2011 V39 2: pp. 313–344
DOI: 10.1111/j.1540-6229.2010.00297.x
REAL ESTATE
ECONOMICS
Explaining Asset Mispricing Using the
Resale Option and Inflation Illusion
Darren K. Hayunga∗ and Peter P. Lung∗∗
We investigate the overconfidence theory and inflation-illusion hypothesis of
asset mispricing. Both concepts address subjective asset valuation but place
the impetus on differing explanations within the standard dividend-growth
model. We find that one of the theoretical outcomes of overconfidence—asset
turnover—consistently explains mispricing in U.S. housing markets. Further, we
find that asset turnover subsumes expected inflation in certain specifications,
suggesting that dispersion in investors’ beliefs is a better explanation of asset
mispricing than the investors’ inability to properly discount future cash flows.
We examine the ability of the inflation-illusion hypothesis originally proposed
by Modigliani and Cohn (1979) and the overconfidence theory of Scheinkman
and Xiong (2003) and Hong, Scheinkman and Xiong (2006) to explain the
subjective valuation of assets. Whereas both concepts offer insight into asset
mispricing, the contrasting nature of the two within the standard dividendgrowth model suggests a quantitative analysis examining whether mispricing
is attributable to one in lieu of the other or if both are predictive. The joint
determination of the empirical value of the rationales addresses an omittedvariable bias, which has not been generally addressed in the literature.
The inflation-illusion hypothesis contends that investors suffer from an incorrect assessment of expected inflation that causes them to discount real dividends
by nominal interest rates.1 Investors fail to recognize that an increase in expected inflation also leads to an increase in the nominal dividend-growth rate.
Accordingly, this error results in an inflation-induced mispricing in assets such
that prices are above their fundamental value when expected inflation is low
and vice versa.
∗
University of Texas at Arlington, 701 South West Street, Box 19449, Arlington, TX
76019 or hayunga@uta.edu.
∗∗
University of Texas at Arlington, 701 South West Street, Box 19449, Arlington, TX
76019 or lungpeip@uta.edu.
1
The inflation-illusion hypothesis is sometimes referred to as the money–illusion
hypothesis.
C 2011 American Real Estate and Urban Economics Association
314 Hayunga and Lung
Recent studies revive the inflation-illusion hypothesis to explain asset mispricing in the U.S. stock and bond markets as well as the U.S. and U.K. real estate
markets. Campbell and Vuolteenaho (2004) find that the hypothesis better fits
the empirical relation between U.S. stock prices and inflation than the standard explanations that inflation (i) either hurts the profitability of a corporation
or (ii) makes the economy more risky. Cohen, Polk and Vuolteenaho (2005)
address the issue of risk with respect to inflation illusion by examining the
joint hypotheses of inflation illusion and the capital asset pricing model. Their
empirical results support inflation illusion as a phenomenon in the U.S. stock
market. Brunnermeier and Julliard (2008) use the inflation-illusion hypothesis
to examine the U.S. and U.K. housing markets and find that nominal interest
rates explain a significant portion of the variation in real estate mispricing. Fehr
and Tyran (2001) find that a fully anticipated negative nominal shock can cause
long-lasting real income losses—results suggesting direct and indirect effects
of inflation illusion.
At about the same time as Modigliani and Cohn suggested inflation-illusion,
Harrison and Kreps (1978) formulated a theory of speculative investor behavior
due to the right an investor has to resell the asset in a later period (the resale
option). Scheinkman and Xiong (2003) and Hong, Scheinkman and Xiong
(2006) extend the model to continuous time. The resale-option theory shows that
when investors believe they possess more precise knowledge than is actually
the case, these agents gain an overconfidence which results in heterogeneous
beliefs in asset fundamentals. Because current buyers feel they can resell an
asset to a future purchaser who will pay an even greater price, current buyers
pay amounts greater than the fundamental value.
Thus, for even small divergent beliefs, asset bubbles develop and are sufficient
to generate a transaction between the current owner and overconfident buyer
because the current owner will sell the asset whenever the price surpasses his
or her fundamental valuation. Accordingly, speculative bubbles will cause a
trading furor, which increases asset turnover as well as price volatility. Chen,
Lung and Wang (2009) demonstrate that asset turnover explains U.S. stock
market mispricing.
Considered jointly, both the overconfidence theory and the inflation-illusion
hypothesis address the difference between fundamental dividend growth and
subjective valuation, but the impetus manifests in differing ways. Consider
the Gordon (1962) static growth model, D/P = R − G, where D/P is the
dividend-price ratio, R is the objective valuation of the expected long-term
discount factor, and G is the objective valuation of the expected long-term
growth rate. Both R and G are the rates in excess of the risk-free rate. Under
either mispricing explanation, there is a subjective valuation of the growth rate,
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 315
Gs , such that D/P = R − G = R s − Gs = − G + R s − (Gs − G), where
− G is the objectively expected dividend-growth rate, R s is the subjective risk
premium, and (Gs − G) is a mispricing term (Campbell and Vuolteenaho 2004,
Brunnermeier and Julliard 2008).
The divergence in the mispricing explanations lies in the final term of (Gs −
G). According to inflation illusion, irrational investors fail to adjust the nominal
growth rate of dividends to match the nominal discount rate. Hence, Gs decomposes into two parts: the objective growth rate, G, and inflation. Consequently,
asset mispricing is driven by expected inflation, which we denote by E(π ).
Alternatively, the overconfidence theory shows that the mispricing term is due to
divergence in buyers’ beliefs. Consider two heterogeneous groups of investors
with the corresponding subjective components of the dividend growth rate
denoted by GA and GB . These components decompose into two additional terms
as GA = G + ξ A and GB = G + ξ B , where G is the same objective expected
growth rate net of the risk-free rate, and ξ is the subjective component driven
by the agent’s respective belief based on their private signal. Heterogeneous
beliefs between the two buyers due to the subsequent resale of the asset cause
a transaction because the current asset owner will sell when a bid exceeds her
or his valuation. Thus, the mispricing term becomes Gs − G = [G + max (ξ A ,
ξ B )] − G = max (ξ A , ξ B ).
Scheinkman and Xiong (2003), Hong, Scheinkman and Xiong (2006) as well
as Cao and Ou-Yang (2009) show that the greater the divergence between
subjective and objective growth rates, the higher the asset turnover. Consequently, asset mispricing is positively related to agents’ heterogenous beliefs
and turnover. We denote by g̃ the turnover measure.
We empirically investigate the two mispricing concepts using the well-suited
U.S. housing market. The residential real estate market offers advantages for
mispricing analysis such as limited short selling, reduced market efficiency due
in part to negotiation and heterogeneous products and inelasticity of supply in
the short term.
Overall, we find considerable evidence that asset turnover better explains mispricing than expected inflation. Across multiple specifications that address
econometric issues and differing time periods, turnover exhibits a persistent relation with mispricing. Time-series tests using Granger-casuality, variance decomposition and impulse response affirm the multivariate correlations. Because
resale-option theory provides insight into or hypothesizes about the relation between the second central moment of asset mispricing and g̃, we investigate and
find asset turnover consistently explains mispricing volatility.
316 Hayunga and Lung
We do not observe the same consistent results for expected inflation. Individually, E(π ) is at times predictive; however, in the presence of other mispricing
predictors, the inflation-illusion proxy rarely exhibits explanatory value. In
addition, expected inflation does not perform well in time-series tests. For
instance, E(π ) does not Granger-cause mispricing in any of a number of specifications.
We provide further detail of these findings in the remainder of this paper. We
discuss the U.S. housing market relative to mispricing in the next section. We
describe the model in the third section along with econometric issues in the
fourth section. Subsequently, we present the results and briefly conclude.
U.S. Residential Real Property Markets
To disentangle the two explanations of mispricing, we examine prices in the
U.S. housing market. This is foremost due to the fact that real estate markets
often experience disequilibria. Hence, if inflation illusion and/or resale option
are to be championed, the explanations should account for mispricing in real
property markets. Further, real estate markets are an ideal natural laboratory
based upon some specific characteristics.
The first unique characteristic is the difficulty in short selling the asset. Classic
finance theory posits that informed arbitrageurs will trade away any excess
returns resulting from asset mispricing in reasonably frictionless markets. This
theory assumes the ability to sell short; however, the real estate market has
historically shown little to no capacity to facilitate such a transaction.2 Because
of this difficulty, real estate optimists should increase prices during bubbles, all
else equal. In addition, high transaction prices further confound the ability of
pessimists to trade against any mispricing.
A second attribute of real estate markets is the greater propensity for speculative bubbles due to the less-than-strong-form efficiency of property markets.
On the one hand, real estate is liquid enough such that there exist quarterly
price indices composed of same-property repeat sales. On the other hand, the
2
The Chicago Mercantile Exchange launched housing derivatives in May of 2006 that
allow for a short position linked to a home price index. In June of 2008 the founder of the
market-making firm for the futures contracts stated that “liquidity during the first two
years has been disappointing, at best.” Another potential short-sell vehicle preparing
to launch is an exchange-traded product from MacroMarkets, co-founded by Shiller
and Weiss, which will be based on the S&P/Case-Shiller Composite-10 Home Price
Index. Bertus, Hollans and Swidler (2008) consider in an academic study the ability of
a homebuilder to short sell a futures contract. They find the results mixed, conditional
on the time period.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 317
heterogeneous and localized nature of real estate markets introduces bargaining power, information inefficiency and behavioral limitations. For example,
Harding, Rosenthal and Sirmans (2003) find that gender, age, income and education have an impact on bargaining power and existing-home transaction
prices. Other studies find that information asymmetries exist for out-of-town
buyers due to an anchoring-induced bias and search costs (Lambson, McQueen
and Slade 2004, Clauretie and Thistle 2007).
The short-term inelasticity of supply offers another contribution of the asset
class to a study of mispricing. Equilibrium in residential housing markets will
be problematic if there exists any excess quantity demanded because it cannot
be matched quickly. The short-term result will be a shortage of supply and the
resulting increase in prices—prices that are potentially in excess of fundamental
values. A theoretical paper by Glaeser, Gyourko and Siaz (2008) shows how
the inelasticity of housing supply has an impact on asset bubbles.
A fourth feature of the real estate market is the influence of financing on asset
values—a point not lost on the credit crunch during the later portion of the
2000s decade. Herring and Wachter (2005) show how the real estate lending
process can contribute to mispricing. As real estate prices increase, the supply
of credit to the real estate industry increases, which subsequently is likely to
lead to further increases in the price of real estate. Alternatively, if there is a
so-called pop of the asset bubble, bank behavior may exacerbate the collapse
of real estate prices as credit capital shrinks with the reduction in value of loans
collateralized by real estate.3
Theoretical Dynamic Model
Before we can examine expected inflation and asset turnover as determinants, we need to identify mispricing. As in prior studies by Campbell and
Vuolteenaho (2004) and Brunnermeier and Julliard (2008), we use the Campbell and Shiller (1988) valuation framework. The model is a reduced-form
vector autoregressive specification that obtains the fundamental component of
the log price-rent ratio and, consequently, also identifies the mispricing value.
We provide a detailed description of the econometric model in the next section.
In this section, we discuss the mispricing theory in a dynamic setting and its
application to inflation illusion and the resale option.
The VAR system uses four variables, one of which is the realized log price–rent
ratio, denoted by pt − dt . Three components form this term: (i) the discounted
3
The additional characteristics of incomplete markets, myopic pricing behavior and
unique regulations further promote real estate as an experimental environment.
318 Hayunga and Lung
∞ τ −1
expected excess log rent growth rates,
ρ Et (Gt+τ ), (ii) the discounted
∞ τ =1
expected excess log house returns τ =1 ρ τ −1 Et (Rt+τ ) and (iii) the estimated
mispricing term, t , such that
pt − dt =
∞
ρ τ −1 Et (Gt+τ ) −
τ =1
∞
ρ τ −1 Et (Rt+τ ) + t .
(1)
τ =1
The excess log rent growth rates and log house returns are τ step-ahead VAR
forecasts conditional
observed up
t. The fundamental value in
to time
onτ data
−1
τ −1
Et (Gt+τ ) − ∞
Et (Rt+τ ), whereas the estiEquation (1) is ∞
τ =1 ρ
τ =1 ρ
mated mispricing term t is the difference between the realized price-rent ratio
on the left-hand side and the fundamental value component on the right.
More formally, Campbell and Shiller (1988) express the log ratio of pt − dt as
pt − dt = c +
∞
ρ τ −1 (Gt+τ ) −
τ =1
∞
ρ τ −1 (Rt+τ ),
(2)
τ =1
where c is a constant less than unity and is equal to k/1 − ρ, ρ = 1/(1 +
1
), and G and R are real returns as
exp(d̄ − p̄), k = −log(ρ) − (1 − ρ)log( ρ−1
above. |ρ| is a constant less than one.
Under the transversality condition that rules out intrinsic bubbles, Equation (2)
holds in expectation for any probability measure. It can be written as
pt − dt = c +
∞
ρ τ −1 Et (Gt+τ ) −
τ =1
=c+
∞
τ =1
∞
ρ τ −1 Et (Rt+τ )
τ =1
ρ
τ −1
Est (Gt+τ )
−
∞
(3)
ρ
τ −1
Est (Rt+τ ),
τ =1
where E is the rational expectations operator and Es is the subjective expectations operator. By adding and subtracting the objective growth rate and
rearranging, Equation (3) can be rewritten as
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 319
pt − dt = c +
∞
ρ τ −1 Est (Gt+τ ) −
τ =1
+
ρ τ −1 Et (Gt+τ ) −
τ =1
=c+
ρ τ −1 Et (Gt+τ ) −
∞
∞
ρ τ −1 Et (Gt+τ )
τ =1
τ =1
+
ρ τ −1 Est (Rt+τ )
τ =1
∞
∞
∞
∞
ρ τ −1 Est (Rt+τ )
τ =1
ρ
τ −1
Est (Gt+τ )
τ =1
−
∞
ρ
τ −1
Et (Gt+τ ) ,
(4)
τ =1
τ −1 s
τ −1
where [ ∞
Et (Gt+τ ) − ∞
Et (Gt+τ )] is defined as mispricing in
τ =1 ρ
τ =1 ρ
Campbell and Vuolteenaho (2004) as their Equation (2) and in Brunnermeier
and Julliard (2008) as their Equation (A.1).
Subsequent to identifying the mispricing component, we investigate the relationship of asset turnover and expected inflation with the mispricing component.
Because inflation illusion contends that investors fail to distinguish between
nominal and real discount rates and mistakenly discount rents, the hypothesis
gives a specific relation between the subjective and objective expectations for
the excess rent growth rate such that Est (Gt+τ ) = Et (Gt+τ − πt+τ ), where π t+τ
denotes the inflation at time t + τ ∀ t and τ . Therefore, Equation (4) can be
rewritten as
pt − dt = c +
∞
ρ τ −1 Et (Gt+τ ) −
τ =1
+
∞
∞
ρ τ −1 Est (Rt+τ )
τ =1
ρ τ −1 [Et (Gt+τ − πt+τ ) − Et (Gt+τ )],
(5)
τ =1
=c+
∞
ρ τ −1 Et (Gt+τ ) −
τ =1
∞
∞
ρ τ −1 Est (Rt+τ ) + t ,
τ =1
τ −1
where t = − τ =1 ρ Et (πt+τ ). Consequently, the inflation-illusion hypothesis suggests that both the observed log price–rent ratio and mispricing decrease
with expected inflation.
The alternative overconfidence theory shows that investors use subjective expectations for the excess log growth rate to value assets. The subjective beliefs may stem from investors’ overconfidence about their private signals as in
models by Kyle and Wang (1997) and Daniel, Hirshleifer and Subrahmanyam
(1998). To capture such differences in opinion in the real estate markets, we
320 Hayunga and Lung
consider two heterogeneous groups of buyers with their corresponding subjecB
tive components of the rent growth rate denoted by ξ A
t and ξ t . The subjective
expectations for the two buyers can be written as
A
EA
t (Gt+τ ) = Et (Gt+τ + ξt+τ ) and
B
) for τ = 1, 2, . . . .
EBt (Gt+τ ) = Et (Gt+τ + ξt+τ
Given the short-sale constraint in the real estate market, only the opinion of the
buyer group with the higher valuation is prominently reflected in the market—
the buyers with the lower valuation decide not to participate. Harrison and
Kreps (1978) and Scheinkman and Xiong (2003) show that the heterogeneous
beliefs between the two buyers should induce a nonnegative resale option that
causes asset prices to exceed the current owner’s valuation. Subsequently, the
current owner chooses an optimal stopping time to exercise his or her resale
option, the value of which increases in the heterogeneous beliefs between the
two groups. Put differently, the subjective components of the growth rate for
O
A
B
the owner group, ξ O
t , is given by ξ t ≡ max (ξ t , ξ t ).
Thus, the relation between the subjective and objective expectations of the
growth rate is
O
A
B
EO
t (Gt+τ ) = Et (Gt+τ + ξt+τ ) = Et (Gt+τ + max(ξt , ξt )) for τ = 1, 2, . . . ,
where EO
t denotes the subjective expectations of the growth rate for the buyer,
who becomes the new owner. From Equation (4), the observed log price–rent
ratio is rewritten such that
pt − dt = c +
∞
ρ
τ −1
Et (Gt+τ ) −
τ =1
+
∞
∞
ρ τ −1 Est (Rt+τ )
τ =1
ρ τ −1 Et (Gt+τ ) + max ξtA , ξtB − Et (Gt+τ ) ,
τ =1
= c+
∞
τ =1
=c+
∞
τ =1
ρ
τ −1
Et (Gt+τ ) −
∞
ρ
τ =1
ρ τ −1 Et (Gt+τ ) −
∞
τ −1
Est (Rt+τ ) +
∞
ρ τ −1 max ξtA , ξtB ,
τ =1
ρ τ −1 Est (Rt+τ ) + r ,
(6)
τ =1
τ −1
max(ξtA , ξtB ), the excess optimism regarding growth
where t = ∞
τ =1 ρ
rates in the future.
Scheinkman and Xiong (2003) and Hong, Scheinkman and Xiong (2006) show
that such excess optimism increases asset turnover. Because turnover is a proxy,
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 321
which is not the case with expected inflation, we elaborate on the direct link
between mispricing and the asset-turnover proxy by including selected equations from the Hong, Scheinkman and Xiong (2006) paper in the appendix.
In addition, we provide the theory of Cao and Ou-Yang (2009), who also directly link overconfidence to turnover but do so using a different analytical
framework.
The intuition of the link between mispricing and trading/turnover is as follows.
Assume two groups of investors observe the same publicly available signals
about the value of an asset, but they have different beliefs about the fundamental value. One group is, in general, more optimistic than the other. As
information flows into the market, their forecasts change and the group that
is relatively more optimistic at one point in time may become relatively more
pessimistic at a later date. These fluctuations in expectations generate trade. As
heterogeneous beliefs widen, the assets are more likely to be overvalued and
deviate from the value of the current owner’s expectations in the presence of
short-sale constraints. Thus, the current owner sells the asset to the party with
the more optimistic expectations and turnover occurs. Consequently, the greater
the heterogeneous beliefs, the greater the asset mispricing and turnover.4
Noted previously in this section, mispricing attributed to inflation illusion in
Equation (5) and to overconfidence in Equation (6) holds under the assumption
of the transversality condition. To fully describe the estimation of the VAR
coefficients this assumption is relaxed and explosive paths are allowed as in
Brunnermeier and Julliard (2008). Equation (4) becomes
pt − dt = c +
∞
ρ τ −1 Ẽt (Gt+τ ) −
τ =1
∞
ρ τ −1 Ẽt (Rt+τ ) + t ,
(7)
τ =1
where Ẽt is the conditional expectation at time t computed using the VAR, and
Ẽt (Gt+τ ) and Ẽt (Rt+τ ) are the τ -step ahead VAR forecasts conditional on the
data observed up to time t.
Econometric Model and Data
Following previous studies, we use the VAR model to obtain the fundamental
component of the log of price–rent ratio and thereby extract the mispricing
component of real estate prices. As detailed in the theoretical section, the
4
The intuition is the reason that asset turnover is used commonly as a proxy for heterogeneous beliefs that drive asset mispricing. See, for example, Harris and Raviv (1993),
Shefrin and Statman (1994), Kyle and Wang (1997), Odean (1998), Scheinkman and
Xiong (2003), Hong, Scheinkman and Xiong (2006), Chen, Lung and Wang (2009) and
Cao and Ou-Yang (2009).
322 Hayunga and Lung
VAR system uses four variables, which are all demeaned: (i) the realized log
price–rent ratio, pt − dt , (ii) the realized excess log rent growth rate, Gt , (iii)
the realized excess log house return, Rt and (iv) the smoothed moving average
of inflation, π t . We define xt as a 4 × 1 vector at time t as
xt = (pt − dt , Gt , Rt , πt ) ,
Pt
t
t
where
pt − dt = log( D
) − Rf,t , Gt = log( DDt−1
) − Rf,t , Rt = log( PPt−1
)−
t
Rf,t , and π is inflation exponentially smoothed using 12 monthly lags. In these
equalities, P is the price, D is the rent and Rf is the risk free rate, which is
the three-month Treasury-bill rate corresponding to time t. The expected xt is
E(xt+τ ) = β τ xt , where β is the matrix {β pd , β G , β R , β π }, the coefficients of
the four variables in the VAR system.
Econometric Considerations
A necessary condition of the VAR model is that the processes must possess timeinvariant first and second central moments, i.e., the time series must not have
trends, fixed seasonal patterns or time-varying variances. Unless the means and
covariance matrices are bounded and the polynomial defined by the determinant
has all its roots outside the complex unit circle, the finite-order VAR is not welldefined and subsequent findings are spurious.5
As is the case with other applications of the dividend-price ratio, the rent–price
process is a submartingale. We use two methods to address the nonstationarity.
The first is to use the Bayesian approach because it is robust to nonstationarity.
Please refer to the appendix for discussion of how the Bayesian approach
is robust to nonstationarity. This method is consistent with the other studies
of mispricing by Campbell and Vuolteenaho (2004) and Brunnermeier and
Julliard (2008). Although the Bayesian approach provides us a natural and
principled way to estimate the coefficients in the VAR model in the presence
of unit roots, it is not flawless. The Bayesian approach requires a prior that can
be subjective and affects posterior distributions. Therefore, we also follow the
classical method of first differencing.6
After obtaining the mispricing series using either Bayesian or differencing in
the first stage, we model it as the dependent variable in the second stage with
E(π ), g̃ and other control variables. We may experience another econometric
issue in the second stage—endogeneity of prices with trading volume. Clayton,
5
Refer, for example, to Lütkephols (2005) for proofs and support of the finite-order
VAR specifications
6
Note that cointegration is not an alternative because the rent–price ratio as a nonstationary process is not cointegrated with the other stationary variables.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 323
Miller and Peng (2010) provide evidence that housing cycles demonstrate a
positive correlation between the two attributes. We use seemingly unrelated
regression (SUR), Bayesian and instrumental variables (IV) to control for the
simultaneous determination of contemporaneous price and asset turnover.7 We
find the results are robust to using ordinary least squares, Bayesian, SUR or
IV to model the second stage. Thus, we report the findings from using the
Bayesian approach in the first stage to obtain mispricing followed by the use of
SUR in the second stage. In addition, we report results using first differences
in the first stage and then OLS in the second.
Data
We use two measures of housing prices as our samples. The first is from the U.S.
Office of Federal Housing Oversight Enterprise (OFHEO). It is a repeat-sales
index based upon mortgage transactions on single-family properties whose
mortgages have been purchased or securitized by Fannie Mae or Freddie Mac.
While a shortcoming of the OFHEO Index is that it focuses on conventional
financing, it provides broad geographic coverage and has been in existence
since 1975. To address the OFHEO Index’s concentration on conventional
financing, we also use the S&P/Case-Shiller Index (SPCS), which begins in
1987. This index may better represent the depth of the U.S. residential asset
market as it includes homes that are financed with nonconventional financing
such as subprime and jumbo loans. Conversely, SPCS Index does not have the
geographic coverage of the OFHEO Index. The difference between the two
indices became evident during the housing-price runup of the mid-2000s (see,
e.g., Cooper 2008).
We construct the two main determinants of interest as in prior studies. We estimate E(π ) based on the exponentially smoothed consumer price index using 12
monthly lags, which is the same process as in Campbell and Vuolteenaho (2004)
and Brunnermeier and Julliard (2008). The quarterly housing turnover ratio is
Housing Sold/Housing Inventory, both levels in the same time period. Similar
to the smoothed inflation measure in Campbell and Vuolteenaho (2004), the
turnover ratio is exponentially smoothed using 12 monthly lags. The smoothed
measure is further detrended. This measure is consistent with previous models of overconfidence by Kyle and Wang (1997) and Odean (1998) as well as
divergence-of-opinion from Harris and Raviv (1993).
In addition to investigating the informational value of E(π ) and g̃, we examine
specifications that control for additional determinants of housing rents and
7
In using IV, we lag asset turnover one quarter because lagged trading volume is highly
correlated with the contemporaneous vector but uncorrelated with the contemporaneous
error term.
324 Hayunga and Lung
Table 1 The table presents summary statistics of the four variables in the Campbell
and Shiller (1988) VAR decomposition.
Obs.
Mean
SD
Min.
Max.
Dickey–Fuller
p-value
OFHEO price index (quarterly observations 1975–2007)
Levels
P/R
131
G
131
R
131
π
131
First difference
P/R
130
G
130
R
130
π
130
5.305
−0.007
−0.003
0.009
0.109
0.007
0.013
0.007
5.144
−0.030
−0.042
−0.006
5.602
0.008
0.033
0.035
0.989
0.009
0.002
0.009
0.003
0.002 × 10−2
−0.008 × 10−2
−0.005 × 10−2
0.011
0.005
0.009
0.002
−0.038
−0.016
−0.039
−0.012
0.030
0.029
0.023
0.012
0.000
0.000
0.000
0.000
S&P/Case–Shiller price index (quarterly observations 1987–2007)
Levels
P/R
83
G
83
R
83
π
83
First difference
P/R
82
G
82
R
82
π
82
4.597
−0.004
0.001
0.008
0.231
0.005
0.023
0.003
4.342
−0.018
−0.070
0.002
5.956
0.008
0.063
0.016
0.702
0.017
0.013
0.033
0.006
0.017 × 10−2
−0.001
−0.008 × 10−4
0.022
0.004
0.015
0.004
−0.072
−0.010
−0.035
−0.005
0.061
0.010
0.044
0.004
0.003
0.000
0.000
0.000
prices. Clearly, the new construction of residential real property, changes in
employment and national interest rates will affect fundamental house prices
but may also predict mispricing as well as asset turnover. Thus, we model these
and other economic determinants in an unrestricted specification. We detail the
covariates in the Appendix.
Empirical Results
In the first stage, we determine the VAR coefficients and mispricing. Table 1
reports the summary statistics of the four factors in the dynamic model. Note
the Dickey-Fuller test statistics indicate the presence of a unit root for the log
price–rent time series. This holds for both price indices.
Figure 1 graphs the resulting mispricing values along with the levels of asset
turnover and expected inflation using Bayesian analysis. Although the top
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 325
Figure 1 The figure displays the time series of asset mispricing, asset turnover and
expected inflation. The mispricing values reflect the prices from the Office of Housing
Enterprise Oversight Index in the top graphs and from the S&P/Case-Shiller Index in
the bottom figures. The two graphs on the left are the time-series levels, while the two
on the right exhibit the time-series volatility.
graphs in Figure 1 note some relation between the three attributes using OFHEO
prices, the lower two graphs present a strong relation between asset turnover
and mispricing using the SPCS price vector. Specifically, we observe that asset
turnover exhibits Pearson correlations of 0.36 with the OFHEO mispricing level
0.30 with the OFHEO mispricing volatility, 0.79 with the SPCS mispricing
level and 0.66 with the SPCS mispricing volatility. The expected-inflation time
series demonstrate less correlation with mispricing: −0.31 with the OFHEO
mispricing level −0.18 with the OFHEO mispricing volatility, −0.24 with the
SPCS mispricing level and −0.04 with the SPCS mispricing volatility.
Mispricing Levels
We formalize these vectors into multivariate models, initially employing SUR.
The results in Table 2 report the mispricing levels. Models (1) and (2) in
Table 2 demonstrate that both variables are significant using either price index
when g̃ or E(π ) is the single predictor. Notably, g̃ as the sole determinant
is quite explanatory with an adjusted R 2 of 0.59 when the SPCS Index is the
326 Hayunga and Lung
Table 2 The table reports results regressing asset mispricing on asset turnover,
expected inflation and control variables using a SUR model.
(1)
(2)
(3)
(4)
(5)
OFHEO price index (quarterly observations 1975–2007)
g̃
E(π )
7.21∗∗∗
(0.88)
−4.65∗∗∗
(0.02)
6.83∗∗∗
(0.84)
−3.58∗∗∗
(1.11)
9.64∗∗∗
(1.87)
−1.40
(1.79)
0.00
(0.04)
0.10
(0.08)
−3.58∗
(2.11)
−1.45
(2.81)
0.09
0.14
0.19
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment
Supply
Adjusted R2
0.04
11.01∗∗∗
(1.60)
0.97
(5.07)
−0.04
(0.05)
−0.03
(0.10)
0.47
(2.45)
4.45
(6.90)
−0.01
(0.01)
−0.00∗∗
(0.00)
0.34
S&P/Case–Shiller price index (quarterly observations 1987–2007)
g̃
E(π )
16.12∗∗∗
(0.88)
−12.12∗∗
(5.57)
16.21∗∗∗
(0.92)
0.40
(2.27)
16.98∗∗∗
(1.58)
−4.05
(4.08)
−0.05
(0.05)
0.08
(0.07)
−1.80
(1.91)
5.98
(6.82)
0.59
0.59
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment
Supply
Adjusted R2
0.59
0.04
15.94∗∗∗
(1.53)
−7.30∗
(4.05)
−0.05
(0.05)
0.03
(0.07)
−0.30
(1.93)
7.15
(6.55)
−0.04∗∗∗
(0.01)
−0.00
(0.00)
0.73
Note: The mispricing regressand is obtained using the Bayesian approach to address
nonstationarity. Standard errors are in parentheses. ∗∗∗ , ∗∗ and ∗ denote statistical significance at the 1%, 5% and 10% levels, respectively.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 327
regressand. Expected inflation does not exhibit the same individual power—the
adjusted R 2 is 0.04. Moreover, when in Model (3) both proxies are in the same
specification, E(π ) is surprisingly not a determinant of asset mispricing using
the SPCS Index. Given that the adjusted R 2 is the same without E(π ) in the
model, g̃ appears to subsume the explanatory value of expected inflation when
the SPCS Index is the regressand.
We next introduce dichotomous and interaction variables to capture potential
asymmetric behavior during unique market cycles. As examples, heterogeneous beliefs may be greater during periods of high inflation, or investors
may not correctly account for inflation changes during cycles with high asset
turnover. Hence, we add a dummy variable to identify intervals with lower versus higher heterogeneous beliefs in market agents. Dg̃ = 1 when g̃ is greater
than its median and 0 otherwise. Likewise, we add a dichotomous variable
for high versus low inflationary periods such that DE(π) = 1 if E(π ) is greater
than its median and 0 otherwise. Further, we interact these qualitative variables with E(π ) and g̃. We denote by g̃ ∗ DE(π) and E(π ) ∗ Dg̃ the interaction
variables.
The results in Model (4) demonstrate that g̃ continues to explain asset mispricing in the presence of the additional controls using either price index.
Conversely, E(π ) is not a predictor of mispricing using either price index.
The last specification, Model (5), introduces the other possible determinants
of mispricing. As noted in the Appendix, we examine 10 additional drivers of
supply and demand. We find that labor markets and the supply of completed
housing are the first-order determinants, i.e., some of the remaining controls
can be predictive of mispricing but are collinear with employment and housing
supply. With the inclusion of the two additional controls, the findings in Model
(5) demonstrate that g̃ is still significant using either price index. Conversely,
E(π ) does not exhibit a relation with OFHEO prices.
Table 3 cites the coefficients and standard errors when we first difference to
obtain the mispricing series. Turnover continues to exhibit a strong relation
with asset mispricing, individually and when combined with any of the control
variables. Indeed, g̃ is the sole significant regressor in Model (5) using OFHEO
prices, yet the adjusted R 2 increases to 0.57 despite the loss of degrees of
freedom.
Expected inflation is a determinant of OFHEO mispricing as the lone regressor;
however, the adjusted R 2 is 0.00 (specifically 0.0002). With the exception being
this particular model, E(π ) does not exhibit a relation with mispricing using
either price index across any of other specifications. In fact, the adjusted R 2
328 Hayunga and Lung
Table 3 The table cites coefficients and standard errors (in parentheses) of the
determinants describing asset mispricing.
(1)
(2)
(3)
(4)
(5)
OFHEO price index (quarterly observations 1975–2007)
g̃
E(π )
0.37∗∗∗
(0.04)
−0.60∗∗
(0.29)
0.35∗∗∗
(0.04)
−0.18
(0.37)
0.38∗∗∗
(0.08)
−0.04
(0.29)
−0.00
(0.00)
−0.00
(0.00)
−0.02
(0.07)
0.35
(0.42)
0.00
0.42
0.41
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment
Supply
Adjusted R2
0.42
0.26∗∗∗
(0.06)
−0.61
(0.39)
−0.00
(0.00)
−0.00
(0.00)
−0.06
(0.08)
0.05
(0.35)
−0.00
(0.00)
−0.00
(0.00)
0.57
S&P/Case–Shiller price index (quarterly observations 1987–2007)
g̃
E(π )
0.32∗∗∗
(0.05)
−0.05
(0.29)
0.32∗∗∗
(0.05)
−0.14
(0.23)
0.28∗∗∗
(0.09)
−0.57
(0.46)
−0.00
(0.00)
0.00
(0.00)
−0.04
(0.12)
0.88
(0.59)
−0.03
0.40
0.46
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment × 10−2
Supply
Adjusted R2
0.38
0.23∗∗∗
(0.08)
−0.16
(0.43)
−0.00
(0.00)
0.00
(0.00)
−0.04
(0.11)
0.45
(0.56)
−0.06∗∗∗
(0.01)
−0.00
(0.00)
0.49
Note: We use first differencing to obtain asset mispricing. The results in this table use
OLS in the second stage. ∗∗∗ , ∗∗ and ∗ denote statistical significance at the 1%, 5% and
10% levels, respectively.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 329
becomes −0.03 in Model (2) using SPCS prices—expected inflation being the
sole independent variable.
Overall, we find that the proxy for the overconfidence theory demonstrates
an enduring relationship with mispricing no matter the econometric method or
accompanying control variables. In contrast, expected inflation is not consistent;
in the presence of asset turnover and other covariates, E(π ) lacks correlation
with asset mispricing.
Mispricing Volatility
We next investigate the relation of g̃ and E(π ) with the second central moment
of asset mispricing. Scheinkman and Xiong (2003) show that the asset-turnover
proxy is positively correlated with mispricing volatility. Inflation illusion does
not offer a specific hypothesis for the sign of the slope of expected inflation.
We report the findings in Table 4 using Bayesian/SUR and Table 5 using
differencing and OLS.
Using either price index and across all models in Table 4, g̃ consistently exhibits
a positive relation with mispricing volatility. In the unrestricted Model (5), the
turnover coefficient is greater than five standard errors from zero using either
price index. Again, turnover is the only significant predictor in Model (5)
using OFHEO prices. g̃ is especially salient in explaining the variance in SPCS
mispricing. Individually in Model (1), it addresses 0.37% of the variation in
mispricing volatility. When combined with the other controls, the adjusted R 2
becomes 0.55. Alternatively, E(π ) has marginal impact on mispricing variance.
Expected inflation is significant as the lone regressor using OFHEO prices and
marginal in Model (3) when controlling for turnover in the model. Otherwise,
it is not a determinant.
There is no difference in the conclusions when we difference to obtain mispricing and use OLS in the second stage. The results in Table 5 demonstrate that g̃
consistently explains mispricing in each model. E(π ) continues to exhibit inconsistency. As the models of OFHEO prices become less restrictive, expected
inflation offers less value. E(π ) offers no relation with mispricing volatility
using SPCS prices. We note that some of the interaction and dummy variables
are predictive, although their economic impact is marginal.
Subperiods
Looking back at Figure 1, note that the vertical scale on the graphs indicates
undervaluing at levels less than zero and overvaluation over zero. The overconfidence theory speaks to asset bubbles and overpricing due to the ability
330 Hayunga and Lung
Table 4 The table details the determinants of the second central moment of asset
mispricing using a SUR model in the second stage.
(1)
(2)
(3)
(4)
(5)
−0.50∗∗
(0.24)
1.16∗∗∗
(0.17)
−0.39∗
(0.22)
1.47∗∗∗
(0.39)
−0.30
(0.37)
0.00
(0.01)
0.01
(0.02)
−0.39
(0.44)
−0.21
(0.58)
0.02
0.04
0.03
2.05∗∗∗
(0.39)
0.51
(1.26)
−0.02
(0.01)
−0.01
(0.02)
0.28
(0.61)
1.80
(1.71)
−0.15
(0.18)
−0.03
(0.03)
0.15
OFHEO price index (quarterly observations 1975–2007)
g̃
E(π )
1.19∗∗∗
(0.17)
Dg̃
DE(π)
g̃ ∗ DE(π)
E(π ) ∗ Dg̃
Employment × 10−2
Supply × 10−2
Adjusted R2
0.02
S&P/CaseShiller price index (quarterly observations 1987–2007)
g̃
E(π )
0.76∗∗∗
(0.06)
0.77∗∗∗
(0.06)
0.23
(0.17)
−0.09
(0.29)
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment × 10−2
0.83∗∗∗
(0.10)
−0.20
(0.28)
−0.01∗∗
(0.00)
0.01
(0.01)
−0.20
(0.13)
1.02∗∗
(0.48)
Supply × 10−3
Adjusted R2
0.37
−0.01
Note: Standard errors are in parentheses.
the 1%, 5% and 10% levels, respectively.
0.39
∗∗∗ ∗∗
,
∗
0.45
0.81∗∗∗
(0.10)
−0.29
(0.28)
−0.01∗∗
(0.00)
0.00
(0.01)
−0.09
(0.13)
1.04∗∗
(0.45)
−0.15∗∗∗
(0.06)
0.04
(0.11)
0.55
and denote statistical significance at
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 331
Table 5 The table presents regressors of the variance of asset mispricing using OLS
after differencing to obtain mispricing, the regressand.
(1)
(2)
(3)
(4)
(5)
−0.35∗∗
(0.17)
0.13∗∗∗
(0.03)
−0.32∗
(0.17)
0.12∗∗∗
(0.06)
−0.83
(0.55)
−0.15∗∗
(0.06)
0.00
(0.00)
−0.00
(0.00)
0.72∗∗∗
(0.27)
0.06
0.09
0.15
0.17∗∗∗
(0.06)
−0.48
(0.29)
−0.07
(0.04)
0.00
(0.00)
−0.00
(0.00)
0.51∗∗
(0.20)
−0.87∗∗∗
(0.14)
−0.00
(0.00)
0.19
OFHEO price index (quarterly observations 1975–2007)
g̃ × 10−2
E(π ) × 10−2
0.13∗∗∗
(0.03)
Dg̃ × 10−3
DE(π)
g̃ × DE(π)
E(π )Dg̃ × 10−2
Employment × 10−4
Supply
Adjusted R2
0.07
S&P/Case-Shiller price index (quarterly observations 1987–2007)
g̃ × 10−2
E(π ) × 10−2
0.34∗∗
(0.15)
Dg̃ × 10−4
−0.61
(1.10)
0.31∗∗
(0.15)
−0.42
(1.60)
0.30∗∗
(0.14)
−0.31
(2.53)
−0.75∗∗
(0.31)
0.26∗∗
(0.12)
−0.00
(0.00)
0.41∗∗∗
(0.13)
0.05
0.11
0.09
DE(π) × 10−4
g̃ × DE(π)
E(π ) × Dg̃ × 10−2
Employment × 10−5
Supply
Adjusted R2
0.06
Note: Standard errors are in parentheses.
the 1%, 5% and 10% levels, respectively.
∗∗∗ ∗∗
,
0.53∗∗∗
(0.15)
−0.47
(2.30)
−0.72∗∗
(0.31)
0.22
(0.22)
−0.00
(0.00)
0.62∗∗∗
(0.13)
−0.44∗∗
(0.19)
−0.00
(0.00)
0.12
and ∗ denote statistical significance at
332 Hayunga and Lung
of the current buyer to find a “greater fool” later that will pay an even higher
price. The resale option does not provide guidance for underpricing. However,
the turnover proxy may still correlate with undervaluing an asset. That is, on a
relative basis, turnover decreases during underpricing periods.
We can think of a few scenarios. As discussed previously, financing can exacerbate cycles. Hence, during a downturn in the real estate cycle, lenders may
restrict credit and slow turnover. A real illustration is the market from 2008 to
2010. Also, sellers who are not forced to sell due to a job change or similar
lifestyle adjustments will not sell because the market value is below their reservation price. Conversely, turnover may not correlate with undervaluation since
one can expect turnover to increase as the market bottoms out and prices begin
to increase back to fundamentals.
A lack of clear relation with undervaluation is not true of expected inflation.
The hypothesis suggests that prices will be undervalued when inflation is high.
Overall, the ability of turnover and expected inflation to predict mispricing in
undervaluation markets is an empirical question, which we explore next.
Note that Figure 1 displays two relatively distinct time periods for both price
indices. Until approximately 1998, mispricing exhibits levels below zero. Subsequently, mispricing increases and is generally above zero. This division is
also apparent in the mispricing volatility minus the very beginning of each
variance time series. Therefore, we split the samples into subperiods pre- and
post-1998 and re-execute the same models as before.8
Table 6 reports the results. We use the unrestricted model that accounts for all
the control variables. Overall, we observe a greater ability to explain mispricing
in overvalued markets. That is, the coefficients of determination are greater in
the 1998–2007 models than in the pre-1998 specifications. In two models—
OLS using OFHEO prices and SUR using the SPCS Index—the adjusted R 2
is 0.80 and 0.83. Nevertheless, a number of variables correlate with mispricing
in the pre-1998 period. Asset turnover is robust and significant in underpricing
periods as well as the overpricing periods. Employment levels are also robust
across time periods. In contrast, E(π ) offers no explanatory power in any of
the pre-1998 subperiods.
Similarly, expected inflation is an inconsistent regressor in the overvaluation
periods from 1998 to 2007. There is some evidence of correlation in two of the
eight models: OLS using OFHEO and SUR using SPCS prices. Alternatively,
8
We thank the reviewer for suggesting a closer examination of the bubble period.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 333
Table 6 The table reports the results of splitting the sample across periods of
underpricing and overpricing.
Bayesian/SUR
OFHEO Price Index
g̃
E(π )
Dg̃ × 10−2
DE(π) × 10−2
g̃ × DE(π)
E(π ) × Dg̃
Employment × 10−2
Supply × 10−2
Adjusted R2
S&P/Case-Shiller
Price Index
g̃
E(π )
Dg̃
DE(π)
g̃ × DE(π)
E(π ) × Dg̃
Employment × 10−2
Supply × 10−2
Adjusted R2
1975–1997
∗∗
First Difference/OLS
1998–2007
∗∗∗
1975–1997
∗∗
1998–2007
3.10
(1.41)
−1.20
(0.99)
−2.41
(1.90)
−1.71
(3.78)
−0.56
(1.09)
2.54
(2.20)
−1.19∗∗∗
(0.20)
−0.03∗∗∗
(0.01)
0.09
13.75
(1.10)
−6.57
(5.65)
−5.97∗
(3.44)
−4.91
(7.58)
−1.01
(1.95)
12.72∗∗
(6.50)
−2.38∗∗∗
(0.57)
−0.59∗∗∗
(0.23)
0.67
0.31
(0.13)
−0.50
(0.36)
−0.22∗
(0.13)
−1.30∗∗
(0.64)
−0.36∗
(0.19)
0.06
(0.62)
−0.07∗
(0.04)
−0.01∗∗
(0.00)
0.35
0.39∗∗∗
(0.06)
−1.20∗
(0.67)
−0.16∗∗
(0.07)
−0.15
(0.33)
−0.07
(0.08)
0.48
(0.41)
−0.03∗∗∗
(0.01)
−0.01∗∗∗
(0.00)
0.80
1987–1997
1998–2007
1987–1997
1998–2007
11.56∗∗∗
(2.14)
−2.31
(2.04)
−0.04∗
(0.02)
0.08
(0.09)
−0.33
(0.27)
2.70
(1.80)
−2.82∗∗∗
(0.18)
−0.21
(0.13)
0.27
18.05∗∗∗
(1.05)
−15.18∗
(8.38)
−0.06∗∗
(0.03)
0.01
(0.06)
−0.49
(1.35)
11.29∗∗
(5.72)
−5.67∗∗∗
(0.51)
−0.11
(0.19)
0.83
0.42∗∗∗
(0.17)
−0.54
(0.41)
−0.00
(0.00)
0.01
(0.01)
−0.34∗
(0.21)
0.22
(0.33)
−0.03∗∗∗
(0.01)
−0.05
(0.08)
0.28
0.31∗∗∗
(0.10)
−0.66
(0.72)
−0.00
(0.00)
0.01
(0.01)
−0.09
(0.15)
0.30
(0.79)
−0.04∗∗∗
(0.02)
−0.05
(0.02)
0.51
Note: Bayesian/SUR denotes that we obtain mispricing using Bayesian in the first
stage and model mispricing as the dependant variable using SUR in the second stage.
Similarly, we use differencing to obtain mispricing and subsequently model using OLS.
Standard errors are in parentheses. ∗∗∗ , ∗∗ and ∗ denote statistical significance at the 1%,
5% and 10% levels, respectively.
334 Hayunga and Lung
Table 7 The table reports Granger-causality tests of asset turnover, expected inflation
and mispricing.
Bayesian
OFHEO Price Index
g̃ → Mispricing
Mispricing → g̃
E(π) → Mispricing
Mispricing → E(π)
S&P/Case-Shiller
Price Index
g̃ → Mispricing
Mispricing → g̃
E(π) → Mispricing
Mispricing → E(π)
1975–2007
First Difference
1975–1997
∗
∗
1998–2007
∗
1975–2007
∗
1975–1997
∗
1998–2007
2.97
(0.04)
0.12
(0.73)
0.92
(0.34)
1.14
(0.29)
7.66
(0.01)
1.01
(0.31)
1.42
(0.22)
0.07
(0.80)
15.64
(0.00)
3.32
(0.07)
1.12
(0.29)
1.60
(0.20)
8.60
(0.00)
1.39
(0.24)
0.01
(0.92)
1.39
(0.24)
10.02
(0.00)
0.93
(0.34)
0.72
(0.39)
0.36
(0.44)
10.04∗
(0.00)
1.59
(0.21)
0.84
(0.36)
1.17
(0.28)
1987–2007
1987–1997
1998–2008
1987–2007
1987–1997
1998–2007
3.19∗
(0.02)
0.41
(0.52)
1.92
(0.17)
0.66
(0.42)
5.15∗
(0.02)
0.15
(0.70)
0.65
(0.42)
0.05
(0.82)
10.30∗
(0.00)
1.12
(0.29)
2.00
(0.16)
0.39
(0.53)
12.27∗
(0.00)
0.56
(0.45)
1.07
(0.30)
0.01
(0.91)
4.45∗
(0.03)
0.39
(0.53)
0.85
(0.36)
1.20
(0.27)
13.88∗
(0.00)
0.12
(0.73)
0.00
(0.95)
1.32
(0.25)
Note: → denotes the direction of Granger-causality. p-values are in parentheses. ∗ denotes significance at the 5% level or less.
significance is not uniform across models or price indexes and the t-statistics
are marginal at 1.78 and 1.81, respectively. Overall, the Table 6 findings demonstrate that asset turnover remains predictive regardless of mispricing type.
Intertemporal Relationships
We next investigate intertemporal relations using Granger-casuality, variance
decomposition and impulse response tests. We use values from the unrestricted
SUR model. We compute the intertemporal tests using the full time period for
both indices as well as the pre- and post-1998 subsamples.
Granger-casuality. Because a cause cannot come after the effect, we examine
if changes in either g̃ or E(π ) induce changes in mispricing. If either asset
turnover or expected inflation affect mispricing, g̃, or E(π ) may help improve
the predictions of an asset bubble in a larger economic context. Table 7 reports
the results.
We find a consistent unidirectional causality between asset turnover and mispricing. Using either price index, the results in Table 7 demonstrate that the
null hypothesis of g̃ not Granger-causing mispricing is rejected with p-values
of 0.04 or less using the OFHEO Index and 0.02 or less using SPCS prices.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 335
Figure 2 The figure exhibits the response of mispricing to a shock in asset turnover
in the upper panels and expected inflation in the lower panels.
This is true across the full sample period as well as both subperiods. We do
not observe bi-directional feedback as mispricing does not Granger-cause asset
turnover using either price index.
We find no evidence of expected inflation Granger-causing mispricing. In fact,
in six periods, such as 1998–2007 using SPCS prices, mispricing exhibits more
causation of E(π ) than the expected converse.
Impulse response. Granger-causality analysis explains whether asset turnover
or expected inflation contains useful information for improving the prediction of
mispricing. However, Granger-causality may not explain the entire intertemporal interactions among g̃, E(π ) and mispricing. We use impulse response
analysis to further understand the response of mispricing to an exogenous
shock on asset turnover or expected inflation. In a VAR model, it is difficult to
describe adequately long-run equilibrium behavior of the components due to
the autoregressive nature of the system. By using the orthogonalized impulse
response function, we can simulate an exogenous shock to the residuals of g̃
and E(π ) and observe the response of mispricing.
Figure 2 displays the mispricing effect of postulating a one-standard-deviation
innovation. All panels plot the dynamic path of mispricing over a period of 1
year (four quarters). The upper panels in Figure 2 exhibit the shock of asset
336 Hayunga and Lung
Table 8 The table presents variance decomposition of the impulse response
functions, which gauges the relative contribution of mispricing, asset turnover and
expected inflation to the forecast error variance of mispricing.
g̃
E(π )
87.52
90.69
17.78
10.33
8.04
71.02
2.16
1.27
11.20
79.07
86.10
77.21
20.11
13.02
21.58
0.82
0.88
1.21
83.66
89.15
55.96
12.28
9.38
36.71
4.07
1.47
7.33
87.15
91.45
83.38
12.34
7.83
15.15
0.51
0.72
1.47
Mispricing
OFHEO Price Index
Bayesian
1975–2007
1975–1997
1998–2007
Differencing
1975–2007
1975–1997
1998–2007
S&P/Case-Shiller Price Index
Bayesian
1987–2007
1987–1997
1998–2007
Differencing
1987–2007
1987–1997
1998–2007
Note: The values are 12 lead quarters and stated as percentages.
turnover, whereas the lower panels cite the affects of expected inflation. The
solid line indicates the dynamic path of an innovation. Not only are we looking
for significant response values but also 95% confidence intervals different from
zero (the dotted lines).
We find that the response of shocking asset turnover exhibits statistical significance out to two quarters before the lower confidence interval falls below
zero. Conversely, an exogenous shock to expected inflation does not cause a
response in mispricing as the confidence intervals begin both above and below
zero.
Variance decomposition. Since impulse response analysis measures the onestep-ahead forecast errors of a VAR process, the shocks are sometimes termed
forecast errors. A subsequent analysis of the relation between mispricing, asset
turnover and expected inflation is to decompose the variance of the forecast
errors. The values of forecast-error variance decomposition attribute the proportion of the mispricing-predicted error variance to own innovations as well
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 337
as shocks to g̃ and E(π ). In our analysis, we extend the calculations out 5
years after evoking the innovation. Table 8 details the findings at the 12th lead
quarter as we observe general stability of the proportions past this point in time.
We again employ both the Bayesian approach and differencing across the full
sample period as well as the two subperiods.
Using the OFHEO national prices, the first row of Table 8 cites asset turnover
accounting for 10.33% of the forecast error variance, whereas inflation accounts
for 2.16%. During the 1975–1997 subperiod, neither g̃ and E(π ) are as strong.
However, from 1998 to 2007, a turnover shock forecasts more than mispricing
itself—71.02 versus 17.78. The trend continues throughout the results in Table
8. g̃ shocks are much more informative than E(π ) by a magnitude ranging from
5 to 24 times greater.
Conclusion
As the first decade of the 21st century closed, questions were posed as to
why economists did not better predict—and accordingly, better address—the
problems that presented themselves during the period. Central to the issues
during the 2000s decade were the effects of asset bubbles, both in the stock
market at the beginning of the decade and in real estate prices toward the end.
The results of this study encourage a theory as well as a proxy for asset
mispricing that may help identify problem markets in the future. Overall,
asset turnover—one of the proxies of the overconfidence theory—exhibits a
persistent relationship with mispricing no matter the model covariates, time
period or econometric method. The same cannot be stated for expected inflation,
the proxy for the inflation-illusion hypothesis. The robustness of asset turnover
is noteworthy as the high transaction costs associated with residential real estate
should bias the results against the overconfidence theory and the asset-turnover
proxy. Further muddling the results should be the fact that the investment
component of housing is only part of the utility to an owner occupant. Because
consumption of shelter is the other portion, the strength and consistency of the
relationship between turnover and mispricing is striking.
We are grateful to John Campbell, Ji-Chai Lin, Albert Wang and Wei Xiong for
helpful comments.
References
Bauwens, L., M. Lubrano and J.F. Richard. 1999. Bayesian Inference in Dynamic
Econometric Models. Oxford University Press: New York, NY.
Bertus, M., H. Hollans and S. Swidler. 2008. Hedging House Price Risks with CME
Future Contracts: The Case of Las Vegas Residential Real Estate. The Journal of Real
Estate Finance and Economics 37(3): 265–279.
338 Hayunga and Lung
Brunnermeier, M. and C. Julliard. 2008. Money Illusion and Housing Frenzies. Review
of Financial Studies 21(1): 135–180.
Campbell, J. and R. Shiller. 1988. The Dividend-price Ratio and Expectations of Future
Dividends and Discount Factors. Review of Financial Studies 1(1): 195–228.
Campbell, J. and T. Vuolteenaho. 2004. Inflation Illusion and Stock Prices. American
Economic Review (Papers and Proceedings) 94: 19–23.
Cao, H. and H. Ou-Yang. 2009. Differences of Opinion of Public Information and
Speculative Trading in Stocks and Options. Review of Financial Studies 22(1):
299–335.
Chen, C., P. Lung and A. Wang. 2009. Stock Market Mispricing: Money Illusion or
Resale Option? Journal of Financial and Quantitative Analysis 44(5): 1125–1147.
Clauretie, T. and P. Thistle. 2007. The Effect of Time-on-Market and Location on Search
Costs and Anchoring: The Case of Single-Family Properties. The Journal of Real Estate
Finance and Economics 35(2): 181–196.
Clayton, J., N. Miller and L. Peng. 2010. Price-Volume Correlation in the Housing Market: Causality and Co-Movements. The Journal of Real Estate Finance and Economics
40(1): 14–40.
Cohen, R., C. Polk and T. Vuolteenaho. 2005. Money Illusion in the Stock Market: The
Modigliani-Cohn Hypothesis. Quarterly Journal of Economics 120(2): 639–668.
Cooper, J. 2008. Tallying the True Size of the Housing Bust. Business
Week June 29. Retrieved from http://www.businessweek.com/magazine/content/
08 27/b4091010291983.htm.
Daniel, K., D. Hirshleifer and A. Subrahmanyam. 1998. Investor Psychology and Security Market Under- and Overreactions. The Journal of Finance 53(6): 1839–1885.
Fehr, E. and J-R. Tyran. 2001. Does Money Illusion Matter? American Economic Review
91(5): 1239–1262.
Glaeser, E., J. Gyourko and A. Siaz. 2008. Housing Supply and Housing Bubbles.
Journal of Urban Economics 64(2): 198–217.
Harris, M. and A. Raviv. 1993. Differences of Opinion Make a Horse Race. Review of
Financial Studies 6(3): 473–506.
Harrison, J.M. and D. Kreps. 1978. Speculative Investor Behavior in a Stock Market
with Heterogeneous Expectations. Quarterly Journal of Economics 92(2): 323–336.
Harding, J., S. Rosenthal and C.F. Sirmans. 2003. Estimating Bargaining Power in the
Market for Existing Homes. The Review of Economics and Statistics 85(1): 178–188.
Herring, R. and S. Wachter. 2005. Bubbles in Real Estate Markets. W. Hunter, G. Kaufman, and M. Pomerleano, editors. Asset Price Bubbles: The Implications for Monetary,
Regulatory, and International Policies. MIT Press: Cambridge, MA.
Hong, H., J. Scheinkman and W. Xiong. 2006. Asset Float and Speculative Bubbles.
The Journal of Finance 61(3): 1073–1117.
Kim, J. 1994. Bayesian Asymptotic Theory in a Times Series Model with a Possible
Nonstationary Process. Econometric Theory 10(3): 764–773.
Kyle, A. and A. Wang. 1997. Speculation Duopoly with Agreement to Disagree: Can
Overconfidence Survive the Market Test? The Journal of Finance 52(5): 2073–2090.
Lambson, V., G. McQueen and B. Slade. 2004. Do Out-of-State Buyers Pay More for
Real Estate? An Examination of Anchoring-Induced Bias and Search Costs. Real Estate
Economics 32(1): 85–126.
Lütkephols, H. 2005. New Introduction to Multiple Time Series Analysis. Springer:
Berlin, Germany.
Miles, M., G. Berens, M. Eppli and M. Weiss. 2007. Real Estate Development. Urban
Land Institute: Washington, DC.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 339
Modigliani, F. and R. Cohn. 1979. Inflation, Rational Valuation, and the Market. Financial Analysts Journal 35(2): 24–44.
Odean, T. 1998. Are Investors Reluctant to Realize Their Losses? The Journal of Finance
53(5): 1775–1798.
Safrin, H. and M. Statman. 1994. Behavioral Capital Asset Pricing Theory. Journal of
Financial and Quantitative Analysis 29(3): 323–349.
Scheinkman, J. and W. Xiong. 2003. Overconfidence and Speculative Bubbles. Journal
of Political Economy 111(6): 1183–1219.
Voith, R. 1999. The Suburban Housing Market: The Effects of City and Suburban Job
Growth. Real Estate Economics 27(4): 621–648.
Appendix
A1: Linking Resale Option to Asset Turnover
Both Hong, Scheinkman and Xiong (2006) and Cao and Ou-Yang (2009)
provide the direct link between mispricing and turnover, but they take different
approaches. The framework of Hong, Scheinkman and Xiong (2006) has the
same features as Scheinkman and Xiong (2003). Namely, short-sales constraints
combined with heterogeneous beliefs can cause asset prices to become higher
than they would be in the absence of the short-sales constraints. When beliefs
are sufficiently heterogeneous, short-sale constraints insure that asset prices
reflect the opinion of the more optimistic investors and, in a multiple-period
setting, mispricing arises. As shown in their paper, the mispricing component
is similar to a call option with the underlying asset the difference in opinion and
the strike price the overconfidence function. As the difference of opinion and
overconfidence increase, current owners are more likely to exercise the resale
options. Consequently, turnover increases.
We summarize several of the key equations in their model and the accompanying
insight showing the asset turnover result. They first divide investors into two
groups—A and B. At time = 0, the prior beliefs of the two groups of investors
about the asset payoff in the future are specified to be normally distributed with
the precision τ 0 . Namely, τ10 is the volatility of the asset’s future payoff pattern.
The prior beliefs for A and B are denoted by N (f̂0A , τ10 ) and N (f̂0B , τ10 ), where
N is the normal distribution and f̂ is the respectively asset’s future payoffs.
The normal distributions indicate that A and B share the same precision, τ 0 ,
but different means, f̂0A and f̂0B , regarding the asset’s payoff in the future. At
time = 1, A and B receive two public signals regarding the asset’s payoff in
the future. The signals are specified as
SfA = f̃ + fA
and
SfB = f̃ + fB ,
B
where f̃ is the asset payoff in the future and A
f and f are respective signal
noise. Both of the noises are normally distributed as N (0, τ1 ). τ is the precision
340 Hayunga and Lung
of public signals for both groups A and B at t = 1. The beliefs of the two groups
of investors at t = 1 are also normally distributed, denoted by N (f̂1A , τ11 ) and
N(f̂1B , τ11 ), respectively for A and B. With the overconfidence among investors,
the precision at t = 1, τ 1 , is given by
τ1 = τ0 + τ + φ · τ .
(A.1)
Equation (A.1) shows that at t = 1 the precision of the future asset payoff pattern
can be divided into three components. τ 0 is the previous period precision, τ is the precision of public signals for both groups A and B at t = 1, and φ
is a parameter of overconfidence with a value greater than one. Because of
overconfidence, investors overestimate the precision of signals as φ · τ . The
means for A and B are specified as
f̂1A = f̂0A +
τ B
φτ A
Sf − f̂0A +
Sf − f̂0A
τ1
τ1
and
f̂1B = f̂0B +
τ A
φτ B
Sf − f̂0B +
Sf − f̂0B .
τ1
τ1
(A.2)
Equation (A.2) shows that the difference of beliefs between A and B at t =
1 is attributed to two reasons—different prior beliefs and overconfidence that
makes investors place too much weight on their own signals. Given this setting,
the resale option value is derived as
Q
Q
Resale Option Value = E l1 −
,(A.3)
Il1 −
r·(τ0 +τ +φ·τ )
r · (τ0 + τ + φ · τ )
where l1 = f̂1A − f̂1B is the difference of expected payoff between A and B at
t = 1, l 1 is the underlying asset for the resale option, Q is the total shares of
the asset in the market, and r is the investors’ risk-bearing capacity. I denotes
the integral function.
Equation (A.3) shows that the resale option value is similar to a call option with
the underlying asset value of l1 and a strike price of r·(τ0 +τQ +φ·τ ) . The wider the
difference in belief, the larger the underlying asset value, l1 , and the more likely
the current owner will exercise the call option. Consequently, trading activities
will increase. As the overconfidence parameter, φ, increases, the strike price,
Q
, decreases. As the difference between the underlying asset price
r·(τ0 +τ +φ·τ )
and strike price increases, the current owner will be more likely to exercise the
call option and, consequently, trading activities will increase. Thus, turnover
reflects the difference in beliefs and overconfidence.
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 341
Cao and Ou-Yang (2009) use a different analytical framework, which yields the
same result of increased turnover with the dispersion of beliefs among investors.
The intuition of the Cao and Ou-Yang (2009) model is as follows. Investors who
have higher confidence about a public signal put more weight on the signal and
thus trade in the direction of the signal. If the public signal is very positive, the
price will go up. But investors with high confidence still believe that the price
has not fully incorporated the positive signal due to the presence of investors
with low confidence. Hence, investors with high confidence believe that the
asset price will go up even further and demand more, for example, shares of
the stock. On the other hand, investors who have low confidence about a public
signal put less weight on it. When the stock price goes up, they believe the price
is overreacting to the public signal due to the presence of investors with high
confidence. Hence, investors with low confidence sell the asset. Therefore, the
bigger the difference between the investors with high and low confidence about
the signal, the more trades occur, and, consequently, the higher the turnover.
The model assumes investors have constant absolute risk aversion utility, believe that the asset payoff distribution is normal and have differences of opinion.
After the first round of trade, there exist new public signals about the final asset
payoff arriving at the market. Investors have the opportunity to trade again in the
market. These new public signals create differences of opinion across investors
because investors interpret them differently. One of the major factors causing
the differences in beliefs among investors is the disagreements on the precision
of signals, which captures the heterogeneity of the investors’ confidence level
in the signal.
Consider a setting in which information about the final payoff μ at time T is
made available gradually by a series of public signals yt at time t = 1, . . . , T
− 1. Investors disagree about how to interpret yt and μ. Investor i believes that
yt = μ + ηt ,
1
μ ∼ N μ̄,
h
and
1
ηt ∼ N mit , i .
nt
(A.4)
Equations (A.4) shows that the public signal at time t can be decomposed into
two parts—the information about the final payoff, μ, and a noise of the signal
at time t of ηt . According to the framework, the final payoff follows a normal
distribution with the precision of h. Investor i believes that ηt has a mean of
mit and a precision of nit . As a result, investors disagree about the mean and the
precision of yt . Let nt denote the average precision of the public signal, then
ni
the relative confidence level for investor i can be estimated as ρti ≡ ntt . If ρ >
1, then investor i is said to have high confidence about the public signal at time
t, and vice versa.
342 Hayunga and Lung
Cao and Ou-Yang (2009) show the demand of the asset for investor is
⎡
⎤
t
i
i
n
m
k
t
t+1 t+1 ⎦
Dti = r ⎣hμ̄ +
nit yj − ktt Pt +
nt+1
j =0
⎡
⎤
t
i
= r ⎣hμ̄ +
nit yj − kit Pt + ρt+1
· kt mit+1 ⎦ ,
j =0
where r is the risk tolerance of investors, kit is the conditional precision of μ
for investor i at time t, kt denotes the average precision of all investors and Pt
is asset price at time t. This function at time t shows investor i’s demand for
the risky asset increases with the precision about the signal ni t+1 . To focus on
analyzing trading due to differences in opinion under the condition that noise
of the signal, assume that the mean, mit , equals zero and the confidence for
investor i is constant at ρ i . Thus, the trading of investor from current period to
the next period is
i
Dt+1
− Dti = r(ρ i − 1) · h(Pt+1 − Pt ).
(A.5)
Note that the left-hand side of Equation (A.5) is asset turnover. The result is
that investors who have high confidence, i.e., ρ i > 1, about public signal put
more weight on the signal and thus trade in the direction of the signal. On a
larger scale, the wider the dispersion of investors’ confidence levels, the more
aggressively the high (low) confidence investors will buy (sell). Thus, asset
turnover increases.
Equation (A.5) also shows that the demand of investors with high confidence
or ρ i > 1 at time t are positively correlated with the price change from current
period to the next period, and vice versa for the demand of low confidence
investors. This implies that price increase will motivate more high-confidence
investors to buy and more low-confidence investors to sell. Consequently,
turnover exaggerates during the period of price soaring; an implication that the
Cao and Ou-Yang (2009) dynamic model shares with the Hong, Scheinkman
and Xiong’s (2006) model. With the short sale constraints and difference in
opinion among investors, asset price could exceed the fundamental value, and
turnover reflects the difference in opinion.
A2: Bayesian Approach
Under a diffuse prior, the posterior distribution of the estimated coefficients in
a VAR can be factorized as the product of an inverse Wishart and a multivariate
Explaining Asset Mispricing using the Resale Option and Inflation Illusion 343
normal distribution as
β|
∼ N (β̂, ⊗ (X X)−1 )
ˆ n − m),
−1 ∼ Wishart(n
,
where β is the vector of slope coefficients in the VAR system, is the covariance matrix of the residuals, the variables with a hat denote the corresponding
estimates, X is the matrix of regressors, n is the sample size, and m is the number
of estimated parameters per equation (see Schervish 1995, Bauwens, Lubrano
and Richard 1999). This result is exact under normality and the Jeffreys’ prior,
but it can also be obtained as an asymptotic approximation around the posterior
maximum likelihood estimation.9 The use of this Bayesian approach allows
us to draw inference that is robust to the potential presence of nonstationary
behavior in our VAR system because the likelihood will have an asymptotically
Gaussian shape even in the presence of unit roots (see Kim 1994).
A3: Control Variables
In modeling asset mispricing, we control for standard demand and supply
covariates. We seasonally adjust each predictor.
The creation or reduction of jobs along with the accompanying change in
population are the preponderant drivers of the demand for residential real
estate. Changes in quantity demanded as well as changes in demand materialize
when people with purchasing power increase in number within the localized
market (Miles et al. 2007, p. 20). For the period from 1950 to June 2008,
the correlation coefficient of the U.S. population and employment is 0.997.
Because we hypothesize that an employed individual is more apt to state his
or her status as compared to an unemployed person, we use the Total NonFarm Employment Index from the Bureau of Labor statistics as a main demand
covariate. Clearly, another demand-side variable is the national interest rate for
mortgage financing. We thus use the 30-year, fixed-rate, conventional home
mortgage contract rate.
On the supply side, we proxy for changes in quantity supplied using the U.S.
Price Index of New One-Family Houses Under Construction compiled by the
U.S. Department of Commerce. As a proxy for own price change, this cost
index of new supply should account for movement along the supply curve. We
find that this index yields a 0.965 correlation coefficient with the alternative
cost proxy of the U.S. Construction Expenditures from the Department of
9
Jeffreys’ prior distribution is specified as f (β, ) ∝ |
|−(p+1)/2 , where p is number of
variables on the left-hand side.
344 Hayunga and Lung
Commerce. We also account for changes in supply using the U.S. Department
of Commerce Housing Completions. This proxy is the number of new privately
owned housing units completed and under construction for the United States.
We also examine the following additional demand and supply controls: (i)
to the measure of market liquidity, we use Months’ supply from the U.S.
Census Bureau—the ratio of homes for sale scaled by homes sold; (ii) the
three-month U.S. Treasury Bill rate as a cost of capital; (iii) the U.S. OwnerOccupied Residential Improvement Expenditure as a proxy for the change
in quantity demanded by homeowners that improve or remodel their existing
residence instead of moving to a new home and (iv) the amount of land within
each census region to account for its relative scarcity (Voith 1999). We find
that the liquidity measure is highly correlated with housing supply and causes
multicollinearity in the model if both are used. We find the other three regressors
are not economically or statistically significant.