The U.S. Housing Market and the Pricing of Risk:

Fundamental Analysis and Market Sentiment

Changha Jin 1, Gökçe Soydemir 2 and Alan Tidwell 3

1 Department of Economics, College of Business and Economics, Hanyang University ERICA campus, 1271 Sa 3-dong, Sangnok-gu, Ansan-si, Gyeonggi-do 426-791, Korea, (031) 400-5602 (Phone), (031) 436-8180 (Fax), cjin@hanyang.ac.kr

2 Department of Accounting and Finance, California State University One University Circle, Turlock, CA 95382, (209)667-3296 (Phone), gsoydemir@csustan.edu

3 Department of Accounting and Finance, Turner College of Business, Columbus State University; 4225 University Avenue, Columbus, GA 31907, (706) 507-8160 (Phone), (706) 568-2184 (Fax), atidwell@columbusstate.edu

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ABSTRACT

We explore the pricing patterns of the U.S. residential real estate market in the context of the

recent housing bubble and subsequent deflation. We examine 10 consolidated metropolitan

statistical areas and calculate excess residential market return per risk. Then, using an error

correction model, we regress excess residential market return per risk on fundamental market

risk factors from a range of demand- and supply-side variables together with a non-fundamental

based sentiment variable. Our long-run findings reveal that non-fundamental based (irrational)

consumer sentiment is a significant exogenous variable in the pricing pattern of U.S. residential

real estate.

Keywords: housing market, market sentiment, fundamental analysis, market behavior, excess

return per risk

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1. Introduction

Although there has been justifiable discussions pertaining to the impact of consumer sentiment

particularly nonfundamental (irrational) sentiment on residential real estate pricing, an empirical

study examining the relationship between the residential real estate market and consumer

(market) sentiments is absent in the literature. The testing procedures in most previous housing

studies are grounded in “rational” theoretical models which use fundamental economic variables

contingent upon the supply and demand side of the housing market when explaining the

residential housing market.1 This approach to explaining market behavior assumes that investors

and homebuyers are fully rational and will only make decisions that reflect knowledge of all

available fundamental information. Given the increased importance of real estate on consumer

consumption and the business cycle post 1980s financial deregulation (Miles, 2009),

investigations into the rationality of the pricing patterns of residential real estate are warranted.

Case and Shiller (2003) contend that a real estate bubble can be characterized as a state in which

housing prices experience rapid appreciation due to excessive public expectations of future

prices (Case and Shiller, 2003). As the authors suggest, patterns in fundamentals such as income

growth and declining interest rates may account for some but not all of observed price increases

in the housing markets as price increases are likely to be a result of fundamental variables and

irrational expectations. Wheaton and Nechvey (2008) empirically observe that the increase in

housing prices from 1998 to 2005 could not be explained by demand fundamentals, and that

MSAs characterized with high levels of speculative purchasing and subprime mortgage activity

had greater forecast errors. Brooks and Ward (forthcoming) find evidence that the US housing

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market recently experienced a rational bubble, where buyers nonlinearly extrapolated historic

growth patterns in house prices rather than relying on fundamentals. In this study we consider

consumer sentiment, particularly the portion of sentiment unexplained by fundamental variables,

as a possible explanatory variable in explaining residential real estate pricing patterns.

Shiller (2007) argues that fundamentals do not explain the recent housing boom. Rather, a

psychological theory better explains the phenomenon, since it can describe as a so-called

feedback mechanism or social epidemic, formulating perception on real estate as an investment

vehicle (Shiller 2007). Likewise, behavioral studies (see, for example Diaz 1990; De Bondt

1998; Hansz and Diaz 2001) reveal that participants in real estate are not fully assumed to be

rational, so that they tend to show systematic biases. In addition, market sentiment is conceived

of as expectations or judgments that are not fully justified by available information on market

fundamentals, and thus beliefs on future market conditions can be misguided resulting in noise

traders who misprice investments against rational expectations (see Shiller 1989; De Long et al.

1990; Baker and Wurgler 2007). We assert that the behavior driven by market sentiment

particularly irrational market sentiment does not have a negligible impact, but rather

considerable economic impact on residential markets.

Theoretically this phenomenon can be explained by a behavioral concept referred to as

overreaction. In this study, the concept of overreaction posits that homebuyers respond

disproportionately to new information. This causes housing prices to fluctuate more than

fundamentals might suggest as homebuyers overreact to fundamental market information; in turn,

at any given point the price of a house will not fully reflect the property’s fundamental value.

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Despite the relevance of market sentiment to real estate consumers and investors, there is only

limited literature examining the relationship between market sentiment and the real estate market.

Case and Shiller (2003) attribute the excess return exceeding the predicted values to an increase

in sentiment. This is verified through a survey of home buyers conducted in 2003 on subjects in

4 metropolitan areas. They find that homebuyers who recently purchased a home expect home

prices to increase between 7 to 11 percent annually indicating that people generally viewed

housing investment as an on-going escalator, meaning that this market state will remain as it was

in the early 2000’s (i.e. status quo bias). This mentality is consistent with prior periods (e.g.

1980’s) of exuberant market sentiment, which eventually resulted in price declines. The linkage

between this suspected belief and market condition can be explained from a behavioral concept

known as a status quo; the state in which naïve expectations on future events are similar to the

way they presently are (see Kahneman et al 1991). If mispricing is driven by a deviation from

current market fundamentals, then the deviation may be from a naïve expectation that current

price increases will remain the same in following years.

The research expectation for this study is that market sentiment unexplained by fundamental

variables significantly impacts subsequent pricing patterns of the U.S. residential real estate

market. This contention suggests that the changes in price are not sufficiently explained by

fundamental variables, but rather are influenced by nonfundamental (irrational) sentiment. We

test to see if the market sentiment unexplained by fundamental variables is a significant factor,

and suppose that price changes are not completely dependent on fundamentals. Support for our

research expectation is based on the behavioral concepts of overreaction and status quo.

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Correspondingly, we make the following contributions to the existing literature: First, our study

is contingent upon the consideration of a behavioral factor, e.g., non-fundamental based

(possibly irrational) consumer sentiment, as an important exogenous variable in analyzing the

pricing patterns of residential real estate. We hypothesize that consumer (market) sentiment

unexplained by fundamental variables is a significant explanatory factor in future housing prices.

If market mispricing is driven by a deviation in housing prices from what current fundamental

economic and finance conditions would indicate, then the deviation may be a result of naïve

consumer expectations that the contemporaneous price changes will reoccur in following years.

This expectation or sentiment could lead to artificial (nonfundamental based) pricing patterns.

Consistent with Baker and Wurgler (2006), we decompose consumer sentiment by regressing

consumer sentiment on a set of fundamental variables. We then use the residual as the

decomposed and orthoganalized irrational sentiment factor in error correction and OLS

regression models examining residential real estate pricing patterns.

This study provides empirical evidence of the impact of nonfundamental consumer sentiment on

residential real estate markets and also provides information on the dynamic relationship

between nonfundamental based consumer sentiment and fundamental economic, financial, and

real estate variables. We identify both long-run and short-run models from a set of potential

explanatory variables. The long-run and short-run models hypothesize their relationship as a

function that assumes the deviation from the short-run model will converge to a long-run model.

Also, both the long- and short-run models provide dynamic models of the pricing of the

residential housing markets in recent years. Our findings are generally consistent with the

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conjecture that nonfundamentally based consumer sentiment explains a significant amount of

variation in residential housing risk adjusted and unadjusted returns in the long-run, and that this

behavior is dynamic in the short-run.

This paper is comprised of the following sections: Section 2 describes the literature; Section 3

provides a description of the data; Section 4 outlines the methodology used to test our

hypothesis; Section 5 presents empirical results; and finally, Section 6 is the conclusion.

2. Literature Review

Recent research on the role of individual and institutional sentiment in the pricing pattern of

stocks generally finds significant co-movements between stock market returns and sentiment.

Sentiment measures include direct measures of investor sentiment (i.e. Conference Board

Consumer Confidence Index, the Investors’ Intelligence Survey Index, and the University of

Michigan Consumer Sentiment Index) and indirect measures (i.e. closed-end fund discounts,

mutual fund flow based measures, trading activity based measures, derivative variables, and IPO

related variables).

Closed-end fund discounts were one of the first measures modeled as proxies of investor

sentiment. These early studies, Lee, Shleifer, and Thaler (1991), Chopra, Lee, Schleifer, and

Thaler (1993), Swaminathan (1996) and Neal and Wheatley (1998), argued that the discount (or

premium) between Net Asset Value (NAV) and the price closed-end fund shares were trading

could be treated as an indicator of investor sentiment. Where, optimistic sentiment results in a

price premium and conversely pessimistic sentiment results in shares selling at a discount to

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NAV. However, more recent studies question the validity of the closed-end fund discount as

measure of sentiment (see Brown and Cliff, 2004; Qiu and Welch, 2006; Baker and Wurgler,

2006; Lemmon and Portniaguina, 2006; Canbas and Kandir, 2009).

Brown, Goetzmann, Hiraki, Shiraishi, and Watanabe (2003) and Randall, Suk and Tully (2003)

contend that mutual fund flows may be a proxy for investor sentiment in the stock market.

Frazzini and Lamont (2008) find that mutual fund flows should be used as contrarian tools, with

bullish investor sentiment evidenced by high fund flows capable of predicting low future returns.

The authors attribute these findings to the idea that inflows into mutual funds push prices higher

in the short-run as described by Wermers (2004) and Coval and Stafford (2007).

Trading activity based measures have also been shown to proxy investor sentiment. Kumar and

Lee (2006) find that the volume of retail investor trades as a proxy for retail investor sentiment

often plays a role in the pricing of stocks. Specifically, the authors find that retail trades are

correlated across individuals, and that the summation of these individual retail trades, which are

partially motivated by sentiment, is sufficient enough to influence stock returns. Similarly,

Barber, Ocean, and Zhu (2009) find that retail investors herd by systematically purchasing stocks

based on strong recent pricing performance and high trading volume. Amihud (2002), and Jones

and Lamont (2002) also use trading volume as a measure of investor sentiment to illustrate that

an increase in sentiment (trading volume) is associated with lower future stock returns.

In addition to the commonly applied indirect sentiment measures previously discussed, there are

several alternative indirect measures linking investor sentiment to derivative variables and IPO

related variables. Dennis and Mayhew (2002) use the put-call ratio as an indicator of sentiment.

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A high ratio indicating a large trading volume in puts is indicative of bearish investor sentiment.

Whaley (2009) suggests that the market volatility index (VIX) generated from the daily spread

between options traded at the CBOE is a good indicator of sentiment. Kaplanski and Levey

(2009) find that the VIX may contain an irrational component of risk which is inversely related

to stock returns. Baker and Wurgler (2000 & 2006) use IPO activity as a proxy for investor

sentiment.

Lastly, and most relevant to this study, one of the most common sentiment proxies are direct

survey based measures to gauge sentiment. These surveys typically attempt to measure either

consumer, individual or institutional sentiment. The literature is rich with studies documenting

the efficacy of direct sentiment based measures. Brown and Cliff (2004 and 2005) and Kalotay,

Gray, and Sin (2007) use the Conference Board Consumer Confidence Index, the Investors’

Intelligence Survey Index, and The University of Michigan Consumer Sentiment Index

(UMichCCI) as proxies of U.S. investor sentiment. Chen (2008) and Charoenrook (2003)

contend that the inclusion of survey based consumer confidence measures enhance market

forecast. Additionally, Qiu and Welch (2006) show that the UMichCCI has a strong positive

relationship with investor sentiment (UBS/Gallup Survey of investor Sentiments) but the closed-

end fund discount did not exhibit a significant relationship with investor sentiments measures

A recent study by Verma, Baklaci and Soydemir (2008) builds upon the existing literature by

dividing investor sentiment into rational and irrational components. They then examine the

unique but simultaneous impact of both rational and irrational sentiment on U.S. stock market

returns. The study finds that the rational component of investor sentiments has a larger impact on

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future stock market returns than the irrational component. However, irrational sentiment has a

greater immediate positive impact on stock market returns, which, however, is corrected by

negative responses in upcoming periods. These results provide evidence that in a publicly traded

securities market periods of high irrational sentiments often times are followed by low returns as

market prices revert to intrinsic values. However, Hirschleifer, Subrahmanyam, and Titman

(2006) provide a model in which “irrational” (nonfundamental based) investors can in some

cases earn greater risk adjusted returns than informed rational investors.

In the private real estate markets typically characterized by relative market inefficiencies when

compared to the public security markets one might expect the role of sentiment and particularly

irrational sentiment to have a larger impact on pricing. Lamont and Stein (1999) and Stein (1995)

find that collateral constraints in the housing market, through the use of leverage, can lead to

price changes which are greater than fundamental market changes suggest. The use of leverage

has a substantial impact on market pricing because in the housing market the stabilizing effects

of arbitrage traders is lacking. Also, the ability of market participants to borrow is related to the

value of the assets, so an increase (decrease) in asset values can result in an increase (decrease)

in demand. Lamont and Stein (1999) refer to this notion as “key” to the amplifying effect of

observed housing prices compared to fundamental price expectations. Variations of this theme

have been examined in a variety of markets including corporate asset sales (Shleifer and Vishny,

1992), and the stock market (Garbade, 1992).

In addition to the constraining influence of leverage on the housing markets, Miller (1977)

suggests that asset overpricing may increase with valuation dispersion, and Daniel, Hirschleifer,

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Subrahmanyam (1998) contend that investors overact to privately gathered information. Chen,

Hong and Stein (2002) and Diether, Malloy and Scherbina (2002) examine stock returns and find

supportive evidence of Miller’s (1977) contention. Hong and Stein (1999) examine overreaction,

underreact ion and momentum trading, and find that as information diffuses slowly across

market participants; prices underreact in the short run, but overreact in the long run as

momentum traders enter the market. Daniel, Hirschleifer, Subrahmanyam (1998) find that

investors are overly confident about their ability to generate private information and thus

overreact to private information signals and underreact to information publicly available. In the

real estate context momentum traders may be thought of as speculators; additionally, valuation

ambiguity and privately gathered information is more prevalent in the housing markets than in

more efficient securities markets due to heterogeneity and liquidity constraints often leading to

greater opportunities for speculation and mispricing.

In the real estate domain there has been limited research on the role of sentiment and the pricing

pattern of real estate. Barham and Ward (1999) find that sentiment and United Kingdom’s (UK)

property company’s discounts to NAV are inversely related. As sentiment increases (decreases)

discounts decline (increase). While, Gallimore and Gray (2002) examine the role of investor

sentiment in the United Kingdom’s commercial market using a direct survey approach. They

conducted a survey with actively involved commercial real estate investors who are members of

the UK investment property forum and find that UK commercial property investors consider

investor sentiment to be an important factor when analyzing property. The lack of transparency

and informational asymmetry in the private commercial real estate markets results in investors

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having incomplete (in some cases incorrect) information, which may compromise investment

decision models. Therefore, property investors turn to nonfundamental indirect signals in the

form of market and or investor sentiment when formulating their investment decisions.

Clayton, Ling, and Naranjo (2009) examined the role of fundamentals and investor sentiment in

determining capitalization rates, revealing a dynamic variation in capitalization rates across time.

In the short-run, using an error correction procedure with fundamental control variables, the

authors find a positive relationship in investor sentiment and subsequent quarter returns.

However, in the long-run sentiment-induced mispricing are eventually followed by price

reversal. The findings document a distinction between the public and private commercial real

estate markets, with the private markets susceptible to a more prolonged sentiment-induced

mispricing presumably due to market inefficiencies. In the context of REITs, Lin, Rahman and

Young (2009) examine REIT asset-pricing factors and find investor sentiment to be a significant

contemporaneous factor. The authors use changes in fund discounts based on NAV as the proxy

for sentiment, contending that when investors are optimistic (pessimistic) the discount should be

smaller (larger). They find that the size of the discount is a significant variable in the pricing

patterns of REITs. More specifically, a large (small) discount results in lower (higher)

contemporaneous price returns, thus indicating investor sentiment should be included in REIT

pricing models.

In the context of residential housing prices, in a series of studies Clayton (1996, 1997 and 1998)

investigates the efficiency of both the single-family and multi-family condominium residential

real estate markets using data collected from the city of Vancouver, British Columbia. He finds

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that models of fundamental variables failed to adequately explain observed house price

dynamics. These studies provide evidence that residential price movements were predictable and

not always rational. Periods of sharply increasing values signaled a looming correction in which

prices reverted to values supported by market fundamentals. The author attributed these sharp

run-ups in housing prices to “irrational expectations”.

More recently, Case and Shiller (2003) investigates whether the U.S. residential real estate

markets were experiencing a market bubble. They empirically analyzed residential housing

market prices at the state level and a vector of fundamental economic variables, with per capital

income being the most influential, during the time period 1985 to 2002. They find fundamental

variables only partially explain the recent increase in housing prices in years after 2000. More

specifically, the fundamental model under forecasts home prices in years 2000 and 2002. The

authors attribute the excess return exceeding the predicted values to an increase in sentiment.

This is verified through a survey conducted in 2003 on subjects in 4 metropolitan areas (Los

Angeles, San Francisco, Boston, and Milwaukee) who purchased houses in 2002. They find that

homebuyers who recently purchased a home in 2002 expect home prices to increase between 7 to

11 percent annually. Suggesting, that, at that time, people generally viewed housing investment

as an escalator, meaning that if they do not buy now, they will not be able to buy later. This

mentality is consistent with prior periods (e.g. 1980’s) of exuberant market sentiment, which

eventually resulted in price declines.

Archer and Smith (2010) construct an integrated model of residential mortgage default risk and

empirically test the model based on mortgages originated in twenty Florida counties from 2001

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to 2008. Their findings as related to sentiment, suggests that lenders’ and borrowers’

interpretation of risk is subject to “euphoria” generated by past price appreciation. The authors

recommend that because residential real estate pricing is subject to euphoric behavior,

underwriting standards should be standardized and consistent across varying market conditions.

The results from the extant literature in real estate and elsewhere provide evidence that lenders,

borrowers and investors are subject to sentiment-based behavioral influences. And, as a result

studies examining the pricing patterns of various assets should consider sentiment as a potential

exogenous variable. While recognizing that the proxy for sentiment may vary depending on the

purpose of the study, the literature offers that direct measures of sentiment, especially those

based on the UMichCCI, have a high degree of fidelity to actual sentiment. The present study

parcels the effect of sentiment into rational sentiment based on fundamentals and irrational

sentiment; therefore we are able to examine the unique effect of irrational sentiment on the

residential real estate markets. This allows us to empirically examine the impact of sentiment and

explain whether the causal effect of sentiment on housing market returns can be attributed

entirely to rational risk factors, noise, or to a mixture of both.

3. Data

3.1 Home Price Data

This study employs the 10-City Standard and Poor’s Case-Shiller Home Price Indices as a proxy

of residential housing market prices for the time period January 1998 to December 2008. The

indices cover housing markets in 10 metropolitan regions across the United States2: Boston,

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Chicago, Denver, Las Vegas, Los Angeles, Miami, New York, San Diego, San Francisco, and

Washington D.C. The indices are calculated monthly, using a repeat sales methodology

employing a 3-month moving average of paired sales, and is published monthly.

{Insert Table 1 here}

Table 1 contains descriptive statistics on the annual return for the respective housing markets for

the 10 MSAs included in this study. The annual returns indicate that Los Angeles, San Diego,

and New York, experienced the highest average (median) annual returns while Denver, Chicago,

and Las Vegas exhibited the smallest returns in the sample period. Las Vegas had the highest

annual increase in home prices along with the highest decrease of housing prices. To control for

difference in volatility between cities, we divided excess housing returns by a city-specific

standard deviation to standardize regional home price changes on a risk adjusted basis.

Excess Housing Market Return per Risk

We calculated excess housing market return per risk (MPR), MPRtiR , , a Sharpe measure with a

specification in equation 1:

ti

ftiMPRti

rrR

,

,, σ

−= (1)

First, we calculated annual home price change ( tir , ) by subtracting the annual home price in time

“t-12” from the annual home price at time “t” for each regional market “i” at time “t.” Second,

we calculated a moving average standard deviation ( 2σ ) for the period t-1 to t-12. Then we

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subtracted the annual risk-free rate from each regional market return at each month “t”. The

MPR for each region can be defined by dividing the excess return with the moving average

standard deviation at time “t”.

{Insert Figure 1 here}

Figure 1 plots the relationship between housing market MPR, United States average GDP excess

return per risk, and market sentiment. We derived the U.S. average GDP excess return per risk

similarly to MPR, as shown in Eq. 1. The housing market had a positive MPR from 1998 to

2005, while GDP excess return remained generally lower than the housing market even

exhibiting negative adjusted returns from late 2002 to the end of 2003, declining again in January

2008. Interestingly, GDP excess return per risk exhibited negative growth from 2000 to 2003;

however the U.S. average housing market experienced positive growth in that same period. The

peaks in housing market excess return occurred around September 1999 and July 2005.

Consumer sentiment remained relatively level between 110 and 120 prior to 2000 and although it

fluctuated from 2003 to 2007, sentiment generally was increasing. Consumer sentiment is our

primary variable of interest in the study, as we utilized the Conference Board Consumer

Sentiment Index as a proxy for market sentiment. The Conference Board publishes this

composite index as a representative sample of U.S. households. The confidence index provides a

measurement of consumer perception on market conditions such as business conditions,

employment, inflation rate, purchasing willingness, interest rate, and expectation of stock price.

We consider, from a structural perspective, the explanatory power of current consumer market

sentiment on future housing returns. The Conference Board provides nine regional confidence

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indexes; so, this study adopts the confidence index of the region closet to the city being analyzed

as to increase the fidelity of measuring market sentiment.

3.2 Non Fundamental Market Sentiment

The volatility in consumer confidence reflects changes in market fundamentals as well as more

expectations which may or may not be perfectly rational based given market fundamentals. So,

we can think of the consumer’s beliefs as reflecting the consensus that can be explained by

fundamental variables as rational market sentiment with the remaining variance attributed to

irrational market sentiment. Using an approach similar to Baker and Wurgler (2006), we

attempted to decompose market sentiment ( )tSentt into two components, a rational market

expectation and an irrational (non fundamental) market expectation.

∑=

++=n

jtjtjt FundrSentt

10 ξγ (2)

Where, 0γ is constant, jγ are the parameters to be estimated. The term tξ is the random error

term, and tSentt represents the relative changes in sentiment on market. This sentiment can be

explained by jtFund , a vector of fundamental variables that represent rational expectations based

on market risk factors. Therefore, the predicted value in equation 2 captures the rational

component of sentiment, while the residual, tξ , captures the irrational component of sentiment.

We adopt the residual as a proxy for the irrational market component used in our analysis.

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3.3 Fundamental Variables

In our analysis we include both the 1-year adjustable rate mortgage (ARM) interest rate and the

30-year mortgage interest rate. We also calculate the spread between the 30-year mortgage

interest rate and 1-year ARM; both interest rates were obtained from Fannie Mae. The spread

serves as a measure for the relative attractiveness for ARMs with a lower “teaser” rate and can

be viewed as a proxy for many alternative loans, e.g., subprime loans and option ARMs.

{Insert Figure 2 here}

In Figure 2, 30-year fixed-rate mortgages (FRMs) and 1-year ARMs are depicted, along with the

percentage of ARM market share. We obtained both sets of data from the Federal Home Loan

Mortgage Corporation (Freddie Mac). The 30-year FRM began at 7% and increased up to 8.5%

in early 2000, prior to settling in the 5 to 7% range from 2000 to 2008. ARM rates followed a

similar pattern before 2001 but diverged substantially, making them more attractive, beginning in

December 2000. The percentage of ARM market share peaked from 2004 to 2006. However, the

interest rate gap between FRM and ARM rates began to close in 2005, when ARM rates

increased sharply. The spread was largest from 2003 to 2004. By mid-2006, just before MPR

became negative, the spread was the lowest in our analysis.

We used the Engineering News Record’s national Construction Cost Index to measure change in

construction costs. The construction costs include material and labor costs for construction. The

data covers 20 major cities across the U.S. We include state income from the Bureau of

Economic Analysis and CMSA monthly unemployment rates from the Bureau of Labor Statistics.

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Additionally, extended models include two national economic variables: Term structure (spread

between 10 year treasury notes and 3-month t-bill rates) and default risk (spread between AAA

rated bonds and BAA rated bonds), two new real estate regional variables: market volatility,

building permits, and trading volume.

4. Methodology

In this study we adopted error correction models (ECMs) to identify both the long-run

relationships and the short-run adjustment process in which the model shows how the long-run

relationship is achieved through error correction (Harvey 1990). We followed the Engle-Granger

two-step method, in which we specify a long-run model using variables in a level series and a

short-run adjustment model using the first difference of the variables. Our methodology is

similar to Hendershott and MacGregor (2005) and Clayton, Ling, and Naranjo (2009).

Regression of time series data may produce spurious results if the explanatory variables are

nonstationary. Under certain conditions, we may expect nonspurious regression results of level

series, if modeled with a long-run error correction term. These conditions are satisfied if the

variables are integrated to the order of I(1) or first-difference stationary, and have a cointegrating

relationship. In order to investigate our posited relationship, we applied the cointegration test

suggested by Johansen (1991).

4.1 Structural Modeling for Long-run and Short-run Models

We adopt the Engle-Granger two-step method in which a long-run model is specified in levels,

and a short-run adjustment model is specified in first differences, but includes a long-run error-

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correction term derived from the estimation of the long-run equilibrium model.

In the first stage, a long-run model can be specified in levels, as:

tit

n

it Xy υββ ++= ∑

=10 (3)

where, ty is the dependent research variable and itX are theoretical-based research variables i at

time t. From this regression, residuals can be estimated as the difference between the actual and

estimated equilibrium between testing factors. If the residuals from equation 3 are stationary,

they may be used as an error correction term in the short-run model as follows:

ttit

n

iit Xy ευγαα +−∆+=∆ −

=∑

^

11

0 (4)

where, 1−−=∆ ttt yyy is the first difference of the dependent variable for the study, residential

home prices, itX∆ , are the first differences of the explanatory variables, and ^

1−tυ is the error-

correction term (lagged residuals from the long-run regression). Estimation of equation 4

provides evidence of a short-run residential market dynamic and adjustments to the previous

disequilibrium in the long-run relation, γ (the speed of adjustment parameter). If 1=γ , then

there is full adjustment, while 0=γ suggests no adjustment. A more general specification of the

short-run model may also include multiple lags of the explanatory and dependent variables.

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5. Empirical Results

A unit root test was conducted as the first stage in investigating the relationship between the

variables. The unit root results are reported in Table 2.

{Insert Table 2 here}

We test for stationary using the Augmented Dickey-Fuller (ADF) procedure which test for the

presents of a unit root, the results are presented in Table 2. The hypothesis test show evidence of

“nonstationary” in the level series, thus we could not reject the null of nonstationary. When

examining the first difference in the data series there is strong evidence that all fundamental

variables modeled are stationary, therefore rejecting the null of nonstationarity. This result

confirms that the research variables may have a cointegrated, nonspurious long-run relationship.

{Insert Table 3 here}

Since we cannot reject the hypothesis of the number of cointegrating vectors at r ≤ 2, there can be

at most two integrating vectors, i.e., r ≤ 2.

5.1 Long-Run Fundamental Model

As outlined previously, we can specify a long-run model by the Engle-Granger two-step method

in levels, since the data series are cointegrated. The long-run equilibrium relationship is

embedded into the specification so that it restricts the long-run behavior of the endogenous

variables to converge to their cointegrating relationships, while allowing for short-run adjustment

dynamics. The cointegration term is known as the error correction term since the deviation from

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long-run equilibrium is corrected gradually through a series of partial short-run adjustments. One

condition for long-run equilibrium is that the relationship between excess return, fundamental

variables and market sentiment is not changing. The fundamental long-run model with irrational

sentiment is specified in the following equation:

ttititiARMFRMttitMPRti SenttIrrUnemplGDPSpreadCCFRMR υβββββββ +++++++= ,7,6,4_,3,210, _ (5)

where MPRtiR , is the excess housing market return in monthly home prices; tFRM is the 30-year

FRM rate; tiCC , is the natural logarithms of construction cost; ARMFRMtSpread _, is a rate spread

between the 30-year FRM and the 1-year ARM rate, corresponding to the measure “relative

attractiveness for variable interest loans”; ,,tiGDP is a growth rate on state income; and tiUnempl ,

is the unemployment rate in each region; tiSenttIrr ,_ represents irrational market sentiment and

is the orthogonalized market sentiment residual, tξ , from equation 2. 0β is a constant, and υ t is

the error term. Table 4 contains these fundamental variables.

In Model 1, we find that the estimated coefficient on ARMFRMtSpread _, , the interest rate spread

between a 30-year FRM and a 1-year ARM, was positive and statistically significant in nine of

ten regions. The parameter estimate for the FRM rate was negative and statistically significant in

four of the ten cities studied. The estimated coefficient on construction costs, tiCC , , was negative

and statistically significant in all ten regions. The estimated coefficient on ,,tiGDP , the state

income, was positive and statistically significant in Chicago and Denver, and negative and

significant in four regions, all were regions where home prices had sharply increased while state

23

income remained stable or decreased. Otherwise, state income had marginally increased after

excess return on the housing market significantly decreased. The estimated coefficient on region

unemployment rate, tiUnempl , , was negative and statistically significant in five regions: Las

Vegas, Los Angeles, Miami, New York, and San Francisco. The extent of relative changes in

FRM rate, construction costs, and unemployment rates is inversely related to excess housing

return per risk.

The orthogonalized (irrational) market sentiment used in this analysis represents lagged market

sentiment not supported by market fundamentals. Table 4 presents the results with a 9-month lag

in the irrational sentiment component. 3 The parameter estimate on orthogonalized irrational

sentiment is negative and significant in 7 of the 10 regions. The negative irrational

(orthogonalized) sentiment coefficients observed in the markets suggests that an increase in

irrational market sentiment resulted in a future decrease in excess return per risk, implicating that

the historic irrational sentiment component is an additional explanatory factor in predicting

contemporary excess return per risk at the MSA level. The adjusted R2 for the long-run model

ranged from 35% to 75% across regions.4

As a matter of practical consideration, we modify our model to examine housing price returns

instead of excess risk adjusted returns. In general, the findings for the long run model as well as

the short run error correction model are robust across MSA’s when substituting the risk adjusted

housing returns with unadjusted housing returns.

{Insert Table 4 here}

24

5.2 Short-Run Error Correction

Error correction models (ECM) use a combination of first differenced and lagged levels of

cointegrated variables. Here, the ECM was specified as follows:

1,7,6,4_,3,210, ˆ_ −+∆+∆+∆+∆+∆+∆+=∆ ttititiARMFRMttitMPRti SenttIrrUnemplGDPSpreadCCFRMR υγβββββββ (6)

where, ∆ represents the first difference of each research factor and γ is the speed adjustment

parameter. The change in excess housing return per risk was associated with the change in

fundamental variables and orthogonalized market sentiment, but it also acts with regard to adjust

or “correct” for any disequilibrium that was observed in the previous period.

Table 5 presents the results for the short-run model from December 1998 to December 2008. In

general, γ in equation (6) describes the speed of adjustment to the long-run fundamental model.

The short-run relationships are shown in Table 5. In our research, the change in excess return is

associated with prior changes in fundamental variables and unexplained market sentiment but

also acts in part to “correct” for any disequilibrium that existed in the previous period. Broadly,

γ describes the speed adjustment back to the equilibrium measuring the proportion of the last

period’s equilibrium error that is corrected. We find that the estimated coefficients generally

shared the same sign as presented in the long-run model; however the effect was subdued in the

short-run model as the differences in the variables do not appear to be as rich as the level series

of the variables. Additionally, the short run model generally lacks explanatory power with

adjusted R2 ranging from 0.04 to 0.20. In fact, most of the explanatory power is attributed to the

error correction term γ . The error correction term has a statistically significant coefficient

25

estimate in eight of ten regions. The short-run model confirms that returns per risk exhibit a

short-term dynamic adjustment toward long-run equilibrium between variables. The error

correction term (constrained to -1 to 1) can be interpreted as the speed our model returns to

equilibrium one month following an exogenous shock. The adjustment back towards equilibrium

ranges from 10% to 2% one time period after a shock.5 Estimated coefficients on the change of

the lagged orthogonalized irrational sentiment variable were negative and statistically significant

across only two of the regions, suggesting the first differenced model lacks explanatory power

relative to the long-run model.

{Insert Table 5 here}

5.3 Causality Test for Sentiment and Fundamental Variables

Based on the previously reported results, we test to see if changes in “sentiment” will affect

“fundamental” variables. In this case, we would expect that changes in fundamental variables

will lead to changes in sentiment. If the direction were reversed and changes in sentiment

precede changes in fundamental variables then we might conclude that the negative coefficients

produced for lagged orthoganalized sentiment in prior models might be spuriously calculated. In

this scenario, sentiment levels would result in a subsequent change in fundamental variables

which would affect house price returns. To test for this inverse relationship, we conduct a test for

relative sensitivity of changes in sentiment to the changes in fundamental economic variables

using the Granger causality test. The Granger causality test attempts to answer the question of

whether variable X “Granger causes” Y. Thus, Y is Granger-caused by X if X improves the

prediction of Y, or equivalently if the coefficients on the lagged X’s are statistically significant.

26

We can specify the Granger Causality test as

tlltltltt xxyyy εββααα +∆++∆+∆++∆+=∆ −−−− ...... 11110 (7)

tlltltltt uyyxxx +∆++∆+∆++∆+=∆ −−−− ββααα ...... 11110 (8)

for all possible pairs of ),( yx series in the study. The estimates of p-value are from the Wald

statistics for the joint hypothesis:

0 ... 21 ==== lβββ (9)

Therefore, the null hypothesis is that X does not Granger-cause Y in the Eq. (7) and that Y does

not Granger-cause X in the Eq.(8)

{Insert Table 6 here}

In Table 6, each panel (panels 1-8) indicates that the change in fundamental variables relates

significantly to our research variable sentiment, indicating fundamental variables “Granger

cause” changes in sentiment. However, we were not able to find the inverse relationship where

the sentiment variable precedes fundamentals except for the unemployment rate; in the case of

unemployment, sentiment and unemployment are tightly connected. Although not reported in

Table 6, as a robustness check of the sentiment index, we compare the Michigan Sentiment Index with

the Conference Board Index and find consistent results with the Conference Board Sentiment Index.

The previous model (Model 1) explained the role of irrational sentiment at the MSA level using a

combination of real estate related local and national exogenous variables. We extend the existing

27

model by including additional possible explanatory variables, including real estate variables

collected for a broader regional use. Model 2 includes all fundamental variables adopted in Table

6 and Eq. 5, and two additional national economic variables: term structure (spread between 10

year treasury notes and 3-month t-bill rates) and default risk6 (spread between AAA rated bonds

and BAA rated bonds), and two additional real estate regional variables: market volatility and

building permits. Considering data availability related to the additional variables, we have classified

each MSA into four unique regions for our variables based on regional data: Northeast, West, Midwest

and South. Similarly to the previous model, we report the 9-month lag in the orthogonalized (non

fundamental) sentiment index. See Table 7 and 10 for Model 2 results.

In the long-run equation, we find that the estimates from many of the explanatory variables,

FRM, Construction Cost, ARM Spread, Income, and Unemployment Rate, previously modeled

are robust to our respecified model. The two new national “economic” variables, Default Risk

and Term Structure, generally produce significant parameter estimates. As expected, an increase

in both the default risk and term spread will negatively impact house price returns (dependent

variable). The two new regional “real estate” variables, Regional Housing Market Volatility and

Regional Building Permits issued, both produce negative coefficients; however, the number of

buildings permits issued is not significant. Real estate market volatility tends to have a

significant negative impact on house prices across all MSA’s. The coefficients produced by the

lagged orthogonalized sentiment variable are negative and statistically significant in six of the

ten MSA’s. Thus it appears that the influence of non fundamental or irrational sentiment is

robust to the inclusion of the additional “economic” and “real estate” variables in the long-run

model. Compared to the prior more parsimonious model, the respecified model is a substantial

28

improvement with the adjusted R2 for the long-run model ranging from 67% to 92% across

MSA’s.

In the short-run model, the error correction term is generally significant across the regions,

however is positive suggesting in this model housing price returns do not exhibit a short-term

adjustment toward a long-run equilibrium between variables. This is perhaps an artifact to the

time period of this analyses and the interaction of house prices with market volatility. The newly

added market volatility variable is significant and negative across eight of the ten CMSA’s. The

coefficients produced by the lagged orthogonalized (non fundamental) sentiment variable are

generally not significant in the short-run. It appears that the influence of non fundamental or

irrational sentiment is less invasive in the short-run then the previous more parsimonious model

might confer, but remains influential in the long-run model.7

{Insert Table 7 here}

{Insert Table 8 here}

5.4 Summary of Results

In summary of the ECM models, the long-run models suggest that non-fundamentally induced

market sentiment does indeed impact housing prices. Further, this sentiment is inversely related

to future housing prices indicating that high non-fundamentally based sentiment will put

downward pressure on future housing prices. The estimates in the long-term model cannot be

interpreted similarly to partial derivatives, however the combined variables in model 1 explain

between 35% and 75% of the variability in housing returns per risk. Extending the model to

29

include two national variables (term structure and default risk) and two regional real estate

variables (market volatility and building permits) improves our understanding of real estate

returns, with variance explained ranging from 67% to 92% in Model 2. Variables such as the

CMSA unemployment rate, CMSA market volatility, and regional nonfundamentally based

market sentiment, along with the national ARM spread, default risk, and term structure seem to

impact housing returns the most consistently across Models 1 and 2. Local economic, sentiment,

and real estate variables cannot fully explain local housing price patterns, national financial

variables are important to the model.

The short-run equations provide us with the error correction term (constrained to -1 to 1) which

can be interpreted as the speed our model returns to equilibrium following an exogenous shock.8

Model 1 has an error correction term ranging from -0.10 to -0.02, suggesting 10% to 2%

movement back towards equilibrium one month subsequent an exogenous shock to the model.

The error correction term in Model 2 across all regions is positive (10% to 1%) suggesting slight

movement away from equilibrium following a shock to the model during the time period studied.

This is likely attributed to the market volatility variable, not included in Model 1, impacted by

the run-up in house prices followed by the credit crises.

A third model, results presented in Table 9, is derived to control for the impact of the internal

dynamics of the housing markets, particularly changes in lagged house price returns and house

volume, and to also provide greater economic interpretability of the partial coefficients. The

parameter estimates derived from a set of regional fundamental variables as well as national level

variables; default risk and term structure risk. Due to limited data availability regional variables

30

previously in 10 CMSA level was transformed into four regions, North East, South, West, and

Mid-West. The ∆ Housing Returnt-1 measures one lag of regional average housing market return.

Our four regional models indicate that the internal housing dynamics, particularly lagged return

on residential real estate markets explains most of short-run variation observed at a regional level.

The lagged residential real estate market returns show highly significant estimates, 0.80, 0.95,

0.55, and 0.88 respectively. This suggest that the expected impact of a one dollar change in

housing returns from the previous month has a contemporaneous impact on housing returns

ranging from $0.55 to $0.95. We also find that trading volume has a marginal impact on returns

in the Mid-west. The spread between ARM and FRM has a positive impact on the residential

market in West and South region, as a one unit increase in the spread results in an expected 1.06

and 1.24 increase in housing price changes, respectively. While, again, sentiment does not seem

to impact housing returns in the short-run.

{Insert Table 9 here}

6. Conclusion

This study builds on existing fundamental residential real estate market models by implementing

a systematic procedure to account for irrational (non-fundamental based) market sentiment.

Specifically, we investigate the role irrational market sentiment and excess return per risk in the

U.S. residential real estate market over a 10-year period (January 1998 to December 2008)

covering periods of high and low sentiment and corresponding housing prices. We generally find

responding information on each fundamental variable with the expected directional relationship

in the long-run models. The inclusion of our derived irrational (orthogonalized) sentiment

31

measure to the vector of fundamental variables has important structural and predictive

implications, and increases the understanding of residential real estate pricing.

These results empirically support Shiller’s (2007) argument that market fundamentals do not

fully explain the recent housing market price movement, but rather an approach incorporating

consumer psychology may describe it better. This study can be considered a novel approach to

empirically investigate this relationship within the residential real estate market context. The

findings empirically support the existence of a long-run relationship between irrational market

sentiment and the pricing pattern of residential real estate during the 1998 to 2008 time period.

These findings suggest that consumer irrational (non-fundamental based) sentiment does indeed

impact subsequent housing prices and can lead to euphoric behavior, therefore real estate pricing

models should include a variable capable of measuring irrational sentiment.

32

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Acknowledgment

The authors gratefully acknowledge Paul Gallimore, and 2010 American Real Estate Society participants; especially discussant Fabrice Barthelemy, and the anonymous referees for their many insightful comments.

37

Table 1 Descriptive Statistics for Annual Home Price Change

Mean Median Max Min Std. Dev. Skewness Kurtosis

Boston 0.07 0.09 0.17 -0.08 0.07 -0.73 2.10 Chicago 0.05 0.07 0.10 -0.15 0.06 -1.90 5.69 Denver 0.05 0.04 0.14 -0.06 0.06 0.07 2.16

Las Angeles 0.08 0.11 0.29 -0.33 0.14 -1.59 5.10 Las Vegas 0.05 0.05 0.43 -0.40 0.16 -0.49 4.70

Miami 0.07 0.10 0.28 -0.34 0.15 -1.38 4.66 New York 0.08 0.11 0.16 -0.10 0.07 -1.22 3.23 San Diego 0.08 0.12 0.29 -0.31 0.14 -1.33 4.14

San Francisco 0.07 0.11 0.27 -0.37 0.14 -1.42 4.92 Washington D.C. 0.07 0.10 0.24 -0.22 0.11 -0.86 3.18

Note : Dec. 1998 as beginning and Dec 2008 as an ending period.

38

40

50

60

70

80

90

100

110

120

130

140

-10

-5

0

5

10

15

20

25

30

35

40

Janu

ary 1

998

June

199

8No

vem

ber 1

998

April

199

9Se

ptem

ber 1

999

Febr

uary

200

0Ju

ly 2

000

Dece

mbe

r 200

0M

ay 2

001

Oct

ober

200

1M

arch

200

2Au

gust

200

2Ja

nuar

y 200

3Ju

ne 2

003

Nove

mbe

r 200

3Ap

ril 2

004

Sept

embe

r 200

4Fe

brua

ry 2

005

July

200

5De

cem

ber 2

005

May

200

6O

ctob

er 2

006

Mar

ch 2

007

Augu

st 2

007

Janu

ary 2

008

June

200

8No

vem

ber 2

008

U.S. Average Housing Market Excess Return Per RiskU.S. Average State GDP Excess Return Per RiskConsumer Market Sentiment

Note : The study inclues a monthy observations from January 1998 - December 2008. The S&P/Case-Shiller Home Price Index are used as a proxy for home priceof U.S.national level (10 CMSA). The GDP has been derivd from the growth in each state income where these 10 CMSA are located. The 3-month T-bill has beed used as proxy for risk-free rate. The excessive return per risk for GDP and Housing Markets is similar to Sharpe ratios where exessive return by subtracting risk free rate return at time t and moving average standard deviation for the period t-1 and t-12. We devided the exess return by the moving average stadnard deviation at time t to derive excessive market return per risk for both GDP and Housing Makret, respectively.

Exce

ss H

ousin

g R

etur

n Pe

r Risk

(%)

Market Sentim

ent (1998: 12 =120)

Figure 1 Market Sentiment and Housing Market Excess Return

39

0102030405060708090100

0

1

2

3

4

5

6

7

8

9

Janu

ary

1998

July

199

8Ja

nuar

y 19

99Ju

ly 1

999

Janu

ary

2000

July

200

0Ja

nuar

y 20

01Ju

ly 2

001

Janu

ary

2002

July

200

2Ja

nuar

y 20

03Ju

ly 2

003

Janu

ary

2004

July

200

4Ja

nuar

y 20

05Ju

ly 2

005

Janu

ary

2006

July

200

6Ja

nuar

y 20

07Ju

ly 2

007

Janu

ary

2008

July

200

8

Percentage of ARM Share 30-Year FRM Rate1-Year ARM Rate

Note : The study inclues a monthy observations from January 1998 - December 2008. The Mortgage Rate has been derivd from the Fannie Mae.

Inte

rst R

ate

(%)

Percentage of AR

M Share

(1998:1 =10)

Figure 2 Market Sentiment and Housing Market Excess Return

40

Table 2 Unit Roots Test

Level First Difference Research Variables t-statistic p-value t-statistic p-value

ERR (Housing Market Return) -1.624 0.467 -3.690 0.005 FRM Rate -1.136 0.701 -7.917 0.001 ARM rate -1.213 0.667 -6.703 0.001

GDP Growth -2.176 0.216 -2.456 0.015 ARM Share -1.624 0.467 -3.690 0.005

Construction Cost -2.170 0.218 -8.479 0.000 Rate Spread(FRM-ARM) -1.418 0.571 -4.514 0.003

Consumer Sentiment 0.044 0.960 -6.627 0.001 Note. We adopt the Augmented Dickey- Fuller test statistic (ADF). * and ** indicate significance at the 1% and 5% levels. We only report national level data where we generate an equally weighted state or CMSA average to create national level data (Market Excessive Return Per Housing and Market Sentiment Index).

41

Table 3 Johansen's Cointegration Test Fundamental Model

Number of Cointegrating Vectors ( r ) at Null Hypothesis

Eigenvalue Trace Statistics Critical Value at 5% p-value

r = 0 0.29 116.93 95.75 0.00

r ≤ 1 0.23 73.14 69.81 0.02

r ≤ 2 0.13 39.31 47.85 0.24

r ≤ 3 0.08 20.17 29.79 0.41

r ≤ 4 0.03 8.34 15.49 0.42

r ≤ 5 0.02 3.42 3.84 0.64 Note: Trace test indicates two cointegrating eigenvalues. The parameter estimates are from the Johansen's test using monthly data over the time period from December 1998 to December. 2008. The variables are excess housing return per risk, U.S. average state income, FRM rate, rate spread between ARM and FRM, unemployment rate, and construction cost.

42

Table 4 Model 1, Long Run Residential Market Excess Return Level Models with Market Sentiment

Boston Chicago Denver Las Vegas L.A. Miami New

York San Diego

San Francisco

Wash. D.C.

Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Constant 4.43*** 1.32** 4.82*** 0.71** 3.69*** 1.57** 6.50*** 3.53*** 2.36*** 1.39**

(6.55) (2.38) (7.50) (2.37) (4.89) (2.05) (7.34) (7.22) (5.22) ( 2.35) FRM Rate -0.73 -1.80** 2.10** -0.23 -1.45 -3.58*** -3.34** -0.84 -2.81 -1.04*

(-0.21) (-2.09) (2.07) (-0.49) (-1.29) (-4.16) (-2.70) (-1.22) (4.03) (-1.18) Construction Cost -0.49*** -0.14** -0.55*** -0.07** -0.38*** -0.14** -0.65*** -0.39*** -0.23*** -0.15*

(-6.52) (-2.49) (-7.93) (-2.33) (-4.91) (-1.90) -(7.24) (-7.52) (-4.86) (-2.29) ARM Spread(FRM-ARM) 2.54** 4.24*** 4.45*** 2.21*** 3.95*** 8.92*** -0.01 2.59*** 3.36** 7.48***

(2.15) (3.48) (3.13) (3.83) (2.71) (7.06) (-0.02) (2.95) (3.26) (5.84) State Income 0.02 0.73** 0.38** -0.39** -0.60** 0.26 -1.08*** 0.26 0.21 -0.71***

(-0.19) (2.45) (2.21) (-4.07) (-3.21) (0.87) (-4.02) (0.01) (1.49) (-4.41) CMSA Unemployment Rate

-1.29 0.73 0.14 -0.99*** -2.32*** -2.02** -7.38*** -0.03 -3.26*** -1.82 (-1.27) (0.82) (0.17) (-3.12) (-3.08) (-2.25) (-5.61) (-0.05) (-5.33) (-1.25)

Ortho. Sentiment (Lag) -0.01 0.14*** -0.07** -0.07*** -0.29*** -0.10*** -0.13** -0.05** -0.05** 0.13*** (0.10) (4.65) (-1.87) (-3.76) (-6.24) (2.19) (-2.36) (-2.01) (-2.12) (4.36)

Adj. R^2 0.68 0.35 0.75 0.411 0.35 0.59 0.44 0.65 0.62 0.55

Note: t statistics are in parentheses. *, ** and *** * and ** indicate significance at the 10%, 5% and 1% levels. The parameter estimates are from the Equation 10. Using monthly data over the Jan. 1998 to Dec. 2008 time period, the dependent variable is the monthly excessive return per risk in 10 CMSA Housing Markets. The independent variables are monthly ARM rate, percentage of ARM shares, State GDP growth, Construction Cost, and Rate Spread between FRM and ARM. Although we have not reported in the results section, Johanson conintegration test shows that fundamental variables and irrational market sentiment has two cointegrating vectors at 5% significant level. We used State Income data and the unemployment rate is level of CMSA obtained from census. We use 9-month lag in sentiment index. We also estimate the model with 1, 3 and 6 lags for orthogonalized consumer sentiment and found 9-month lag has been confirmed by SBC criterion. We also confirm that other different lags provide a similar coefficient with 9 month lag.

43

Table 5 Model 1, Short Run Residential Market Excess Return Level Models with Orthogonalized Sentiment Effect

Boston Chicago Denver Las Vegas LA Miami New

York San

Diego San

Francisco Wash. D.C.

Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Constant 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

(-0.33) (-0.48) (0.03) (-0.21) (0.03) (-0.18) (-0.19) (0.09) (-0.82) (0.05) ∆FRM Rate 1.873** 0.28 0.47 0.46 2.25 -2.99** 0.47 -3.52*** -0.52 -1.77*

(1.67) (0.34) (0.31) (0.88) (0.96) (-2.03) (-0.23) (-3.44) (-0.60) (-1.74) ∆ Construction Cost -0.11 0.01 -0.57 0.01 -0.62 0.36 -0.24 -0.06 0.05 -0.21

(-0.39) (0.05) (-1.33) (0.14) (0.98) (0.89) (-0.44) (-2.04) (0.23) (-0.77) ∆ ARM Spread -2.40** 0.03 1.29 1.14* -1.83 4.43** 0.95 5.33*** -0.19 2.40*

(-1.66) (0.03) (0.53) (1.61) (-0.57) (2.19) (0.34) (3.73) (-0.16) (1.75) ∆ State Income -0.43** 0.05** 0.49* 0.13 -0.30 0.96** 0.03 0.05** -0.26* -0.14

(-2.09) (1.85) (0.16) (1.18) (-0.63) (2.03) (0.10) (2.23) (-1.46) (-0.83) ∆ CMSA Unemployment Rate

-0.01 -0.00 -0.03 0.00 -0.01 -0.05 -0.03 -0.01 -0.02 0.01 (-1.28) (-0.25) (1.10) (0.38) (-0.33) (-1.53) (-0.68) (-0.71) (-1.92) (0.18)

Error Correction Term -0.09*** -0.02 -0.10** -0.02 -0.09** -0.08** -0.06** -0.07** -0.06** -0.02* (-3.04) (-0.99) (2.31) (-1.09) (-2.00) (-2.22) (-1.69) (-2.01) (-1.91) (-1.71)

∆ Ortho. Sentiment (Lag) 0.001 0.02* -0.03* 0.01 0.01 0.00 0.02 -0.02* 0.02 -0.01 (0.67) (1.62) (-1.70) (0.12) (0.83) (0.08) (0.87) (1.78) (0.24) (-0.24)

Adj. R^2 0.12 0.04 0.11 0.11 0.06 0.11 0.05 0.20 0.10 0.06 Note: t statistics are in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% levels. We use the data over the Jan. 1998 to Dec. 2008. The dependent variable is the monthly excessive return per risk in 10 CMSA Housing Markets. The independent variables are change (∆) in monthly ARM rate, State GDP growth, Construction Cost, and Rate Spread between FRM and ARM. We adopt state income data and the unemployment rate is level of CMSA. Orthogonalized Sentiment is the residual calculated from regressing fundamental variables on market sentiment index. In order to match each CMSA cities with regional sentiment measure, we use U.S. consumer confidence index which provides the ten standard Federal Regions. For example, we use regional confidence index: U.S. Confidence Index for New England (Boston), Pacific (Los Angeles, San Francisco, and San Diego), East North Central (Chicago), South Atlantic (Miami and District of Columbia), Mid-Atlantic (New York) and Mountain (Las Vegas, and Denver), respectively.

44

Table 6 Granger Causal Tests for the Change in Sentiment Index and Fundamental Variables

Null Hypothesis F-Stat. P-value

Panel 1 ∆FRM does not Granger Cause ∆ Sentiment 3.82 0.01 ∆Sentiment does not Granger Cause ∆ FRM 1.03 0.39 Panel 2 ∆ARM Spread does not Granger Cause ∆ Sentiment 2.55 0.04 ∆Sentiment does not Granger Cause ∆ ARM Spread 0.52 0.68 Panel 3 ∆Construction Cost does not Granger Cause ∆ Sentiment 2.54 0.04 ∆Sentiment does not Granger Cause ∆ Construction Cost 0.42 0.79

Panel 4 ∆Income does not Granger Cause ∆ Sentiment 2.75 0.03 ∆Sentiment does not Granger Cause ∆ Income 0.21 0.93

Panel 5 ∆Building Permit does not Granger Cause ∆ Sentiment 0.27 0.89 ∆Sentiment does not Granger Cause ∆ Building Permit 0.35 0.84

Panel 6 ∆Unemployment does not Granger Cause ∆ Sentiment 1.64 0.10 ∆Sentiment does not Granger Cause ∆ Unemployment 2.48 0.04

Panel 7 ∆default risk does not Granger Cause ∆ Sentiment 0.49 0.74 ∆Sentiment does not Granger Cause ∆ Unemployment 0.91 0.45

Panel 8 ∆Term risk does not Granger Cause ∆ Sentiment 0.74 0.56 ∆Sentiment does not Granger Cause ∆ Term risk 0.45 0.76 Note: Using monthly data over the Jan. 1998 to Dec. 2008 time period. We include conference board sentiment index as proxy for sentiment variable and also include fundamental variables; Income, Building Permit, Unemployment Rate, Term Structure (a spread between 10 year treasury note and 3-month t-bill rate), Default Risk(a spread between 10 AAA rated bond and BAA rated bond). As a robustness check of sentiment index, we also compare the Michigan Sentiment Index with the Conference Board Index. However the results are consistent with the Conference Board Sentiment Index and thus omit for a concise manner of presentation. Results are available based upon a request.

45

Table 7 Model 2, Long Run Residential Market Annual Return Level Models with Market Sentiment

Boston Chicago Denver Las Vegas L.A. Miami New

York San Diego

San Francisco

Wash. D.C.

Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Constant 0.16** -0.01 -0.06 0.52*** 0.69*** 0.76*** 0.23*** 0.46*** 0.04 0.24**

(2.18) (-0.27) (-1.29) (3.14) (9.40) (6.79) (5.34) (3.38) (0.27) ( 2.36) FRM Rate 1.86** 1.45*** 4.15*** -5.55*** -8.22*** -7.69*** -1.38** -3.09** 2.89 -2.74***

(2.27) (5.46) (7.79) (-4.10) (-9.11) (-7.62) (-2.51) (-2.08) (1.60) (2.82) Construction Cost 0.01* -0.01 0.01 -0.02 -0.02 -0.01 -0.01*** -0.01 -0.01 -0.01

(0.17) (-0.95) (0.03) (-1.01) (1.12) (-0.78) (-0.63) (-0.51) (-0.51) (-0.99) ARM Spread(FRM-ARM) 7.92*** 4.24*** 2.46** 3.44*** 18.84*** 9.26*** 12.01*** 14.79*** 11.31*** 16.23***

(5.08) (6.42) (2.55) (0.37) (8.36) (3.13) (9.18) (4.46) (3.01) (6.68) State Income -1.08*** -0.52** -0.59** 1.65*** 0.55** 0.63 -0.51*** -0.01 -0.30 -1.15***

(-7.90) (-3.90) (5.38) (3.13) (2.54) (1.26) (-3.58) (-0.05) (-0.77) (-5.36) CMSA Unemployment Rate

-4.18*** -1.03 -1.95*** -1.97 -2.52** -3.80*** -1.14* -4.46*** -3.26*** -4.04* (-4.92) (0.82) (-4.69) (-0.99) (-2.03) (-2.97) (-1.68) (-2.74) (-5.33) (-1.94)

Term Structure -0.06 -0.02*** -0.01** 0.02 -0.04*** -0.03*** -0.04*** 0.01 -0.05** 0.13*** (0.10) (-7.06) (0.83) (1.60) (-3.40) (-2.51) (-5.71) (0.12) (-2.12) (4.36)

Default Risk -0.06*** -0.01*** -0.04*** -0.14*** -0.06** -0.01 -0.03** -0.15*** -2.64 -0.15*** (-3.75) (-7.70) (-4.87) (-3.62) -2.54 (-0.51) (-2.33) (-4.38) (-1.49) (-6.72) Regional Building Permit 0.01 -0.01 0.01 -0.04 -0.05 0.01 0.01 -0.03 -0.01 -0.04 (0.10) (-0.50) (0.45) (-0.83) -1.28 (0.13) (0.25) (-0.61) (-0.06) (-1.20) Market Volatility -0.02*** -0.04** -0.08*** -0.02*** -0.03*** -0.03*** -0.03*** -0.01** -0.01*** -0.02*** (3.87) (-1.80) (-3.64) (-5.48) (-5.19) (-7.97) (-9.56) (-2.46) (-2.40) (-4.83) Ortho. Sentiment(Lag) -0.10*** 0.04** -0.08*** -0.05 -0.04 -0.27*** -0.12*** -0.12* -0.19** 0.03 (-3.87) (2.34) (-3.64) (-0.74) (-0.97) (-4.30) (-4.04) (-1.69) (-2.38) (0.78) Adj. R2 0.75 0.92 0.83 0.78 0.86 0.84 0.78 0.71 0.67 0.76 Note: t statistics are in parentheses. *, ** and *** * and ** indicate significance at the 10%, 5% and 1% levels. The parameter estimates is based on a set of fundamental variables adopted in Table 5 and also include national level variables; default risk and term structure risk. The market volatility is measured as a moving average market standard deviation of last 12-month. We also include a supply side variable; building permit available at four regional levels, North East, South, West, and Mid-West. We also estimate the model with 1, 3 and 6 lags for orthogonalized consumer sentiment and found 9-month lag has been confirmed by SBC criterion. We also confirm that other different lags provide a similar coefficient with 9 month lag.

46

Table 8 Model 2, Short Run Residential Market Annual Return Level Models with Market Sentiment

Boston Chicago Denver Las Vegas L.A. Miami New

York San Diego

San Francisco

Wash. D.C.

Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Constant -0.01 -0.01*** -0.01*** -0.00* -0.01** -0.01* -0.01** -0.01 -0.01** -0.01

(-2.27) (-2.58) (-3.16) (-1.77) (-2.80) (-1.88) (-2.21) (-3.15) (-1.91) ( -2.13) ∆FRM Rate 0.13 0.56 1.64*** 1.16 0.12 -0.62 0.15 0.36 2.64** -0.01

(0.25) (1.41) (4.78) (0.94) (0.14) (-0.78) (0.31) (0.43) (2.31) (-012) ∆Construction Cost 0.01 -0.01 0.00 -0.00 0.00 0.01 0.15 0.01 0.00 0.01

(1.10) (-0.26) (-0.09) (-0.08) (-0.02) (0.27) (0.37) (0.29) (0.36) (0.19) ∆ARM Spread(FRM-ARM) 0.23 0.15 2.13** -1.79 0.92 2.10* 0.58 -0.65 -2.59 0.86

(0.31) (0.25) (4.26) (-0.95) (0.72) (1.73) (0.83) (-0.53) (-1.53) (0.83) ∆State Income -0.23** -0.09 0.01 0.87*** 0.28 0.61** 0.02 0.31* 0.22 -0.04

(-2.31) (-0.63) (0.11) (3.17) (1.62) (2.36) (0.31) (1.80) (0.95) (-0.40) ∆CMSA Unemployment Rate

-0.08 -0.01 -0.01 -0.01 -0.01 -0.01 0.01 -0.01 -0.01 -0.01 (-1.18) (-0.14) (-0.42) (-0.69) (-0.36) (-0.46) (0.06) (-0.12) (-0.23)) (-0.06)

∆Term Structure -0.01 -0.01** 0.01 0.00 -0.01 -0.01 -0.01 0.01 -0.01** -0.01* (-1.17) (-1.98) (1.52) (0.81) (-0.62) (-1.34) (-1.94) (0.33) (-2.19) (-1.81)

∆Default Risk -0.01** -0.01*** -0.04 -0.01 -0.01 -0.01 -0.01* -0.01 -0.02* -0.01** (-2.21) (-3.04) (-1.15) (-0.62) (-0.66) (-1.34) (-1.81) (-0.88) (-1.81) (-2.59) ∆Regional Building Permit -0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.00 -0.01 -0.01 (-0.89) (-0.60) (-0.07) (-0.09) (-0.13) (-0.23) (-0.03) (-0.03) (-0.51) (-0.79) ∆Market Volatility -0.01*** -0.01* -0.08*** 0.01 -0.01** -0.01*** -0.01** -0.01 -0.01*** -0.01*** (-2.78) (-1.86) (-3.50) (1.36) (-2.40) (-4.53) (-2.37) (-0.14) (-3.41) (-3.05) Error Correction Term 0.01 0.10** 0.04** 0.04* 0.05*** 0.03* 0.03 0.04*** 0.02 0.01 (0.90) (2.52) (2.59) (1.85) (2.73) (1.73) (1.37) (3.16) (1.29) (0.64) ∆Ortho. Sentiment(Lag) 0.01 0.01** -0.01 0.01 -0.01 -0.01 0.01 -0.01 0.01 0.01 (0.12) (1.99) (-0.41) (0.28) (-0.32) (-0.75) (0.21) (-0.78) (0.62) (1.06) Adj. R2 0.18 0.21 0.30 0.14 0.15 0.28 0.13 0.13 031 0.17 Note: t statistics are in parentheses. *, ** and *** * and ** indicate significance at the 10%, 5% and 1% levels. The parameter estimates is based on a set of fundamental variables adopted in Table 5 and also include national level variables; default risk and term structure risk. The market volatility is measured as a moving average market standard deviation of last 12-month. We also include a supply side variable; building permit available at four regional levels, North East, South, West, and Mid-West. We also estimate the model with 1, 3 and 6 lags for orthogonalized consumer sentiment and found 9-month lag has been confirmed by SBC criterion. We also confirm that other different lags provide a similar coefficient with 9 month lag.

47

Table 9 Model 3, Regional Residential Market Return Models with Market Sentiment Model Controlling for internal Housing Dynamics NE

∆ Housing Return

West ∆ Housing Return

MW ∆ Housing

Return

South ∆ Housing Return

Constant -0.00 -0.00 -0.001 -0.000 (0.00) (0.00) (0.000) (0.000) ∆ Housing Returnt-1 0.80*** 0.95*** 0.550*** 0.879*** (0.05) (0.04) (0.080) (0.040) ∆ Income -0.04 -0.06 -0.015 0.216*** (0.06) (0.09) (0.124) (0.118) ∆Unemployment rate -0.03 0.11 -0.016 0.162 (0.12) (0.14) (0.107) (0.159) ∆Building Permit -0.01 -0.00 0.000 -0.001 (0.01) (0.01) (0.002) (0.003) ∆Trading Volume -0.01 0.01 0.015*** -0.007 (0.01) (0.08) (0.009) (0.013) ∆FRM rate 0.34 0.80*** 0.321 -0.200 (0.25) (0.34) (0.330) (0.353) ∆ARM Spread 0.43 1.06*** -0.162 1.239*** (0.365) (0.53) (0.514) (0.546) ∆Construction cost 0.01*** 0.00 -0.001 0.002 (0.01) (0.00) (0.001) (0.001) ∆ Default_Risk -0.01 0.01 -0.009*** 0.001 (0.01) (0.01) (0.004) (0.004) ∆ Term Structure -0.01*** 0.00 -0.001 -0.005*** (0.00) (0.01) (0.002) (0.002) ∆Sentiment -0.01 0.01 -0.000 0.006 (0.01) (0.01) (0.003) (0.003) R-squared 0.71 0.84 0.394 0.825 Adj.R 0.68 0.83 0.337 0.809 Note: Note: t statistics are in parentheses. *, ** and *** * and ** indicate significance at the 10%, 5% and 1% levels. The parameter estimates is based on a set of regional fundamental variables adopted in Table 6 and also include national level variables; default risk and term structure risk. Our regional variables previously in 10 CMSA level has transformed into four regions, North East, South, West, and Mid-West. We transform a set of CMSA level fundamental variables into regional equal-weight fundamental variables including consumer sentiment. The ∆ Housing Returnt-1 measures one lag of regional average housing market return. We also include a supply side regional variable and construction cost.

48

1 This study denotes the fundamental analysis as a model based on a microeconomic framework that often uses macroeconomic variables. Chen, Ross and Rolls (1987) uses arbitrage models as premised on cash flow analysis using systematic aggregated variables. Fundamental variables often combined to simulate cash flow measures include inflation measure, volatility in mortgage interest rates, regional population and income growth, and changes in money supplies and other capital market activities. The validation of specification on fundamental analysis is challenged by the selection of right fundamental exogenous variables. To avoid, this argument against on our study, the selective economic variables included in the model can be referred as parsimonious fundamental model. 2 The description of area coverage is available at S&P/Case-Shiller web site (http://www.standardandpoors.com). 3 We also estimate the model with 1, 3, and 6 month lags for irrational consumer sentiment and found that the 9-month lag was confirmed by SBC criterion. 4 The adjusted R2 for the long-run model with the orthogonalized market sentiment variable increased in all regions compared to the fundamental model without the orthogonalized market sentiment variable (not presented).

5 Negative one indicates full adjustment to equilibrium one time period later, while 0 indicates no adjustment towards equilibrium. A positive error correction coefficient suggests movement away from equilibrium. 6 In the extended model the authors have added term spread and default spread, as in Yang, Zhou and Leung (2012) 7 Considering data availability, we also classified each state into four different regions; North East, West, Mid-West and South Region and regressed the monthly return in regional (North East, West, Mid-West and South) housing markets on the regional (we combined state income and unemployment rate data respective of region to proxy for regional level data) and national variables, along with a broad regional irrational sentiment index. We find that the coefficients produced by the lagged orthogonalized (non fundamental) sentiment variable generally are not significant in this regional analysis. These results combined with the previous MSA level results, suggests that the impact of irrational sentiment is highly localized. Where local irrational sentiment has a substantial impact on subsequent local housing price patterns, but we were unable to detect a regional effect as regional irrational sentiment levels do not substantially impact subsequent regional house pricing.

49

8 Negative one indicates full adjustment to equilibrium one time period later, while 0 indicates no adjustment towards equilibrium. A positive error correction coefficient suggests movement away from equilibrium.