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
1
Modeling Space Market Dynamics: An Illustration Using Panel Data
for US Retail
1.
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.1 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.2
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.
1
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).
2
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.
3
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.
2
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
three-equation system, and tests of asymmetric and interactive responses. Section 5 provides a
detailed analysis of MSA natural vacancy rates and simulations of the model. Section 6 summarizes
our main conclusions and discusses further work.
2.
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 RS t 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 , RS t )  (1  v*)SUt ( Rt )
(2)
Substituting equation (1) into (2) and solving for R, we obtain5:
4
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.
5 For simplicity of presentation, we replace SU (R ) with SU but the assumption that supply is a function of rent
t t
t
remains.
3
Rt   0 RS t  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,6 the
underlying elasticities can be computed from the coefficients as 1  1 /  2 and 2   1 /  2 . The
estimated constant term is  2 (ln( 1  v*)  ln 0 ) . Because  0 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 1. Note that we do
not assume that the sales to floorspace ratio is constant,7 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:8
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 RS t i    3,i  ln SU t i    4,i (vt i 1  v*)    5,i t i 1
(5)
where  t 1 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:
6
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.
7
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.
8
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.
4
n1
n2
n3
n4
n5
i 0
i 0
i 0
i 0
i 0
 ln Rt   0   1,i  ln Rt i    2,i  ln RS t i    3,i  ln SU t i    4,i vt i 1    5,i t i 1
n4
n4
i 0
i 0
(6)
where  0  v *   4,i , so   0   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   0   1,i vt i    2,i  ln RS t i   3,i  ln SU t i    4,i vt i 1   5,i t i 1
n4
m4
i 0
i 0
(7)
where  0  v *   4,i , and   0   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 do 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 do 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.9 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.
9
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.
5
l1
l3
m5
i 0
i 0
i 0
St   0   1,i St i    2,i vt i 1    3,i t i 1
(8)
l3
We again have an estimate of the natural vacancy rate from   0   2,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 do 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 4 below.
3.
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 19822007.
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.
6
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:
‘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 1 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
12
The input data omit overage rent, but we do 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.
7
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 1 around here]
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 2 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 do 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
8
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 2 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 3 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 5 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 4 percent.
15 Estimates by the BOC show that online sales represented about four percent of total retail sales in 2009.
9
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 4 around here]
4.
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 1 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 1 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
16
The normal econometric requirements of co-integration and order of integration are met throughout our
estimations and are not reported here.
10
positive and γ2i is always negative, lnλ0i must be positive and greater than ln(1 - vi*) (=-vi*). We
would expect the constant to be negatively correlated with γ2i and this effect to dominate the
negative correlation with the average vacancy rate, all depending on the variations in γ0i. The
correlations of the constant with γ2i and with the average vacancy rate are, respectively, -0.57 and 0.04, as expected.
Further, the higher the value of λ0i, the higher is the space demand for any given level of income
(retail sales) and any given price (rent).
This suggests that λ0i is positively associated with
profitability or sales per unit of space and so the constant term above (  2i [ln(1  v * i )  ln 0i ] )
should be negatively correlated with sales per unit of space. The correlation is –0.36.
We expected that γ1i and γ2i would be highly negatively correlated, and they are: -0.78. This is a
precondition for relative constancy of income elasticities across MSAs. On the other hand, the large
range of γ2i estimates gives a range in price elasticities of -0.7 to -5.6. In an attempt to explain this
large variation, we correlated the cross section coefficients for retail sales (γ1i) and supply (γ2i) and
the income elasticity (the negative of the ratio of γ1i to γ2i) and price elasticity (the inverse of γ1i) with
a number of possibly relevant variables from our dataset17 and with three from Saiz (2010).18 There
were few significant correlations in our dataset and none in Saiz’s. Both cross-section coefficients
are significantly correlated with the standard deviation of real rental growth (0.77 for retail sales and
-0.79 for supply), the standard deviation of supply growth (-0.59 and 0.60) and the standard
deviation of the rent level (0.72 and -0.76). The supply coefficient is, in addition, significantly
correlated (0.60) with the mean absorption rate.
The price elasticity is significantly correlated with the standard deviations of rental growth (0.64), of
the rent level (0.66), of retail sales growth (0.59) and of supply growth (-0.56). That is, demand for
space responds more to changes in rent in MSAs where rent and the variables determining it are
volatile. The income elasticity is significantly correlated with only the mean rental growth (0.58) and
its standard deviation (-0.57). That is, if retail sales increase, the demand for space increases more
in areas where sales growth is more volatile, and increases less in areas where rents are high.
17
These were the mean and standard deviation of: real rental growth, real retail sales growth, supply growth,
the vacancy rate, the real rent level, the supply level, the absorption rate, real sales/ space, and real sales/
space/ real rent. We set this analysis in the context of an option pricing framework. The value of a
development, and therefore market responses, should be linked to the level and volatility of these variables.
18
There are two measures of development constraints (the percentage of undeveloped land and the Wharton
Restriction Index) and his estimated housing supply elasticities.
11
While the correlations between the two Saiz measures of development constraints, and the
correlations of each of these measures with retail sales and supply coefficients and the price and
income elasticities are signed as we expected,19 none is significant and the lowest p-value is 0.12.
We also find plausible, but insignificant, correlations between Saiz’s estimate of the supply elasticity
of housing and these variables. These correlations provide weak evidence of a link between the
parameters of our model and land supply constraints.
To determine whether we can reasonably group the MSAs, we proceed as follows:

For each retail sales and supply coefficient, we order the cities according to the magnitude
of the coefficient;

Starting from the smallest in magnitude, we test whether there is a significant difference
between it and the next city;

If there is not, we include the second city in the same group as the first and compare the
second and third cities to see whether the third city should be in the group;

If there is, we start a new group and compare the second and third cities;

We repeat until all cities have been allocated to groups.
The results are shown in Table 2. The retail sales coefficients do not exhibit significant differences
between any of the ordered pairs of MSAs, suggesting that all MSAs should be in a single group. The
supply coefficients, on the other hand divide between Chicago and Philadelphia, giving two groups,
comprising four and seven MSAs.
[Insert Table 2 around here]
Table 3 reports estimates of the long run rent model for the groups of four and seven MSAs. The
constant and the retail sales and supply coefficients are significantly higher in absolute magnitude
for the first group than for the second as we knew they would be. The income elasticity is half again
as large for group 1, and the price elasticity is three times larger.
[Insert Table 3 around here]
19
Our thinking here is as follows: (1) the less undeveloped land is available, the greater would be the impact of
a change in demand on rent, so the higher would be the retail sales coefficient (γ 1), so the Saiz correlation
would be negative; (2) the more undeveloped land is available, the lower will be the magnitude of the impact
on rent of an increase in supply so, with a negative impact, the correlation with the supply coefficient (γ 2)
should be positive; (3) as the price elasticity is 1/γ2, we expect the correlation to be negative; and (4) as the
income elasticity is -γ1/γ2, we expect a positive correlation.
12
Short run adjustment models
We proceeded as follows in our estimates of the short run models with different calculation of long
run equilibria for the two groups of MSAs. First, separately for the two groups, we estimated three
single equations (growth rates in rent, the vacancy rate and supply) with the constant term allowed
to vary in cross-section, thus allowing the natural vacancy rate to vary across MSAs. We tested up to
four lags of the dependent variables to eliminate residual autocorrelation. The first lag is important
and significant for rent and the vacancy rate. Three lags are important for supply. Our shock
variables are change in retail sales and change in supply, and we also include the lagged rent error
and the lagged vacancy error. This procedure produced the basic structure of the three equations.
Next, using SUR, for each MSA group, we estimated two three-equation systems. In the first, we
allow the cross section constants to vary differently in the three equations, thus producing three
separate estimates of the natural vacancy rate; in the second, we impose a series of constraints to
ensure that each system equation produces the same sets of natural vacancy rate estimates.20
Then, in the two sets of systems estimates (unconstrained and constrained), we tested for significant
differences between coefficients (at 10% initially) in the two panels. With only one exception did
these differences vary between the constrained and unconstrained systems - the change in retail
sales coefficient in the constrained rent equation. Change in supply was different in both the rent
and vacancy equations and the lagged change varied in the vacancy equation. Lastly, both the
lagged three period rent error and change in supply differed in the supply equation. The appearance
of supply differences in all three equations is not surprising given that it was variation in the supply
coefficients that led to our partitioning the MSAs in the first place.
We then estimated two systems (one unconstrained and one constrained) for all MSAs, in which the
long run equilibria varied between groups and dummy variables allowed the significantly different
coefficients to vary between groups. We then removed the insignificant dummy variables to
produce the final models that are presented in Table 4. In these versions, in the rent equation,
change in supply is different in the constrained but not the unconstrained system. Change in supply
and its lagged value remain different in the vacancy equation, and the third lags of change in supply
and the rent error are different in the supply equation.
20
As explained at equations (6)-(8), we can extract separate estimates of natural vacancy rate from the three
equations. In each equation, the estimate is the negative of the ratio of the constant to the coefficient (or sum
or coefficients) on the lagged vacancy rate. In the constrained system, we impose a constraint on the lagged
vacancy rate coefficient in two of the equations. This ensures that the ratio of the lagged coefficient to the
constant in that equation is the same as in the third equation. Similar constraints are required on each of the
dummy variables representing the fixed effects. The exact formulation is available from the authors.
13
[Insert Table 4 (symmetric systems) around here]
Growth in rent is driven by its lagged value, by retail sales growth and by the lagged rent error. Of
special note is the magnitude and significance of the rent error (0.24 with t-ratio of 10). Supply
growth is not significant, except in partition 1 in the constrained model and, even then, the
magnitude of the coefficient (0.01) is small. Particularly surprising is the insignificance of the lagged
vacancy rate, the ultimate driver of rents in the traditional literature. This suggests the superiority of
our ECM approach but may also point to concerns about the vacancy rate data.21 Further, given that
the vacancy rate coefficients are used to estimate natural vacancy rates, our confidence in these
rates is limited.
Growth in the vacancy rate is driven by its lagged value, by current and lagged retail sales growth, by
supply growth and by the lagged vacancy rate. The rent error has a significant, but small coefficient
(0.02); just as rent responses mostly to its own error, vacancies respond mostly to their error. The
responses to supply are complicated. Supply growth initially lowers vacancies, but this is offset in
the next period. Also, both the initial effect and the lagged adjustment are about 50 percent larger
in group 1.
Growth in supply is driven by three lags of the dependent variable, and by the third lag of the rent
error and the second lag of the vacancy rate. Both the third lag of supply growth and the third lag of
the rent error are significantly different between the groups, with larger magnitude responses again
occurring in group 1.
The adjusted-R2s of the three equations, whether in the unconstrained or constrained system, range
from 46% to 58%, with the supply equation being highest, owing largely to the importance of three
lags, and the vacancy rate equation being the lowest. Constraining all three equations to produce
the same estimates of the natural vacancy rate across MSAs reduces the R2s by only about 1%. The
coefficient values are little changed although it should be noted that, given the low values of the
constants, only small changes in their magnitude are required to produce common estimates of the
natural vacancy rates. Before turning to discussion of these estimates, we consider asymmetries
and interactive variables in the adjustment processes.
Asymmetries and interactive variables
21
Both the first and second lags of the vacancy were (barely) significant in early estimations with a single long
run equilibrium and without the supply coefficients allowed to vary between groups.
14
Adjustment in property markets is slow owing to long lived assets and the time required to build
them. Moreover, long-term leases and high moving costs slow adjustments in rental markets even
further. All of these characteristics motivate the use of ECMs in property research. Three recent
papers also suggest several types of asymmetries in office market adjustment where the space
driver is employment: EGHS (2008a), HLM and Brounen and Jennen (2009a).
EGHS emphasize that neither the vacancy rate nor gross investment can be negative. Thus when the
vacancy rate is low, increases in employment will have small impacts on vacancy and large impacts
on rent. In contrast, at high vacancy rates, increases in employment will largely lower vacancy with
small increases in rents. Also, (lagged) positive rent gaps and negative vacancy rate gaps will trigger
increases in supply while reverse gaps will have little impact.22 EGHS (2008a) find strong support for
these propositions in their rent and supply equations.
HLM posit that rent and vacancy responses to positive employment shocks will be greater than
responses to negative shocks because, being locked into long-term leases, tenants cannot easily
abandon space or bargain for lower rents. Further, not only will adjustment to positive employment
shocks depend on the level of the vacancy rate, but the size of the rent error will matter; with rent
below equilibrium, a positive shock will raise rent more than if it is above equilibrium. And a positive
supply shock will lower rent more if it is above equilibrium than if it is below. HLM, too, find support
for their hypotheses regarding rental adjustment.
Brounen and Jennen test similar hypotheses with a panel of 15 US MSA office markets. They divide
employment shocks into positive and negative components and interact the former with a dummy
variable for when the vacancy rate is below average. Positive shocks have a 2.5 times larger impact
on rents when the vacancy rate is below average than when it is above. The division into positive
and negative and the vacancy interaction strongly support the EGHS and HLM results. Brounen and
Jennen do not report vacancy rate adjustment equations.
We have tested for all the asymmetries found in the earlier studies. We separated retail sales
growth into positive and negative components and interacted them with both the vacancy rate and
dummy variables for when the vacancy rate was above and below average for the MSA. We also
interacted supply growth with these vacancy rate variables. For the change in supply model, the
22
The importance of asymmetries in supply adjustment has been emphasized, in the context of a model of
urban growth and residential housing, by Glaeser and Gyourko (2005). They show empirically across U.S.
metropolitan areas that positive shocks to the local economy tend to increase population and employment
more than they increase prices, whereas the opposite holds for negative shocks: prices fall more than
population and employment. A key driving force in their model is a kinked supply curve with a high upward
elasticity but with downward elasticity limited by depreciation.
15
lagged rent error was split into positive and negative components as was the lagged gap between
the actual and average vacancy rate. Few of these asymmetries were significant.
In our final models, the only asymmetries are for responses to retail sales growth in the rent and
vacancy equations. The variable is growth divided by the first lag of the ratio of the vacancy rate to
its average value during our sample period. Thus, a rise in retail sales increases rent more and
decreases the vacancy rate less the lower is the vacancy rate. We had expected a difference
between increases and decreases in retail sales and that an increase would have had a stronger
effect in the rent equation and a decrease would have a stronger effect in the vacancy rate equation.
But we could not detect such effects. The final versions of the unconstrained and constrained
asymmetric systems are shown in Table 5.
[Insert Table 5 (asymmetric systems) around here]
When compared to the symmetric system, the increases to the R2s are trivial – no change in the
vacancy and supply equations and little more than a half of a percent increase in the rent equation.
The structures of the systems, whether symmetric or asymmetric, unconstrained or constrained are
remarkably robust. The only notable difference is in supply in the rent equation. In the constrained
symmetric system, there is small but significant coefficient for group 1 but, in the constrained
asymmetric system, group 2 has a larger and significant coefficient.
5.
Overview
Natural vacancy rates
Eight different estimates of the natural vacancy rates and the average vacancy rates in the MSAs are
presented in Table 6. Looking at the unconstrained estimates, the rates calculated from the vacancy
and supply equations are similar and relatively close to the observed sample means for the 11 MSAs.
Estimates from the vacancy equation never differ by a percentage point from the mean and in only
two cases do estimates from the supply equation differ by this much. In contrast, estimates from
the rent equation are always less than the mean and average two percentage points less in the
symmetric system and three points less in the asymmetric system.23 Clearly calculating natural
vacancy rates from the rent equation estimates alone would be a mistake.
[Insert Table 6 around here]
23
Recall that these estimates are based on low, statistically insignificant, vacancy rate coefficients.
16
In the constrained estimations, the rent measures are effectively pulled up to the vacancy and
supply measures. The correlation of the constrained estimates and the sample means is nearly 0.99.
The natural rates range from a low of 4 to 5 percent for NY, Seattle and Washington to 10 to 12
percent for Atlanta, Chicago, Dallas, Houston and Phoenix.
We considered the correlations between the estimated natural vacancy rate, from the asymmetric
constrained system (see Table 6), and the potential explanatory variables considered for the retail
sales and supply coefficients and the price and income elasticities in section 4 above. Only four were
significant at 5%: the level of rent; the level of supply; the standard deviation of supply and the level
of sales/floorspace. Plots of the natural vacancy rate against these four variables are shown in
Figure 5 below. We find that the natural vacancy rate is higher where rents are low, supply is high,
the volatility of supply is high and sales/floorspace is low. However, in each case, the correlations
are influenced by outliers, respectively: New York; Chicago; Atlanta and Chicago; Chicago.
The first two of these may seem contradictory as high rents and high supply, other things being
equal, would suggest a large market. The combined result may, however, point to the importance of
diversification of the local economy. The other two results are, perhaps, more straightforward: the
supply volatility may create an option value to hold space vacant; and greater possible income from
high sales per unit of floorspace and so reduce vacancies. Nonetheless, this is clearly an area that
requires further research with a larger cross-section of cities.
[Insert Figure 5 around here]
Finally, recall our assumption of a constant natural vacancy rate. To investigate the constancy in our
data, we divide the sample into two equal sub-periods and calculate the average vacancy rates. The
second sub-period has a higher rate in five areas and a lower rate in six areas. However, none of the
differences is significant - the highest magnitude for the t-stat is 1.1. Thus, we conclude that there is
no difference in the natural rate between the two sub-periods, and we remain comfortable with the
assumption of a constant natural rate.
The impact of a shock
To illustrate properties of the model, we ran it with a trend rate of real retail sales growth of 2.6%
(equivalent to the average across MSAs for the period) and we simulated both a 10 percent increase
in real retail sales and then a ten percent decrease. We did this separately for each of the MSA
groups and for the symmetric and the asymmetric systems. It turns out that differences between
the symmetric and asymmetric systems are trivial (the asymmetries were minimal) and negative
17
shocks gave results that are close to mirror images of positive ones. Given that the US experienced a
major negative shock in 2008, only negative shocks with the symmetric system are reported. There
are, however, significant differences in responses for the two MSA groups owing to their different
equilibrium rent equations.24
Figures 6 and 7 illustrate the impacts on equilibrium and actual rent, supply and the vacancy rate for
our two groups of MSAs. We run the system in equilibrium and then shock it. The permanent fall of
10% from the trend in real retail sales directly reduces real rent by 2.5% from trend for group 1 (real
equilibrium rent falls from trend by nearly twice as much – 4.4%) and the vacancy rate increases by
nearly a percentage point. In the second period, the vacancy rate falls by another third of a
percentage point, and the combination of the previous real rental fall, the positive real rent error of
and the previous increase in the vacancy rate decrease real rent by over another one percent. By
the third period, the vacancy rate starts to return toward the natural rate, but the other factors
continue to reduce real rents for four periods when they bottom at nearly six percent below their
initial value. The absence of new supply and reversal of the vacancy rate kick in to reverse over half
of the fall in real equilibrium rent and actual real rent adjusts towards the new equilibrium. Owing
largely to the excess supply, full equilibrium is not reached for about 20 years when real rent is down
by nearly two percent, although it is within a half of a percent of the equilibrium by the twelfth year.
By then, supply has fallen by over five percent with another one percent still to go.
[Insert Figures 6 and 7 around here]
For group 2, the timing of the directional responses is similar, but the decline in rents is greater. The
initial decrease in real equilibrium rent is about twice as large, and, as a result, the initial cumulative
fall in actual rents is about 60 percent greater (nine percent). The vacancy responses are similar for
the two groups.
The main explanation for the difference lies in the constants in the difference models (the ‘drifts’).
These are higher for LA than Washington for rent and the vacancy rate. Thus, when faced with the
same negative shock, rent is less affected and the vacancy rate is more affected in group 1. The
combined effect is to reduce the impact on rent. The differences in supply responses do not have an
impact until three periods after the initial shock.
24
A striking feature of all of the shocks is how the system returns to a stable equilibrium. This underlines the
robustness of the models.
18
Our results can be compared to the simulation results obtained by EGHS and HLM with their office
market models.25 They also have most of the adjustment occurring in 12 years, but the magnitude
of their short run adjustments is much greater than we have estimated. According to EGHS (their
Figure 5), a ten percent employment increase raised rents in year one by 13 percent and lowered
the vacancy rate by 3.5 percentage points. The impact fell more heavily on rents (up 21 percent)
and less on vacancy (down 2.7%) according to HLM (their Figure 7). After three years, rents were 25
percent higher in both studies, versus the six to ten percent found here. That is, we have smaller
temporary (and permanent) impacts on rents and a lesser and shorter impact on vacancies.
Potentially the most interesting comparison would be with the Brounen and Jenner (2009b) panel
study of US office MSAs, the differences reflecting solely different property types. Unfortunately, no
simulations are reported. Moreover, Brounen and Jenner do not have an ECM (no vacancy rate
error and the coefficient on the rent error is effectively zero). Thus, we are limited to comparing
long run price and income elasticities. The income elasticities are similar for the two property types,
near unity, and the price elasticity for our group 2 and the office market are similar (-0.8). It is the
price elasticity for our group 1 (-2.6) that is the outlier.
Comparison of shock impact with the actual 2008-11 market decline
Between 2008 and 2011, real retail rents in the US fell by 20 percent owing to the ’great recession’.
This recession was marked by a 5.5% decline in real retail sales during 2008 and 2009, although this
was largely reversed by a 4% rise during 2010 and 2011. We do not have MSA level data beyond our
estimation period to 2007, but we have national level data (in levels) from 1989 to 201126, so we
perform a simple analysis for the forecasting ability of our model. We shock real retail sales growth
by using the actual figures for 2008-2011.
Table 7 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. Retail
sales and supply growth are virtually identical, but the fall in rents is greater in our MSAs (-0.3%
against -0.6%) and the vacancy rate is lower by nearly a percentage point. Comparing our MSA data
for the study period and the shorter period for which we have national data, shows that the shorter
period had lower real retail sales growth, greater real rental decline, lower supply growth and
almost an identical vacancy rate.
25The
26
office studies are of single cities (Stockholm and London) with employment as the demand variable.
The data for the national analysis were supplied by CBRE EA.
19
[Insert Table 7 about here]
For the same two representative MSAs (LA for group 1 and Washington for group 2), we test the
forecasting ability of our model. As in the previous simulations, we set it to an initial equilibrium
with a 2.6% annual growth in retail sales. As we do not start the forecast period (2008-2011) with
the system in equilibrium, we have to make some initial adjustments.
For the period 2004-2007, real retail sales growth was 0.4% above the 1990-2007 averages, supply
growth was 0.2% above average and the vacancy rate was 0.9% below average. So, we make these
adjustments from equilibrium for the period 2004-2007 and then shock retail sales for the period
from 2008-2011 using the actual rates: -2.6%; -2.8%; +3.2%; and +0.7%. The effect in our models is a
cumulative decline in real rents of 16.5% for 2008-2011 in group 2, but only 7.9% in group 1. This
compares with a fall in actual national real rents of 20%;
The simulations also show a good fit with trends in the vacancy rate. But they do not track the
supply changes – in the national figures, supply growth falls from an average of 2.5% during 20042007 to 0.3% in 2010 and 2011. In contrast, our simulations show supply continuing to grow above
trend as a lagged response to above trend real retail sales growth.
So, overall, for MSAs in group 2, the model performs well for forecasting rents and the vacancy rate;
and in group 1, although it does well for the vacancy rate, it does poorly for rents. However, group 1
comprises only four of the 11 MSAs in the study, and cross-section differences are to be expected
against a national average. Further, we do not have a national model but have applied two models
for two sets of MSAs (with constants varying by MSA in each of the three component equations) to
national data in order to produce the forecasts. Nonetheless, the disappointing group 1 rent result
and the general supply result point to a number of issues.
First, it is, perhaps, not a surprise that model performance is mixed during the downturn. The
consequences of the sub-prime crisis mean that the period was not one of ‘business as usual’, so
there were no data to calibrate the model for such an event. Second, it is also possible that agents
in the market (occupiers, owners and developers) overreacted to the economic fundamentals. The
ability and desire to negotiate lower rents, to remove supply (particularly poorer quality) from the
market, and to stop developments are all likely to have been affected by the crisis.
6.
Conclusions
20
In the above analysis, we have confirmed the value of the Error Correction Model (ECM) approach to
the modeling of space markets. The key variables of rents and vacancy rates adjust to shocks in
retail sales and supply, and to deviations of rents and the vacancy rate from their long run equilibria.
In the case of rents, this is time-varying and defined by the long run equation. The speed of
adjustment is consistent with that found in other studies.
The analysis has substantially extended work on panel data in the investigation of the dynamics of
real estate space markets. These extensions include: partitioning of the markets into groups
according to the parameters in the long run rent equation; consideration of how the underlying price
and income elasticities vary in cross section; analysis of the different short run dynamic adjustment
processes in the groups derived from the long run models; and the estimation of systems.
Our analysis of the long run parameters confirms the existence of significantly different relationships
in different areas. In particular, we derive two groups that have substantially different coefficients
and implied price elasticity. We follow this through to investigate possible differences in the short
run adjustments to shocks.
Overall, the short run analysis shows that, within period, rent responds partially to changes in the
activity measure, in this case, retail sales. Responses to supply take place over time through the
lagged rent and vacancy rate errors. The vacancy rate, in contrast, responds to both retail sales and
to supply and to the vacancy error but not the rent error. The essential structure of these models is
robust.
Although we estimate the adjustment processes within common systems, we allow the long run rent
relationships and short run adjustment coefficients to vary between groups and the natural vacancy
rate to vary across MSAs. There are significant differences to supply shocks in all three equations
and to adjustments to the rent error in the supply equation.
We find only limited evidence of asymmetric responses. We constructed an interactive variable,
designed to moderate the impact of retail sales change depending on the level of the vacancy rate.
There is evidence of the dampening effect of high vacancies on rental responses to retail sales
changes. We find no convincing evidence of the impact of supply change being so dampened.
Overall, we have strong evidence of the differences in the long run relationships and of differences
in the adjustment processes. While the basic structure of the error correction model is robust, the
details of the short run dynamics vary. And we produce remarkably good and consistent estimates
21
of the natural vacancy rates. Moreover, we use the model to forecast the sharp decline in real rents
in the US during 2008-11 and obtain acceptable results.
Further investigation of the different dynamics across markets is merited as is further work on
asymmetric. Identifying these effects systematically is the first challenge; explaining their temporal
and cross-section variation would require a more substantial dataset than we have had available. A
first step might be to seek to explain cross-section variation in the long run elasticities and in the
natural vacancy rate. All of these quests would benefit from consideration of other property types
and countries.
22
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23
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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 1: Proportional changes in real retail rents per square foot
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
24
Figure 2: Vacancy rates (%)
24
20
20
16
16
12
12
8
8
4
4
0
0
25
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
26
Figure 5: Natural vacancy rate and explanatory variables
27
Figure 6: Simulated impact of a permanent 10% fall in retail sales on equilibrium rent, actual
rent, supply and the vacancy rate (Group 1 - LA)
Figure 7: Simulated impact of a permanent 10% fall in retail sales on equilibrium rent, actual
rent, supply and the vacancy rate (Group 2 - Washington)
28
Table 1: Long run coefficients and elasticities
Implied elasticities
Retail sales
Atlanta
Chicago
Dallas
Houston
LA
Minneapolis
New York
Philadelphia
Phoenix
Seattle
Washington
Supply
Income
Price
0.64
-0.82
0.77
-1.21
(6.93) ***
(-8.52) ***
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
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) ***
Notes: Table 1 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.
29
Table 2: Determining groups
Retail sales coefficient
Coeff.
SD
LA
0.19
0.12
Seattle
0.21
0.09
Minneapolis
0.34
0.08
Dallas
0.50
0.11
Washington
0.57
0.12
Chicago
0.58
0.07
Atlanta
0.64
0.09
Philadelphia
0.64
0.15
Phoenix
0.92
0.07
Houston
1.15
0.10
New York
1.45
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
-0.82
0.10
Phoenix
-0.93
0.11
Washington
-1.02
0.11
Dallas
-1.31
0.13
Houston
-1.35
0.14
New York
-1.38
0.17
LA
Seattle
Minneapolis
Dallas
Washington
Chicago
Atlanta
Philadelphia
Phoenix
Houston
New York
-0.11
-1.1
-1.19
-0.43
-0.03
-0.51
-0.03
-1.73
-1.82
-1.04
Supply coefficient
Minneapolis
Seattle
LA
◊
◊
Chicago
◊
◊
Minneapolis
Seattle
LA
Chicago
Philadelphia
Atlanta
Phoenix
Washington
Dallas
Houston
New York
0.48
0.85
0.94
3.4 ◊
0.54
0.75
0.54
1.69
0.19
0.15
◊
Notes: Diagonal figures in Table 2 are z-values; indicates significantly different from preceding MSA
30
Table 3: Long run models
Group 1
constant
ln(real retail sales)
ln(supply)
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) ***
Fixed Effects
Chicago
0.007
Los Angeles
0.000
Minneapolis
0.027
Seattle
-0.034
Atlanta
0.000
Dallas
-0.217
Houston
-0.007
New York
0.204
Philadelphia
-0.001
Phoenix
0.018
Washington
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
t-Statistic for
difference between
groups
(6.49) ***
(7.78) ***
(-13.47) ***
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.
31
Table 4: Symmetric systems
Constant
rental growth (-1)
Change in rent
retail sales growth
supply growth
Constrained
0.008
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 1 only)
(0.01)
-0.010
(-2.42) **
rent error (-1)
vacancy rate (-1)
vacancy rate (-2)
Adj R2
Constant
vacancy rate growth (-1)
retail sales growth
retail sales growth (-1)
Change in vacancy rate
Unconstrained
supply growth
supply growth (partition 1 only)
supply growth (-1)
supply growth (-1) (partition 1 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
Constrained
0.013
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) ***
2
Adj R
0.472
0.461
32
Table 4: Symmetric systems (Cont’d)
Constant
supply growth (-1)
Change in supply
supply growth (-2)
supply growth (-3)
supply growth (-3) (partition 1 only)
rent error (-3)
rent error (-3) (partition 1 only)
vacancy rate (-2)
Unconstrained
Constrained
0.030
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) ***
2
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.
33
Table 5: Asymmetric systems
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 1 only)
0.307
(2.41) **
rent error (-1)
vacancy rate (-1)
vacancy rate (-2)
Adj R
2
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 1 only)
supply growth (-1)
supply growth (-1) (Part 1 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
34
Table 5: Asymmetric systems (Cont’d)
Constant
supply growth (-1)
Change in supply
supply growth (-2)
supply growth (-3)
supply growth (-3) (partition 1 only)
rent error (-3)
rent error (-3) (partition 1 only)
vacancy rate (-2)
Unconstrained
0.030
Constrained
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.
35
Table 6: Estimates of natural vacancy rates
Symmetric system
Time
series
average v
Unconstrained
Change
Change
in
Change
in rent
vacancy in supply
equation
rate
equation
equation
6.1%
10.2%
10.8%
Asymmetric system
Constrained
Common
10.3%
Unconstrained
Change
Change
in
Change
in rent
vacancy in supply
equation
rate
equation
equation
4.8%
9.9%
10.8%
Constrained
Common
Atlanta
9.6%
10.1%
Chicago
12.2%
11.1%
11.3%
11.9%
11.8%
10.7%
11.4%
11.9%
11.6%
Dallas
10.3%
6.0%
11.0%
10.9%
10.8%
4.4%
10.8%
10.9%
10.6%
Houston
10.5%
8.4%
10.7%
10.4%
10.5%
7.6%
10.5%
10.4%
10.4%
LA
6.8%
6.3%
5.8%
6.6%
6.5%
6.2%
6.0%
6.6%
6.2%
Minneapolis
7.9%
7.1%
7.7%
7.3%
7.7%
6.8%
7.7%
7.3%
7.5%
New York
3.7%
0.6%
4.1%
4.2%
4.0%
-0.4%
3.9%
4.2%
3.8%
Philadelphia
8.6%
6.0%
8.6%
9.3%
8.9%
5.1%
8.5%
9.3%
8.7%
Phoenix
11.2%
9.7%
11.8%
12.8%
12.3%
8.8%
11.6%
12.8%
12.0%
Seattle
5.2%
3.3%
5.2%
4.7%
5.1%
2.7%
5.2%
4.7%
4.8%
Washington
4.2%
1.8%
4.5%
5.1%
4.7%
0.6%
4.5%
5.1%
4.6%
Cross section mean
8.2%
6.0%
8.3%
8.6%
8.4%
5.2%
8.2%
8.6%
8.2%
Cross section SD
Correlation with
average
2.9%
3.2%
2.9%
3.1%
3.0%
3.3%
2.9%
3.1%
3.0%
92.9%
97.9%
97.1%
98.7%
87.9%
98.7%
97.1%
98.7%
Notes: Table 6 shows eight different estimates of the natural vacancy rates and the actual average vacancy (availability) rates in the MSAs.
36
Table 7: Key MSA and national variables
Real retail sales growth
Real rental growth
Supply growth
Vacancy rate
All
Group 1
Group 2
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 7 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.
37