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Interest Rate and Investment under Uncertainty: Evidence from Commercial Real Estate Capital Improvements Liang Peng Leeds School of Business University of Colorado at Boulder Email: liang.peng@colorado.edu Thomas G. Thibodeau Leeds School of Business University of Colorado at Boulder Email: Tom.thibodeau@colorado.edu Abstract This paper empirically analyzes the non-monotonic influence that interest rate changes have on irreversible investment in income producing properties. Using the complete history of quarterly capital improvements for 1,416 commercial properties over the 1978 to 2009 period, we find strong evidence of the non-monotonic effect for apartment, office, and retail properties, but not for industrial properties. For the first three property types, a decrease in the Treasury yield dramatically increases capital improvements when property values are high, but has a weak or negative effect when property values are low. This result has important implications for monetary and fiscal policies. JEL classification: E22, E52 Key words: interest rate, investment under uncertainty, commercial real estate  The authors thank the Real Estate Research Institute for a research grant and thank Marc Louargand and David Watkins for valuable comments. Liang Peng thanks the National Council of Real Estate Investment Fiduciaries (NCREIF) for providing the data. The authors take responsibility for any errors in this manuscript. 1 I. Introduction Investment under uncertainty is one of the most important economic decisions that investors make (e.g. Dixit and Pindyck (1994)). Among all variables that might affect investment, interest rate changes have important implications for monetary and fiscal policies, and have drawn a lot of attention from economists. While the neoclassical theory of investment (e.g. Jorgenson (1963)) predicts that a decrease in the interest rate increases investment by reducing the cost of capital, recent theoretical analyses (e.g. Capozza and Li (1994), Capozza and Li (2002), and Chetty (2007)) suggest that, when firms make irreversible investments with uncertain pay-offs, the effect of an interest rate change on investment is non-monotonic. Chetty (2007) specifically suggests that investment is a backward-bending function of the interest rate. This means that a decrease in the interest rate reduces investment when the interest rate is “low”, in the sense that the difference between the interest rate and the expected future income growth rate is small, and increases investment when the interest rate is “high”. While focusing on empirical analyses, Capozza and Li (2001) also show that the difference between the discount rate and the expected future income growth rate influences the investment responses to interest rate changes. We empirically analyze the non-monotonic effect of interest rate changes on irreversible investment using a unique dataset of individual capital improvements of 1,416 large commercial properties, including apartment, office, industrial and retail properties, in a sample period from 1978 to 2009. In our empirical model, the non-monotonic effect is captured by an interaction term between the change in the interest rate and the capitalization rate of properties. The capitalization rate, which is also called the cap rate by real estate professionals, equals the ratio of net operating income (NOI) to the property value. Real estate professionals conventionally use the cap rate as a measurement of the valuation of properties: a low (high) cap rate indicates high (low) property valuation. We show that, under reasonable assumptions, the cap rate measures the difference between the cost of capital and the expected future income growth rate. Therefore, the theory by Chetty (2007) predicts that a decrease in the interest rate increases (reduces) the capital improvement when the cap rate is low (high). We find strong evidence for the non-monotonic effect of interest rate changes on the capital improvements in apartment, office, and retail properties, but not for industrial properties. For the first three types of properties, a decrease in the Treasury yield dramatically increases 1 expenditures on capital improvements when property values are high (low cap rates), but has little or negative effect when properties have low valuation (high cap rates). For example, when the cap rate is 4%, a decrease of 50 basis points in the Treasury yield increases the capital improvement by 18% for apartments, 15% for offices, and 31% for retail properties, but the same interest rate decrease has no or negative effect when the cap rate is 10%. This result indicates that a decrease in the interest rate may strongly stimulate investment in a booming economy when asset values are high, but will have no or negative effect on investment in a recession when assets values are low. This result has important policy implications. If a decrease in the interest rate does not necessarily stimulate investment, then monetary authorities should take extreme care when they try to use interest rate changes to stimulate investment. The empirical evidence described above is novel. In fact, the existing literature provides little empirical evidence regarding the non-monotonic effect of interest rate changes on investment. The only empirical analysis prior to this paper is Capozza and Li (2001), which, however, differs from this paper in research questions, data, method, and findings. For example, Capozza and Li (2001) empirically analyze and substantiate the effect of the population growth rate and its uncertainty on the likelihood of positive investment response to interest rate changes, while we analyze and provide direct evidence that investment is a backward bending function of the interest rate. Overall, the finding in this paper that the investment effect of interest rate changes is related to asset valuation is original, has important policy implications, and makes an important contribution to the literature. The novel empirical evidence in this paper is made possible by the unique and high quality dataset employed, which has a few important advantages. First, the real estate market is an ideal environment to analyze investment under uncertainty, since real estate investments, including capital improvements and development, are not only irreversible but also affected by real options (e.g. Williams (1997)). Second, the dataset contains accurate measurements of both the timing and the amount of capital improvements at the property level over the entire investment period of each property. Property level data, or firm level data in a non-real estate environment, are desirable for testing investment theories but are rarely available. Many researchers, including Guiso and Parigi (1999), argue that property or firm level data are superior to aggregate data in testing investment theories because investment decisions are made at the firm/property level. 2 Third, the sample period of the data is 30 years. This period covers several economic cycles and provides valuable opportunities to observe dramatic changes in interest rates, which makes the empirical tests in this paper powerful. Finally, the dataset contains accurate information on the net operating income and owners’ appraised property values, which allows the calculation of the cap rate and thus facilitates the measurement of property owners’ expectation of future income growth. While investors’ expectation is an important variable that affects investment, it is rarely observed in empirical research, with Guiso and Parigi (1999) being a notable exception. The rest of this paper is organized as follows. Section II reviews the literature. Section III discusses the empirical model. Section IV describes the data. Section V presents empirical results, and section VI concludes. II. Literature review Pindyck (1991), Dixit and Pindyck (1994), Trigeorgis (1996), and Schwartz and Trigeorgis (2001) provide good summaries of theoretical and empirical analyses on irreversible investment under uncertainty. Below we briefly review more recent literature, which focuses more on real option-based theories, the relationship between the cost of capital and investment, and the influence of market structure on investment. On the theory side, recent contributions to this literature include Grenadier (2002), Wang and Zhou (2006), Novy-Marx (2007), and Chetty (2007). Grenadier (2002) demonstrates that competition reduces the value of an investor’s real option and consequently increases investment. Novy-Marx (2007) shows that, even in competitive markets, as long as products and opportunity costs are heterogeneous, the option to delay can be valuable and thus investment can be lumpy. Wang and Zhou (2006) demonstrate that the value of real options depend on market structure (e.g. competitive, monopolistic, etc.). Chetty (2007) shows that a change in the interest rate affects not only the net present values (NPVs) of possible projects but also the value of waiting. More importantly, the effect on the value of waiting is stronger (weaker) than the effect on the NPVs when the interest rate is “low” (“high”).1 Therefore, a decrease in the interest rate reduces 1 The “low” and “high” is defined according to the difference between the interest rate and the expected future income growth rate. An interest rate is “low” if the difference is small. 3 investment when the interest rate is low, but increases investment when the interest rate is high. This non-monotonic effect of interest rates on investment is the main hypothesis of this paper. On the empirical side, many recent analyses focus on non-real estate industries. For example, Leahy and Whited (1996) use a panel of 772 manufacturing firms over the 1981 to 1987 period to examine the response of investment to uncertainty. They demonstrate that firms postpone investments when the uncertainty of the payoff increases. Guiso and Parigi (1999) use crosssectional data for 549 Italian manufacturing firms to examine whether uncertainty in future expected benefits influences current investment. Their survey data provide a unique opportunity to observe, rather than estimate, managers’ expectations of future expected benefits. They find strong evidence for the value of real options, and that uncertainty has a substantially stronger influence on investment in firms that cannot easily dispose of excess capital equipment in secondary markets. Moel and Tufano (2002) use a Probit model to examine the openings and closings of 285 mines over the 1988-1997 period. They conclude that the probability of opening depends on gold prices, volatility in gold prices, mining costs, and capital costs. Bloom, Bond and Reenen (2007) fit data for 672 publicly traded U.K. manufacturing companies over the 19721991 period to an Error Correction Model (ECM), which relates the investment of a firm to sales growth rates, cash flow, transformations of these variables and uncertainty in investment returns. They conclude that uncertainty reduces the responsiveness of investment to demand shocks. Some important papers in the literature analyze real estate investments. Titman (1985), Quigg (1993) and Capozza and Li (1994) examine the option component of undeveloped land value. Capozza and Li (2001) and Bulan, Mayer and Somerville (2009) use option-based models to analyze residential property development. Holland, Ott and Riddiough (2000), Sivitanidou and Sivitanides (2000), Schwartz (2007), and Fu and Jennen (2009) use real options to analyze commercial property development. Below we briefly review these papers. Titman (1985) uses option theory to value vacant land, and is arguably the first paper on real options. He argues that vacant land can have a variety of different end uses, each with its own market value. The uncertainty in how the vacant land will ultimately be used (and the corresponding rents those properties will generate) is best modeled using real options. Quigg (1993) estimates the real option value associated with real estate development using data on 4 2,700 land transactions in Seattle. She reports a mean option value premium (over intrinsic value) of 6%. Capozza and Li (1994) use real options to model the intensity and timing of capital intensive investment decisions (like real estate). They use an optimal stopping framework that incorporates the value, intensity and timing of the project. Capozza and Li (2001) use annual data on single-family building permits in 56 metropolitan housing markets over the 1980 to 1989 period to analyze the relationship between interest rate changes and housing development. They report that the housing permit growth rate more likely positively responds to interest rate increases when the population growth rate and its volatility are higher. Bulan, Mayer and Somerville (2009) use data for 1,297 condominium transactions in Vancouver over the January 1979 through February 1998 period to analyze the effect of risk on condo development. They estimate a reduced form hazard model, and conclude that the probability of condo development is lower with greater idiosyncratic risk and greater market risk, and that competition significantly reduces the sensitivity of option exercise to volatility. Holland, Ott and Riddiough (2000) provide empirical evidence that option-based investment models outperform neoclassical models in explaining commercial real estate new construction. They estimate a two equation model – one equation for property prices and a second for the stock of commercial real estate space – using quarterly national price indices over the 1972-1992 period from the National Council on Real Estate Investment Fiduciaries (NCREIF) and the National Association of Real Estate Investment Trusts (NAREIT). Sivitanidou and Sivitanides (2000) also empirically examine commercial property development. They analyze CB Richard Ellis/Torto Wheaton survey data for 15 metropolitan office property markets over the 1982 to 1998 period, and conclude that uncertainty in demand growth, increases in the real discount rate, and increases in construction costs reduce investment while rental income growth and expected demand growth increase investment. Using quarterly CoStar data from 1998:3 to 2002:2 for 14 metropolitan office markets, Schwartz (2007) analyzes the determinants of the number of office building starts. They conclude that volatility in lease rates reduces building starts; more competition increases starts; and competition reduces the value of the developer’s option to delay. Fu and Jennen (2009) examine office space new construction in Singapore and Hong Kong (semi-annual data beginning in 1980 5 for Singapore and annual data beginning in 1978 for Hong Kong). They conclude that market volatility reduces the influence that real interest rates and growth expectations have on office starts. This paper has a key difference from existing empirical papers that analyze investment except Capozza and Li (2001): this paper focuses on the non-monotonic effect of interest rate changes on investment predicted by Chetty (2007) and Capozza and Li (2001). It is worth noting that while Capozza and Li (2001) and this paper both analyze non-monotonic effects of interest rate changes, the two papers use different data, methods, and most importantly report different findings. Further, the two empirical analyses are different. While Capozza and Li (2001) examine the effect of population growth rate and its volatility on the investment effect of interest rate changes, this paper analyzes the influence that interest rate changes have on real property capital investments. This paper has other noticeable differences from all existing empirical papers that study real estate investment, including Capozza and Li (2001). First, the existing real estate investment papers analyze real estate development, while this paper is the first that analyzes capital improvements. Second, the dataset we use provides accurate measurement of the timing and the amount of investment, while existing empirical papers estimate investment timing and amount. Third, this paper analyzes investment at the property level, while all existing papers on real estate investment employ indirect investment measurements at aggregate levels. Finally, this paper uses property level cap rates to help capture property owners’ expectation of future income growth, while existing papers assume that investors’ expectation is affected by variables such as population growth etc. III. Research Design This paper uses a model that is similar with the ones in Guiso and Parigi (1999) and Bloom, Bond and Reenen (2007) to test the non-monotonic effect of interest rate changes on investment. We use “interest rates” and “discount rates” interchangeably thereafter, as the literature often does. We model the optimal capital investment of property i in period t , Invi ,t , using the following process: 6   Invi ,t   i  1   2  Disi ,t  Growthi ,t  Disi ,t  3Growthi ,t   4Voli ,t  5Growthi ,t  Voli ,t   6 Phyi ,t  7 Buyi ,t  8 Selli ,t   i ,t (1) In equation (1),  i is a property specific intercept term; Disi ,t is the property owner’s discount rate for future cash flows; Growthi ,t is the expected growth rate of future income, which captures demand changes; Disi ,t is the change in the discount rate from period t  1 to t ; Voli ,t measures the uncertainty of the expected income growth rate Growthi ,t ; Phyi ,t captures the physical condition of the property in period t ; Buyi ,t is a dummy variable that equals 1 if the property was acquired in quarter t  1 ; Selli ,t is a dummy variable if the property was sold in quarter t  1 ;  i ,t is an error term that captures all other variables that might affect the investment. Equation (1) uses the interaction between the change in the discount rate, Disi ,t , and the difference between the discount rate and the expected income growth rate, Disi ,t  Growthi ,t , to capture the non-monotonic effect of interest rate changes on investment that is predicted by Chetty (2007) and Capozza and Li (2001). Both papers suggest that the effect of changes in the interest rate have on investment relates to the difference between the discount rate and expected future income growth. A statistically significant estimated coefficient for the interaction term,  2 , would provide empirical evidence of the non-monotonic influence that changes in interest rates have on investment. Equation (1) includes a variety of factors that likely influence irreversible investment. First, the property specific intercept term helps capture investment needs associated with unobserved time invariant property attributes, such as property type, location, etc. Second, theory predicts that investment responds positively to increases in the expected income growth rate Growthi ,t , so Growthi ,t is expected to have a positive coefficient. Third, investment is expected to negatively react to the uncertainty in the expected income growth rate Voli ,t . Consequently, Voli ,t is expected to have a negative coefficient. Fourth, the option to wait is more valuable with greater uncertainty Voli ,t , and the investment responses to expected income growth is likely to be 7 weaker. As a result, the interaction term Growthi ,t  Voli ,t is expected to have a negative coefficient. Fifth, Phyi ,t captures the physical condition of the property in period t , such as the age or condition of the roof, the HVAC, etc, which affects the need for capital improvements. Finally, we use period dummies to control for possible unusual capital improvements right after the acquisition or before the disposition that are driven by transactions. It is important to note that the actual investment amount cannot be negative and thus is left censored. A panel Tobit model, therefore, is appropriate. However, since the final sample only includes properties with positive capital improvements over their entire holding periods, the Tobit model is reduced to a simple panel linear model. The next section provides a detailed discussion regarding the data cleaning process and the rationale for us to exclude properties with zero capital improvement, which basically cannot be distinguished from properties with missing capital improvement information. Equation (1) is not estimable because some right side variables are not observed. First, the property owner’s expected future income growth rate Growthi ,t , is unobserved. To overcome the problem, this paper employs the Gordon growth model (Gordon (1962)), which relates the cap rate to the discount rate Disi ,t and the expected income growth rate Growthi ,t . Specifically, the cap rate of property i in quarter t , denoted by Capi ,t , is defined as the ratio of annualized income in quarter t , Fi ,t , to the property value at the end of quarter t  1 , Vi ,t 1 . Capi ,t  Fi ,t Vi ,t 1 (3) In the Gordon growth model, the income is assumed to be a growing perpetuity, and the property value Vi ,t 1 equals the present value of all future income. Vi ,t 1  Fi ,t Disi ,t  Growthi ,t (4) Relating equations (3) and (4), we have Capi ,t  Disi ,t  Growthi ,t . 8 (5) Two issues are worth noting regarding the cap rate. First, for Growthi ,t in (5) to capture the property owner’s expectation, the cap rate should be calculated using the property owner’s valuation of the property. We assume that the quarterly appraised property values in the NCREIF database reflect property owner’s valuation. This seems reasonable since appraised values in the database are produced by property owners themselves or appraisers hired by them. Second, the cap rate should be calculated using the normal or stabilized income for the property. However, in the data, the reported NOI is very volatile and thus may differ from what property owners think the stabilized NOI should be. To overcome this problem, we use the median cap rate of all properties of the same type (e.g. apartments or office) in the same Central Business Statistical Area (CBSA) as property i ’s cap rate Capi ,t . The difference between the true property cap rate and the median CBSA cap rate is absorbed by the error term. Now replace Disi ,t  Growthi ,t in (1) with the median CBSA cap rate, Capi ,t , and replace the expected growth rate Growthi ,t with Disi ,t  Capi ,t . Equation (1) becomes Invi ,t   i   1   2Capi ,t  Disi ,t  3  Disi ,t  Capi ,t    4Voli ,t  5  Disi ,t  Capi ,t   Voli ,t  6 Phyi ,t  7 Buyi ,t  8 Selli ,t   i ,t . (6) The model in (6) still contains two unobserved variables. One is the physical condition of the property in period t , Phyi ,t . To overcome this problem, we decompose Phyi ,t into two parts: the condition when the property is acquired, which is unobserved but can be captured by the property specific intercept term, and the change in the condition from the acquisition period to period t . We specify the second component as a linear function of three variables: the average capital improvement per period from acquisition to the previous period Coni ,t , the duration of the holding period from acquisition to period t Holdi ,t , and the squared duration Hold 2i ,t . The duration and its squared value help capture nonlinear relationships between the property age since acquisition and the need for capital improvements. The average capital improvement from 9