Is a bubble emerging in the U.S. commercial real estate market?

(1)

Is a Bubble Emerging in the U.S.

Commercial Real Estate Market?

Mulin Tang

Supervisor: Natalya Martynova

Master Thesis of Real Estate Finance Faculty of Business and Economics

Student ID: 10605274

(2)

Abstract

This paper studies the recent speculative commercial real estate bubble in the United States. The real estate bubble is characterized by a discrepancy between asset price and asset fundamental value. Sufficient evidences against the emergence of bubble have been found by analyzing the price-rent ratios of 52 real estate investment trusts from 2000 to 2013. This research also contributes to the knowledge of bubble testing and the understanding of investment risk of commercial real estate in the United States.

Statement of Originality

This document is written by Student [Mulin TANG] who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

I. Introduction

During the recent global financial crisis of 2008, the price of real estate had fallen at historical low for the past decade. However in the subsequent years, a sharp growth of the commercial real estate prices in the United States draws considerable attention to this research. In the aftermath of collapse of housing markets, researchers have found extensive evidences on residential real estate bubble throughout time, see- Sornette and Zhou (2003), Case and Shiller, (2004), Himmelberg, Mayer and Sinai (2005), Sornette and Zhou (2006). However few have attempted to assess the existence of bubble in the field of commercial real estate.

Table 1: The Moody’s and RCA price index of U.S. commercial real estate, data from

https://www.rcanalytics.com/Public/rca_cppi.aspx 60 80 100 120 140 160 180 200 4q 2000 2q 2001 4q 2001 2q 2002 4q 2002 2q 2003 4q 2003 2q 2004 4q 2004 2q 2005 4q 2005 2q 2006 4q 2006 2q 2007 4q 2007 2q 2008 4q 2008 2q 2009 4q 2009 2q 2010 4q 2010 2q 2011 4q 2011 2q 2012 4q 2012 2q 2013 4q 2013 2q 2014

U.S. Commercial Property Price Indices

(5)

As can be observed from the above table provided by Real Capital Analytics (RCA), the recent price of commercial real estate in the United States has grown substantially. The office segment, for instance, has virtually reached at the level equivalent to the historical peak before the global financial crisis started to occur.

It is noted that the scope of commercial real estate includes properties that are intended to generate profits, such as office building, industrial property, hospitals, warehouse and multifamily housing and etc. Therefore one possible reason behind this sharp growth of commercial real estate is that there was a decline in underwriting standards of commercial mortgage backed security (CMBS) loan, which has been one of the primary financing sources of commercial real estate (Levitin and Wachter, 2012). Moreover, due to the asset price sliding to historical low level during the recession, investors may have strong expectations on the recovery of yields in commercial real estate markets. Thus the increasing demands of transactions also contribute to the growth of price levels. Moreover, the recovery of national economy such as growing domestic GDP and CPI also to some extent lead to the growth of demand and asset prices. Considering factors such as low credit cost and strong investor expectation, it is logical to think of the following research question of this paper: is a bubble emerging in the commercial real estate markets of the United States?

The emergence of bubble is characterized by a discrepancy between the fundamental value and the market price of asset. Following this definition, investors who perceive a continuing growth of market price would opt for buying assets notwithstanding they are over charged against economic fundamentals. The reason behind this is investors deem that the piece would keep arising and they are able to sell assets at higher price in the future. As various investors expect this sort of price growth as arbitrage opportunity, the increasing demand on assets would stimulates a further rise of asset price and in return contribute to the development of bubble. Therefore the capital market will see a significant growth of market price that consists of both asset fundamental value and a bubble term.

Historical examples can be found from the Dutch Tulip Mania in 1634, the Mississippi Bubble in 1719 and the more recent Dot-Com Bubble (IT Bubble) at the end of 2000. However, according to Rappoport and White (1993), it is important to point out that misconception on the presence or bubble is also critical. A lack of investor confidence resulting from insufficient knowledge about market condition while

(6)

concerning the burst of speculative bubble would also substantially jeopardizes market performance and sustainability. Therefore it is essential to examine the mergence of bubbles and assess situations under which commercial real estate prices can deviate from their fundamental value. Therefore the research on the sustainability of this growth becomes critical, and this paper is going to contribute the knowledge of bubble testing and market analysis of current commercial real estate market.

In order to test for the evidence on the existence of commercial real estate bubble, the methodology of this paper has utilized a pool of unit root tests as empirical testing method. In a sense of economics, the hypothesis is to check if the fundamental asset value is able to identify its corresponding market price. And the research hypothesis is that if there were no bubble emerging in commercial real estate markets, the series of asset log price-rent ratios should be stationary. The theories for the tests of stationarity will be further explained in the next sections. However, this paper understands that there are various obstacles in terms of constantly and accurately observing market price of commercial assets or directly calculating their fundamental value. Hence the Total Enterprise Value (TEV) of Real Estate Investment Trust (REIT) has been introduced as a measurement of asset market price. Moreover, the fundamental value is then expressed by incorporating quarterly pure rental income of REIT.

The REIT investment vehicle was firstly introduced by the congress of the United States in 1960 through legislation called the Real Estate Investment Trust Act, which authorized a following real estate ownership structure: a pass-through entity that distributes most of its earnings and capital gains. And the introduction of REITs was to provide retail investors a means to invest in a diversified portfolio of various individual assets without requiring an enormous fortune to do so. REITs thus offer a liquid approach to invest in a transparent portfolio of commercial assets to individual investors. Nowadays REITs are playing significant roles in the commercial real estate industry and also provide considerable sample data for this research. According to Geltner and etc. (2013), REITs as of 2011 owned approximately 800 billion dollars worth of commercial real estate in the United States. Moreover in view of the transparency and liquidity of REITs, this paper has calculated the log rental income from pooled assets that are under management of each REIT.

In this research, the sample database has includes 52 equity REITs listed in the United States and their quarterly rental income and historical enterprise value observed from the 1st_{quarter of 2000 to the 4}th

(7)

quarter of 2013 (totally 56 periods). Although previously bubble tests also studied the performance of REITs - see Campbell, Jirasakuldech and Knight (2006) Brooks, Nneji and Ward (2013), Sun, Titman and Twite (2013), they either focused on the price-return ratios of the common equity, or tried to explain the volatility of REITs’ stock price during the global financial crisis. In addition, their findings did not provide direct evidences on the existence of bubble in commercial real estate market, i.e. the discrepancy between market price and fundamental value. Therefore, the direct investigation of this research will examine whether there was a commercial real estate bubble by analyzing the relationship between asset fundamental value and market price. And the contribution of this paper to the study is that it will provide comprehensive market analysis of the commercial real estate markets.

What’s more, the result of unit root tests has turned out to support the stationarity of the linear combined log price and log rental income, which quantitatively indicates evidence against bubble in commercial real estate. Hence this paper is able to contribute consolidated understanding of current market situation of commercial real estate in the United States. In addition, the analysis of this paper will provide insights not only for researchers but also for governments who can make macro decisions that may enhance the sustainability of investment systems. For example, policy makers could consider adjusting and controlling the sharp growth of asset price by imposing higher tax rate on real estate transactions or on any capital gains. Moreover real estate investors and institutional lenders who are directly exposed to the investment risks may also reference the findings of evidence against bubble in this paper.

The next sections will firstly focus on the review of related literatures that illustrate bubble-testing approaches, which will include efforts not only from commercial real estate markets, but also from stock markets and residential real estate markets. Then the methodology and dataset in this research will be described in the third section. After analyzing the testing result in the fourth section, the fifth section will discuss the robustness of this research from critical perspectives. Finally, it will draw a short conclusion for this research and address potential further studies.

(8)

II. Related Literature

Although this paper is primarily concerned about testing the commercial real estate bubble, a variety of studies focusing bubbles in stocks markets and housing markets have provided empirical lessons and relevant theories for this research. Moreover due to a lack of related literatures that cover the U.S. commercial real estate markets, this paper is going to extend the topic by incorporating bubble-testing efforts from stock markets and housing markets in the section of literature review. A table that summarizes the methodologies and topics of major literatures is given as follow:

Table 2. Overview of Literatures

Literature Methodology Topic

DeLong and Shleifer (1991) Regression analysis 1929 stock bubble Rappoport and White (1993) Regression analysis 1929 stock bubble

Diba and Grossman (1988) Unit root tests Simulated data

Campbell and Shiller (1998a) Unit root tests 1926-1986 stock market Bonn, Breitung and Homm

(2009)

Unit root tests 1995 stock market

Sornette and Zhou (2003) Log-periodic pattern 2003 housing market Case and Shiller (2004) Regression analysis 2003 housing market Himmelberg, Mayer and

Sinai (2005)

Regression analysis 2003 housing market

Levitin and Wachter (2013) Qualitative analysis 2008 commercial real estate market

Campbell, Jirasakuldech and Knight (2006)

Unit root tests and cointegration analysis

1973-2000 commercial real estate market

Brooks, Nneji and Ward

(9)

Bubbles in stock market

The sharp rise and crash of the U.S. stock prices in 1929 has addressed the attention of researchers such as DeLong and Shleifer (1991) and Rappoport and White (1993). DeLong and Shleifer (1991) have regressed index price on stock fundamental value observed from close-end mutual funds in order to and they pointed out that at the peak the stock index was more than one third above its fundamental value. Moreover, it has been interpreted that the emergence of the bubble in 1929 was a consequence of overly optimistic expectation among investors (DeLong and Shleifer, 1991).

However, Rappoport and White (1993) argued that the term of burst of bubble, which was used to describe the slide of stock prices in DeLong and Shleifer (1991), was a matter of contention. They have run a set of regressive analysis on the index price and brokers’ loan rates to analyze the dramatic change of stock prices. It has been pointed out that the market boom of 1929 stock market was a preeminence of stock companies who adopted new technologies. However the radical decline of stock price is argued as a consequence of drastic rise of interest rate of brokers’ loans during 1928, instead of a consequence of

bubble burst. Hereby, the high interest rate, which was imposed due to misperception of lenders who

deems the emergence of stock bubble, had dramatically jeopardized the performance of stocks and resulted into a collapse of stock markets in 1929 (Rappoport and White, 1993). It is clear that DeLong and Shleifer (1991) and Rappoport and White (1993) hold significantly different views due to the set of independent variables in their regression analysis. Researchers such as Blanchard and Watson (1982), Flood and Garber (1980), pointed out that regression analysis of bubble economy based on diversified economic regressors would have low power in that bubbles may follow several different types of process.

Diba and Grossman (1988) have added that in the case of the bubble presence, the price of assets will depend on variables that are irrelevant to the fundamental values or macro economic variables. One instance could be the diversified investor expectations that are difficult to measure and quantify into empirical models. Hence biased results would be observed from analyzing the contribution of fundamental values to asset prices. According to Diba and Grossman (1988) an alternative approach which tests the property of stationary of the joint distribution from returns and prices would avoid the problems that have been addressed in Blanchard and Watson (1982) and Flood and Garber (1980).

Furthermore, Campbell and Shiller (1998a) applied a vector autoregressive model to examine the log dividend-price ratios derived from annual observations for Standard & Poors Composite Stock Price

(10)

Index, and monthly returns on the value-weighted New York Stock Exchange (NYSE) index from 1926 to 1985. Although they have argued that log-dividend price ratio does Ranger-causes the future expected dividend growth, it has been pointed out that economic fundamentals such as short-term interest rates, consumption growth and even stock returns cannot not significantly explain the volatility of stock price (Campbell and Shiller, 1998a).

The proposed log dividend-price ratios approximation model in the research of Campbell and Shiller (1998a) has provided insight and reference for later researchers, see- Bonn, Breitung and Homm (2009) and Wu and Yu’s (2007). For instance Bonn, Breitung and Homm (2009) have investigated into the testing of rational bubbles in stock markets based on the analysis of stock yields. They claimed that explosive stock prices together with non-explosive dividends of stocks would imply the presence of bubbles in the price process. In their research, the outcome of Bhargava statistic, Busetti-Taylor statistic, Kim statistic, Phillips et al. statistic, and Chow-type unit root statistic indicated that the emergence of bubble in the NASDAQ started in the first half of the year 1995. The stationary-test model mentioned in Diba and Grossman (1988), developed by Phillips, Wu and Yu (2011) have been adopted into this research and will be further discussed in Section III.

Bubbles in residential real estate

Chronically, the topics of bubbles in residential real estate markets have been extensively studied. Numerous bubble-testing approaches have been introduced and developed by a variety of investment institutes and scholars, see- Sornette and Zhou (2003), Case and Shiller, (2004), Himmelberg, Mayer and Sinai (2005), Sornette and Zhou (2006) Leamer (2007). Nonetheless, based on different perceptions of housing bubble and testing methodologies, various testing results and corresponding theories will be reviewed in the following part of paper.

For example, Sornette and Zhou (2003) described the indication of housing as the existence of faster-than-exponential growth rate in real estate prices. They fit housing index since December 1992 to December 2002 into a proposed log-periodic harmonics model to test the exponential growth rate of asset price. They argued that no significant log-periodicity or power law criticality has been found during the U.S housing markets of 1992 to 2002. The testing results suggest that the growth of house price does not qualify the assumption of super-exponential growth with significant log-periodicity, indicating no

(11)

housing bubble in the United States during 1992 to 2002 (Sornette and Zhou, 2003). This claim has been revised and confirmed by Sornette and Zhou (2006) who consistently describe the housing prices in U.S. during 2003 as “not overpriced”. However, after incorporating updated housing prices as of the mid of 2005, Sornette and Zhou (2006) recalculated the log-periodic harmonics and found evidence for the faster-than-exponential rates in terms of 2005 housing prices. Thereafter, they claimed that a bubble in the residential real estate markets was emerged during 2003-2005.

However Case and Shiller (2004) disagrees with the findings on no evidence of ex-ante 2003 housing bubble in Sornette and Zhou (2003) and Sornette and Zhou (2006). Case and Shiller (2004) have considered different versions of bubble definitions, and assessed the U.S. housing market based on surveys of investor expectation and regression analysis on the relationship among housing prices and economic fundamentals. With regard to the measurement of house prices, Case and Shiller (2004) used Case-Shiller index, which is derived from the weighted-repeat sales data provided by Fiserv CSW, Fannie Mae and Freddie Mac, spanning the period from the 1st_{quarter in 1985 to 2}nd_{quartet in 2002. Moreover,} with regard to the variables of fundamentals, Case and Shiller (2004) have included data about personal income per capita, population, employment at the state level, data on housing starts, and data on average mortgage interest rates. By benchmarking the testing results of housing bubbles in 1988, Case and Shiller (2004) confirmed the existence of the bubble in residential real estate in 2003. They have also pointed out that the burst of bubble, i.e. decline of houses prices in the near future would lead to a considerable number of bankruptcies due to the high average personal debt to personal income ratios.

Findings from Case and Shiller, (2004) have been supported by Himmelberg, Mayer and Sinai (2005) who defined the housing bubble as a significant discrepancy between imputed rent and market rent. The term of imputed rent in real estate identifies annual opportunity costs by assuming that tenants occupied the properties. And the imputed rent concept is, to some extent, a macro-economic approach compared the concept of using micro economic fundamentals as explanation to housing prices in Case and Shiller (2004). Himmelberg, Mayer and Sinai (2005) have assessed the 2003 housing bubbles for 46 metropolitan areas in the United Sates via analyzing the relationship between imputed rents and market rents. In addition, the imputed rent variable in Himmelberg, Mayer and Sinai (2005) has been constructed by considering the total costs from six sub fundament variables. Frist of all, the one-year opportunity cost is included as pricing of house multiplied by corresponding risk-free rate. The second cost, which is the property tax, is calculated as house price multiplied by property tax rate. Third, the amount of tax benefits

(12)

from bearing a housing mortgage is waived from the calculation of total cost, and is calculated as tax rate multiplied by estimated mortgage and tax payment. The fourth variable, which is the maintenance costs, is calculated by taking a fraction from the value of real estate. The last two terms incorporated to the model have taken capital gains/loss and risk premium into account. By creating a price index of imputed rent using the proposed cost variable, Himmelberg, Mayer and Sinai (2005) then see potential evidence of deviation from imputed rent-to-actual rent ratio as the indication of housing bubble. It has been pointed out that, in most cities of the United States, from the period of 1995 to 2004, the cost of owning rose is somewhat related to the cost of renting, however still not to the magnitudes that market prices of housing have achieved. According to Himmelberg, Mayer and Sinai (2005), the high value of imputed rent-to-actual rent ratios and the significant discrepancy between imputed rent and market rent have confirmed the existence of bubble in 2003 residential real estate markets.

Bubbles in commercial real estate

Nonetheless there are different methodologies and different voices toward the bubble residential real estate, the collapse of housing markets surrounding the recent financial crisis have confirmed the bubble’s existence and burst in countries such as the United States, the United Kingdom and the Netherlands. In contrast, the same topic of pricing bubble but in the dimension of commercial real estate, did not receive adequate discussions. It appears that there is no such academic paper or institutional research that has provided announcement about collapse or abnormal fluctuations relating to commercial real estate markets.

A small number of studies, however, did report inefficiencies in the market for commercial real estate, while the empirical evidences and methodologies were far from uniform. Several studies, for example, Levitin and Wachter (2013) tentatively studied the real estate markets in the United States and perceive that there were two parallel bubbles in both residential and commercial real estate markets between 2004 and 2008. It is has been extensively argued that an environment conducive to the development of speculative commercial real estate bubble been provided by the markets of commercial mortgage backed security (CMBS), which are deemed as private and inefficient (Levitin and Wachter 2013). Notwithstanding they also compare and contrast the commercial real estate markets with the housing markets and CMBS markets from the perspectives such as the source of financing, risk of default and regulation by government, they did not provide quantitative evidences which are able to confirm the existence of the commercial real estate bubble.

(13)

From the perspective of REITs, Campbell, Jirasakuldech and Knight (2006) attempted to test for the presence of rational speculative bubbles using Augmented-Dickey Fuller (ADF) test. What’s more, Campbell, Jirasakuldech and Knight (2006) analyzed macroeconomic fundamentals of equity REITs during 1973–2000 taken from NAREIT index and Russell 2000 index. The ADF unit root test results showed that both REIT price index and the macroeconomic factors are non-stationary but stationary at their first difference. Due to the stationarity found in the first difference of sotck prices of REITs, Campbell, Jirasakuldech and Knight (2006) rejected the null hypothesis of bubble existence in favor of the alternative hypothesis of no bubble in commercial real estate market.

In order to further examine the conclusion of absence of bubble, they have also incorporated a vector of econometric methods testing the property of stationary of residuals. Macroeconomic variable such as CPI index, industrial production (IP), risk free rate (RP) and Federal fund rate were included into their model. According to their study, the stationarity of residuals in their model has indicated that the prices and fundamentals are co-integrated, which confirms the absence of bubble. In accordance to their empirical testing results, Campbell, Jirasakuldech and Knight (2006) argued that the pricing inefficiency is not due to speculative bubbles but economic fundamentals.

Brooks, Nneji and Ward (2013) hold different opinions. They have integrated 166 tax-qualified mortgage and equity REITs from 1978 to 2012 into their test for commercial real estate bubble. The sample data of Brooks, Nneji and Ward (2013) are taken from S&P 500 Composite index was seen as benchmark of the performance of stock market in their research. Moreover, they use NCREIF Property Index to track the price changes in commercial real estate markets. Based on a regime-switching bubble model of returns, Brooks, Nneji and Ward (2013) claimed significant evidence on the existence of periodically partially collapsing speculative bubbles has been found not only in in direct real estate market but also in indirect real estate market. The volatility of REIT prices during the financial crisis, which has been suggested by Brooks, Nneji and Ward (2013), is supported by Sun, Titman and Twite (2013) who argued that a decline in REIT prices was substantially due to anticipated costs associated with financial distress. In addition, Sun, Titman and Twite (2013) also pointed out that share prices of REITs with higher Loan to Value (LTV) ratios or with shorter maturity debt fell more during the initial time period.

(14)

III. Methodology and Data

Based on the study of REITs financials, this paper will examine the emergence of bubble starting from its essence, i.e. the relationship between the market price and asset fundamental value. In this paper, therefore, this relationship will be studied based on unit root test approaches in a panel data of price-rent ratios. The testing methodology of this paper basically follows the recursive unit root test, which has been introduced by Phillips, Wu and Yu (2011) while analyzing the bubble in stock market. However this paper will focus on the ratios of price-rents of commercial real estate. The methodology part will firstly describe the empirical approach in terms of bubble testing. Then it will explain and support the theoretical assumptions behind this method. The followed section will then describe the properties and sources of data used in this research.

Methodology

Empirical strategy

The hypothesis in this paper is that bubble is not emerging in the U.S. commercial real estate. Therefore the empirical strategy of this research is to find evidence against unit root in the series of log price-rent ratios within the sample panel data that has been observed in this research. The logic behind this connection will be further explained in the section of theoretical evidence part.

Hence the null hypothesis for empirical testing is that unit root in the series of log price-rent ratio would be detected, which indicates the series of log price-rent ratios are stochastic. The empirical explanation is the fundamental value of assets fail to explain the changes of market price. The alternative hypothesis is that unit root cannot be found from sample data, which indicates that the series of price-rent ratios are stationary. The model is described as follow:

𝐻!: 𝛿 = 0 𝑣𝑠. 𝐻!: 𝛿 < 1

∆𝑍_! = 𝛽_!+ 𝛿𝑍_!!!+ 𝜇_! 𝑤ℎ𝑒𝑟𝑒

𝑍_! = ln 𝑃_! − ln 𝑅_! ≡ ln 𝑃! 𝑅_!

The variable 𝑍_! is the linear combination of log price and log rent, which is equal to the log of price-rent ratio. And the dependent variable ∆𝑍_! is defined as the first differences of log price-rent ratios. If the null

(15)

hypothesis can be rejected, tis paper is then able to conclude that bubble does not exist in commercial real estates. If, however, unit root in the log price-rent ratio is detected, i.e. the research fails to reject 𝐻!; it

does not necessarily mean that a bubble is emerging due to potential Type II error. In that case, further research on testing the critical value of 𝛿 > 1.02 is inevitable in order to conclude the bubble emergence according to Phillips, Wu and Yu (2011).

Theoretical evidence

This part of paper will describe theories that illustrate the advantages and relevance of unit root tests. First of all, with regard to bubble detecting, regression analysis has low power and obstacles in terms of modeling and data collection according to Diba and Grossman (1988). Other approaches, however, seem to focus more on mathematics rather than economics, such as Sornette and Zhou (2003) and Sornette and Zhou (2006). Furthermore, the theoretical evidences that explain the connections between unit root tests and bubble testing will be detailed in the below part of paper.

Following Phillips, Wu and Yu (2011) and Breitung, Homm, Ulrich (2012), this paper assumes the standard no arbitrage condition and defines the rate of return, also known as discount rate of commercial real estate investments, as follow (this paper does not consider tax payment):

𝑌_!!! =𝑃!!!− 𝑃!+ 𝑅!!!

𝑃! =

𝑃!!!+ 𝑅!!!

𝑃! − 1

Where 𝑌_!!! denotes the yield, which is unknown until the period 𝑡 + 1. And 𝑃_!, 𝑃_!!! denote the market price of assets at 𝑡, 𝑡 + 1;𝑅!, 𝑅!!! denote the rental income from leasing assets at period 𝑡, 𝑡 + 1

respectively. In accordance to Diba and Grossman (1988), Phillips, Wu and Yu (2011), assuming discount rate Y!!! time invariant will not influence the results of unit root tests, but will simplify the

empirical model. Therefore, the fundamental value could be obtained:

𝑃_!! = 𝐸 𝑃!!!+ 𝑅!!! 1 + 𝑌

Where 𝑃_!! denotes the fundamental value of assets at time t. Furthermore the fundamental value of the asset can be derived from the present value of all expected income. By utilizing the law of iterated expectations, the equation of fundamental value can be rewritten into:

(16)

𝑃_!! = 𝐸 1 1 + 𝑌 ! 𝑅_!!! ! !!! + 𝐸 1 1 + 𝑌 ! 𝑃_!!!

The final term _!!!! !𝑃!!! denotes the present value from selling proceeds of assets at the end of

holding period 𝑘. In the case of this paper, the expected current value of the sales is deemed to converge into zero, which is based on long-term discounting factors and natural depreciation of property. First, under the standard assumption of no arbitrage, the value of holding period 𝑘 is virtually equal to the real estate asset’s lifespan, which can be seen as significantly large in this paper. Therefore the first part of the term coefficient _!!!! ! will yield substantially small value as Y > 0. Furthermore, after a considerably long holding period, the selling proceeds 𝑃!!! is proposed based on the residual value of property

considering the factor of depreciation thought out time. In empirical cases, those properties would be either demolished or re-innovated, yielding insufficient returns. Therefore, the value of an asset has been written as the sum of expected present value exclusively from future rental income:

𝑃_!! = 𝐸 1 1 + 𝑌 ! 𝑅!!! ! !!!

Therefore, theoretically if there were no bubble in the commercial real estate market, then the asset price would be equal to the fundamental value of assets. In addition, this paper understands that it has been an acute misunderstanding to simply define the volatility or variation of REIT stock prices, or the sharp decline or growth of price index as indications of bubble- see Levitin and Wachter (2013) and Brooks, Nneji and Ward (2013). This paper has followed the definition of bubble that has been commonly pointed out by Campbell and Shiller (1998b), Brunnermeier (2001), Brunnermeier and Nagel (2004), Case and Shiller (2004), Temin and Voth (2004) as asset’s prices that exceed an asset’s fundamental value. Once the market returns and potentials are over rated by investors and the demand of assets increases, the discrepancy between market price and fundamental value, i.e. bubble, will emerge:

𝐵_! = 𝑃_!− 𝑃_!!

𝑎𝑛𝑑 𝐵! = 𝐸

𝐵_!!! 1 + 𝑌

Here 𝑃! denotes the market price of assets, and 𝐵! denotes any bubble when the asset starts trading.

Following the log-linear approximation introduced by Campbell and Shiller (1989), the model could be rewritten as:

(17)

ln 𝑃_! = ln 𝑃_!!− ln 𝐵_! ln 𝑃_!! = 𝜅 − 𝛾 1 − 𝜌+ (1 − 𝜌) 𝜌! ! !!! 𝐸(ln 𝑅!!!!!) ln 𝐵_! = lim !→!𝜌 !_{𝐸(ln 𝑃} !!!!!) 𝐸(ln 𝐵_!!!) =1 𝜌ln 𝐵! = (1 + ln 𝑃_! 𝐵! ) ln 𝐵! 𝑤ℎ𝑒𝑟𝑒 𝛾 = ln 1 + 𝑅 , 𝜌 = 1 (1 +𝑃! 𝐵!) 𝜅 = − ln 𝜌 − 1 − 𝜌 ln(1 𝜌− 1)

It is necessary to point out the log approximation suggested by Campbell and Shiller (1989) is observed from simulated data, thus difficult to impose economic definitions or explanations for its composing terms. However Phillips, Wu and Yu (2011), rewrites the log approximation through assuming no bubble case, i.e. 𝐵_!= 0, it yields:

ln 𝑃! 𝑅_! ≡ ln 𝑃! − ln 𝑅! = 𝜅 − 𝛾 1 − 𝜌+ 𝜌! ! !!! 𝐸(Δ ln 𝑅!!!!!)

In terms of the observation of bubble absence, the fundamental value and market price are integrated of same order (Diba and Grossman 1988). Intuitively, if there is absence of bubble, the fundamental value, which is exclusively determined by rental income, will be equivalent to the market price. And the series of rents and prices would be co-integrated. Accordingly, the linear combination of the two series i.e. ln !!

!! would be stationary. Therefore, by performing unit root test, this paper will examine the property

stationary of the linear combination of fundamental value and market price, i.e. log price-rent ratios. The logic behind this is that if the series of price-rent ratios are stationary, it indicates the no-bubble assumption in Phillips, Wu and Yu (2011) does hold within the sample data. Therefore this research is able to claim the absence of bubble in commercial real estate. Alternatively, if unit root is detected from

(18)

the price-rent ratios, it is able to conclude that the no-bubble assumption in Phillips, Wu and Yu (2011) is not applicable in the case of this paper.

Data

As it has mentioned in the methodology section, the data needed for the bubble testing are log price-rent ratios. This research has utilized financials from REITs, i.e. total enterprise value (TEV) and pure rental income (RI) to build variables that measure price-rent ratios. The sample panel consists of information from 52 REITs located in the United States. Moreover this research spans the period between 2000(Q1) and 2013(Q4) [n=56 quarters]. In total, 2056 observations have been included.

Table 3. Frequency of REITs based on property categories

Theoretically, the optical dataset for testing bubble in commercial real estate is to monitor the rental income and property price at asset levels. And researchers would receive robust and unbiased data by enlarging the entity numbers,. However in case of real world, it is necessary to point out that commercial assets are characterized by infrequently trading history. In terms of measuring the price of commercial

0 2 4 6 8 10 12 14 16 18

Diversified Health Care Hotel Office ResidenHal Retail Unclassified

(19)

real estate, it is essentially difficult to directly trace the market prices of assets without any lag or inaccuracy. Moreover, the location, utility, and volumes of commercial assets are virtually heterogeneous; it becomes relatively less applicable and accurate to construct a repeat-sale price index, which was introduced by Case and Shiller (1993) into residential real estates.

Due to the transparency and liquidity of REITs, price of REITs in stock market can be utilized to construct a daily-based repeat-sale price index. The stock price is seen as an accurate indication that is jointly determined by the performance of underlying assets, which has already been discussed in the literature review section, and by the expectation of market yields among investors. In terms of data availability, apart from the irregularity of commercial real estate valuation reports, the valuation process, timing, and rental levels of specific properties make the results not as liquid or transparent as stock price. Furthermore, observing rent at individual assets level would have bias in that in commercial real estate markets, there are circumstances that tenants may have rent free period offered by landlord. Hence an innovative and more accurate approach of studying the price-rent ratios of commercial real estates is crucial in this paper.

This paper has used quarterly accumulative rents from a pool of assets that are under REITs’ management to reduce the impact of biased results from observing rental income by individual asset. It has also attempted to construct a time-varying total enterprise value (TEV) variable for each REIT that has been included in this paper, which has been seen as a proxy to the total assets value (TAV) under management. Intuitively, the assumption that the TEV of REIT is approximately equal to the TAV is not only logical but also valid because of the following facts. First, the Total Enterprise Value is a term that defines the essential value for the acquisition of business:

𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒

= 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 + 𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑡 − 𝐶𝑎𝑠ℎ 𝑎𝑛𝑑 𝑐𝑎𝑠ℎ 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡

In this paper, the TEV identifies the market price of taking over the ownership of assets that are currently under REITs’ management. Second, the type of REITs that has been included into this paper is equity REITs, whose revenues are principally generated from rents. In addition, REITs are regulated to invest in real estate exclusively. Therefore, it is authentic to see the total enterprise value (TEV) of REITs approximately stands for to the total value of assets (TAV) in this paper. The value of REITs is also

(20)

largely correlated with the performance of fundamental assets that are under the management of REITs. The reason is that after the payment of debt service and other operating costs, REITs are obligated to pay out the majority of funds available for attribution (FAD), which is principally from rental income. Moreover, the assets of REITs are financed by investor’s equity, inter-company loan and third party debt. Therefore, it is logical to argue that the total value of underlying assets of REITs could be represented by adjusting its market capitalization to the financial structure of each specific REIT, namely, common and preferred equity, total debt, cash and cash equivalent, which will be further explained in the next sections. Therefore, the prices of a pool of assets that are under the management of REITs could be studied by assessing the total enterprise value of REITs.

Based on this conception, observing the market capitalization of REITs at a quarterly frequency, which has been provided by CRSP/Ziman Real Estate Database, becomes practical. What’s more, data about preferred equity, total debt, cash and the pure rental income of REITs S&P Capital IQ, which is a division of McGraw Hill Financial that provides data of company financials, markets, pricing, analytic measures, reference, rating, and research. The research of this paper has collected financial information of REITs from synchronized data stream by coding Capital IQ syntax and REITs’ tickers into Excel. Additionally, in order to construct a strongly balanced panel, which is required when performing unit root tests such as Levin–Lin–Chu test and Harris–Tzavalis test, this paper has excluded entities in Capital IQ that did not provide continuous information on market capitalization and other financials. Overall, the panel data has included 2912 observations. Additionally, a name list of REITs that have been studied in this research has been provided in the section of appendix.

Table 4. Panel Statistic on TEV and RI

Mean ($) Max ($) Min ($) Median ($)

Standard Deviation

Total Enterprise Value (TEV)

4,986 million 72,092 million 84 million 2,773 million 7,098 million

Rental Income

(RI) 103 million 939 million 277 thousand 64 million 119 million

In addition, a short description of mean, maximum, minimum, median value and standard deviation of the panel could be found in the above table:

(21)

IV. Results

This paper has adopted a pool of panel data unit root test approaches developed by Dickey and Fuller (1979), Phillips and Perron (1988), Harris and Tzavalis (1999), Breitung (2000), Hadri (2000), Levin, Lin and Chu (2002), and Im, Pesaran and Shin (2003) to help test for the evidence of bubble emergence. A summary on the null and alternative hypothesis of these tests is given in the appendix. This part of paper will first describe the corresponding testing results from econometric perspectives and integrate the analysis of testing results from economic perspectives.

First of all, the Levin-Lin-Chu test is suitable for panels with moderate size that matches the characteristics sample data in this research. Levin, Lin and Chu (2002) describe this moderate size as having between 10 and 250 panels and 25 to 250 observations per panel, Accordingly, this paper finds out that the null hypothesis of unit roots existence is rejected at 5% significance level, indicating that the alternative hypothesis of stationarity in log price-rent ratios is true. Therefore evidence against bubble emergence has been found based on Levin-Lin-Chu test.

Second, the Harris Tsavalis (1999) pointed out that their unit root test is suitable for datasets dealing with microeconomics that have small time dimension but have entities larger than 25. In this paper, the database spans REITs financials from 2000 to 2013, which is relatively short compared to other bubble studies such as Campbell and Shiller (1998a), Campbell, Jirasakuldech and Knight (2006) and Brooks, Nneji and Ward (2013) who have time dimension that are larger than 20 years. Moreover, the number of entities in this paper, i.e. the number of REITs (52) is also larger than the preferred value of 25 in Harris-Tsavalis test. Based on it, this paper has rejected the hypothesis of unit roots in favor of the alternative that log price-rent ratios are stationary. And it shows evidence against the emergence of commercial real estate bubble.

Although Breitung test has more favorable power for panels with smaller size of entities and time dimension (N=25, T=25) according to Breitung (2000) the testing result still rejected the hypothesis of unit roots and in favor of the alternative that log price-rent ratios are stationary.

(22)

Hereby, as the first three unit root tests: Levin-Lin-Chu test, Harris Tsavalis test, and Breitung assume that all panels share a common autoregressive parameter, Im, Pesaran and Shin (2003) have altered the assumptions of identical autoregressive parameter. Moreover, the Im-Pesaran-Shin null hypothesis that all panels contain a unit root has been rejected in this research. Therefore, evidence against bubble emergence has been indicated based on Im-Pesaran-Shin test.

What’s more, the classic Augumented Dicky Fuller tests and Phillips-Perron unit root tests both provide evidence against bubble emergence. However, all the tests mentioned so far take as the null hypothesis that the series contain a unit root. As unit root tests have low power against alternative hypotheses, Hardri LM test has proposed null hypothesis that all panels are stationry versus alternative hypothesis that at least one panel contains a unit root. And this paper finds out that the null hypothesis that all panels are stationary has been strongly rejected in favor of the alternative that at least one of the panels has stochastic trend. However, this does not necessarily mean that all panels are not stationary, but it provides critical evidence and thus necessities for robustness check.

Table 5. Summary of tests results

Test Method Empirical Result

Levin-Lin-Chu test Evidence against bubble

Harris Tsavalis test Evidence against bubble

Breitung test Evidence against bubble

Im,-Pesaran-Shin test Evidence against bubble

Augumented Dicky Fuller tests Evidence against bubble

Phillips-Perron test Evidence against bubble

Hardri-LM test Evidence for bubble from specific panels

In a short conclusion, the majority of tests in this paper show strong signals of absence of unit roots in the series of log price-rent ratios, which means the linear combination of log price and log rent is stationary. This stationarity of price-rent ratios hence confirms the no bubble hypothesis mentioned in section of

(23)

methodology. Empirically it shows that the price changes of commercial real estate can be explained by the corresponding adjustments in asset fundamental value. Hereby this paper concludes that commercial real bubble is not emerging in the United States.

In addition, a tentative explanation of the price changes in earlier in Table 1 one will be provided in the following part of paper.

Table 6. Index of US GDP, employment rate and CIP

Data available from http://www.bea.gov/

According to the movements of U.S. GDP, CPI and employment rate, the national economy of United States has seen compelling growth in the early phase of 21st_{century. During this period, the price of} commercial real estate also increased significantly. However, due to the outcome of global financial crisis, the national economy has seen a slide during 2008 and 2009. During this period, commercial real estate prices have seen a sharp decline. However, this is not a burst of bubble as it has been described in Levitin and Watcher (2012) in that the fundamental value of assets also decreased significantly. Evidences can be found from via unit root tests of this paper. In a short conclusion, the arising commercial real estate price is in line with the underwriting standards financing, a growing demand of transactions and the recovery U.S. national economy.

80 90 100 110 120 130 140 150 160 170 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 US GDP US emlpyment US CPI

(24)

V. Robustness Analysis

In terms of the assumption where total enterprise value (TEV) is approximately equal to total assets value (TAV), this research has to some extent augmented the real value of underlying assets. The explanation is that in real world cases, the total enterprise value of REITs is relatively larger than the total value of fundamental assets. This assumption may have risk of Type II error, where the research may not be able to reject the hypothesis on the existence of unit, i.e. the augmented total real estate value cannot be explained by the rental income. Therefore biased evidence on the existence of bubble may be found during this research. However, this does not influence the conclusion of no pricing bubble in commercial real estate. Therefore, it can be argued that, the theoretical assumptions of did not jeopardize the robustness of results in this paper.

In terms of unit root tests on price-rent ratios of REITs, it needs to be pointed out that different categories of commercial real estate may have considerably different ratios. For instance, offices are more risky investments but have higher yields compared to self-storage warehouses. And tests methods such as Levin-Lin-Chu, Harris-Tzavalis and Breitung assume common Auto Regressive (AR) parameter for all panels. This will not have issues on the outcome of stationarity test. However, unit roots will probably still exist under specific category of assets among panels.

Nonetheless, this paper has run another series of unit root tests of based on REITs property types in order to check the robustness of the testing results. It finds that Hardri-LM testing results suggested at least 1 out of 12 REITs in the office segment is over priced. However considering the relatively small sample size in respect to office REITs, this does not sufficiently indicates there is a bubble in the office markets. In addition, other approaches such as Harris-Tzavalis test and Levin-Lin-Chu test still significantly confirmed the evidence against bubble. One possible explanation according to Geltner and etc. (2013) could be that office markets are the most risky investment segment compared to other categories of commercial real estate. Therefore the price-rent ratios of REITs that exclusively invested into office are more likely to contain a stochastic trend due to the essence of underlying assets with higher investment risks.

(25)

VI. Conclusion

In recap, the speculative bubble of U.S. commercial real estate during 2000-2013 has been extensively investigated in this paper. The critical hypothesis of this research is that if there was no bubble emerging in the commercial real estate markets, the linear combination of asset price and rental income of properties should be stationary. The theoretical evidences behind this hypothesis are primarily based on the log approximation suggested by Campbell and Shiller (1989) and bubble-absence assumption suggested by Phillips, Wu and Yu (2011). In terms of empirical approaches, this paper has followed a set of unit root tests developed by Dickey and Fuller (1979), Phillips and Perron (1988) Harris and Tzavalis (1999), Breitung (2000), Hadri (2000), Levin, Lin and Chu (2002), Im, Pesaran and Shin (2003). In terms of the constructing variables, this research has collected financial data of 52 REITs that are listed in the United States through Capital IQ. In terms of the sample database, it includes total enterprise value and rental income data spanning through the 1st_{quarter of 2000 to the 4}th_{quarter of 2013.}

Unit root testing results from the panel data have significantly confirmed the stationarity of log price-rent ratios, which indicates the absence of bubble in U.S. commercial real estate. Although the Hardri-LM test detects a weak signal that at least one panel contains unit root, the robustness analysis locates the speculative problem in office segment. However, it cannot be interpreted as a bubble is emerging in the office markets in that other testing results of log price-rent ratios in the segment office still strongly indicate evidence against bubble. What’s more, office as an asset is one of the most risky real estate investments. This paper hence concludes bubble is not emerging in the U.S. commercial real estate markets.

In terms of the enhancement and future study of this paper, there are several potential aspects. First of all, as this research has used total enterprise value of REITs as a proxy to the market price of assets, one could probably improve the accuracy of testing results by incorporating more advanced data for assessing the property prices. What’s more, the span of the dataset could be further extended, as it appears that the moderate time dimension in this research may have problems considering real estate market cyclicity. Furthermore, more sophisticated researchers may have better choices on the length of lags while performing unit root tests. Last but not least, this paper has primarily focused on finding evidence on the absence of commercial real estate bubble thus only tentatively analyzed the economic connections between asset price and economic fundamentals. Therefore, one can conduct further comprehensive analysis that thoroughly explains the factors behind the recent growth of commercial real estate prices.

(26)

Reference List

Blanchard, O. and Watson, M. (1982). ‘Bubbles, Rational Expectations, and Financial

Markets’ in P. Wachtel, ed., Crisis in the Economic and Financial Structure. Lexington Books.

Breitung, J. (2001). ‘The local power of some unit root tests for panel data’ (Vol. 15, pp. 161-177). Emerald Group Publishing Limited.

Brunnermeier, M. (2001), ‘Asset Pricing under Asymmetric Information – Bubbles,

Crashes, Technical Analysis, and Herding’. Oxford University Press

Brunnermeier, M. and Nagel, S (2004).’Hedge Funds and the Technology Bubble’.

Journal of Finance, October, 59(5), pp. 2013-40.

Case,K. E. and Shiller, R.J. (2004), ‘Is There a Bubble in the Housing Market’. Brookings Papers on Economic Activity, 2, 299-342.

Campbell, J. Y., and Shiller R. J. (1988a): ‘The dividend-price ratio and expectations of future dividends and discount factors’. Review of Financial Studies, 1(3), 195–228.

Campbell, J. Y., and Shiller, R. J. (1998b). ‘Valuation ratios and the long-run stock market outlook’. The Journal of Portfolio Management, 24(2), 11-26.

Craine, R. (1993) ‘Rational Bubbles – A Test’, the Journal of Economic Dynamics and

Control 17, 829–846.

DeLong, J. B., and Shleifer, A. (1991). ‘The stock market bubble of 1929: evidence from clsoed-end mutual funds’. The Journal of Economic History, 51(03), 675-700.

Diba, B. T., and Grossman, H. I. (1988). ‘Explosive rational bubbles in stock prices?’. The American Economic Review, 520-530.

Dickey, D. A., and Fuller, W. A. (1979). ‘Distribution of the estimators for autoregressive time series with a unit root’. Journal of the American statistical

(27)

Flood, R. P., and Garber, P. M. (1980). ‘Market fundamentals versus price-level bubbles: the first tests0’. The Journal of Political Economy, 745-770.

Frehen, R. G., Goetzmann, W. N., and Geert Rouwenhorst, K.G. (2013). ‘New evidence on the first financial bubble’. Journal of Financial Economics, 108(3), 585-607.

Geltner, D.M., Miller N.G., Clayton, J., and Eichholts, P. (2013) Commercial Real

Estate Analysis and Investment. 3rd edition. Mason: OnCourse Learning

Hadri, K. (2000). ‘Testing for stationarity in heterogeneous panel data’. Econometrics

Journal 3: 148–161

Harris, R. D., and Tzavalis, E. (1999). ‘Inference for unit roots in dynamic panels where the time dimension is fixed’. Journal of econometrics, 91(2), 201-226.

Himmelberg, C., Mayer, C., Sinai, T. (2005) ‘Assessing High House Prices: Bubbles, Fundamentals, and Misperceptions’. Journal of Economic Perspectives 19 (4), 67-92.

Im, K. S., Pesaran, M. H., & Shin, Y. (2003). ‘Testing for unit roots in heterogeneous panels. Journal of econometrics’, 115(1), 53-74.

Levitin, A. and Wachter, S.M. (2013), ‘The commercial real estate bubble’, Harvard

Business Law Review, Vol. 3, pp. 83-118.

Levin, A., Lin, C. F., and Chu, C. S.J. (2002). ‘Unit root tests in panel data: asymptotic and finite-sample properties’. Journal of econometrics, 108(1), 1-24.

Phillips, P. C., and Perron, P. (1988). ‘Testing for a unit root in time series regression’. Biometrika, 75(2), 335-346.

Phillips, P. C., Wu, Y., and Yu, J. (2011). ‘Explosive behavior in the 1990s NASDAQ: when did exuberance escalate values?’, International economic review, 52(1), 201-226.

(28)

Sornette, D and Zhou, W.X. (2003) ‘2000-2003 real estate bubble in the UK but not in the USA’, Physica A 329, 249-263.

Sornette, D and Zhou, W.X.. (2006). ‘Is there a real-estate bubble in the US?’ Physica A:

Statistical Mechanics and its Applications, 361(1), 297-308.

Sun, L., Titman, S., and Twite, G. J. (2013). ‘REIT and Commercial Real Estate Returns: A Post Mortem of the Financial Crisis’. Real Estate Economics, Forthcoming.

Temin, P. and Voth, H. (2004) ‘Riding the South Sea Bubble’. American Economic

Review 94, 1654-1668

(29)

Appendix

Data for RCA price index

US - Commercial US - Office US - Industrial 4q2000 100 100 100 1q2001 101 101 101 2q2001 101 99 100 3q2001 99 97 99 4q2001 97 95 98 1q2002 97 95 97 2q2002 99 96 99 3q2002 101 97 102 4q2002 103 99 104 1q2003 106 101 107 2q2003 109 103 108 3q2003 110 106 107 4q2003 112 107 106 1q2004 114 108 108 2q2004 116 111 111 3q2004 120 115 115 4q2004 125 118 119 1q2005 131 125 123 2q2005 138 132 128 3q2005 144 138 133 4q2005 148 142 136 1q2006 151 145 141 2q2006 153 147 145 3q2006 156 151 149 4q2006 161 156 153 1q2007 168 164 159 2q2007 174 172 164 3q2007 180 179 168 4q2007 180 182 167 1q2008 177 179 166 2q2008 169 171 160 3q2008 158 160 152 4q2008 145 145 142 1q2009 130 128 128 2q2009 117 111 120 3q2009 109 101 115 4q2009 106 97 113

(30)

1q2010 107 100 113 2q2010 110 107 114 3q2010 112 112 112 4q2010 116 117 112 1q2011 119 121 113 2q2011 121 123 113 3q2011 124 125 116 4q2011 127 130 121 1q2012 128 131 123 2q2012 129 132 123 3q2012 130 134 122 4q2012 134 139 123 1q2013 138 144 123 2q2013 144 149 126 3q2013 151 156 132 4q2013 156 162 136 1q2014 160 166 142 2q2014 166 174 149 3q2014 170 180 152

(31)

(32)

Description of pooled unit root tests

Test Method Null Hypothesis (H0) Alternative Hypothesis (H1) Levin-Lin-Chu test Panels contain unit roots Panels are stationary

Harris Tsavalis test Panels contain unit roots Panels are stationary Breitung test Panels contain unit roots Panels are stationary Im,-Pesaran-Shin test All panels contain unit roots Some panels are stationary Augumented Dicky Fuller tests All panels contain unit roots At least one panel is stationary

Phillips-Perron test All panels contain unit roots At least one panel is stationary

(33)

Pooled unit root tests results (panel unified)

Unit Root Test Test Method

AR parameter

Panel Balance Requirement

Statistic Pro. Result

Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -6.9898*** 0.0000 Rejection of H0 Harris-Tzavalis Common Strongly balanced -41.0466*** 0.0000 Rejection of H0

Breitung Common Strongly

balanced -3.4998*** 0.0002 Rejection of H0 Hadri LM Stationarity Not applicable Strongly blanced 87.3822*** 0.0000 Rejection of H0 Augmented Dickey-Fuller

Panel-specific Not required -12.1333*** 0.0000 Rejection of H0

Phillips-Perron

Im-Pesaran-Shin

Panel-specific Not required -10.5733*** 0.0000 Rejection of H0 Panel Means: Included Time Trend: included Levin-Lin-Chu Common Strongly balanced -5.2253*** 0.0000 Rejection of H0 Harris-Tzavalis Common Strongly balanced -35.5472*** 0.0000 Rejection of H0

Breitung Common Strongly

balanced -7.2190*** 0.0000 Rejection of H0 Hadri LM Stationarity Not applicable Strongly blanced 49.0534*** 0.0000 Rejection of H0 Augmented Dickey-Fuller

Phillips-Perron

Im-Pesaran-Shin

(34)

Pooled unit root tests (panel specified based on property type) REIT Type (number) Unit Root Test Test Method AR parameter Panel Balance

Property Type: Diversified (5) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -3.2313*** 0.0006 Reject H0 Harris-Tzavalis Common Strongly balanced -31.7768*** 0.0000 Reject H0

Breitung Common Strongly balanced -1.6844 0.0461 Fail to reject H0 REIT Type (number) Unit Root Test Test Method AR parameter Panel Balance

Property Type: Health Care (6) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -4.3340*** 0.0000 Reject H0 Harris-Tzavalis Common Strongly balanced -7.8484*** 0.0000 Reject of H0 Breitung Common Strongly

balanced

-0.8796 0.1895 Fail to reject H0

(35)

REIT Type (number) Unit Root Test Test Method AR parameter Panel Balance

Property Type: Hotel (2) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -1.2144 0.1123 Fail to reject H0 Harris-Tzavalis Common Strongly balanced -3.3205*** 0.0004 Reject H0

Property Type: Industrial, Office (12) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -2.4931*** 0.0063 Reject H0 Harris-Tzavalis Common Strongly balanced -21.0557*** 0.0000 Reject H0

Breitung Common Strongly balanced

(36)

Property Type: Residential (9) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -1.8131* 0.0349 Fail to reject H0 Harris-Tzavalis Common Strongly balanced -6.3935*** 0.0000 Reject H0

Property Type: Retail (17) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -4.0197*** 0.0000 Reject H0 Harris-Tzavalis Common Strongly balanced -11.8000*** 0.0000 Reject H0

(37)

Property Type: Unclassfied (1) Panel Means: Included Time Trend: Not included Levin-Lin-Chu Common Strongly balanced -0.8244 0.2049 Fail to reject H0 Harris-Tzavalis Common Strongly balanced - - -

(38)

List of REITs

Company Name Property Type

Cousins Properties Incorporated (NYSE:CUZ) Diversified

Vornado Realty Trust (NYSE:VNO) Diversified

Alexander's Inc. (NYSE:ALX) Retail

Pennsylvania Real Estate Investment Trust (NYSE:PEI) Retail Washington Real Estate Investment Trust (NYSE:WRE) Diversified Monmouth Real Estate Investment Corp. (NYSE:MNR) Industrial/Office

Federal Realty Investment Trust (NYSE:FRT) Retail

Health Care REIT, Inc. (NYSE:HCN) Health Care

Weingarten Realty Investors (NYSE:WRI) Retail

Equity Commonwealth (NYSE:EQC) Industrial/Office

Universal Health Realty Income Trust (NYSE:UHT) Health Care Duke Realty Corporation (NYSE:DRE) Industrial/Office Ramco-Gershenson Properties Trust (NYSE:RPT) Retail

Ventas, Inc. (NYSE:VTR) Health Care

PS Business Parks Inc. (NYSE:PSB) 4Industrial/Office Omega Healthcare Investors Inc. (NYSE:OHI) Health Care

Taubman Centers, Inc. (NYSE:TCO) Retail

Healthcare Realty Trust Incorporated (NYSE:HR) Health Care Tanger Factory Outlet Centers Inc. (NYSE:SKT) Retail

Post Properties Inc. (NYSE:PPS) Residential

Camden Property Trust (NYSE:CPT) Residential

Equity Residential (NYSE:EQR) Residential

Saul Centers Inc. (NYSE:BFS) Retail

CBL & Associates Properties Inc. (NYSE:CBL) Retail

Regency Centers Corporation (NYSE:REG) Retail

Associated Estates Realty Corporation (NYSE:AEC) Residential

Simon Property Group Inc. (NYSE:SPG) Retail

Sun Communities Inc. (NYSE:SUI) Residential

Glimcher Realty Trust (NYSE:GRT) Retail

(39)

The Macerich Company (NYSE:MAC) Retail

Agree Realty Corp. (NYSE:ADC) Retail

First Industrial Realty Trust Inc. (NYSE:FR) Industrial/Office Highwoods Properties Inc. (NYSE:HIW) Industrial/Office Liberty Property Trust (NYSE:LPT) Industrial/Office Apartment Investment and Management Company (NYSE:AIV) Residential

Home Properties Inc. (NYSE:HME) Residential

Mack-Cali Realty Corp. (NYSE:CLI) Industrial/Office

Realty Income Corporation (NYSE:O) Retail

Sovran Self Storage Inc. (NYSE:SSS) Self-storage Hospitality Properties Trust (NYSE:HPT) Lodgin/Resorts Alexandria Real Estate Equities, Inc. (NYSE:ARE) Industrial/Office

Boston Properties Inc. (NYSE:BXP) Industrial/Office EastGroup Properties Inc. (NYSE:EGP) Industrial/Office SL Green Realty Corp. (NYSE:SLG) Industrial/Office Investors Real Estate Trust (NYSE:IRET) Diversified

EPR Properties (NYSE:EPR) Unclassified

LaSalle Hotel Properties (NYSE:LHO) Lodging/Resorts

Equity One Inc. (NYSE:EQY) Retail

Senior Housing Properties Trust (NYSE:SNH) Health Care National Retail Properties, Inc. (NYSE:NNN) Retail

Is a bubble emerging in the U.S. commercial real estate market?