φ2,10
1 0
φ3,1 · · · φ3,10
1 0
φ4,1 · · · φ4,10
1 0
φ5,1 · · · φ5,10
1 0
We follow Kim and Nelson (1999) to maximize the log-likelihood func-
tion written via the Kalman filter to obtain the estimates of the hyper-
parameters. Once the hyper-parameter estimates are found the smoothing
algorithm is invoked to calculate the smoothed estimates of the national
and local factors: E[∆dt|IT ] and E[∆di,t|IT ], i = 1, 2, . . . , 17. The smoothed
estimates are based on the most available information in the sample and
thus provide the best estimates of these factors.
Iterating forward the dynamics of the unobserved national factor and
observed macroeconomic variables, we can derive the growth component
and interest rate component in the Campbell-Shiller decomposition (5) as
12
follows:
Et
∞∑τ=0
ρτ∆dt+1+τ = e′1 · F · (I − ρF )−1 ·Wt (14)
Et
∞∑τ=0
ρτrf,t+1+τ = e′3 · F · (I − ρF )−1 ·Wt (15)
where Wt = (∆dt,∆dt−1, rf,t, rf,t−1, gt, gt−1, st, st−1, πt, πt−1)′, i.e. the sec-
ond half of the state variable in the transition equation (13); F is the cor-
responding companion matrix in the VAR model. ej is a selection column
vector which has 1 as the j-th element and zero elsewhere. In the same
way, the idiosyncratic local growth component Et∑∞
τ=0 ρτ∆di,t+1+τ can be
computed relatively easily since it is by construction independent of the
macroeconomic variables.
The aggregate and local risk premium components are obtained as the
residual terms in the Campbell-Shiller accounting identity (5) and (6), re-
spectively. We first apply the DFM to the price-rent ratio and extract the
national and local factors from this series.8 Assume each price-rent ratio is
the sum of the unobserved national factor and local factor:
xi,t = βx,ixt + xi,t, i = 1, 2, . . . , 17 (16)
and the national and local price-rent ratios both follow the stationary AR(2)
processes:
xt = α1xt−1 + α2xt−2 + et, et ∼ i.i.d. N(0, σ2e) (17)
xi,t = γi,1xi,t−1 + γi,2xi,t−2 + ςi,t, ςi,t ∼ i.i.d. N(0, σ2ς,i) (18)
Again, the national and local factors are orthogonal to each other for
8Before applying the DFM to the log price-rent ratio data, we ran a panel unit roottest and rejected the unit root hypothesis. This is consistent with the finding in Ambroset al (2011) that house price and rent are cointegrated.
13
identification purposes following Stock and Watson (1991). This model can
be put into its state-space form and the estimation is done by following Kim
and Nelson (1999). The risk premium term is then obtained by subtracting
the rent growth and interest rate components from the price-rent ratio.
Also notice that in the dynamic factor models, the scale of the common
factor and the factor loading are not identified independently. We can either
normalize the factor loading to be 1 (i.e. βx,i = 1) or normalize the standard
deviation of the shocks to the common factor to be 1 (i.e. σ2e = 1). We
estimated both versions of the model and obtained similar results.
4 Results
4.1 Factor Decomposition
We first estimate a dynamic factor model of the price-rent ratios of the 17
cities in our sample. The model decomposes each price-rent ratio into a
common national factor and a local factor. We estimated two versions of
the model. In one model, we restricted the loadings on the national factor
to be 1 across the 17 cities in our sample. In the other model, the factor
loading is allowed to change but the standard deviation of the national factor
is normalized to be 1 in order to achieve identification. The results from
the two models are very similar and are summarized in Table 3. We find
that across the 17 cities local factors drive a significant portion of the total
volatility in the housing markets. We measure the volatility of a housing
market by the standard deviation of the annual price-rent ratio. As Table
3 shows, in the model with restricted factor loadings, an average of 47% of
the total volatility of the housing markets is attributable to local factors. In
some cities, the local factor shares are more than 60%. If we allow the factor
loadings to vary, the average local factor share is slightly lower, but is still
more than 40%. This is consistent with the results of Del Negro and Otrok
(2007), which finds that historically movements in house prices were mainly
driven by the local components. Figure 1 plots the estimated national factor
14
of the price-rent ratio together with the log Case-Shiller house price index
(normalized by the CPI index). We can see that these two series track each
other closely with a correlation coefficient of 0.86. Our series of the national
factor of the price-rent ratio is also very similar to the one estimated by
Davis et al. (2008). This confirms that the dynamic factor model provides
a good summary of housing market movements.
Table 3 also shows that the local factor shares vary greatly from city to
city. For example, while local factors contribute more than 60% of the total
volatility of the price-rent ratio in New York City and Los Angeles, the lo-
cal factor share is only 24% in Chicago. The log-linearized Campbell-Shiller
present value formula provides insights about what drives these local volatil-
ities. The Campbell-Shiller formula is an accounting identity that expresses
the (log) price-rent as a sum of two components: the present value of the
expected future rent growth rates and the present value of expected future
discount rates. House prices increase today either because people expect
higher future growth or a lower discount rate or both. As we have demon-
strated in Section 2, the growth component can be further decomposed into
a common national growth factor and an independent local growth factor.
The discount rate components can be thought of as consisting of three fac-
tors, a risk-free interest rate, an aggregate or national risk premium which
are common to all cities, and an idiosyncratic local risk premium. Therefore,
in cites where the local factors contribute a large share to the housing mar-
ket volatility there must be either volatile local growth or volatile local risk
premiums or both. In Table 4 we report the standard deviations of the local
growth rate and local risk premiums (see below for more on the estimation
of different components in the Campbell-Shiller accounting idendity). We
can see that local risk premiums are about 5 times more volatile than local
growth rates. There are also greater variations in the standard deviations
of local risk premiums. In Figure 2 we plot the scatter graph of the local
factor shares of the price-rent ratio against the standard deviations of the
local risk premiums. In Figure 3 we plot a similar graph with the standard
deviations of the local growth rate instead. We can clearly see from these
15
two figures that the local factor shares are mostly due to the volatility of
local risk premiums. Variations in the local growth rate have some, but very
limited, explanatory power for the local factor shares.
4.2 Economic Fundamentals of Housing Markets
We next examine the economic fundamentals that underlie the national and
local factors of the house price-rent ratios. Using the Campbell-Shiller log-
linear present-value formula, we are able to equate the national factor of the
log price-rent ratio to the sum of the present value of the expected national
growth rate in rent, the present value of the expected real interest rate
and an aggregate risk-premium term. Similarly, the local factor of a price-
rent ratio can be written as the sum of the present value of the expected
local growth rate in rent and a local risk premium term. To get reliable
estimates of the expected future rent growth rates and interest rates, we
use a long duration of historical data from 1936-2009 on rent and interest
rate. We embed a vector regression model into a dynamic factor model of
rent growth rates. This allows us to obtain joint estimates of the national
and local factors of rent growth as well as the expected future interest rates.
The national and local risk premium terms are then obtained as residuals
in the Campbell-Shiller accounting identity using our previous estimates of
the national and local factors of the log price-rent ratios. The results are
summarized in Table 4 and 5.
Table 5 shows that the long-run growth rate in rent is estimated to be
around 1.40% at the aggregate level. Our model also yields an estimate
of the expected long-run real interest rate of 2.27%. Since we can only
obtain index data on rent, the log price-rent ratio used in our study is
different from the true log price-rent ratio by a constant. Therefore we can’t
obtain the correct estimates of the mean of the national and local factors of
the log price-rent ratios, as well as that of the national house market risk
premium. Nonetheless this scale problem doesn’t affect our estimate of the
standard deviations of the log price-rent ratios and the underlying economic
16
variables as well as their correlations. Among the three economic variables
underlying the national factor of log price-rent ratio, the interest rate term
has the biggest standard deviation of 17.25%. The risk premium term has a
standard deviation of 11.95%, indicating strong evidence of time-varying risk
premium in housing markets. The growth term is the least volatile variable
with a standard deviation of 6.91%. Moreover, these three variables are
also highly correlated. The growth term and real interest rate are positively
correlated. The risk premium is negatively correlated with both the growth
term and real interest rate.9
To assess the impact of the economic fundamentals on housing markets,
we report in Table 6 the results from simple regressions of log price-rent
ratios on the growth and interest rate variables. Notice that our estimates of
the national growth factor and the real interest rate term are obtained from a
separate dynamic factor model than the one for price-rent ratio, and the risk
premium is obtained as the residual term in the Campbell-Shiller accounting
identity. Therefore a meaningful regression is a one that only includes the
growth and interest rate variables. Table 6 shows that the growth and
interest rate variables jointly explain up to 46.47% of the total variation
in the aggregate log price-rent ratios. The interest rate alone accounts for
about 17% of the variation in the aggregate log price-rent ratios. Moreover,
consistent with standard economic theory, a higher expected real interest has
a significant negative effect on house price while a higher growth expectation
has a significant positive effect. The regression result also indicates that a
large portion (more than 50%) of the variation in the national house market
is due to changes in the aggregate risk premium term. Table 6 also reports
the results from regressing local price-rent ratios on local growth variables.
Consistent with the result on the local factor shares in the previous section,
we find that local growth explains very little of the variation in local price-
rent ratios for most cities. The idiosyncratic volatilities in local housing
markets seem mostly due to time-variations in local risk premiums. Given
9The negative correlation between housing market risk premium and growth is consis-tent with the counter-cyclical risk premiums in stock market documented in many studiessuch as Campbell and Cochrane (1999).
17
that local price-rent ratios contribute to more than 40% of the total volatility
of house markets, it seems safe to conclude that variations in risk premiums
are the most important factor that drives housing market volatility. Changes
in the interest rate have the expected, but limited, direct effect on housing
market volatility.10
4.3 Housing Market Risk Premiums and the Pricing Error
The residual term from the Campbell-Shiller present value formula (5) is the
expected excess return or risk premium in the housing market, Et∑∞
τ=0 ρτ ert+1+τ .
This is a valid decomposition if investors have rational expectations and the
transversality condition holds, i.e., limT→∞ ρTEtxt+T = 0, where xt is the
national factor of log price-rent ratio. In general, however, the residual term
from the Campbell-Shiller formula may include a pricing error. This pricing
error can arise because either investors hold irrational expectations or there
is a speculative bubble that violates the transversality condition. We now
rewrite the Campbell-Shiller present value formula as
xt = Et
∞∑τ=0
ρτ∆dt+1+τ−Et∞∑τ=0
ρτrf,t+1+τ−Et∞∑τ=0
ρτ ert+1+τ+ limT→∞
ρTEtxt+T
(19)
or
xt = yt − lt − ηt + νt (20)
where yt, lt and ηt are, as before, the expected rent growth, the real interest
rate and the risk premium respectively, and νt denotes a possible pricing
error in the housing market. Our dynamic factor models produce estimates
of xt, yt and lt, and the residual term from the account identity (20) now
contains two components, the risk premium and the pricing error, ηt and νt.
It is well documented that the excess return in equity market can be
predicted by some state variables such as yield spread and dividend yield
10Kishor and Morley (2010) reports a similar finding that variations in risk premiums ex-plain a large fraction of housing market volatility. Cochrane (2011) argues that most assetmarket puzzles and anomalies are related to large discount-rate/risk premium variations.
18
etc. To distinguish between the risk premium and the pricing error in the
housing market, we project via OLS regression the residual term from the
Campbell-Shiller formula (20) onto the same state variables that are known
to predict stock market returns. We interpret the fitted value as the housing
market risk premium and the OLS residual as the pricing error. The results
are reported in upper panel of Table 7. We can see that both the yield
spread (the difference between the yield on Treasury bonds and that on
Treasury bills) and S&P 500 dividend yield are significant predictors of
the housing market return. We also used the S&P earning-price ratio in
the linear projection and obtained similar results. The R2 from the OLS
regression is high, indicating a large part of the Campbell-Shiller residual
is the housing market risk premium that varies over time. Nonetheless the
pricing error is also significant. The estimated housing market risk premium
and pricing error are plotted in Figure 4. We can clearly see that during the
housing market frenzy between 2000 and 2006, there was a large increase in
the pricing error, νt, and an even larger decrease in the risk premium, ηt,
both contributing to the sharp increase the housing market price before the
2007-2008 financial crisis (Figure 1). In contrast, during the early sample
period (1979 to 1985), the pricing error was decreasing and the risk premium
was increasing. As a result, the housing price declined during that period.
It is interesting to notice that in the risk premium regression (the upper
panel of Table 7), the coefficient on the yield spread is positive while the
coefficient on the stock dividend yield is negative. A large positive yield
spread indicates that interest rates are likely to rise in the future, and rising
interest rates decrease values of long-term assets such as houses. Therefore
a large yield spread increases the risk to participate in the housing market,
resulting in a higher risk premiums. On the other hand, it is well known that
the dividend yield has strong forecasting power for future stock returns. For
example Cochrane (2011) shows that a one percentage point increase in the
dividend yield forecasts a nearly four percentage point higher excess return
in the stock market. In states where the dividend yield is high, investors
perceive a larger risk in the stock market and demand a higher expected
19
return. As a result they are more willing to accept a lower expected return
in the housing market. A higher dividend yield in the stock market predicts
lower returns in the housing market. Housing assets provide a hedge against
stock market risk. Of course, such interpretations are subject to the caveat
that part of the estimated risk premium may actually be the projection of
the pricing error on the state variables or that the two state variables fail
to capture all the variations of the housing market risk premium.
The orthogonal residual term from the above OLS regression can be
interpreted as an estimate of housing market pricing error. One possible
source of the pricing error is money illusion. For example, as pointed out by
Modigliani and Cohn (1979), investors may fail to distinguish between the
real interest rate and nominal interest rate. They may interpret a decline in
the nominal interest rate due to changes in inflation as a decline in the real
interest rate, and therefore bid up the real housing price. As pointed out by
Brunnermeier and Julliard (2008), in the simplest case with constant real
rents and real interest rates, the price-rent ratio will be simply determined
asP
D=∞∑τ=1
1
(1 + rf )τ=
1
rf(21)
where rf is the real interest rate. Under money illusion, however, investors
would value the housing asset as
P
D=∞∑τ=1
1
(1 + i)τ=
1
i(22)
where i is the nominal interest rate. And if i declines due to a reduction
in inflation, the price-rent ratio will increase even if the real interest rate
remains constant.
To see if the estimated pricing error is indeed related to money illusion,
we run an OLS regression of the pricing error on the inverse of the nominal
interest rate as well as the inverse of inflation. The results are reported in the
second panel of Table 7. We can see that the estimated pricing error is indeed
20
positively related to the inverse of the nominal interest rate and inflation.
Since a change in inflation may reflect a change in inflation volatility rather
than its level, we also include the square of inflation in the regression to
control the effects of inflation volatility and obtain the same result. Notice
that the R2 of the regressions are not very high, suggesting that money
illusion may not be the only source of the pricing error.11 The pricing error
and its fitted value are plotted in Figure 5. It is interesting to note that
while the fitted value of the pricing error remains close to 0 and is very
different from the actual value in most periods (which explains the low R2),
it increases sharply in between 2000 and 2003 and tracks the actual value of
the pricing error closely. The short-term nominal interest rate was pushed
down to a very low level in a short period of time by the monetary policy in
the aftermath of the tech bubble and the subsequent economic recession. It
was also during that period the increase in housing prices accelerated (see
Figure 1). We can also see from Figure 5 that the money illusion effect
explains most of the pricing errors during the early 1980s as well. These
results suggest that money illusion is most severe during periods of drastic
changes in the nominal interest rate such as the early 2000s and the early
1980s. And the monetary policy may have contributed to the initial stage of
the last housing market bubble indirectly through the money illusion effect.
5 Conclusions
This paper is an empirical analysis of housing market dynamics. The hous-
ing asset is probably the single most important component of an average
household’s financial portfolio. Housing market movements also have great
impacts on macroeconomic fluctuations. Compared to equity and bond mar-
kets, however, there have relatively fewer studies on the nature and sources
of housing market volatility. We contribute to a growing literature on hous-
ing market by estimating a dynamic factor models of the price-rent ratios
11This is in contrast to the result in Brunnermeier and Julliard (2007) where the pricingerror is almost entirely explained by money illusion.
21
of 17 major metropolitan areas of the U.S. The model allows us to disen-
tangle the common and idiosyncratic local components of housing market
volatility. We find that a large fraction of housing market volatility is lo-
cal. Our dynamic factor model is based on a present-value representation
of the price-rent ratio of the housing asset and is jointly estimated with
a forecasting VAR that includes important macroeconomic variables. This
approach enables us to relate otherwise unobservable latent factors to eco-
nomic fundamentals of the housing markets. Our results indicate that at
both the local and the aggregate levels time-variation in risk premiums is
the most important source of housing market volatility. Interest rates play a
smaller role in driving the movements of the housing markets. Nonetheless,
changes in the interest rate can have a direct and indirect impact on the
housing market. A decrease in the interest rate directly lowers the discount
rate, and therefore pushes up home prices. Moreover, a sharp decline in
the interest rate can also fuel housing market speculations through a money
illusion effect. We find evidence that the housing market bubble leading to
the 2008 financial crisis was indeed accompanied by both a large decrease in
the housing market risk premium and a large increase in the pricing error
associated with money illusion.
22
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25
A Data
Rent growth. Nominal rent indexes are the rent of primary residence for
major U.S. metropolitan areas from Bureau of Labor Statistics (BLS).12
The beginning periods of these indexes vary for different cities: for some
cities such as Boston or San Francisco we start to have observations from as
early as 1915 but for some other cities such as Miami or Denver we do not
have observations until as late as 1978 and 1971, respectively. To explore
as much information as possible in the long-run time series data and at the
same time to include as many cities as possible to span wide geographic re-
gions, we choose to start our sample period from 1935 and we have to drop
many cities such as Dallas, Miami, Tampa, Anchorage, Denver, Honolulu,
San Diego. Furthermore we have to drop St. Louis because of the lack of
house price data. This leaves us with a set of observations of the annual
rent indexes from 1935 to 2009 for 17 cities: New York City, Philadelphia,
Boston, Pittsburgh, Chicago, Cincinnati, Cleveland, Detroit, Kansas City,
Milwaukee, Minnesota, Atlanta, Houston, Los Angeles, Portland, San Fran-
cisco, and Seattle. Evidently the data covers most major cities ranging from
the east coast to the midwest and west coast. The nominal rent then is
deflated by the consumer price index (CPI). The real rent growth is the
difference of the logarithms of the real rent.
Log price-rent. Nominal housing price indexes are the repeat-transaction
house price indexes from the Federal Housing Finance Agency (FHFA). The
original data start from 1975 for most cities. But we do not have observations
for some cities, such as St, Louis, until as late as 1983. Therefore, we choose
to start our sample period from 1979 and this, together with the considera-
tion of the rent data as described earlier, leaves us with a set of observations
of the annual housing price data from 1979 to 2009 for 17 cities: New York
City, Philadelphia, Boston, Pittsburgh, Chicago, Cincinnati, Cleveland, De-
12These indexes are the Consumer Price Index (CPI) rent components whose construc-tion has been criticized by a number of studies such as the Boskin Commission Report.While we are aware of this problem, these indexes are the only long-run rent series avail-able.
26
troit, Kansas City, Milwaukee, Minnesota, Atlanta, Houston, Los Angeles,
Portland, San Francisco, and Seattle. We then divide the nominal housing
price by the nominal rent and take the logarithm to get the log price-rent
ratio. Notice that since both price and rent are indexes, the log price-ratio
deviates from its true value by a constant. This caveat, however, won’t
affect our analysis of housing market volatility.
Other macroeconomic variables. Annual real GDP growth rate and the
consumer price index are from the FRED website. The Case-Shiller home
price index and the short and long rate are taken from Robert Shiller’s book
Irrational Exuberance, available on Shiller’s website. The real interest rate
used in our estimation is the short rate minus the CPI inflation rate. The
sample period for the macro variables is 1935 to 2009.
27
Ta
ble
1S
um
ma
ry S
tati
stic
s o
f H
ou
sin
g M
ark
ets
, P
rice
Ch
an
ge
s 1
97
9-2
00
9
NY
CP
HIL
BO
ST
PIT
TC
HIC
CIN
CC
LEV
DE
TK
CM
ILW
MIN
NA
TL
HO
US
LAP
OR
TL
SF
RS
EA
Log
Pri
ce C
ha
ng
e0
.06
77
0.0
55
90
.06
79
0.0
36
50
.04
08
0.0
35
80
.03
23
0.0
35
30
.03
50
0.0
40
40
.04
56
0.0
42
80
.03
08
0.0
58
00
.03
32
0.0
63
90
.05
78
Std
De
v0
.07
47
0.0
54
60
.08
11
0.0
22
90
.03
36
0.0
24
80
.02
93
0.0
63
40
.02
67
0.0
31
40
.04
31
0.0
31
60
.04
60
0.0
97
00
.10
15
0.0
85
40
.05
70
Co
rre
lati
on
1.0
00
00
.81
51
0.8
92
90
.10
81
0.3
99
40
.39
55
0.1
86
10
.38
18
0.5
75
10
.21
28
0.5
56
90
.71
29
-0.3
66
70
.58
52
0.5
67
00
.58
78
0.0
94
3
1.0
00
00
.54
53
0.2
90
00
.60
97
0.5
24
50
.27
63
0.4
10
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.43
85
0.4
11
90
.52
80
0.5
67
6-0
.19
17
0.8
45
10
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94
0.7
58
30
.41
50
1.0
00
0-0
.00
99
0.2
60
40
.30
21
0.1
90
30
.35
37
0.5
16
90
.06
79
0.4
77
90
.70
35
-0.3
78
50
.39
98
0.3
80
40
.48
66
-0.0
79
9
1.0
00
00
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50
0.5
33
20
.59
51
0.2
83
50
.03
05
0.6
22
30
.27
95
-0.1
28
4-0
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07
0.2
39
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02
0.2
46
80
.31
62
1.0
00
00
.79
05
0.7
59
50
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66
0.3
15
80
.73
75
0.4
81
10
.30
47
-0.2
35
50
.68
00
0.6
48
80
.64
84
0.6
03
5
1.0
00
00
.87
94
0.9
13
50
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24
0.7
66
20
.64
23
0.4
26
2-0
.26
60
0.5
52
40
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23
0.6
69
00
.39
68
1.0
00
00
.84
20
0.3
19
70
.74
05
0.4
27
40
.16
38
-0.3
74
80
.36
85
0.4
03
20
.44
44
0.3
45
1
1.0
00
00
.66
58
0.6
10
90
.64
45
0.5
15
9-0
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84
0.5
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.51
67
0.6
26
20
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59
1.0
00
00
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85
0.8
68
80
.76
39
0.0
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0.5
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40
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46
0.2
10
5
1.0
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00
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86
0.1
16
0-0
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49
0.5
16
20
.61
79
0.5
33
40
.59
39
1.0
00
00
.69
00
0.2
30
20
.64
80
0.7
83
60
.70
08
0.4
07
3
1.0
00
00
.08
42
0.5
39
90
.58
89
0.6
45
20
.24
13
1.0
00
00
.13
70
0.1
75
60
.10
56
0.3
15
0
1.0
00
00
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13
0.9
03
60
.62
00
1.0
00
00
.73
39
0.6
46
7
1.0
00
00
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69
1.0
00
0
Ta
ble
2S
um
ma
ry S
tati
stic
s o
f H
ou
sin
g M
ark
ets
, Lo
g P
rice
/Re
nt
Ra
tio
s 1
97
9-2
00
9
NY
CP
HIL
BO
ST
PIT
TC
HIC
CIN
CC
LEV
DE
TK
CM
ILW
MIN
NA
TL
HO
US
LAP
OR
TL
SF
RS
EA
log
(P/D
)-0
.41
05
-0.4
37
1-0
.35
78
-0.3
48
5-0
.51
28
-0.3
83
0-0
.41
85
-0.3
65
0-0
.27
00
-0.3
92
0-0
.23
66
-0.3
41
4-0
.07
83
-0.2
66
6-0
.27
48
-0.3
92
6-0
.42
53
Std
De
v0
.22
36
0.1
50
90
.21
00
0.1
12
40
.08
76
0.0
91
00
.08
71
0.2
00
10
.08
78
0.1
70
90
.19
21
0.0
93
40
.10
84
0.2
25
40
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93
0.2
27
20
.22
85
Co
rre
lati
on
1.0
00
00
.87
15
0.9
77
30
.54
29
0.4
69
60
.46
05
0.3
63
80
.46
65
0.2
27
40
.50
92
0.6
42
00
.65
04
-0.1
47
50
.75
50
0.6
07
40
.77
44
0.7
15
2
1.0
00
00
.79
27
0.7
71
10
.77
82
0.6
76
50
.58
35
0.5
61
40
.52
13
0.7
58
20
.81
90
0.8
34
60
.03
77
0.9
32
80
.70
83
0.9
48
60
.88
14
1.0
00
00
.54
54
0.4
18
30
.48
34
0.3
89
60
.52
40
0.1
97
90
.50
67
0.6
34
90
.60
67
-0.2
25
90
.68
35
0.5
04
20
.71
17
0.6
99
5
1.0
00
00
.91
04
0.9
40
50
.91
39
0.8
51
40
.68
02
0.9
40
80
.89
56
0.7
81
8-0
.09
59
0.8
03
90
.37
60
0.8
39
00
.90
67
1.0
00
00
.90
67
0.8
95
70
.77
68
0.7
77
10
.92
05
0.8
68
50
.79
79
0.0
48
70
.85
02
0.5
40
20
.86
37
0.8
50
8
1.0
00
00
.93
62
0.8
99
40
.82
31
0.9
68
60
.93
13
0.8
14
50
.02
76
0.7
75
50
.42
90
0.7
94
90
.83
97
1.0
00
00
.94
36
0.6
54
10
.85
94
0.7
85
40
.61
05
-0.2
35
20
.68
47
0.2
36
60
.71
43
0.7
68
2
1.0
00
00
.55
28
0.7
98
50
.77
57
0.5
88
4-0
.33
69
0.6
75
90
.22
26
0.7
02
40
.75
48
1.0
00
00
.85
73
0.8
25
30
.83
72
0.5
51
60
.65
04
0.5
92
80
.63
94
0.5
76
4
1.0
00
00
.97
25
0.9
01
40
.15
79
0.8
26
10
.54
25
0.8
44
50
.89
36
1.0
00
00
.95
43
0.1
80
30
.88
19
0.6
66
00
.88
91
0.9
12
5
1.0
00
00
.39
94
0.8
97
30
.81
09
0.8
86
50
.83
49
1.0
00
00
.12
48
0.4
96
10
.07
51
-0.0
92
9
1.0
00
00
.77
83
0.9
91
30
.88
34
1.0
00
00
.72
22
0.5
60
3
1.0
00
00
.90
91
1.0
00
0
Table 3 Factor Decomposition of Log Price/Rent Ratios 1979-2009
Restricted Model Unrestricted Model
Nat'l Factor Local Factor Local Share Nat'l Factor Local Factor Local Share
NYC 0.0943 0.1885 0.6666 0.1579 0.1838 0.5379
PHIL 0.0943 0.0959 0.5043 0.1637 0.0922 0.3604
BOST 0.0943 0.1773 0.6528 0.1292 0.1750 0.5754
PITT 0.0943 0.0355 0.2735 0.1147 0.0310 0.2127
CHIC 0.0943 0.0300 0.2412 0.1062 0.0301 0.2208
CINC 0.0943 0.0182 0.1614 0.0611 0.0389 0.3888
CLEV 0.0943 0.0397 0.2964 0.0778 0.0350 0.3099
DET 0.0943 0.1289 0.5775 0.0928 0.1302 0.5837
KC 0.0943 0.0540 0.3640 0.0813 0.0616 0.4311
MILW 0.0943 0.0792 0.4564 0.1198 0.0673 0.3597
MINN 0.0943 0.1042 0.5249 0.1099 0.1000 0.4764
ATL 0.0943 0.0460 0.3281 0.0684 0.0530 0.4367
HOUS 0.0943 0.1386 0.5952 0.0434 0.1187 0.7324
LA 0.0943 0.1517 0.6168 0.1999 0.1078 0.3504
PORTL 0.0943 0.1862 0.6638 0.2004 0.2079 0.5092
SFR 0.0943 0.1509 0.6154 0.2209 0.0992 0.3098
SEA 0.0943 0.1493 0.6129 0.2138 0.0867 0.2886
Average 0.0943 0.1044 0.4795 0.1271 0.0952 0.4167
Note: this table reports the standard deviations of the national factor and local factors of the price-rent
ratios in 17 cities. In the restricted model, the loading on the national factor is restricted to be 1. In the
unrestricted model, the factor loading can change across different cities. Local share is the percentage of
the total standard derivation attributable to local factors.
30
Table 4 Volatility of Local Economy
Local Growth Rate Local Risk Premium Correlation
NYC 0.0588 0.1516 -0.7652
PHIL 0.0347 0.0838 -0.1945
BOST 0.0353 0.1743 0.0199
PITT 0.0066 0.0357 0.1280
CHIC 0.0078 0.0303 0.1421
CINC 0.0018 0.0185 0.2547
CLEV 0.0083 0.0378 -0.1972
DET 0.0110 0.1281 -0.1022
KC 0.0116 0.0546 0.1636
MILW 0.0174 0.0819 0.3492
MINN 0.0071 0.1057 0.2321
ATL 0.0145 0.0505 0.4200
HOUS 0.0292 0.1531 0.5383
LA 0.0385 0.1377 -0.1863
PORTL 0.0212 0.1903 0.2386
SFR 0.0293 0.1692 0.6132
SEA 0.0142 0.1482 -0.0134
Average 0.0204 0.1030 0.0965
Note: this table reports the standard deviations of the present value of the expected local rent growth
rates and the standard deviations of the local risk premiums (first two columns). The last column
includes the correlation coefficients between local growth rate and local risk premium.
31
Table 5 Macroeconomic Fundamentals of House Markets
Nat'l Growth Interest Rate Nat'l Risk
Mean 0.0140 0.0227 n/a
Std dev 0.0691 0.1725 0.1195
Correlation 1.0000
0.8342 1.0000
-0.8140 -0.7826 1.0000
Note: this table reports the summary statistics of the present value of the expected national rent growth
(2nd
column), the present value of the expected real interest rates (3rd
column) and the aggregate house
market risk premium (4th
column). The first two series are estimated on the annual data from 1936 to
2009 using a dynamic factor model. The last series is obtained as a residual term from the Campbell-
Shiller formula using data from 1979 to 2009.
32
Table 6 Price-Rent Ratio and Economic Fundamentals
Nat'l Price-Rent Real Interest Rate Nat'l Rent Growth R2
-0.8878** 2.2318** 0.4647
(0.1885) (0.5767)
-0.2076**
0.1783
(0.0827)
Local Price-Rent Local Rent Growth R2
NYC
3.5609** 0.7320
(0.4001)
PHIL
1.4930** 0.2650
(0.4617)
BOST
0.9026 0.033
(0.9066)
PITT
0.3475 0.0047
(0.9387)
CHIC
-0.1076 0.0002
(1.4329)
CINC
-1.8497 0.0284
(2.0093)
CLEV
2.1090** 0.1276
(1.0240)
DET
3.0455 0.0228
(3.6983)
KC
0.2930 0.0047
(0.7917)
MILW
-2.1878 0.0614
(1.5885)
MINN
-2.2109 0.0263
(2.4985)
ATL
-0.2518 0.0086
(0.5023)
HOUS
-1.5951** 0.13335
(0.7545)
LA
1.5961** 0.2050
(0.5836)
PORTL
-1.0367 0.0154
(1.5390)
SFR
-2.0719** 0.2152
(0.7348)
SEA
1.1211 0.0152
(1.6741)
Note: Coefficient estimates with ** indicate that they are significant at 5% level.
33
Table 7 Housing Market Risk Premium and Pricing Error
Risk Premium Yield Spread Dividend Yield Earning/Price R2
0.0542** -1.7722*
0.7248
(0.0070) (0.9351)
0.0459**
-1.3901** 0.7883
(0.0067)
(0.3845)
Pricing Error 1/Rate 1/Inflation Inflation2 R2
0.0843
0.0854
(0.0512)
0.1141**
0.0005 0.1556
(0.0538)
(0.0003)
0.0940* 0.0434
0.159
(0.0504) (0.0277)
Note: The first panel of this table contains the results of an OLS regression of the Campbell-Shiller
residuals on the yield spread, S&P 500 dividend yield and S&P 500 earning/price ratio. The second panel
reports the results of an OLS regression of the regression residual from the first OLS on inverse interest
rate and inflation. Numbers in parentheses are standard errors.
34
Figure 1: National Factor of Price-Rent Ratio and House Price Index
-.8
-.6
-.4
-.2
.0
.2
1980 1985 1990 1995 2000 2005
LOG(NP/CPI) PDN
This figure plots the estimated national factor of log price-rent ratio, PDN, and log Case-
Shiller house price index over the CPI index, LOG(NP/CPI).
35
Figure 2: Local Factor Share vs Local Market Risk Premium Volatility
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vo
lati
lity
of
Idio
syn
cra
tic
Ris
k P
rem
ium
s
Price/Rent Volatility Due to Local Factors
This figure plots the fraction of the total volatility in the house price-rent ratio due to the
local factor (the horizontal axis) versus the volatility of local risk premium (the vertical
axis) across the 17 housing markets.
36
Figure 3: Local Factor Share vs Local Growth Volatility
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vo
lati
lity
of
Loca
l R
en
t G
row
th
Price/Rent Volatility Due to Local Factors
This figure plots the fraction of the total volatility in the house price-rent ratio due to
the local factor (the horizontal axis) versus the volatility of local rent growth (the vertical
axis) across the 17 housing markets.
37
Figure 4: Housing Market Risk Premium and Pricing Error
-.6
-.4
-.2
.0
.2
-.10
-.05
.00
.05
.10
.15
1980 1985 1990 1995 2000 2005
RISK_PREMIUM MIS_PRICING
This figure plots the estimated aggregate housing market risk premium (left scale) and
the pricing error (right scale).
38
Figure 5: Housing Market Pricing Error
-.12
-.08
-.04
.00
.04
.08
.12
1980 1985 1990 1995 2000 2005
Pricing Error Fitted Value
This figure plots the estimated housing market pricing error and its fitted value from a
regression on the inverse of the nominal interest rate and the square of inflation.
39