maeve maloney stuart s. rosenthal
TRANSCRIPT
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Why Do Home Prices Appreciate Faster in Center Cities? The Role of
Risk-Return Trade-Offs in Real Estate Markets
April 21, 2021
Maeve Maloney
Syracuse University
Email: [email protected]
Stuart S. Rosenthal
Maxwell Advisory Board Professor of Economics
Syracuse University
Email: [email protected]
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Abstract
Using Zillow data, this paper shows that central city housing appreciates faster than in suburban
markets, echoing evidence of higher rates of appreciation in superstar cities (e.g. Gyourko et al
(2013)). Additional results confirm that housing supply constraints within and across cities
contribute to these patterns by increasing volatility and investor exposure to risk. Allowing for
other mechanisms, zip code and CBSA-level CAPM betas explain up to half of cross-sectional
variation in appreciation rates. These patterns confirm that risk-return trade-offs are important
drivers of returns across markets, and that different rates of home price appreciation across
markets do not necessarily indicate opportunities for arbitrage.
JEL Codes: R0, G1
Key words: CAPM, Risk-Return, Home price appreciation rates, supply constraints
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1. Introduction
This paper establishes a new stylized fact that helps to highlight market mechanisms that
drive home price appreciation rates. Among large cities, year-over-year neighborhood level
single family home price appreciation rates decline almost monotonically both with distance to
the central city (Figure 1a) and as density declines (Figure 1b).1 In some respects, these patterns
echo more widely recognized tendencies for metropolitan level home price appreciation rates to
vary across urban areas, as is evident in Table 1. Recent work by Gyourko et al (2013) suggests
that for highly attractive supply constrained “superstar” cities, such cross-metro differences can
be sustained if a growing population of high-income households are drawn to such cities with
their scarce mix of amenities.
The superstar city argument is compelling when comparing higher appreciation rates for
amenity rich cities like San Jose to less sought after locations like Milwaukee or Cleveland, as in
Figure 2. It does not, however, explain differences in appreciation rates among cities with similar
appeal (e.g. New York and Los Angeles based on quality of life estimates in Chen and
Rosenthal, 2008). A different explanation is also needed for within-city variation in appreciation
rates. This is especially apparent if central city and suburban locations are viewed as close
substitutes on the demand side of the market, consistent with growing tendencies for central city
gentrification (Couture and Handbury, 2020). It will also be true because of equilibrating forces
from the supply side as developers direct investment to higher yielding locations, creating
pressure for similar rates of within-city home price appreciation across neighborhoods (e.g. Liu
et al, 2016).
1Estimates in Figures 1a and 1b are based on all CBSAs in the United States with population over 100,000 using
monthly zip code-level home price indexes from Zillow Inc. for the period 1996-2019. Additional detail will be
provided later in the paper.
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We draw on standard finance principles to provide a simple but unified explanation for
both the macro (cross-city) and micro (within city) patterns just described. As with previous
literature in the urban area (e.g. Glaeser, Gyourko and Saiz (2008)), we argue that cross-sectional
differences in housing supply elasticities and related supply constraints contribute to differences
in market volatility across locations. To the extent that supply constraints are known to investors
and perceived as enduring, systematic differences in investor exposure to risk should then be
offset by higher rates of home price appreciation in more volatile locations. Controlling for other
factors, our empirical work provides support for this idea both across and within metropolitan
areas.
To establish these and related results, we begin by estimating a CAPM model that
measures local housing market risk relative to the broader housing market to which a community
belongs, as in Case, Cotter, and Gabriel (2011). When we examine within-CBSA patterns of
home price appreciation we adopt two different approaches to measuring local markets. In some
models we divide the CBSA into just two locations, central city and suburb, and estimate
separate betas for each treating the entire CBSA as the broader market. In other models we
estimate separate betas for each zip code in the CBSA, again treating the entire CBSA as the
broader market. When we examine cross-CBSA patterns, we estimate separate betas for each
CBSA treating the entire set of CBSAs as a broader national market to which a CBSA belongs.
Our analysis of the relationship between the CAPM betas and cross-sectional indicators
of housing supply constraints yields striking patterns at both the cross-metro and within-metro
levels of geography. For the cross-metro analysis, we proxy for CBSA level housing supply
elasticities using the Wharton Land Use Regulatory Index (WLURI) developed by Gyourko,
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Saiz and Summers (2007).2 Estimates based on the entire population of CBSAs indicate that a
one standard deviation increase in the level of supply restrictiveness is associated with a roughly
20% to 30% increase in CBSA level risk relative to the national market. Moreover, the most
supply constrained quartile CBSAs are exposed to 45% more risk while the least constrained
quartile exhibit 15% lower risk.
Parallel analysis for within-CBSA patterns requires that we specify the center of each
CBSA which, to simplify discussion, we refer to as the CBD for a given urban area. For this we
use coordinates adopted by Holian and Kahn (2012) who code the latitude and longitude of
CBDs based on coordinates provided by Google Earth. Neighborhood level housing supply
elasticities are then proxied in two different ways including distance from the CBD and density.
Both proxies are motived by the idea that pre-existing high-density development makes land
assembly and new development more difficult, lowering housing supply elasticities in central
city and high-density locations (as in Baum-Snow and Han (2019)). Results indicate that CAPM
betas decline with distance from the CBD: zip codes 10 miles distant from the center exhibit 5%
less risk. Analogous estimates are also obtained when we distinguish zip codes by employment
density, and when we segment zip codes into central city versus suburban groups.3 These
patterns confirm that within cities, higher density, central locations tend to be associated with
greater housing market risk.
The final portion of this paper estimates the extent to which spatial variation in CAPM
betas helps to explain the spatial patterns of home price appreciation rates described above, both
2 See also Gyourko, Hartley, and Krimmel (2019) for related work. 3 For these exercises, high-density zip codes were defined as those above 95th percentile zip code employment
density and low-density zip codes were defined as those below the mean zip code employment density for the
national sample of CBSA zip codes. Suburban zip codes were classified as those 4 to 8 miles from the CBD, while
city center zip codes were classified as those within one mile of the city center.
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across and within CBSAs. This portion of the analysis controls for other plausibly important
drivers of price appreciation beyond risk in ways that we elaborate on later in the paper. At both
the metropolitan and zip code level we find a positive and significant relationship between
locally estimated betas and long-run home price appreciation. At the CBSA level a 50-
percentage point increase in beta (e.g. from 1.0 to 1.5) is associated with a 0.36 percentage point
increase in average year-over-year price growth. At the neighborhood level the relationship
between asset risk and home price appreciation is of the same order of magnitude but stronger; a
50-percentage point increase in local risk relative to the market is associated with a 0.58
percentage point increase in growth. We also find that spatial variation in betas accounts for
roughly half of the variation in home price appreciation rates across and within CBSAs.
Our paper contributes to literature on risk-return tradeoffs in housing markets. Crone and
Voith (1999) and Cannon, Miller and Pandher (2006) find positive risk-return patterns in housing
markets. However, Fan, Huszar and Zhang (2012) show that the risk-return relationship is
positive only when risk is low; when risk becomes high, the relationship becomes negative. Han
(2013) finds that while the positive relationship holds for some US metropolitan areas (San
Francisco and San Jose), there is a negative relationship in others (Chicago and Cincinnati).
Relative to these and other related studies, this paper introduces two ideas not previously
emphasized. First, we rely on a simple risk-return argument that allows for a unified explanation
for why long run home price appreciation rates differ both within and across CBSAs. Second, we
show that home price appreciation rates decline as density and related local supply elasticities
increase both across and within cities. We argue that these and other patterns are consistent with
market adjustments for spatial variation in investor exposure to risk.
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We proceed as follows. Section 2 presents a set of stylized facts on long-run price
appreciation and volatility within and across metropolitan areas. Section 3 reviews the capital
asset pricing model and estimates CAPM betas within and across CBSAs. Section 4 establishes a
positive relationship between indicators of housing supply elasticity and asset risk at both levels
of geography. Section 5 examines the extent to which differences in risk contribute to long-run
differences in price appreciation. Section 6 concludes.
2. Spatial Variation in House Price Appreciation and Volatility
2.1 Data
The primary data source is the monthly Zillow Home Value Index (ZHVI) for single
family-homes. We work with both the zipcode and CBSA level versions of the ZHVI, both of
which are seasonally adjusted. For both levels of geography, the index is designed to measure
quality adjusted home price appreciation in the target area. Index values are further scaled so that
the index value for December 2019 is equal to the average home value in the target area in that
month. In this way, the ZHVI captures home price appreciation while facilitating comparison of
home price levels across locations.
More precisely, for a given target location i and period t, ZHVI is computed as follows.
First, for each individual home within i, Zillow computes the home’s value in each month (the
so-called “Zestimate”) based on a comparison to sales of comparable homes in the nearby
community although Zillow does not provide full detail on how this is done. Next, Zillow
measures home price appreciation in the target area based on a weighted average of appreciation
across all homes in the target location, 𝐴𝑖,𝑡 = ∑ 𝑤ℎ,𝑡𝑧ℎ,𝑡𝐻ℎ=1 , where wh,t is the value of home h in
period t divided by the value of all homes in the target area in that period and zh,t is the rate at
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which home h is estimated to have appreciated in the last month. As a final step, Zillow forms
𝑍𝐻𝑉𝐼𝑖,𝑇 =1
𝐻∑ 𝑍𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒ℎ,𝑇
𝐻ℎ=1 , where ZHVIi,T is the average home value in the target
community in the final period of the sample horizon (December, 2019 in our case). Working
backwards from that end point, the ZHVI index for each period prior to T in target location i is
constructed as follows,
𝑍𝐻𝑉𝐼𝑖,𝑡−1 = 𝑍𝐻𝑉𝐼𝑖,𝑡
1+𝐴𝑡, for 𝑡 = 0, … , 𝑇 − 1 (1)
Using this measure, in all of the analysis to follow, house price appreciation in location i is
calculated based on the growth of ZHVIi between periods.
ZHVI is the only publicly available index we are aware of that has extensive coverage at
the zip code level. The index includes all single-family residences outside of condominiums and
co-ops, and in that sense includes both single family attached and single family detached homes.
We use the monthly index from April 1996 to December 2019 at both the zip code and CBSA
level. Throughout the paper, index values are always measured in nominal terms without
adjusting for macro or local general rates of inflation. In adopting this approach, we are
implicitly assuming that month-to-month changes in local cost of living are driven primarily by
home price appreciation and not non-housing goods and services.4
4 Additional details on the Zillow methodology is provided by Zillow at: Zillow Home Value Index Methodology,
2019 Revision: Getting Under the Hood - Zillow Research . The ZHVI is designed to measure the change in
aggregate home values within a given location, holding constant the stock of homes between adjacent periods. Noise
embedded in the ZHVI estimates for individual homes that underlie the index for a given location appear likely to
average away. Also, addition of new possibly more highly valued homes to the local stock of housing is
incorporated into time varying measures of a location’s price appreciation index in a manner that is unlikely to
introduce biases into our estimates. There are two reasons for this. Looking back in time, homes constructed in
period t are not used to measure appreciation in prior to period t, helping to ensure that a common stock of homes is
used to measure price appreciation. Looking forward in time, Liu et al (2016) argue that active new construction in a
given market helps to ensure similar rates of home price appreciation across homes of different size and quality
because of equilibrating effects on the supply side. Both features help to ensure that construction of new homes will
have little effect on the rate at which Zillow’s ZHVI index appreciates in a given location. Any remaining concerns
that might arise from changes in the composition of homes in a given geographic area are further mitigated by our
focus on monthly changes in ZHVI index values since the stock of homes changes little on a month to month basis.
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At the time our data was downloaded the core-based statistical area (CBSA) definition
used by Zillow was the September 2018 US Census definition of CBSAs in the United States.
We use this same definition when constructing CBSA population counts for 1990, 2000, and
2010, ensuring that these measures correspond to the geography used to measure home price
appreciation. We limit our sample to the 364 CBSAs with population greater than a hundred
thousand in 2000.
2.2 Stylized Facts
Here we present three sets of stylized facts about single-family home prices that hold
across and within CBSAs. First, there is significant spatial variation in home price appreciation.
Second, home prices tend to appreciate more quickly in supply constrained locations. Finally,
homes price volatility is higher in supply constrained locations. We describe these patterns at
both the CBSA and within CBSA levels of geography.
2.2.1 Across CBSAs
The urban literature is well aware that long-run home price appreciation rates differ
across CBSAs (Glaeser, Gyourko & Saiz, 2008; Gyourko & Saiz, 2008). Here we reconfirm that
pattern and place it in context within our framework. Table 1 shows the average year-over-year
SF ZHVI growth rates over the 1996-2019 period for the top and bottom fastest growing CBSAs
with population greater than 500,000. Growth rates range from 1.27% in Youngstown, OH to
7.23% in San Jose, CA. There is also considerable variation in growth rates even among CBSAs
with high rates of price appreciation. Washington, DC has average year-over-year growth of
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4.36% while San Francisco, CA experiences price growth almost 3 percentage points higher at
7.22%.
The superstar city framework attributes differences in home price appreciation rates
between metropolitan areas to growing demand for select “superstar” cities that are in scarce
supply. These are cities that exhibit unusual high quality amenities not found elsewhere and
which also often have very inelastic local housing supply. Growing aggregate numbers of high-
income households increase demand for such locations over time pushing home prices higher.
While this may explain differences in growth rates between Cleveland and San Jose, it does not
explain differences in appreciation rates between similarly attractive, metropolitan areas. For
example, non-super star cities like Indianapolis and Minneapolis have average year-over-year
growth rates over the 1996-2019 period of 2.05 and 4.11 respectively.5
The next stylized fact is that price appreciation tends to be higher in more supply
constrained locations. At the CBSA level, supply restrictions are proxied using the Wharton
Land Use Regulation Index (WLURI) (Gyourko, Saiz, and Summers, 2008; Gyourko, Hartley,
and Krimmel; 2019). This index is based on the local regulatory environment including caps on
permitting and construction, density restrictions such as minimum lot size restrictions, affordable
housing requirements, and the number of re-zoning permits required. We match the index to 298
of the 364 CBSAs in our sample. Panel A of Table 2 shows the results from regressing average
CBSA year-over-year SF ZHVI growth on the WLURI. The coefficient on WRLURI is positive
and significant; long-run house price appreciation increases with the level of housing
restrictiveness. We repeat this exercise with the Siaz (2008) housing supply elasticities and find a
5 Amenity comparisons are based on the Chen and Rosenthal (2008) Quality of Life Index. Then mean Index value
for our sample is 231 with standard deviation 1880. The Index values for Indianapolis and Minneapolis are -1839
and -2054.
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negative relationship: CBSAs with more inelastic housing supply experience greater price
appreciation. Only 82 of the CBSAs within our sample can be matched to the Saiz measures,
however, and for this reason, we use the WRLURI as an indicator of CBSA level supply
elasticity in most of the analysis to follow.
Finally, not only do prices appreciate more quickly in supply constrained locations, they
are also more volatile. We measure local price volatility as the variance in the single family
ZHVI over our sample period. Regressing that measure on the WLURI we find that supply
constraints increase price volatility (Panel B of Table 2). Repeating the exercise using the Saiz
proxy for supply restrictiveness confirms this pattern.
2.2.2 Within CBSAs
A further stylized fact documented here is the positive relationship between supply
constraints and price appreciation within CBSAs.6 As noted earlier, we use two proxies for
within-CBSA supply constraints, distance to the CBD, whose coordinates are provided by Holian
and Kahn (2015), and zip code log employment density.
Panel A of Figure 1 plots the estimates from a nonparametric regression of zip code level
single-family ZHVI year-over-year percent growth on miles to the CBD. Observations are
restricted to within 30 miles of the CBD to reduce the tendency to encounter important
population subcenters and other cities situated within the CBSA. Observe that there is a roughly
monotonic negative relationship between distance to the CBD and percentage growth of ZHVI
with growth rates at the center roughly 3.9% versus 3.4% ten miles from the city center. Growth
6 Gleaser (2012) observe that city centers tend to experience more frequent housing bubbles than their suburb
counter parts. However, to our knowledge, we are the first to observe higher price appreciation in city centers/ high
density locations over a significant time horizon.
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rates stabilize thereafter, falling only slightly further to 3.3% by 20 miles distance from the CBD.
An analogous pattern holds for log employment density as well (Figure 1, Panel B). Price growth
is close to 3% when employment is largely absent (1 worker per square mile, or zero log
employment) but increases to over 5% percent for log density of 9, roughly 8,000 workers per
square mile.
Table 3 confirms that the patterns in Figure 1 persist event after controlling for other
factors. Column 1 adds no other controls and is analogous to the non-parametric plots in Figure
1. Column 2 includes CBSA fixed effects, and column 3 includes both CBSA and month fixed
effects. The coefficient on distance to the CBD is significant and similar in magnitude across all
three columns: moving ten miles away from the city center decreases price appreciation by
0.19% per year (Panel A). This is similar to the relationship plotted in Panel A of Figure 1. The
coefficient on log employment density is also significant and positive in all three specifications
but declines somewhat in magnitude with the addition of CBSA and month fixed effects (Panel
B).
We allow for further heterogeneity by estimating the distance and log employment
density models separately for each CBSA. This also addresses the possibility that the patterns in
Table 3 (and Figure 1) could be driven by a small number of large CBSAs with many zipcodes.
Because of the large number of CBSAs, Table 4 presents summary measures of the distribution
of estimates across urban areas.
For the distance model, notice that for 236 of the 352 CBSAs price growth varies
significantly with distance from the CBD. Of those, 58% are negative and 48% display a positive
growth-distance relationship. On the surface, this one measure casts doubt on whether there is a
systematic tendency for home price growth to decline with distance from city centers. Grouping
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CBSAs by population bins, however, reveals a more compelling pattern. For CBSAs with year-
2000 population between 100,000 and 500,000, home price growth does not appear to vary with
distance to the CBD. For CBSAs with population between 500,000 and 1 million, 57% of the
coefficients are negative. Between 1 million and 2.5 million, 86% of the coefficients are
negative, and for CBSAs with population over 2.5 million, all exhibit a negative price growth-
distance relationship. Similar patterns are also evident in Panel B of Table 4 for the log
employment density model.
The flat pattern between distance to the CBD and home price appreciation in small
CBSAs is suggestive of elastic housing supply and similarly stable rates of home price
appreciation throughout such areas. Conversely, the strong negative relationship between home
price appreciation and distance in large CBSAs suggests the presence of within-CBSA
heterogeneity. In these urban areas, it is possible that central city housing supply constraints may
amplify price volatility and investor exposure to risk, triggering risk-return tradeoffs, while more
outlying areas may exhibit more elastic supply, less price risk, and lesser appreciation for that
reason.
Table 5 reinforces this line of thinking. Estimates are presented of zip code level
regressions of the variance in ZHVI over the sample period on miles to the CBD (Panel A) and
log employment density (Panel B). The coefficient on miles to the CBD is negative and
significant, confirming that zip codes closer to the city center experience greater volatility in the
price index. These estimates are robust with and without controls for CBSA and month fixed
effects. Similar estimates are obtained for the density model as well, although here the
relationship is of smaller magnitude upon controlling for CBSA fixed effects.
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3. CAPM Betas
This section briefly reviews the theory behind the capital asset pricing model (CAPM)
and then estimates and presents summary measures of the betas for different locations as
described earlier in the paper. As emphasized earlier, beta is our primary measure of investor
exposure to risk.
3.1 Theory
Under the CAPM assumptions (Fama and French, 2004; Bodie, Kane, and Mohanty,
2009) all investments should offer the same reward-to-risk ratio in equilibrium:
𝐸(𝑟𝑖)−𝑟𝑓
𝐶𝑜𝑣(𝑟𝑖,𝑟𝑀)=
𝐸(𝑟𝑀)−𝑟𝑓
𝜎𝑀2 (2)
where 𝐸(𝑟𝑖) − 𝑟𝑓 is the expected return of asset i in excess of the risk-free asset return, 𝑟𝑓 , and
𝜎𝑀2 is the variance of the market portfolio – the measure of market risk. The standard CAPM
equation is obtained by rearranging the equilibrium condition:
𝐸(𝑟𝑖) − 𝑟𝑓 = 𝛽 ∗ [𝐸(𝑟𝑀) − 𝑟𝑓] (3)
Equation (3) states that the excess return or risk premium for asset i is the product of the
risk premium for the market and beta, where 𝛽 =𝐶𝑜𝑣(𝑟𝑖,𝑟𝑀)
𝜎𝑀2 measures the extent to which the
return on the asset and the return on the market move together. A beta equal to 1 indicates that
the respective returns for asset i and the market move together, and for that reason, asset i is risk
neutral relative to the market portfolio. A beta greater than 1 signals that asset i exposes investors
to greater risk relative to the market portfolio, where beta equal to 1.2, for example, indicates that
the asset’s return is 20% more volatile than that of the market.
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It is important to recognize that beta captures how the asset’s returns fluctuate in response
to systematic risk that cannot be diversified away. This includes broad market shocks as with
changes in interest rates, demand and other macroeconomic conditions, the effect of which
differs across housing markets with the local supply elasticity. Beta does not reflect idiosyncratic
risk that is specific to investment in a local housing market, as with discovery of contaminated
soil from past but forgotten development, or some other unanticipated catastrophic event.
The market in CAPM applications typically refers to a portfolio of all possible
investments. For that reason, CAPM applications often use a composite index to represent the
market, as with the S&P 500, which is based on many different financial assets. In this context,
previous work has found that the correlation between real estate returns and broad financial
market indexes is close to zero (e.g. Geltner, 1989). One reason for this may be that much of the
variation in homes prices is local, while variation in stock prices is not (Goetzmann, 1993). For
these reasons, Case, Cotter, and Gabriel (2009) develop what they refer to as a Housing-Capital
Asset Pricing Model or H-CAPM in which local housing market risk is compared to returns from
a broader real estate market but not to returns from a portfolio of financial assets. Specified in
this fashion, the H-CAPM measures beta for a local housing market relative to volatility of real
estate returns for the broader real estate market to which the local area belongs. We adopt the
same approach in this paper.
3.2 Estimating CAPM betas across and within CBSAs
In this section we apply the CAPM framework outlined above to estimate betas for
individual CBSAs and zip codes. The estimating equation is specified in equation 4 and is
standard in the CAPM literature.
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𝑅𝑖,𝑡 = 𝛽𝑅𝑀,𝑡 + 휀𝑖,𝑡 (4)
When we estimate (4) at the CBSA level, there is one beta for each CBSA. The market here is
defined to be the national single family real estate market and market value is measured as the
average of CBSA level home values for CBSAs within our sample. When we estimate (4) at the
zip code level, there is one beta for each zip code in our sample and the CBSA to which a zip
code belongs is specified as the relevant market.
Figure 4 plots the beta distributions for both levels of geography. The mean beta across
CBSAs is 0.963 with a standard deviation 0.781. The distribution is also centered close to one
indicating that the modal CBSA return follows the market quite closely. The distribution also
displays an elongated right tail, with several CBSAs exposing housing market investors to
considerably more systematic risk relative to the national market. Table 6 lists the CBSAs with
the highest and lowest CAPM betas. CBSAs with especially low betas are often in smaller, less
sought after metropolitan areas that are not growing rapidly, an example of which is Syracuse,
NY. CBSAs with especially high betas mostly include high-amenity locations that have been
growing sharply in recent years, as with Phoenix, San Francisco, and Tampa.
In Figure 4, we also plot the distribution of betas for 17,837 zip codes. These are drawn
from all CBSAs in our sample with population greater than 100,000 in year 2000. Once again the
mean beta is close to one, equalling 0.990 in this instance. The standard deviation of the betas is
0.491. The distribution of zip code level betas are more tightly centered around 1 than the CBSA
levels betas. However, the zip code level beta distribution also has long, thin tails reflecting that
there are a handful of zip code level betas with extreme values.
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4. Supply elasticities, volatility and spatial variation in risk premia
This section examines the relationship between the betas described above and differences
in home price volatility and housing supply restrictions across locations. As before, we first
consider differences across CBSAs and then focus on variation at the zipcode level within a
given urban area.
4.1 Variation across CBSAs
We begin by considering the relationship between a CBSAs local housing market risk
premium and the volatility of its price index. Treating each CBSA as a separate observation,
Panel A of Table 7 reports regressions of the CBSA beta on the log variance of its house price
index over the sample period.7 As anticipated, there is a positive and significant relationship
between volatility and asset risk: a one percent increase in variance is associated with a 0.32
increase in beta. This confirms that at the CBSA level, increased volatility contributes to greater
market allowance for risk.
Next, we regress βi on a proxy for local housing supply restrictions and other CBSA level
attributes that capture potential for demand shocks. The regression equation is specified as:
𝛽𝑖 = 𝛼 + 𝜇 𝑊𝐿𝑈𝑅𝐼𝑖 + 𝛿𝑋𝑖 + 휀𝑖 , 𝑖 = 1, … , 𝑛 (5)
where n is the number of CBSAs.
The term WLURI in expression (4) denotes the Wharton Land Use Regulatory Index and
is used to proxy for local housing supply restrictions. The index has mean zero with standard
7 The variance of price levels is not mechanically related to beta. Beta is equal to the covariance between the growth
rate of the asset and market normalized by the variance in the market growth rate. Both the asset and market growth
rates are measured in excess of the risk free asset.
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deviation one. It is also designed so that urban areas in the lowest quartile of the index are the
least supply constrained while those in the top quartile are the most supply constrained.
The term X in expression (5) includes proxies for potential demand shocks. This includes
log population in 2000, log median income in 2000, and the Chen and Rosenthal (2008) Quality
of Life Index that measures the amount of real wage workers forgo to live in the CBSA. As such,
the index is an indicator of the amenity appeal of the urban area, as in Rosen-Roback.8 Two
additional controls capture whether the urban area grew or lost population between 1990 and
2010, Growing and Shrinking. These are measured as the absolute value of the percent increase
(if growing) or decrease (if shrinking) in CBSA population between 1990 and 2010.
Table 9 presents estimates of equation (5).9 In column 1 beta is regressed just on the
Wharton Land Use Regulatory Index. The coefficient on WLURI is 0.26. This indicates that a
one standard deviation increase in the index corresponds to a 26% increase in local housing
market risk relative to the national market. In Columns 2 through 4 we progressively add in
additional controls for log population and median income, Growing and Shrinking, and the
Quality of Life Index. The coefficient on WLURI remains positive and significant in all
specifications except the last. With the addition of the quality of life index the coefficient on
WLURI loses significance but remains positive.
Table 10 provides further evidence that supply restrictions are associated with higher
values for beta. We group CBSAs into four clusters for the 1st through 4th quartile of the WLURI,
or from the least to the most restricted housing supply. The CAPM model is then estimated
8 The index measures nominal wage adjusted for the local cost of living and is scaled to reflect how many thousand
dollars (in year 2000$) a worker gives up to locate in a given urban area relative to an “average” urban area. The
QOL index from Chen and Rosenthal was based on metropolitan statistical areas (MSAs). We were able to match
that geography to the CBSA data in this study for 261 CBSAs. Matches were formed using the name of the primary
city for each defined area, MSA and CBSA. 9 Table 8 presents summary measures of the variables in expression (4).
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separately for each group of CBSAs, constraining the beta and the constant term to be alike
across CBSAs within a given group. The market is the national real estate market as before when
we estimated individual CAPM models for each CBSA.
In Table 10, there is a monotonic relationship between level of supply restrictiveness and
beta: moving from left to right in the table, more heavily regulated, supply constrained CBSAs
expose investors to a greater level of systematic risk. The magnitude of the pattern is also
noteworthy. The least restricted quartile experiences return volatility approximately 25% less
than the national market, while the most restricted quartile experiences volatility 45% more than
the national market, a 70 percentage point difference.
Summarizing, at the CBSA level, local housing market risk premia increase with the
volatility of local house prices, confirming that volatility exposes housing market investors to
increased risk. Evidence above also confirms that risk premia increase with housing supply
restrictions and demand shocks that drive volatility in local markets.
4.2 Variation within CBSAs
As in the previous section, we first examine the relationship between asset risk and
supply restrictiveness within CBSAs by pooling observations across all zip codes. We also
compare betas estimated for city centers and suburbs as well as high- and low-density areas. In
all exercises we find that locations with greater supply restrictiveness are associated with higher
asset risk. Finally, we look at the relationship between zip code level price volatility and asset
risk finding a positive and significant relationship. However, the magnitude of this relationship is
smaller than it is at the CBSA level.
18
Figure 5A shows the results of a local constant regression of zip code level betas on
distance to the CBD. There is a distinct negative relationship between distance and risk. Zip
codes at the CBD experience 15% more systematic risk than those ten miles out. Running the
analogous regression with log employment density on the right-hand side we observe a strong
positive relationship between employment density and beta (Figure 5B). As log employment
density increases betas increases, rising sharply from 0.95 at natural log 4 (around 60 workers
per square mile) to 1.1 at natural log 8 (around 3000 workers per square mile) where the
relationship flattens.
Running the linear versions of these regressions with CBSA fixed effects confirms that
the patterns are not driven by differences across CBSAs (Table 11). Additionally, coefficients
from the linear specifications are of the same order of magnitude as the results from the
nonparametric model. Moving ten miles from the city center decreases beta by 0.058 (columns 1
and 2 of Table 11). A one percent increase in employment density increases beta by 0.013
(columns 3 and 4). The specifications in columns 5 and 6 include both distance to the CBD and
log employment density. The coefficient on distance to the city center remains significant and
consistent in terms of sign and magnitude to the previous results. However, the coefficient on
log employment density decreases from 0.013 to 0.0038, although it remains significant. This
likely reflects the high correlation between distance to the CBD and employment density.
Next, we stratify zip codes by two indicators of supply elasticity and compare the betas
estimated from pooling observations within stratifications. We classify zip codes into city centers
and suburbs as well as into high- and low-density locations. City centers are defined to be within
1 mile of a CBD while suburbs are defined to be 4-8 miles from a CBD. We are able to define
city centers and suburbs for 134 CBSAs. In part, this number is limited because we only work
19
with CBSAs for which Holian and Kahn (2015) specify the coordinates associated with the
center of the CBD. We also define high-density zip codes as those with employment density of at
least 3,500 workers per square mile (about the 95th percentile density for our sample) and low-
density zip codes as those with less than 1,400 workers per square mile (about the mean density
of our sample). Due to the specified cutoff for employment density, not all CBSAs have a high-
density location. In this instance, we are able to identify both high- and low-density locations in
243 CBSAs.
Table 12 reports the mean beta for each grouping noted above (central city versus suburb
and high versus low density). For both comparisons, average beta is roughly 7% higher in the
more supply constrained areas (central city and high density). Also of note, city center betas are
larger than their suburban counterparts in 61.7% of CBSAs, while high density betas are larger
than their low density counterparts in 63.9% of CBSAs.
Figure 6 provides a more complete picture by plotting the distribution of cross-CBSA
betas for each of the groupings above. A striking pattern is that supply elastic locations – suburbs
and low density – have very tight beta distributions centered close to one. In contrast, the
distribution of betas for supply constrained areas is right shifted and exhibits much greater
dispersion. As a general characterization, while relative risk exposure is elevated on average in
supply constrained areas within CBSAs, the extent to which this occurs differs considerably
across urban areas.
Finally, we examine the relationship between price volatility and asset risk. As in the
previous section price volatility is measured as log variance in home prices. Regressing zip code
level betas on price volatility we find that a one percent increase in volatility is associated with a
0.054 increase in beta (Table 7, panel B). While the magnitude of this coefficient is smaller than
20
the CBSA level regression, it is still highly significant. Running this regression CBSA-by-
CBSA, 75% of significant coefficients are positive.
5. Home price appreciation and CAPM betas
We now return to the central question of the paper – to what extent is spatial variation in
home price appreciation over our sample period (1996-2019) driven by differences in risk across
locations? As above, we consider this question both across and within CBSAs.
5.1 Across CBSAs
This section examines the degree to which CBSA-level measures of beta help to explain
cross-CBSA differences in the rate at which home prices appreciate. We begin by measuring
year-over-year home price appreciation for each CBSA using monthly frequency data. For each
CBSA, year-over-year appreciation is then averaged over the entire sample horizon, 1996-2019,
and scaled by 100. Our analysis is then based on a cross section with one observation from each
location. Across CBSAs, year-over-year home price appreciation averages 3.1 percent.
Table 13 presents a series of regressions for which the dependent variable is the CBSA
average annual rate of appreciation as just described. Column 1 controls for the beta associated
with that CBSA. Column 2 adds in controls for year 2000 CBSA population and median income.
Column 3 adds additional controls for whether the CBSA is growing or shrinking (Growing,
Shrinking). Column 4 adds in a dummy measure for whether Gyourko et al (2013) code the
CBSA as a superstar city. Column 5 adds a final control, the quality of life index for the urban
area as measured by Chen and Rosenthal (2008).
21
The dominant and most notable result in Table 13 is that the coefficient on beta is always
positive, quite significant, and very robust to inclusion of other controls in the model. In the most
robust specification in column 5, the coefficient on beta is roughly 0.7 which suggests that a 0.1
increase in beta is associated with a 0.07 percentage point increase in a CBSAs average annual
rate of home price appreciation over the sample horizon.
5.2 Within CBSAs
Tables 14 and 15 mirror the analysis above but in this instance we focus on within CBSA
patterns. In both tables, our dependent variable is the same as above but measured at the zipcode
level. Table 14 controls for distance to the center of the CBD in addition to the zipcode level
beta. Table 15 controls for log employment density at the zipcode level instead of distance. In
both tables, Panel A reports estimates having pooled CBSAs together and including CBSA fixed
effects. Panels B-G report analogous estimates for groupings of CBSAs by size of urban
population and again controlling always for CBSA fixed effects10.
Several core patterns are evident in these tables. First, the qualitative patterns are largely
identical for the two tables regardless of whether we proxy for housing supply restrictions using
distance to the CBD or local employment density. Second, beta is, with one exception, a positive
and significant predictor of local house price appreciation regardless of the size of the urban area.
The only case in which this does not hold is for CBSAs with population 250,000 to 500,000 for
which the associated estimates are not very precise.
10 We also ran each of these with a partial linear specification, controlling for beta parametrically and allowing the
relationship between average growth and distance to the center of the CBD (log employment density) to vary
nonparametrically. In all cases the nonparametric relationship was roughly linear and thus we have only included the
linear results.
22
Focusing on the spatial patterns, among CBSAs up to 500,000 residents we see little
evidence of within-CBSA variation in home price appreciation both based on distance to the
CBD and local employment density. This is the case regardless of whether beta is included in the
models or omitted. A different pattern is evident among larger CBSAs. For CBSAs with
population over 500,000, omitting beta (column 1), home prices appreciate faster in zipcodes
closer to the CBD and in denser locations. Adding controls for beta (as in column 3), the
coefficient on distance to the CBD (in Table 13) and density (in Table 15) is notably reduced in
magnitude while the coefficient on beta remains highly significant. This pattern indicates that
controlling for risk-return tradeoffs – as summarized by beta – appears to explain an important
portion of systematic spatial variation in home price appreciation observed within cities.
6 Conclusion
This paper presents a new stylized fact and offers an explanation that links to other
previously identified patterns in the literature. We show that housing appreciates faster in central
city markets than in suburban markets and especially so in large cities. Previous literature has
documented unusually high long run rates of home price appreciation in select superstar cities as
characterized by Gyourko et al (2013). We also document persistent differences in home price
appreciation rates across cities.
Our analysis relies on Zillow data which we draw upon both at CBSA and zip code levels
of geography. Using these data, we show that within- and cross-CBSA spatial variation in the
volatility of home prices in a given location increases with indicators of supply restrictions,
consistent with the view that housing supply constraints increase investor exposure to risk.
Building on that pattern, we also demonstrate that home price appreciation rates also increase
with supply constraints and that elevated rates of home price appreciation are partly explained by
23
the local market’s CAPM beta that measures systematic risk relative to the broader geographic
market to which the area belongs.
Our findings support the idea that risk-return tradeoffs help to explain both cross-CBSA
and within-CBSA variation in home price appreciation rates, and that these results are robust to
controls for other possible mechanisms. Differences in home price appreciation rates, even
within a given city, therefore, do not necessarily present opportunities for arbitrage.
24
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26
Tables and Figures
Figure 1
Panel A: Distance to the CBD on percent year-over-year ZHVI growth
Observations are limited to zip codes within 30 miles of a CBD. Estimates are based on a local polynomial
regression of degree 0 using the epanechnikov kernel and bandwidth of 1.11 as determined by the Rule of Thumb
bandwidth selection process.
Panel B: Log employment density on percent year-over-year ZHVI growth
Observations are limited to zip code with log employment density above 0 and are truncated at the top 1% in terms
of employment density. Estimates are based on a kernel regression of degree 0 using the epanechnikov kernel and
bandwidth of 0.27 as determined by Rule of Thumb bandwidth selection process.
27
Figure 2: Normalized single-family home value index growth for CBSAs at the top, middle, and bottom of the
growth distribution
ZHVI is normalized such that April 1996 equals 100.
28
Figure 4: Distribution of CAPM Betas at the CBSA and Zip code Levels
Estimates are based on a kernel density using the epanechnikov kernel and bandwidth determined by the Silverman
(1986) optimal bandwidth. For visual clarity the zip code level distribution is truncated at -6 and 6, this excludes 13
zip codes, less than one percent of the sample.
29
Figure 5: Local Constant Regression of Zip Code Betas on
Within-CBSA Indicators of Supply Elasticity
Panel A: Relationship between Beta and Distance to the CBD
Observations are limited to zip codes within 30 miles of a CBD. Estimates are based on a local polynomial
regression of degree 0 using the epanechnikov kernel and the Rule of Thumb bandwidth (2.7).
Panel B: Relationship between Beta and Log Employment Density
Observations exclude the top 1% in terms of employment density and zip codes with log employment density less
than 0. Estimates are based on a local polynomial regression of degree 0 using the epanechnikov kernel and the
Rule of Thumb bandwidth (0.7).
30
Figure 6: Distribution of within-CBSA stratified betas
Panel A: Distributions of city centers and suburbs betas
Estimates are based on a kernel density using the epanechnikov kernel and bandwidth of determined by the
Silverman (1986) optimal bandwidth. For visual clarity, the St. Louis city center beta has been omitted. It’s value is
-7.69.
Panel B: Distribution of high-density and low-density betas
Estimates are based on a kernel density using the epanechnikov kernel and bandwidth of determined by the
Silverman (1986) optimal bandwidth: 0.0692 for the high-density betas and 0.0056 for the low-density betas.
31
Table 1: Single-family home index growth for
bottom and top 20 CBSAs: 1996-2019
Bottom 20 Top 20
Average one-
year growth
Population in
2000
Average
one-year
growth Population in 2000
Youngstown, OH 1.27 602,964 Washington, DC 4.30 4,849,948
Dayton, OH 1.43 805,816 New York, NY 4.36 18,323,002
Cleveland, OH 1.53 2,148,143 North Port, FL 4.43 589,959
Memphis, TN 1.75 1,205,204 Orlando, FL 4.45 1,644,561
Akron, OH 1.84 694,960 Phoenix, AZ 4.57 3,251,876
Jackson, MS 1.93 546,955 Tampa, FL 4.66 2,395,997
Birmingham, AL 1.94 981,525 Portland, OR 4.71 1,927,881
Scranton, PA 1.95 560,625 Boston, MA 4.77 4,391,344
Toledo, OH 1.96 659,188 Honolulu, HI 4.79 876,156
Chicago, IL 1.98 9,098,316 Fresno, CA 4.84 799,407
Greensboro, NC 1.99 643,430 Denver, CO 4.94 2,157,756
El Paso, TX 2.00 682,966 Miami, FL 5.17 5,007,564
Indianapolis, IN 2.05 1,658,462 Seattle, WA 5.35 3,043,878
Columbia, SC 2.08 647,158 Sacramento, CA 5.48 1,796,857
Rochester, NY 2.20 1,062,452 San Diego, CA 5.88 2,813,833
Albuquerque, NM 2.23 729,649 Riverside, CA 6.17 3,254,821
Wichita, KS 2.23 571,166 Los Angeles, CA 6.33 12,365,627
Cincinnati, OH 2.29 2,016,981 Stockton, CA 6.57 563,598
Winston, NC 2.29 569,207 San Francisco, CA 7.22 4,123,740
Baton Rouge, LA 2.38 729,361 San Jose, CA 7.23 1,735,819
CBSAs in this this table are limited to those with population greater than 500,000 in 2000. The name of each CBSA is
limited to its primary city.
32
Table 2: CBSA level ZHVI growth and variance regressed on indicators of housing supply elasticity
Panel A: Average of one-year SF ZHVI growth
(1) (2)
WLURI 0.535*** -
(0.104) -
Siaz supply elasticities - -0.646***
- (0.138)
Constant 3.198*** 4.698***
Observations
298 82
𝑅2 0.079 0.204
Panel B: variance of SF ZHVI
(1) (2)
WLURI 2.92e09*** -
(5.05E08) -
Siaz supply elasticities - -3.89e09***
- (1.19E09)
Constant 2.49e09*** 1.17e10***
Observations 298 82
𝑅2
0.098 0.106
* p<0.1, ** p<0.05, *** p<0.01
Standard errors are in parenthesis.
33
Table 3: Zip Code Level ZHVI Growth Pooling Across CBSAs
Panel A: Miles to the city center
One Year Growth Rate Five Year Growth Rate
(1) (2) (3) (4) (5) (6)
Miles to CBD -0.0183*** -0.0259*** -0.019*** -0.110*** -0.168*** -0.132***
(.000546) (.000558) (.000429) (.00258) (.002548) (.00176)
Fixed Effects
CBSA - 352 352 - 352 352
Month - - 237 - - 237
Observations 2,949,703 2,949,703 2,949,703 2,358,634 2,358,634 2,358,634
𝑅2 0.0004 0.0321 0.4270 0.0008 0.0956 0.5682
Observations are restricted to zip codes within 30 miles of a CBD.
Panel B: Log employment density
One Year Growth Rate Five Year Growth Rate
(1) (2) (3) (4) (5) (6)
Log employment density 0.185*** 0.0811*** 0.0415*** 1.441*** 0.604*** 0.352***
(.00142) (.00170) (.00130) (.00685) (.00793) (.00541)
Fixed Effects
CBSA - 352 352 - 352 352
Month - - 237 - - 237
Observations 3,953,325 3,953,325 3,953,325 3,151,022 3,151,022 3,151,022
𝑅2 0.0043 0.0327 0.435 0.0139 0.0977 0.581
Observations are restricted to zip codes with employment density greater than 0.
* p<0.1, ** p<0.05, *** p<0.01
Standard errors are in parenthesis.
34
Table 4: Zip code level regressions of ZHVI on within-CBSA indicators of supply elasticity by CBSA
Panel A: Miles to the CBD
Population
groups
Total
Significant
Coefficients
Negative
Coefficients
Percent
Negative
Coefficients
75th
Percentile
Coefficient
50th
Percentile
Coefficient
25th
Percentile
Coefficient
100K – 250K 85 44 52 0.051 -0.022 -0.064
250K – 500K 55 24 44 0.058 0.024 -0.042
500K – 1M 35 20 57 -0.023 -0.019 -0.046
1M-2.5M 28 24 86 -0.018 -0.033 -0.046
Over 2.5 M 17 17 100 -0.049 -0.065 -0.084
Total 236 137 58 0.044 -0.026 -0.054
Counts and percentiles are based on significant coefficients only.
Panel B: Log employment density
Population
groups
Total
Significant
Coefficients
Positive
Coefficients
Percent
Significant
Positive
25th
Percentile
Coefficient
50th
Percentile
Coefficient
75th
Percentile
Coefficient
100K – 250K 90 44 49 -0.165 -0.051 0.178
250K – 500K 48 22 46 -0.260 -0.070 0.148
500K – 1M 35 19 54 -0.101 0.090 0.180
1M-2.5M 24 20 83 0.050 0.109 0.180
Over 2.5 M 15 15 100 0.144 0.256 0.401
Total 229 125 55 -0.147 0.072 0.178
Counts and percentiles are based on significant coefficients only.
35
Table 5: Regressions of home price index variance on supply elasticity indicators
Panel A: Distance to the CBD
(1) (2) (3)
Miles to the city center -3.02E08*** -2.99E08*** -2.99E08***
(2.72E06) (2.54E06) (2.54E06)
Fixed Effects
CBSA - 352 352
month - - 237
Observations 3,519,180 3,519,180 3,519,180
𝑅2 0.004 0.189 0.189
Observations are restricted to zip codes within 30 miles of a CBD.
Panel B: Log employment density
(1) (2) (3)
Log employment density 3.09E09*** 1.37E09*** 1.37E09***
(7.92E06) (8.77E06) (8.77E06)
Fixed Effects
CBSA - 352 352
month - - 237
Observations 4,523,805 4,523,805 4,523,805
𝑅2 0.033 0.172 0.172
* p<0.1, ** p<0.5, *** p<0.01
Observations are restricted to zip codes with employment density greater than 1.
36
Table 6: CBSAs with the highest and lowest betas
Bottom 20 Top 20
Beta Population Beta Population
Wichita, KS 0.221 571,166 Seattle, WA 1.649 3,043,878
Tulsa, OK 0.282 859,532 Providence, RI 1.687 1,582,997
Oklahoma City, OK 0.331 1,095,421 Detroit, MI 1.816 4,452,557
Baton Rouge, LA 0.332 729,361 Jacksonville, FL 1.862 1,122,750
Pittsburgh, PA* 0.375 2,431,087 Washington, DC 1.881 4,849,948
McAllen, TX 0.388 569,463 Tucson, AZ 1.991 843,746
Little Rock, AR 0.393 610,518 San Francisco, CA 1.996 4,123,740
Winston, NC 0.397 569,207 San Diego, CA 2.134 2,813,833
Greenville, SC 0.430 725,680 Los Angeles, CA 2.392 12,365,627
El Paso, TX 0.430 682,966 Tampa, FL 2.511 2,395,997
Columbia, SC 0.430 647,158 Phoenix, AZ 2.619 3,251,876
Rochester, NY 0.434 1,062,452 North Port, FL 2.648 589,959
Buffalo, NY* 0.444 1,170,111 Orlando, FL 2.696 1,644,561
Greensboro, NC 0.454 643,430 Miami, FL 2.821 5,007,564
Oxford, NC 0.455 753,197 Sacramento, CA 2.858 1,796,857
Syracuse, NY 0.474 650,154 Bakersfield, CA 3.057 661,645
Harrisburg, PA 0.475 509,074 Fresno, CA 3.091 799,407
Louisville, KY 0.487 1,090,024 Riverside, CA 3.115 3,254,821
Jackson, MS 0.492 546,955 Las Vegas, NV 3.249 1,375,765
Scranton, PA* 0.497 560,625 Stockton, CA 3.282 563,598
CBSAs shown here are limited to those with population greater than 500 thousand in 2000. Stars indicate CBSAs
with population loss between 1990 and 2010. The North Port, FL CBSA contains Sarasota.
37
Table 7: Regression of CAPM-Betas on local house price volatility
Panel A: CBSA level beta observations
(1) (2)
Log variance in location i house prices 0.324*** -
(.0199) -
Variance of location i house prices - 4.01E-11***
- (6.01E-12)
Constant -5.567*** 0.880***
(0.403) (0.0428)
Observations 362 362
𝑅2 0.424 0.111
Panel B: Zip Code level beta observations
(1) (2)
Log variance in location i house prices 0.0539*** -
(.00316) -
Variance of location i house prices - -1.48E-13
- (1.02E-13)
CBSA Fixed Effects 364 364
Observations 17,837 17,837
𝑅2 0.0262 0.0101
* p<0.1, ** p<0.05, *** p<0.01
38
Table 8: Summary Statistics for CBSA Characteristics
N. Obs. Mean Std. Dev. Min Max
Log population in 2000 362 12.63 1.02 11.52 16.72
Percent change in population: 1990 to 2010 362 28.61 26.51 -12.68 163.17
Log median income 2000 362 9.88 0.17 9.20 10.55
Wharton Land Use Index 298 -0.028 0.737 -1.936 2.982
Chen and Rosenthal (2008) Quality of Life Index 261 0.00 1.97 -4.11 8.90
Note: We divided the Chen and Rosenthal Quality-of-Life Index by 1000 so that it was the same order of
magnitude as the other coefficients.
39
Table 9: Regression of CAPM-Betas on the WLURI
(1) (2) (3) (4)
Wharton Land Use Regulation Index 0.260*** 0.218*** 0.182*** 0.108
(0.0639) (0.0657) (0.0628) (0.0828)
Log Population 2000 0.112** 0.0906** 0.148***
(0.0458) (0.0436) (0.0548)
GROWING 0.00848*** 0.00580*
(0.00183) (0.00233)
SHRINKING -0.0618** -0.0795**
(0.0298) (0.0400)
Chen and Rosenthal Quality of Life Index 0.0783**
(0.0315)
Constant 1.043 -0.384 -0.338 -0.997
Observations 298 298 298 222
𝑅2 0.0497 0.0654 0.157 0.152
* p<0.1, ** p<0.5, *** p<0.01
40
Table 10: CBSA Beta Estimates Grouping Areas by Housing Supply Restrictions
WLURI 1st
Quartile CBSAs
WLURI 2nd
Quartile CBSAs
WLURI 3rd
Quartile CBSAs
WLURI 4th
Quartile CBSAs
Beta 0.749*** 0.909*** 0.981*** 1.45***
(0.009) (0.008) (0.007) (0.010)
Observations 12,200 18,457 23,509 20,418
𝑅2 0.348 0.395 0.446 0.494
* p<0.1, ** p<0.05, *** p<0.01
The unevenness in the size of the quartile groups in due to our restriction of the sample to CBSAs
with population greater than 100 thousand.
41
Table 11: Zip code level Betas regressed on within-CBSA measures of supply elasticity
(1) (2) (3) (4) (5) (6)
Miles to the CBD -0.0052*** -0.0058*** - - -0.0040*** -0.0046***
(0.0006) (0.0006) - - (0.0007) (0.0008)
Log employment density - - 0.0127*** 0.0189*** 0.0135*** 0.0128***
- - (0.0014) (0.00185) (0.0022) (0.0033)
CBSA fixed effects - 286 - 286 - 286
Observations 6,114 6,114 9,853 9,853 5,883 5,883
𝑅2 0.0121 0.0607 0.0083 0.0661 0.0216 0.0719
* p<0.1, ** p<0.05, *** p<0.01
Observations have been Winsorized at the top and bottom 1% in terms of log employment density. We have also
limited the observations to be within 30 miles of a CBD.
42
Table 12: Average Betas for Supply Constrained and Supply Elastic Areas Within CBSAs
Grouping Within-CBSA Location
into City Center and Suburban
Grouping Within-CBSA Location
into High and Low Density
City Center Suburb High Density Low Density
Mean across CBSAs 1.115 1.054 1.075 0.989
Std Deviation 0.408 0.189 0.532 0.027
Observations (No. CBSAs) 128 128 241 241
Note: Two betas are estimated for each CBSA, one for supply constrained and one for supply elastic
areas as defined in the two pairs of columns. Betas for each classification are then averaged across
CBSAs in the sample. St. Louis city center Beta was an extreme outlier and omitted for that reason.
43
Table 13: CBSA-Level Percent Year-Over-Year Home Price Appreciationa
CBSA Attributes (1) (2) (3) (4) (5)
Beta 0.979*** 0.938*** 0.871*** 0.835*** 0.723***
(.0732) (.0757) (0.0810) (0.0969) (0.0897)
Log CBSA population 2000 0.0137 0.00706 0.0637 0.239**
(.0678) (0.0676) (0.0875) (0.0855)
Median CBSA income 2000 0.0000362* 0.0000361* 0.0000309 0.000024
(.0000203) (0.0000203) (0.0000287) (0.0000266)
GROWING 0.00393 0.00484 -0.000335
(0.00254) (0.00322) (0.00305)
SHRINKING -0.0672 -0.0257 -0.044
(0.0419) (0.0489) (0.0502)
Superstar status 0.721** 0.153
(0.321) (0.323)
Quality of Life Index 0.298***
(0.0393)
Observations 362 362 362 243 226
𝑅2 0.330 0.335 0.343 0.361 0.502 a The dependent variable has a mean of 3.1 which indicates that on average, CBSA home prices increase 3.1
percent per year over our sample horizon. Measured in this fashion, if the coefficient on beta above was equal to
1.0, a 0.1 increase in beta would increase house average CBSA home price appreciation 0.1 percentage points.
* p<0.1, ** p<0.05, *** p<0.01
Standard errors are in parentheses.
44
Table 14: Distance from the CBD and Zip Code Level House Price Growth on a Year-Over-Year Basis
Panel A: All CBSAs
(1) (2) (3)
Miles to CBD -0.0258*** - -0.0199***
(.00168) - (.00161)
Beta - 0.953*** 0.920***
- (.0260) (.0260)
CBSA FE 364 364 364
Observations 12,348 12,348 12,348
R2 0.487 0.529 0.535
Panel B: Population between 100K & 250K Panel C: Population between 250K & 500K
(1) (2) (3) (1) (2) (3)
Miles to CBD -0.00222 - -0.00628* 0.00432 - 0.0043
(.00375) - (.00351) (.00420) - (.00420)
Beta - 1.246*** 1.253*** - -0.0471 -0.0467
- (.0666) (.0667) - (.0557) (.0557)
CBSA FE 194 194 194 79 79 79
Observations 2,628 2,628 2,628 2,243 2,243 2,243
𝑅2 0.480 0.544 0.545 0.433 0.433 0.433
Panel D: Population between 500K & 1M Panel E: Population between 1M & 2.5M
(1) (2) (3) (1) (2) (3)
Miles to CBD -0.00775** - -0.00176 -0.0368*** - -0.0134***
(.00378) - (.00361) (.00351) - (.00334)
Beta - 0.651*** 0.647*** - 1.364*** 1.295***
- (.0554) (.0560) - (.0539) (.0565)
CBSA FE 45 45 45 29 29 29
Observations 2,004 2,004 2,004 2,427 2,427 2,427
𝑅2 0.374 0.414 0.414 0.493 0.582 0.585
Panel F: Population between 2.5M & 5M Panel G: Population over 5M
(1) (2) (3) (1) (2) (3)
Miles to CBD -0.0700*** - -0.0611*** -0.0569*** - -0.0470***
(.00458) - (.00382) (.00515) - (.00457)
Beta - 2.0556*** 1.961*** - 1.534*** 1.447***
- (.0754) (.0706) - (.0776) (.0751)
CBSA FE 13 13 13 5 5 5
Observations 1,734 1,734 1,734 1,312 1,312 1,312
𝑅2 0.479 0.587 0.641 0.289 0.401 0.446
* p<0.1, ** p<0.05, *** p<0.01.
Standard errors are in parentheses. Zip codes are limited to be within 30 miles of a CBD.
45
Table 15: Log Employment Density and Zip Code Level House Price Growth on a Year-Over-Year Basis
Panel A: All CBSAs
(1) (2) (3)
Log emp density 0.0855*** - 0.0574***
(.00559) - (.00538)
Beta - 1.001*** 0.977***
- (.0237) (.0248)
CBSA FE 364 364 364
Observations 15665 16217 15665
R2 0.505 0.527 0.551
Panel B: Population between 100K & 250K Panel C: Population between 250K & 500K
(1) (2) (3) (1) (2) (3)
Log emp density -0.0267** - -0.0175 0.00226 0.0012
(.0132) - (.0129) (.0141) (.0141)
Beta - 0.788*** 0.685*** 0.108* 0.116**
- (.0567) (.0576) (.0573) (.0588)
CBSA FE 194 194 194 79 79 79
Observations 3288 3508 3288 2338 2444 2338
R2 0.498 0.477 0.520 0.470 0.430 0.471
Panel D: Population between 500K & 1M Panel E: Population between 1M & 2.5M
(1) (2) (3) (1) (2) (3)
Log emp density 0.035*** - 0.00838 0.0988*** - 0.0424***
(.0129) - (.0128) (.0113) - (.0107)
Beta - 0.678*** 0.673*** - 1.27*** 1.14***
- (.0510) (.0607) - (.0491) (.0513)
CBSA FE 45 45 45 29 29 29
Observations 2356 2443 2356 2972 3069 2972
R2 0.364 0.392 0.397 0.460 0.534 0.537
Panel F: Population between 2.5M & 5M Panel G: Population over 5M
(1) (2) (3) (1) (2) (3)
Log emp density 0.201*** - 0.114*** 0.250*** - 0.187***
(.0146) - (.0125) (.0171) - (.0158)
Beta - 2.28*** 2.11*** - 1.66*** 1.47***
- (.0642) (.0655) - (.0667) (.0663)
CBSA FE 13 13 13 5 5 5
Observations 2427 2459 2427 2284 2294 2284
R2 0.427 0.585 0.599 0.519 0.581 0.605
* p<0.1, ** p<0.05, *** p<0.01
Standard errors are in parentheses. Zip codes are Winzorized at 1% employment density.