Modeling Space Market Dynamics An Illustration Using Panel Data for US Retail

Modeling Space Market Dynamics: An Illustration Using Panel Data for US Retail Pat Hendershott, Maarten Jennen and Bryan MacGregor * Abstract Real estate research has a long and extensive history of analyzing space market dynamics Nonetheless, two areas have been under researched Regional panels of data have been rarely analyzed Moreover, due to data constraints, the retail market has been studied much less than other market segments This paper addresses both of these topics through an analysis of Metropolitan Statistical Area (MSA) level panel data Our study covers almost three decades of annual retail data for 11 of the largest MSAs of the United States We estimate a long run rent model and use Error Correction Models for short run rent, vacancy and supply adjustments We test for differences in local market behavior in both the long run equilibrium relationships and in the short run adjustment processes We identify two groups of similar markets This version: 18 March 2013 Hendershott is a Senior Fellow at the Institute for Housing Studies at DePaul University and a member of the Academic Board of the Homburg Academy He was a part-time Chair in Property Economics and Finance at the Centre for Property Research, University of Aberdeen Business School when early drafts of this paper were written Jennen is Assistant Professor of Finance and Real Estate at Rotterdam School of Management, Erasmus University and Senior Investment Analyst at CBRE Global Investors MacGregor is MacRobert Professor of Land Economy at the Centre for Real Estate Research in the Business School at the University of Aberdeen The authors gratefully acknowledge the generous data support that was offered by CBRE Econometric Advisors (CBRE EA), formerly Torto Wheaton Research, in this project An earlier version was presented at the Annual AREUEA 2010 Meetings * Corresponding author Modeling Space Market Dynamics: An Illustration Using Panel Data for US Retail Introduction Space market research in real estate is directed toward improving understanding of the dynamic responses and interactions of rent, vacancy rate and new supply to changes in the market demand driver Important aspects of this research are the development of better models of the relationships and of the dynamic adjustment of the market to an exogenous shock The empirical testing of more sophisticated models, such as allowing asymmetric responses to shocks, is an important part of the work Such testing requires adding geographic areas and using panel estimation the effective degrees of freedom in analysis of single time series with a limited number of property cycles are too few Panel estimation means a common model for all included localities, but all markets need not adjust similarly, creating a trade-off between obtaining degrees of freedom and allowing for market differentiation An appropriate approach is to identify groups of similarly behaving markets and to estimate separate panels for each group.3 Some caution is required in this general approach as the quality of data likely decreases as more markets are considered The present paper illustrates a way forward in this research We consider the dynamics of the retail space market using annual MSA rent, supply and vacancy data provided by CBRE Econometric Advisors (CBRE EA), formerly Torto Wheaton Research, for the 13 largest US retail markets over the 1982-2007 period While we start with 13 MSAs, we exclude two from the analysis, one because a key data series is simply implausible and the second because the estimated model seems implausible We also systematically test for aggregation of the remaining 11 MSAs based on the long run rent model, determining that panels of four and seven MSAs are appropriate We proceed to estimate separate models for these two groups Research seems to have settled on the error correction model (ECM): see Hendershott, MacGregor and Tse (2002, hereafter HMT) and Englund, Gunnelin, Hendershott and Soderberg (2008, hereafter EGHS) Application of the ECM in panel estimation of real estate markets is limited Hendershott, MacGregor and White (2002) and Hendershott and MacGregor (2005b) estimated panels of regional rents in the UK and of capitalization rates in US MSAs, respectively Mouzakis and Richards (2007) estimated a panel of office rents in 12 European cities and Brounen and Jennen (2009a, 2009b) estimated panels for European and US city office market rents To the best of our knowledge, only Hendershott, MacGregor and White (2002) have tested for differences in markets, concluding that the London region was dissimilar from the other regions In the next two sections, we discuss the framework to be estimated and describe the data employed In Section 4, we report results, including single equation estimates, SUR estimates of the threeequation system, and tests of asymmetric and interactive responses Section provides a detailed analysis of MSA natural vacancy rates and simulations of the model Section summarizes our main conclusions and discusses further work Modeling The model must address analysis of both time series and cross section data We begin with the former Time series modeling The time series analysis is similar to the three-equation model (rent, vacancy rate and change in supply) that EGHS (2008) estimate for the Stockholm office market and Hendershott, Lizieri, and MacGregor [2010, hereafter, HLM] use to test for asymmetric responses to demand and supply shocks in the London office market See EGHS and HMT, who introduce the Error Correction approach to rent modeling, for reviews of the earlier time series literature on rent determination We begin by specifying the long run demand for space by retailers, D, as a logarithmic function of real effective rent on new contracts (R) and real retail sales (RS): Dt 0 Rt 1 RSt 2 (1) where 1 is the ‘price’ elasticity (negative) and 2 is the income elasticity (positive) The market clearing (equilibrium) rent equates demand and supply (SU) when the vacancy rate is at its constant4 ‘natural’ level (v*): Dt ( Rt , RSt ) (1  v*)SUt ( Rt ) (2) Substituting equation (1) into (2) and solving for R, we obtain5: The constancy assumption is standard in the literature on modeling space markets The actual vacancy rate oscillates around its constant natural level depending on the real estate cycle Therefore the estimation of vacancy rate trends is affected by the points on the cycle at the start and end of the estimation period For the MSA’s examined in this study, with one exception, the trends in the vacancy rate lie in the narrow range -0.1% pa to +0.1% pa For simplicity of presentation, we replace SUt(Rt) with SUt but the assumption that supply is a function of rent remains Rt 0 RSt 1 [(1  v*)SUt ]2 (3) where the gammas are constants Taking logs, we obtain: ln Rt ln 0  1 ln RSt  2 ln(1  v*)  2 ln SUt This is a reduced form equation (4) Assuming a very inelastic short run supply response, the underlying elasticities can be computed from the coefficients as 1 1 /  and 2  1 / 2 The estimated constant term is 2 (ln(1  v*)  ln 0 ) Because  is unknown, the natural vacancy rate cannot be solved from this estimation If γ1 and γ2 were equal in magnitude but opposite in sign, equal percentage changes in RS and SU would leave R unchanged In this case, the income elasticity (-γ1/γ2) would be Note that we not assume that the sales to floorspace ratio is constant, and empirically the long run coefficient on sales is less than that on supply in nine of the 11 markets This means that, if the vacancy rate were at its equilibrium level, sales could grow more quickly than stock while rent remains constant, suggesting increased sales per unit of floorspace The short-run rent adjustment equation is: n1 n2 n3 n4 n5 i 0 i 0 i 0 i 0 i 0  ln Rt   1,i  ln Rt  i    2,i  ln RSt  i    3,i  ln SU t  i    4,i (vt  i   v*)    5,i  t  i  (5) where  t  is the lagged error (actual less estimated) from the estimation of equation (4) We expect rents to revert to equilibrium (α5 < 0) and above equilibrium vacancies to cause downward adjustment on rent (α4 < 0) Rents also adjust to changes in the shock variables (RS and SU) – to rise with increases in retail sales and fall in response to increases in supply Because v* is unobservable, equation (5) is estimated as: Supply cannot adjust within a year as the construction period is too long and demolitions are unlikely Instead, the adjustment is in occupied space and hence the vacancy rate To test this assumption, we used the approach advocated by Hilber and Mayer (2009) We estimated a two-stage least squares regression for the response of supply to rent, using retail sales as the instrument We repeated this for changes in these (logged) variables The results offer support for our assumption The trends in the sales to floorspace ratio range from -1.4% pa to +1.4% pa Of these 11 trends, four are insignificant at 5%, five are significantly negative and two are significantly positive The general pattern is a rise for the first three years, then a fall for eight years, a rise for eight and then a leveling off This is the general form of the model that allows lags of the dependent and independent variables In practice, we normally expect no more than one or two lags of the variables The exception in our estimations is the change in supply Lags of the rent error were also tested but were never significant n1 n2 n3 n4 n5 i 0 i 0 i 0 i 0 i 0  ln Rt    1,i  ln Rt  i    2,i  ln RSt  i    3,i  ln SU t  i    4,i vt  i     5,i t  i  n4 n4 i 0 i 0 (6) where   v *   4,i , so     4,i is an estimate of the natural vacancy rate Because the natural (equilibrium) vacancy rate is assumed constant, there is no long-run vacancy equation And an equation for changes in the vacancy rate can be expressed as a direct analogue to the rental change equation m1 m2 m3 m4 m5 i 0 i 0 i 0 i 0 i 0 vt    1,i vt  i    2,i  ln RSt  i    3,i  ln SU t  i    4,i vt  i     5,i t  i  n4 m4 i 0 i 0 (7) where   v *   4,i , and     4,i provides another estimate of the natural vacancy rate Here, the expected signs on the error correction coefficients are the same as in the rent equation; variables revert to equilibrium in the own market and above equilibrium rent encourages greater lease-ups and thus lower vacancy) Shocks, on the other hand, would have opposite effects on rent and vacancy The final equation in the model is for the change in the stock We not have data for development starts Moreover the data we have for completions is identical to the change in supply; that is, there are no ‘discards’ or depreciation in the data set The basic theory underlying the estimation is that a sufficient excess of the estimated value of investments over their cost will trigger development, while a shortfall will prevent even replacement investment Of course, we not have data on either of these estimated values or costs Investment value is the present value of expected future rents Expected rental growth is assumed to be driven by positive gaps between the natural and actual vacancy rates and equilibrium and actual rent The greater are the gaps, the greater will be expected rental growth and thus the greater will be investment We model completions with the lagged values of these variables – we expect two and three periods will be most important as these accommodate the likely development period Thus, we expect that lagged values of the vacancy rate and the rent error (R – R*) will have negative impacts on development As before, we also include lagged values of the dependent variable l1 l3 m5 i 0 i 0 i 0 St    1,i St  i    2,i vt  i     3,i t  i  (8) We use the logs of rent and supply levels, so the log differences approximate the growth rates for these variables, but we use the levels for the vacancy rates and model the change We again have an estimate of the natural vacancy rate from   l3   ,i i 0 Cross section modeling of the long-run rent relationship To let the natural vacancy rate vary across MSAs in the long run model, we have to allow the constant in equation (4) to vary.10 To allow the natural vacancy rate to vary in cross-section in the short run model, we must allow the constants in equations (6), (7) and (8) to vary This permits separate calculations of the natural rate from each of the three short run equations (our final system estimations will constrain these to be equal) Initially we also allow the retail sales and supply coefficients in equation (4) to vary We then partition the MSAs according to significant differences in these coefficients On the assumption that we can derive the price and income elasticities from these coefficients (see above), this is equivalent to partitioning based on the elasticities Note, however, that we not require this assumption to hold to be able to undertake the partitioning The retail sales coefficient amplifies (greater than unity) or dampens (less than unity) the impact of growth in retail sales on rents The supply coefficient has a similar amplifying or dampening effect on the transmission of the impact of a change in supply to a change in rent Because 1 and 2 should be roughly equal and opposite in sign, we expect a negative correlation of the cross section gammas After finding that the coefficients vary significantly across MSAs, we determine whether some MSAs can be aggregated into groups and find that two groups are adequate The procedure is described in section below Data Our private retail real estate data on rents, supply and ‘vacancies’ have been kindly provided by CBRE Econometric Advisors (CBRE EA), formerly Torto Wheaton Research, for the largest 13 US MSAs We supplement these data with MSA level CPI deflators and retail sales data These series are discussed in turn and a range of summary statistics is provided We have annual data for 1982-2007 Real retail rent The rent indices are constructed from both information produced through leasing agreements that CBRE EA has been involved with and property level asking rents from CoStar 11 According to CBRE: 10 Hendershott and Haurin (1988) provide an analysis of the determination of v* and summarize evidence from a number of early empirical studies on variation of office market v* across MSAs 11 ‘The database contains selected information about each lease This includes the term of the lease, rent during each year, and percentage commission (for CBRE vouchers) For the CBRE data when combined, this sums to the total consideration of the lease, or the non-discounted sum of the rental payments These payments take into account any periods of free rent and any step increases, but exclude taxes, any tenant improvements, or payments made as a percentage of sales (overage rent) The data file also contains limited information on the location of the leased space (city, submarket) plus the type of center and the amount of space leased' (Marks, 2008, p 5) CBRE EA has estimated a hedonic rent index alon5g the lines of Wheaton and Torto (1994) and EGHS (2008) The underlying leases are for tenants in neighborhood and community market centers only (regional and super regional center tenants are excluded due to lack of sufficient individual leases) The estimates are for what the average payment would be over a standard lease term for given amount of space TWR’s standard lease has a five year term and is the gross rent for 5000 square feet in an existing center.12 We convert nominal series to real series using the BLS consumer price indices for our MSAs based on the prices paid by urban consumers for a representative basket of goods and services These indices are based at 1982=100 NY, DC and LA had the highest real rents, all being $13 per square foot in 1982 and about the same in 2007 Rent in the other cities was in the $7 to $10 range Figure is a box plot showing the mean percentage change in real retail rents as a solid dot surrounded by a box whose lower and upper boundaries are determined by, respectively, the first and third quartile of observations The horizontal stripes represent the maximum and minimum observations in case of no outliers When outliers, indicated with circles in the graph, are present, the stripes represent the observations with the largest distance from the mean within the nonoutlier range.13 With three exceptions, real rental growth per annum ranged between minus 0.6 and plus 0.8 percent Real rents in Boston and Dallas declined by about two percent each year, while Phoenix had a positive annual average growth of 1.4 percent (As discussed below, Phoenix had far and away the largest percentage growth in real retail sales over the period.) [Insert Figure around here] 12 The input data omit overage rent, but we not believe that this would have a significant effect on changes in market level rent over time unless the relative importance of base rent has changed over time At the beginning of a lease a tenant agrees to a base rent and the portion of the rent that can also be driven by sales What we use in the model is the average market rent at the city level Rent paid within existing leases will change over time as a result of sales level and indexation; however, at the end of a contract, the rent will be adjusted again to some market level that will be driven by supply of retail space and the level of demand for retail services (sales) 13 Outliers are those observations whose value does not fall within an interval determined as first quartile minus 1.5 times IQR or third quartile plus 1.5 times IQR, IQR being the Inter Quartile Range or the difference between the third and first quartile observations All thirteen MSAs had declines in real rents between (roughly) 1984-87 and 1992-94 On average, the decrease was 28 percent with eight of the 13 MSAs showing a decline of more than 25 percent Hendershott and Kane (1992) attribute the general decline in real estate rents and values during the late 1980s and early 1990s to massive overbuilding during the middle 1980s (the 1990-91 recession also contributed) According to Hendershott and Kane, the overbuilding resulted largely from two provisions in 1981 tax legislation First, extremely generous tax depreciation allowances were adopted (complete write-off of structures investment in 15 years) Second, ‘passive losses’ were made deductible against wage income Further, separate legislation encouraged de facto insolvent financial institutions to grow out of their insolvency by investing in 'higher return' commercial mortgages, providing cheap funding for these investments The 1986 Tax Act more than reversed the two tax provisions, and the commercial mortgage option was withdrawn in 1989 legislation Real rents then rebounded somewhat in most markets, with Houston and Phoenix more than reversing their earlier declines The exceptions were Boston and Dallas, which experienced even further declines, ending the sample period at $7 psf; only one other MSA had rent (barely) below $10 in 2007 NY had the greatest volatility, owing to enormous rent increases in the early 1980s (rent rose from $13 to $24), before exactly reversing Vacancy Rate US office and industrial property rent research has emphasized responses to gaps between the actual and natural (constant) vacancy rates Figure reports a box plot of the actual rates for the 13 MSAs There is a huge range of average values, although all but Riverside are between four (NY and Washington DC) and 12 percent (Chicago and Phoenix) Riverside is an incredible outlier, with the rate being in the 15 to 22 percent range throughout the 1982-2004 period, before plunging to six percent in 2006 The Riverside rates seem implausible Not only they suggest an unbelievably high ‘natural’ vacancy rate, but they are inconsistent with the mean positive real rental growth observed Thus, we have dropped the Riverside data from our analysis We actually use what CBRE EA refers to as the ‘availability rate,’ which Marks (2008, p 10) defines as the percentage of the retail stock that is available as of that period, either vacant or occupied In fact we believe availability includes, in addition to vacancies, only leases for space that are coming to the market (space for which the tenant has give notification that the lease will not be continued at the end of the contract).14 CBRE EA argues that availability rates are a better measure of retail market tightness than are vacancy rates [Insert Figure around here] Stock TWR has compiled these series based on information provided by the National Research Bureau Shopping Center Directory (a subsidiary of CoStar) and TRW/Dodge Pipeline Supposedly, these data exclude space in regional and super regional centers Periodical increases in the supply of retail space represent both the opening of new centers and the additional available space as a result of expansion of existing centers The data we use are in thousands of square feet Minneapolis, NY, Riverside and Seattle have less space (starting around 10,000 and rising to 20,000) Chicago has the most space, rising from 40,000 to 94,000 The mean annual percentage change in retail supply in the 13 MSAs varies within a rather tight band of 2.2 to 4.5 percent but with some remarkable positive outliers due to the bulky nature of shopping centers as shown in the box plot (Figure 3) All MSAs, except those on the east coast, exhibited particularly rapid growth in the period 1984-90, consistent with the argument of Hendershott and Kane (1992) [Insert Figure around here] Real retail sales The US Bureau of Census (BOC) publishes retail sales data at the MSA level based on surveys of companies with one or more establishments that sell merchandise and related services to final consumers The monthly series date back to 1951 New samples of national tenants are surveyed every five years.15 The data are in billions of dollars Three MSAs – NY, LA and Chicago have had sales roughly 50 percent greater than the other ten Unfortunately, the geographical coverage of the retail sales data does not correspond perfectly with the CBRE EA data Whereas the major city in each included MSA is part of all series, minor differences occur in the coverage of the smaller municipalities that can be part of the MSAs 14 Note that with an average lease length of years (this is the assumed standard length), the availability rate due solely to the rolling over of leases would be 20 percent; for length of 10 years, it would be 10% The average rates in the data for two of the MSAs is a far lower percent 15 Estimates by the BOC show that online sales represented about four percent of total retail sales in 2009 A box plot contains data on percentage changes in real retail sales per square foot Only one MSA has an average change greater than 0.2 percent (Phoenix with 1.3%), and six MSAs have declines of a half percent or more The largest average declines are 1.5% in Chicago and 1.2% in Los Angeles [Insert Figure around here] Estimation The results are reported in three parts The first considers the long-run rent determination model and the partitioning of MSAs based on its coefficients The second examines the short-run adjustment models for rent, the vacancy rate and the change in the stock These incorporate ECM adjustments and shock responses, and produce estimates of natural vacancy rates Finally, asymmetries in the short run relationships are considered Long run rent estimates and grouping of the MSAs First, we allow all coefficients to vary in cross-section, effectively estimating separate models for each city With one exception, all coefficients are statistically different than zero at the 5% level and most at the 0.1% level All supply coefficients are negative, and all retail sales coefficients are positive, except that for Boston The negative Boston sales coefficient, which is statistically different than zero, implies a negative income elasticity of retail space demand The correlation between rental growth and retail sales growth for Boston is only 0.065, compared to between 0.22 and 0.56 for the other MSAs And the Boston correlation between rental and supply growth is 0.26, in comparison to negative or much lower positive values for other MSAs The rise and fall of rent and supply together is particularly pronounced during the second half of the 1980s Given the implausibility of the negative income elasticity, we drop Boston from the subsequent analysis Table lists the supply and retail sales coefficients with the MSAs ordered from smallest to largest supply coefficient when the model is rerun with the remaining 11 MSAs 16 [Insert Table around here] Recall that the estimated constant term for the ith MSA is  2i [ln(1  v * i)  ln 0i ] , where λ0i is the constant in the demand function [equation (1)] γ2i is in the range -1.38 to -0.18, while the average vacancy rate (a proxy for v*) is in the range 0.04 to 0.12 As the regression constant is always positive and γ2i is always negative, lnλ0i must be positive and greater than ln(1 - vi*) (=-vi*) We would expect 16 The normal econometric requirements of co-integration and order of integration are met throughout our estimations and are not reported here 10 Saiz, A (2010) The Geographic Determinants of Housing Supply, The Quarterly Journal of Economics, 125 (3), 1253-1296 Wheaton, W.C and Torto, R.G (1994), Office Rent Indices and their Behavior Over Time, Journal of Urban Economics 35, 121-139 23 Washington, DC Seattle Riverside Phoenix Philadelphia New York Minneapolis Los Angeles Houston Dallas Chicago Boston Atlanta Washington, DC Seattle Riverside Phoenix Philadelphia New York Minneapolis Los Angeles Houston Dallas Chicago Boston Atlanta Figure 1: Proportional changes in real retail rents per square foot 4 3 2 1 0 -.1 -.1 -.2 -.2 24 Figure 2: Vacancy rates (%) 24 20 20 16 16 12 12 8 4 0 24 Washington, DC Seattle Riverside Phoenix Philadelphia New York Minneapolis Los Angeles Houston Dallas Chicago Boston Atlanta Washington, DC Seattle Riverside Phoenix Philadelphia New York Minneapolis Los Angeles Houston Dallas Chicago Boston Atlanta Figure 3: Proportional changes in retail stock 20 20 16 16 12 12 08 08 04 04 00 00 Figure 4: Proportional change in real retail sales per square foot 15 15 10 10 05 05 00 00 -.05 -.05 -.10 -.10 -.15 -.15 25 Figure 5: Natural vacancy rate and explanatory variables 26 Figure 6: Simulated impact of a permanent 10% fall in retail sales on equilibrium rent, actual rent, supply and the vacancy rate (Group - LA) Figure 7: Simulated impact of a permanent 10% fall in retail sales on equilibrium rent, actual rent, supply and the vacancy rate (Group - Washington) 27 Table 1: Long run coefficients and elasticities Atlanta Chicago Dallas Houston LA Minneapolis New York Philadelphia Phoenix Seattle Washington Retail sales 0.64 Supply -0.82 (6.93) *** (-8.52) *** 0.58 -0.37 (8.71) *** (-10.56) *** 0.50 -1.31 (4.44) *** (-9.87) *** 1.15 -1.35 (11.45) *** (-9.47) *** 0.19 -0.30 (1.67) * (-4.72) *** 0.34 -0.18 (4.4) *** (-2.51) ** 1.45 -1.38 (5.34) *** (-8.21) *** 0.64 -0.75 (4.32) *** (-7.18) *** 0.92 -0.93 (13.15) *** (-8.51) *** 0.21 -0.23 (2.34) ** (-3.34) *** 0.57 -1.02 (4.95) *** (-8.95) *** Implied elasticities Income Price 0.77 -1.21 1.55 -2.68 0.38 -0.76 0.85 -0.74 0.64 -3.29 1.91 -5.63 1.05 -0.72 0.86 -1.34 0.99 -1.07 0.94 -4.45 0.56 -0.98 Notes: Table reports regression results based on Equation (4) and the resulting implied income and price elasticities T-statistics within parentheses *** indicates significance at the 1% level; ** indicates significance at the 5% level, and * indicates significance at the 10% level 28 Table 2: Determining groups Retail sales coefficient Coeff 0.19 0.21 0.34 0.50 0.57 0.58 0.64 0.64 0.92 1.15 1.45 SD 0.12 0.09 0.08 0.11 0.12 0.07 0.09 0.15 0.07 0.10 0.27 Coeff SD -0.18 0.07 -0.23 0.07 -0.30 0.06 -0.37 0.04 Philadelphia -0.75 0.10 Atlanta Phoenix Washington Dallas Houston New York -0.82 -0.93 -1.02 -1.31 -1.35 -1.38 0.10 0.11 0.11 0.13 0.14 0.17 LA Seattle Minneapolis Dallas Washington Chicago Atlanta Philadelphia Phoenix Houston New York LA Seattle Minneapolis Dallas Washington Chicago Atlanta -0.11 -1.1 -1.19 -0.43 -0.03 -0.51 -0.03 Supply coefficient Minneapolis Seattle LA ◊ ◊ Chicago ◊ ◊ Minneapolis Seattle LA Chicago Philadelphia Atlanta Phoenix 0.48 0.85 0.94 3.4 ◊ 0.54 0.75 0.54 Notes: Diagonal figures in Table are z-values; ◊ indicates significantly different from preceding MSA 29 Table 3: Long run models Group constant ln(real retail sales) ln(supply) Fixed Effects Chicago Los Angeles Minneapolis Seattle Atlanta Dallas Houston New York Philadelphia Phoenix Washington Group2 4.36 5.83 (25.26) *** (39.55) *** 0.45 0.90 (11.66) *** (20.5) *** -0.38 -1.15 (-11.29) *** (-24.88) *** t-Statistic for difference between groups (6.49) *** (7.78) *** (-13.47) *** 0.007 0.000 0.027 -0.034 0.000 -0.217 -0.007 0.204 -0.001 0.018 0.003 Weighted Statistics Adjusted R-squared 0.884 0.877 Unweighted Statistics R-squared 0.616 0.676 Elasticities Price Income -2.630 1.180 -0.870 0.780 Notes: Regression based on Pooled EGLS with Cross-section SUR Sample period 1982-2007 T-statistics within parentheses *** indicates significance at the 1% level; ** indicates significance at the 5% level, and * indicates significance at the 10% level 30 Table 4: Symmetric systems Constant rental growth (-1) Change in rent retail sales growth supply growth Constrained 0.011 (0.68) (1.31) 0.456 0.478 (11.1) *** (11.84) *** 0.272 0.250 (3.43) *** (3.31) *** -0.015 0.001 (-0.16) supply growth (partition only) (0.01) -0.010 (-2.42) ** rent error (-1) vacancy rate (-1) vacancy rate (-2) Adj R Constant vacancy rate growth (-1) retail sales growth retail sales growth (-1) Change in vacancy rate Unconstrained 0.008 supply growth supply growth (partition only) supply growth (-1) supply growth (-1) (partition only) rent error (-1) vacancy rate (-1) -0.238 -0.239 (-9.66) *** (-9.67) *** -0.157 -0.118 (-0.75) (-0.56) -0.269 -0.109 (-1.21) (-0.51) 0.533 0.519 Unconstrained 0.013 Constrained 0.015 (4.61) *** (5.49) *** 0.095 0.118 (1.84) * (2.26) ** -0.089 -0.089 (-4.82) *** (-4.96) *** -0.056 -0.056 (-2.95) *** (-2.89) *** 0.293 0.267 (6.52) *** (5.82) *** 0.139 0.144 (2.4) ** (2.48) ** -0.163 -0.154 (-3.32) *** (-3.24) *** -0.116 -0.116 (-2.02) ** (-2.03) ** -0.019 -0.018 (-2.75) *** (-2.63) ** -0.295 -0.312 (-5.83) *** Adj R 0.472 0.461 31 Table 4: Symmetric systems (Cont’d) Constant supply growth (-1) Change in supply supply growth (-2) supply growth (-3) supply growth (-3) (partition only) rent error (-3) rent error (-3) (partition only) vacancy rate (-2) Unconstrained 0.030 Constrained 0.029 (6.47) *** (6.72) *** 0.450 0.453 (7.57) *** (7.48) *** 0.176 0.179 (2.5) ** (2.52) ** 0.153 0.191 (2.04) ** (2.8) *** 0.262 0.199 (2.8) *** (2.68) *** -0.042 -0.047 (-3.32) *** (-3.78) *** -0.113 -0.104 (-3.17) *** (-3.04) *** -0.592 -0.604 (-6.74) *** Adj R 0.577 0.569 Notes: Sample: 1984 2007; included observations: 264 T-statistics within parentheses *** indicates significance at the 1% level; ** indicates significance at the 5% level, and * indicates significance at the 10% level Table 5: Asymmetric systems 32 Constant rental growth (-1) Change in rent retail sales growth/(vt-1/v*) supply growth Constrained 0.016 (0.16) (1.85) * 0.451 0.474 (11.04) *** (11.82) *** 0.296 0.234 (4.03) *** (3.54) *** -0.031 -0.346 (-0.32) (-3.7) *** supply growth (partition only) 0.307 (2.41) ** rent error (-1) vacancy rate (-1) vacancy rate (-2) Adj R Constant vacancy rate growth (-1) retail sales growth/(vt-1/v*) Change in vacancy rate Unconstrained 0.002 retail sales growth (-1)/(vt-2/v*) supply growth supply growth (Part only) supply growth (-1) supply growth (-1) (Part only) rent error (-1) vacancy rate (-1) -0.239 -0.235 (-9.86) *** (-9.68) *** -0.025 -0.009 (-0.12) (-0.04) -0.302 -0.348 (-1.37) (-1.59) 0.54 0.524 Unconstrained 0.016 Constrained 0.016 (5.12) *** (5.69) *** 0.117 0.126 (2.28) ** (2.43) ** -0.077 -0.076 (-4.46) *** (-4.5) *** -0.058 -0.060 (-3.25) *** (-3.27) *** 0.300 0.303 (6.65) *** (6.63) *** 0.131 0.128 (2.27) ** (2.19) ** -0.158 -0.168 (-3.21) *** (-3.49) *** -0.121 -0.111 (-2.1) ** (-1.93) * -0.017 -0.016 (-2.54) ** (-2.42) ** -0.345 -0.348 (-6.48) *** Adj R2 0.472 0.462 Table 5: Asymmetric systems (Cont’d) Unconstrained Constrained 33 Constant supply growth (-1) Change in supply supply growth (-2) supply growth (-3) supply growth (-3) (partition only) rent error (-3) rent error (-3) (partition only) vacancy rate (-2) 0.030 0.029 (6.47) *** (6.84) *** 0.450 0.457 (7.57) *** (7.56) *** 0.176 0.186 (2.5) ** (2.62) ** 0.153 0.210 (2.04) ** (3.13) *** 0.262 0.208 (2.81) *** (2.88) *** -0.042 -0.048 (-3.31) *** (-3.88) *** -0.113 -0.108 (-3.17) *** (-3.18) *** -0.592 -0.623 (-6.74) *** Adj R2 0.577 0.568 Notes: Sample: 1984 2007; included observations: 264 T-statistics within parentheses *** indicates significance at the 1% level; ** indicates significance at the 5% level, and * indicates significance at the 10% level 34 Table 6: Estimates of natural vacancy rates Time series average v Atlanta Chicago Dallas Houston LA Minneapolis New York Philadelphia Phoenix Seattle Washington 9.6% 12.2% 10.3% 10.5% 6.8% 7.9% 3.7% 8.6% 11.2% 5.2% 4.2% Cross section mean Cross section SD Correlation with average 8.2% 2.9% Symmetric system Unconstrained Change Change in Change in rent vacancy in supply equation rate equation equation 6.1% 10.2% 10.8% 11.1% 11.3% 11.9% 6.0% 11.0% 10.9% 8.4% 10.7% 10.4% 6.3% 5.8% 6.6% 7.1% 7.7% 7.3% 0.6% 4.1% 4.2% 6.0% 8.6% 9.3% 9.7% 11.8% 12.8% 3.3% 5.2% 4.7% 1.8% 4.5% 5.1% Constrained Common 10.3% 11.8% 10.8% 10.5% 6.5% 7.7% 4.0% 8.9% 12.3% 5.1% 4.7% Asymmetric system Unconstrained Constrained Change Change in Change in rent vacancy in supply Common equation rate equation equation 4.8% 9.9% 10.8% 10.1% 10.7% 11.4% 11.9% 11.6% 4.4% 10.8% 10.9% 10.6% 7.6% 10.5% 10.4% 10.4% 6.2% 6.0% 6.6% 6.2% 6.8% 7.7% 7.3% 7.5% -0.4% 3.9% 4.2% 3.8% 5.1% 8.5% 9.3% 8.7% 8.8% 11.6% 12.8% 12.0% 2.7% 5.2% 4.7% 4.8% 0.6% 4.5% 5.1% 4.6% 6.0% 3.2% 8.3% 2.9% 8.6% 3.1% 8.4% 3.0% 5.2% 3.3% 8.2% 2.9% 8.6% 3.1% 8.2% 3.0% 92.9% 97.9% 97.1% 98.7% 87.9% 98.7% 97.1% 98.7% Notes: Table shows eight different estimates of the natural vacancy rates and the actual average vacancy (availability) rates in the MSAs 35 Table 7: Key MSA and national variables Real retail sales growth Real rental growth Supply growth Vacancy rate All Group Group National 1982-2007 1990-2007 2.60% 2.20% 2.20% 1.70% 2.90% 2.50% 2.20% 1982-2007 1990-2007 -0.20% -0.60% 0.10% -0.40% -0.40% -0.70% -0.30% 1982-2007 1990-2007 3.00% 2.30% 3.20% 2.30% 2.90% 2.30% 2.30% 1982-2007 1990-2007 8.20% 8.20% 8.10% 7.90% 8.30% 8.40% 9.10% Notes: Table compares the unweighted averages across MSAs with the national data for the four key variables: real retail sales growth; real rental growth; supply growth; and the vacancy rate 36 .. .Modeling Space Market Dynamics: An Illustration Using Panel Data for US Retail Introduction Space market research in real estate is directed toward improving understanding of the... illustrates a way forward in this research We consider the dynamics of the retail space market using annual MSA rent, supply and vacancy data provided by CBRE Econometric Advisors (CBRE EA), formerly... rates in US MSAs, respectively Mouzakis and Richards (2007) estimated a panel of office rents in 12 European cities and Brounen and Jennen (2009a, 2009b) estimated panels for European and US city