Housing Demand and Expenditures:
How Rising Rent Levels affect Behavior and
Costs-of-Living over Space and Time
David Albouy
Gabriel Ehrlich
University of Illinois and NBER
Congressional Budget Office
Yingyi Liu ∗
University of Illinois
October 2014
∗ Albouy:
albouy@illinois.edu; Ehrlich: gabriel.ehrlich@cbo.gov; Liu: liu195@illinois.edu. During
work on this project, Albouy was supported by the NSF grant SES-0922340 and was a David C. Lincoln
Fellow. Any mistakes are our own. The views in this paper are the authors’ and should not be interpreted as
the views of the Congressional Budget Office.
Abstract
Since 1970, the share of income spent on housing grew along with incomes and the relative price of
housing. This rising share is consistent with housing being a necessity when demand is sufficiently
price inelastic. We estimate housing demand parameters using compensated and uncompensated
frameworks over space and time, testing restrictions imposed by demand theory and household
mobility. Estimates are largely consistent, suggesting that housing demand is slightly price and
income inelastic, and obeying the restrictions of demand theory. We construct a non-homothetic
constant-elasticity-of-substitution cost-of-living index that reflects housing’s greater importance
when housing prices are high and incomes are low.
Keywords: Housing demand, affordability, cost-of-living, inflation, non-homothetic preferences, consumer economics.
JEL Numbers: D12, E31, R21
1
Introduction
The share of Americans’ household budgets devoted to housing has risen considerably over the
last four decades. Figure 1 illustrates this trend using several sources of data. The Bureau of
Economic Analysis (BEA) indicates that the share of national income devoted to housing rose by
2 percentage points from 1970 to 2012, while the American Housing Survey (AHS) and Consumer
Expenditure Survey (CEX) indicate a 7 percentage point increase over similar time periods. At the
same time, the AHS, CEX, and Census all indicate that the typical share of income spent on rent
by renting households rose by 10 percentage points, despite similar home-ownership rates of 64
percent in both 1970 and 2012. These trends support the recent claim by the Secretary of Housing
and Urban Development that, “We are in the midst of the worst rental affordability crisis that this
country has known” (Olick 2013).
Economically, these trends are surprising, as household incomes have risen over the past four
decades and housing has historically been viewed as a necessity. This means that the income
elasticity of housing demand is less than one, and the share of expenditures devoted to housing
should fall as incomes rise. Yet, the rising expenditure share suggests that housing may in fact
be a luxury good. One possible resolution to this apparent contradiction lies in the considerable
increase in the price index for shelter (the main component of housing) relative to non-shelter
goods. If housing demand is price inelastic, the expenditure share on housing will rise as housing
becomes more expensive relative to other goods, due to weak substitution effects.
Figure 2 displays this possibility graphically. The production possibility frontier (PPF) may
have expanded more in the direction of non-housing goods, many of which may be traded internationally, than in the direction of housing, the production of which depends on scarcer local factors,
such as urban land, and may be subject to slower technological improvements. In that case, households will optimally increase their consumption of non-housing goods far more than of housing
goods because of both income effects (illustrated by the movement from point A to point B in the
figure) and substitution effects (illustrated by the movement from point B to point C). The income
effect causes the expenditure share to fall, seen in the distance between points B and D. The rise
1
in the relative price, determined by the slope of the PPF, causes housing’s share to rise due to the
limited substitutability between housing and non-housing goods: at the new prices, consumption
would need to be at point E, not C, for the share spent on housing to not rise.
In this paper, we investigate both cross-sectional and time-series data to identify the principal
features of housing demand using an intuitive yet adequately rich framework. We demonstrate that
cross-sectional data lends itself to estimating both uncompensated (Marshallian) and compensated
(Hicksian) housing demand functions. The latter is based on the common assumption that the
mobility of some households across cities acts to equalize the utility households receive from
living in different locations. Since no such assumptions are plausible over time, the time-series
data lends itself only to estimating uncompensated demand. In either case, understanding housing
demand is useful for measuring changes in costs-of-living over space (e.g. across cities) and time
(i.e. inflation) realistically through a price index that incorporates substitution and income effects.
Our investigation employs a parsimonious framework featuring housing expenditures, housing
prices, measures of income, and more originally, non-housing prices. Unlike previous authors, we
use data on non-housing prices to test restrictions imposed by demand theory, which serve as a
check on the validity of our empirical methodology. Under such restrictions, we integrate a demand equation into non-homothetic utility and expenditure functions with a constant elasticity of
substitution. These functions should be useful to researchers interested in housing consumption
behavior or in how changes in cost-of-living affect welfare. The analysis also provides an unconventional examination of demand theory by using spatial variation, rather than more conventional
temporal variation (e.g. Deaton 1986, Blundell et al. 1993).
Combining cross-sectional evidence from various sources, it appears that the uncompensated
own-price, income, and substitution elasticities are all near 2/3 in absolute value. The time series patterns are consistent with the cross-sectional results, but exhibit an additional secular trend
towards greater housing consumption that invites further investigation. We also discuss potential
problems from aggregation bias, as well as how the changing income distribution should affect
overall housing demand.
2
2
Motivation and Related Literature
Mirroring our own findings, the Joint Center for Housing Studies of Harvard University (JCHS,
2013) documents that from 2000 to 2012, the median share of renters’ income devoted to contract
rent rose nearly five percentage points to 27.4 percent and that 28 percent of renting households
now spend more than half of their incomes on rent. Concerns about housing affordability are most
acute when housing is a necessity and demand is price inelastic. This is particularly true for low
income households, who have experienced few income gains in America’s largest, most expensive
cities (Baum-Snow and Pavan, 2013). Low-skilled households’ inability to substitute away from
expensive housing appears to account for their choosing to live in cheaper cities (Moretti 2013),
while those who remain in expensive cities must earn higher wages relative to other skill groups
(Black, Kolesnikova, and Taylor 2009).1
Households’ ability to substitute between housing and non-housing goods is a key factor affecting house prices, tax incidence, and population density within and across metropolitan areas.
When substitutes for housing are limited, housing demand is price inelastic, and increases in demand, for instance due to rising incomes, will lead to large local price increases in places where
housing supply is price inelastic. Regardless of supply, housing will constitute a larger share of
household budgets in areas where, or eras when, it is more expensive. If instead, demand is unit
elastic, housing expenditures for similar households should not change across space or time. Accurately measuring the price elasticity of housing demand is important to understanding whether
the recent resurgence of housing prices in some markets is sustainable or a potential signal of a
new housing bubble. Recent price increases are likely be more sustainable if housing demand is
inelastic. In that case, rents in high-priced markets may continue to take a larger share of income,
and housing policy may need to prioritize problems in housing affordability and production over
issues related to lending and credit.
1
Using grocery data, Handbury (2013) estimates a non-homothetic log-logit utility function with a CES superstructure to argue that high-income households may find large cities to be more “affordable” because they contain a greater
range of groceries suited to their tastes. We reinforce this conclusion by finding the large cities are more affordable
for high-income households as they spend less on housing.
3
Economists’ interest in housing demand and expenditures has a long and distinguished history,
featuring a wide range of estimates of the price and income elasticity of housing demand. Articles
reviewed in Mayo (1981) find uncompensated price elasticities that range from slightly positive
to less than minus one. Popular estimates in the middle include Pollinsky and Ellwood’s (1979)
estimate of -0.7 and Hanushek and Quigley’s (1980) estimates of -0.64 in Pittsburgh and -0.45 in
Phoenix.2 More recently, Davis and Ortalo-Magne (2009) argue that the median expenditure on
housing among rentals is roughly constant metro areas, implying a price elasticity of negative 1.
Few articles estimate elastic price demand, with elasticities great than one.3 While some studies
use non-housing price data to deflate their numbers, none actually use it to test the validity of the
housing demand specification, as we do here.
The income elasticity of demand for housing, which measures households’ propensity to consume more housing services as their incomes grow, also has important implications for house prices
and quantities. Classical studies, such as Engel (1857) and Schwabe (1868), tended to find an income (or more precisely, an expenditure) elasticity for housing demand of less than one, which
became known as “Schwabe’s Law of Rent”.4 As summarized by DeLeeuw (1971), Mayo (1981)
and later Harmon (1988), most studies have been consistent with Schwabe’s Law, with some important exceptions. For instance, Muth (1960) estimated an income elasticity well over one. One
major source of differences among studies is on how to measure income income: most researchers
suggest using a measure of “permanent income” – of which various varieties have been proposed
– to correct for attenuation bias caused by transitory income shocks. For owner-occupiers, it also
makes sense to include implicit rental income from home equity.5
2
There is a large literature on this topic, including Muth (1960), Reid (1962), Rosen (1985), Goodman and Kawai
(1986), Goodman (1988) Ermisch et al. (1996), Goodman (2002), and Ionnides and Zabel (2003). Most estimate
uncompensated price elasticities ranging from -1 to -0.3 and income elasticities from 0.4 to 1.
3
Kau and Sirmans (1979) estimated price elasticity shifting from -2.25 to -1 from year 1876 to 1970 using historical
data from Chicago. However, these are based off land-price gradients and are not robust to expected sorting behaviors
or changes in commuting costs.
4
Some confusion regarding Engel’s findings stems from Wright’s (1875) confused statement of the results in English; see Stigler (1954) for a discussion.
5
See Hansen et al. (1998) and references therein for estimates less than one, Larsen (2002) for an estimate of
approximately one, and Cheshire and Sheppard (1998) for an estimate greater than one, noting that the latter estimate
elasticities for housing attributes rather than for a unified bundle.
4
With such disparate findings, theoretical models of housing demand have taken great latitude
in modeling housing demand. Many models in urban and macro-economics assume a fixed demand for housing, perfectly inelastic to price and income. This provides a simple derivation of the
mono-centric city model, seen in Mills (1967), and used for urban welfare accounting in Desmet
and Rossi-Hansberg (2013). Other models, such as the search and matching one of Piazzesi and
Schneider (2010), assume housing demand is responsive to price but not income, as with quasilinear preferences. Another common approach is to specify preferences as Cobb-Douglas, implying
price and income elasticities of one. Examples include Eeckhout (2004) and Davis and OrtaloMagne (2011), Michaels, Rauch and Redding (2012), and Guerreiri, Hartley and Hurst (2013).
While a certain level of abstraction is a necessary component of a useful and tractable economic
model, we must remain aware of the limitations such assumptions have on the conclusions we
make about housing and its interaction with other markets.
The secular rise in housing expenditures appears to be understudied by economists. Piketty
(2014) finds that the value of residential capital relative to economic output has increased substantially over the last hundred years.6 Gyourko, Sinai, and Mayer (2013) find that the difference
in housing values between the typical and highest-price locations has widened considerably over
the last five decades. In addition, Davis and Heathcote (2007) present evidence of persistent real
growth in land values, which accounts for an increasing share of housing costs over recent history.
These findings are consistent with limited substitution possibilities between land and non-land inputs in housing production, as found in Albouy and Ehrlich (2012). Those authors, as well as
Davis and Palumbo (2007), document that land values are extremely heterogeneous across time
and space. Theoretically, as population and incomes rise, an inelastic derived demand for land can
lead to land values taking up an ever increasing share of the economy.7
6
We note that housing is a capital asset that provides a flow consumption services to its owner. This asset is
a composite of land and structure, the latter of which typically depreciates over time. We follow the bulk of the
literature in estimating demand for a composite housing good, but the shape of the housing demand function can have
important implications for land values separately from housing values. For more on the production of housing services
from local land and construction inputs, we recommend Albouy and Ehrlich (2012).
7
This may happen if land-saving technological improvements are weak or stifled by regulation. Rising demand may
reverse earlier declines in land values engendered by transportation improvements. Even in a modernizing economy,
if the demand for housing is price inelastic, Ricardo’s (1817) and George’s (1879) concerns that land may accrue an
5
3
3.1
Household Demand for Housing in a System of Cities.
Household Budgets and Preferences
We use a standard static model of housing demand, and embed it in a richer equilibrium framework
with local household amenities, similar to Rosen (1979) and Albouy (2008). The national economy contains many cities, indexed by j, which share a population of potentially mobile households.
Households supply labor in their city of residence; they consume a housing good y with price pj ,
and a non-housing good x with price cj .8 Households earn total income mj = I + (1 − τ )wj ,
determined by a constant unearned income, I, and which varies due to local wage levels wj ,
after taxes, τ . In this static setting, household expenditure equals household income. Household preferences over the consumption good, housing, and location are modeled by a utility
function U (x, y; Qj ), where Qj represents a city-specific amenity conceptualized as “quality-oflife”. The indirect utility function for a household in city j is then given by V (pj , cj , mj ; Qj ) =
maxx,y (U (x, y; Qj )|cj x + pj y = (1 − τ )wj + I). The expenditure function for a household in city
j is likewise given by e(pj , cj , u; Qj ) = minx,y (cj x + pj y|U (x, y; Qj ) ≥ u).
3.2
The Housing Expenditure Share and Uncompensated Demand
In order to take the model to the data, we approximate the relationships described above around
their national average values. Denote the fraction of household expenditures on housing in city j
as sjy ≡ (pj y j )/mj . Log-linearizing this equation produces the identity
ŝjy = p̂j + ŷ j − m̂j .
(1)
outsize share of national income may be more relevant than they have seemed for much of the past century. This
reasoning is based on insights from standard two-sector models, although it deserves a full formalization.
8
For simplicity, the exposition of the theoretical model will refer to a system of cities and call individual geographical units as such. However, the empirical work using the Consumer Expenditure Survey data will be at the state level,
and the empirical work using the Census data will also use the non-metropolitan portions of states. Therefore, the geographies considered in this model are more properly conceived as ‘areas’, with the term ‘city’ used for concreteness
rather than precision.
6
A hat over a variable represents its log deviation from the (geometric) national average, i.e., ẑ j =
d ln z j = dz j /z̄. We take local price and income levels as parametric, so that the only behavioral
variable in the share is housing consumption, y. Consumption is determined by the uncompensated
(Marshallian) demand function y j = y(pj , cj , mj ; Qj ). Log-linearizing this function produces
ŷ j = y,p p̂j + y,c ĉj + y,m m̂j + y,Q Q̂j .
(2)
The parameter y,p is the uncompensated own-price elasticity of housing demand, y,c is the uncompensated elasticity of housing demand with respect to non-housing prices (or cross-price elasticity),
y,m is the income elasticity, and y,Q is the elasticity with respect to quality of life. Equation 2
is an identity for infinitesimal changes, and an approximation for larger changes. If housing is a
normal good, then y,m > 0, and housing obeys the law of demand, y,p < 0. It is unclear whether
housing is a gross substitute for non-housing goods, i.e., whether y,c > 0, because the cross-price
elasticity will exhibit positive substitution effects and negative income effects of unknown magnitudes. Housing could also be a gross complement or substitute for non-market quality of life,
i.e. y,Q ≷ 0, if amenities somehow alter the marginal rate of substitution between housing and
non-housing goods.9
We combine equations 1 and 2 to demonstrate how expenditure shares depend on behavioral
responses to local attributes:
ŝjy = (1 + y,p )p̂j + y,c ĉj + (y,m − 1)m̂j + y,Q Q̂j
(3)
Unrestricted, equation (3) is merely definitional. Rationality of preferences requires that the demand function be homogenous of degree zero in prices and income (p, c, m), so that y,p + y,c +
y,m = 0. This restriction requires that there be “no money illusion,” so that proportional increases
9
We have not modeled how households with low tastes for housing may be inclined to seek out more amenable
areas (see Black et al. 2002). Albouy and Lue (2014) present evidence that household sizes, age, and marital status
vary little across metropolitan areas (they vary more within), suggesting such selection issues are not of first-order
importance.
7
in all prices and income do not lead to changes in behavior.
Adding a constant to equation 3 motivates the following regression equation:
ln sjy = α0 + α1 ln pj + α2 ln cj + α3 ln mj + α4 q j + ej
= α0 + α1 (ln pj − ln cj ) + α3 (ln mj − ln cj ) + α4 q j + ej
(4)
(5)
Equation 5 follows 4 from imposing the homogeneity assumption as α1 + α2 + α3 = 0. If we
demean the right-hand side variables, the regression coefficients α0 = ln s¯y , α1 = 1 + y,p , α2 =
y,c , and α3 = y,m − 1. s¯y = eα0 is the geometric mean of expenditure shares. The own-price
uncompensated elasticity is simply the coefficient on housing prices minus one, y,p = α1 − 1,
while the income elasticity is the coefficient on income plus one, y,m = α3 + 1.
Quality of life cannot be observed directly but only proxied by observable amenities, qj , meaning y,Q cannot be identified in a fully cardinal sense without additional assumptions. The same
holds true of other demand shifters. Consistent estimation of this equation requires that nonhousing goods are properly accounted for by the index cj , that preferences across cities are the
same, that preferences can be aggregated across households, and that we have an appropriate (arguably permanent) measure of income mj .
3.3
Compensated Demand with Household Mobility and Heterogeneity
The uncompensated demand function may be converted into a compensated (Hicksian) demand
function by substituting in the expenditure function, i.e. y H (p, c, m; Q) = y(p, c, e(p, c, u; Q); Q).
Alternatively, we may log-linearize the expenditure function directly, yielding
m̂j = s¯y p̂j + (1 − s¯y )ĉj + m,Q Q̂j + m,u ûj
(6)
where m,u is the elasticity of expenditures with respect to utility, and m,Q is the elasticity of
expenditures with respect to quality of life.
8
Substituting equation 6 into equation 3 yields a relatively complicated that may be simplified
using the Slutsky equations. These give the relationships among the uncompensated, or Marshallian, price elasticities, and the compensated, or Hicksian, price elasticities: y,p = H
y,p − s¯y y,m and
H
H
y,c = H
y,c − s¯x y,m . Here y,p and y,c represent the compensated elasticities of housing demand
with respect to housing prices and consumption prices, respectively.10 Rationality requires that
compensated demand functions are homogenous of degree zero in prices. This means that the own
H
and cross-price elasticities of compensated housing demand should sum to zero, H
y,p + y,c = 0.
Combining these insights yields the following equation for differences in the expenditure share
in terms of relative prices, quality of life, and utility:
j
j
H
j
H
j
ŝjy = (H
y,p + 1 − s¯y )(p̂ − ĉ ) + (y,u − m,u )û + (y,Q − m,Q )Q̂
(7)
H
Here H
y,Q is the compensated elasticity of housing demand with respect to quality of life and y,u
is a similar elasticity for income.
To simplify further, we impose the restriction households are equally well-off across cities.
When households are sufficiently mobile, then prices and wages equilibriate so that households
are indifferent across inhabited locations. In that case, utility for a particular type of household
should not vary across cities. Rather, utility differences only represent inherent differences across
households, such as different earnings potentials. We parameterize income in city j as mj = ζ j wj ,
where ζ j is the skill level and wj is the wage level that compensates these household for living in
that city.11
To interpret the coefficient, we posit that our utility function is money metric around national
averages: u(x, y; Q) = e(p̄, c̄, ũ(x, y; Q), Q). This added simplification allows us to write utility
differences in terms of differences in the skill index ûj = ζ̂ j , and impose m,u = 1 and H
y,u = y,m .
The first substitution yields ŝjy = (1 + y,p − s¯y + s¯y y,m )p̂j + [y,c − (1 − y,m )(1 − s¯y )]ĉj + (y,Q − (1 −
y,m )m,Q )Q̂j − (1 − y,m )m,u ûj . Besides the Slutsky equations we also substitute in the identities H
y,Q = y,Q +
H
y,m m,Q and y,u = y,m m,u to get the resulting equation.
11
When household types vary within city, the compensating wage differences will vary according to their tastes for
housing, quality of life, and taxes.
10
9
Note that we implicitly impose the restriction that the skill index affects housing consumption
through income, and not through differences in tastes.12 These simplifications yield
j
j
j
H
j
ŝjy = (H
y,p + 1 − s¯y )(p̂ − ĉ ) + (y,m − 1)ζ̂ + (y,Q − m,Q )Q̂
(8)
Equation 8 then motivates the following empirical specification using data across cities:
ln sjy = β0 + β1 p̂j + β2 ĉj + β3 ζ̂ j + β4 q j + ej
(9)
= β0 + β1 (p̂j − ĉj ) + β3 ζ̂ j + β4 q j + ej
(10)
where β0 = ln s¯y , β1 = H
y,p + 1 − sy = −β2 and β3 = y,m − 1. Similar to the uncompensated
β0
j
case, s¯y = eβ0 and y,m = β3 + 1, but H
y,p = β1 − 1 + e . In practice, ζ̂ is an index estimated
from the average log wages households would earn in a typical city based on their human capital
and other location-invariant characteristics.
The main testable restriction here is that the coefficients on the price of housing and nonhousing goods should be of opposite signs and equal magnitudes, i.e., β1 + β2 = 0. This may be
seen as a joint test of both demand theory and mobility.13 When this restriction holds we use the
elasticity of substitution between housing and non-housing goods, σD ≡ −(ŷ j − x̂j )/(p̂j − ĉj ) =
−H
y,p /(1 − s¯y ), so that β1 = (1 − s¯y )(1 − σD ). When the elasticity of substitution is less (greater)
than one, housing demand is said to be price inelastic (elastic), and the expenditure share of housing
rises (falls) with the relative price of housing, p/c. One advantage of the compensated specification
is that it estimates the elasticity of substitution without directly using information on income.
Quality of life amenities may affect the income share of housing if H
y,Q 6= m,Q , which means
amenities and housing are either are net complements or substitutes. Such relations are not obvious a priori. If 0 > H
y,Q > m,Q , compensated improvements in quality of life reduce housing
12
If households with more skills like housing less (more) than those with fewer skills, the income elasticity estimate
will be biased downwards (upwards).
13
If mobility does not hold, then the coefficients would not be equal. Income effects in the uncompensated elasticities would likely push coefficients on both housing and non-housing prices downwards.
10
consumption less than other consumption. Households could spend more on their properties to
enjoy a nice climate. The opposite could also be true: nice weather may make people spend time
away from their houses, while cold weather could cause them to consume more housing.
3.4
Potential Biases
Most examinations of housing demand do not consider variation in non-housing prices. Yet, these
are potentially important as non-housing prices co-vary positively with housing prices. In places
where housing is expensive, labor-intensive services, such as haircuts and restaurant meals, also
tend to be expensive. This covariance arises because the workers who provide those services must
purchase local housing. Such services may also contain a land component in their cost. We model
this covariance with the projection
ĉj = ρp̂j + v j
(11)
where ρ > 0 and v j is white noise. Substituting this projection into equation 8, together with the
elasticity of substitution, gives
j
ŝjy = (1 − s¯y )(1 − σD )(1 − ρ)p̂j + (y,m − 1)ζ̂ j + (H
y,Q − m,Q )Q̂
(12)
We may write the estimated elasticity of substitution as a function of the parameters σ̂D = 1 −
β1 /[(1 − eβ0 )(1 − ρ)] The higher is ρ, the more ignoring non-housing prices will bias β̂1 towards
zero and σ̂D towards one.14
An upward bias in the estimated price elasticity of housing is likely to occur if worker skill
levels are omitted from the regression. As seen in Moretti (2013), higher skilled individuals tend
to locate in areas with more expensive housing. Formally, if ζ j is positively correlated with pj , and
housing is a normal good, i.e., y,m > 0, then excluding a measure of skill will bias β1 downwards.
14
Technically, Davis and Ortalo-Magne’s (2011) data support an elasticity of substitution 0.85. However, their index
of rental costs differs from ours by controlling for commuting costs, and thus exaggerating the actual price differences
faced by households (e.g. that suburban dwellers in the New York suburbs face Manhattan prices), biasing their results
towards one. Their study also suffers from the other potential biases we correct for.
11
For instance, a negative relationship between prices and expenditure shares induced by households
in more skilled cities spending a smaller fraction of their incomes on housing could lead to the
inference that demand is highly price elastic even if the true elasticity is unity or lower.15
Another potential bias stems from using renters. It could be the case that households are less
likely to own, and more likely to rent, in more expensive areas. In that case, only the poor rent in
cheap cities, while more affluent households also rent in expensive cities. If housing is a necessity, and our controls for utility are incomplete. then selection bias of this kind would make the
estimated expenditure-rent gradient more negative. One may attempt to deal with this problem by
controlling for the home-ownership rate, but this rate is also endogenous.
Finally, there is the issue of unobserved taste in housing. Households that care more for housing
will prefer to locate in areas where housing is less expensive. This selection effect would also
make the expenditure-rent gradient more negative, as those who wish to consume the least amount
of housing locate in the most expensive areas.
3.5
Non-Homothetic Utility and Expenditure Functions for Housing
In modeling housing demand, economists almost invariably use utility functions that are homothetic or quasilinear, imposing income elasticities of one or zero. Since housing is a major consumption item, in many applications we believe it may be worth using a more general utility function
that allows for non-homotheticity. Here, we propose to use non-homothetic separable family CES
function from Sato (1977), with Qj = 1. To minimize on new notation, we write it as
"
U (x, y; 1) =
γσδx
σ−1
σ
+ 1 − σ − γδ
γσ(δ − 1)y
σ−1
σ
+ 1 − σ − γ(δ − 1)
σ
# γ(σ−1)
(13)
This function contains three paramters: a distribution parameter δ, a substitution paramter, σ,
and a non-homotheticity parameter, γ. In the limit, as γ → 0 this function becomes a standard
CES function. Our restricted log-linear model provides three parameters that map well to this
15
Such issues cause us to put less faith in housing demand estimates
12
utility function. We demonstrate in the appendix that when all of the variables are demeaned that
β0 = σ ∗ln(1−δ) = ln s̄y , β1 = (1− s̄y )(1−σ), β3 = −γ(1− s̄y )(1−σ). Inverting, the parameters
can be expressed recursively as σ = 1 − β1 /(1 − eβ0 ), δ = 1 − eβ0 /σ , γ = −β3 /β1 .
We may construct an ideal cost-of-living index using the expenditure function
e(p, c, u; 1) =


1−σ σ γ(1−σ)
1−σ
σ
 1
 1−σ
c δ u
+ p (1 − δ)
iσ
 1 γ + (1 − σ − γδ)(1 − u γ(1−σ)

σ
)
γσ
h
(14)
This expenditure function differs from a standard CES function: when γ(1 − σ) > 0, then at higher
levels of utility, households place greater importance on non-housing costs, c. By choosing a base
level of utility and prices, we may then construct a cost-of-living index, which we detail below.
4
Data
The main variables in our inter-metropolitan analysis are the income or expenditure share devoted to housing, a price index of for housing, a price index for non-housing goods, and intermetropolitan income and potential earnings differentials. We also consider metropolitan amenity
levels. The primary data we use in the analysis comes from the 2000 Census 5 percent microdata
samples from IPUMS, which we use to calculate the expenditure share devoted to housing across
different metropolitan areas, a housing price index across areas, and wage and income differentials
across areas. We measure the prices of non-housing goods across metro areas using the panel of
inter-area price differences for the years 1982-2012 constructed by Carrillo et al. (2013). The
analysis uses several auxiliary data sources, which are cited throughout the paper.
Although the theoretical relationships in section 3.2 are straightforward, in practice several
decisions are necessary to take the model to the data. First is the decision on whether to include
homeowners in the sample. Ideally both renters and homeowners would be included in order
to have a more representative sample. However, the inclusion of homeowners can be problematic
because homeowners’ monthly payments depend heavily on factors such as when they bought their
13
homes and the terms of their mortgages, rather than on the inherent characteristics of the home.
These factors can cause homeowners’ monthly payments to diverge from the theoretical quantity
of interest, the value of the service flow that homeowners receive from their housing. This paper
reports results both including and excluding homeowners from the estimation. In specifications
that include homeowners, they are assigned an imputed annual rent of 6.2 percent of the reported
value of the home, following Albouy and Hanson (2014).
Second, in the static model of the theory, expenditure is equal to income, but this equality
does not hold in dynamic reality. The difference between the two quantities leads to an ambiguity
when calculating the expenditure share devoted to housing. In the main results, we calculate the
expenditure share on housing using wage and salary income as the denominator.
Third, it is necessary to decide whether to include expenditures on utilities such as electricity,
fuel, and water in housing expenditures. The main analysis the inclusive, or ‘gross rent’ concept.
4.1
Rental Indices
To operationalize the concept of relative housing prices across cities, we construct inter-metropolitan
price indices using hedonic regression methods. We run regressions of the form:
P
ln(Pij ) = αP + βX
Xij + δjP + Pij
(15)
where Pij is the rent or imputed rent for unit i in area j, XijP is a vector of unit characteristics, and
δjP is a set of area fixed effects. We take δ̂jP as our inter-area housing price indices, subtracting
the national average so that the indices may be interpreted as the percentage by which housing
prices in a given area differ from the national average. The appendix describes the covariates XijP
in detail.
Appendix table A1 displays the housing price indices indices at the metropolitan level using
the 2000 Census 5 percent data sample. The table displays indices calculated using only rental
units and indices calculated using rental and owner-occupied units. In both cases the indices have
14
been normalized so that the average index value weighted by (the square root of) MSA population
is zero. Generally, large and coastal cities have more expensive housing by these measures. For
instance, the New York, NY-NJ MSA has a rental index 44 log points higher than the national average and San Francisco-Oakland, CA has a rental index 66 log points higher than national average.
Smaller cities and those located in the interior of the country, as well as non-metropolitan areas,
tend to have below average rental indices. For instance, the non-metropolitan areas of Alabama
have rents 64 log points below the national average. The standard deviation of the rental index
across areas is 21.8 percent. The housing price index that includes owner-occupied units follows
the same general pattern, although it is slightly more dispersed with a standard deviation of 24.5
percent.
4.2
Expenditure Shares
Appendix table A1 also displays the median expenditure shares on housing across metropolitan areas, calculated from the 2000 Census data. As noted above, these shares are calculated as shares of
wage and salary income, and include expenditures on utilities as well as on contract rent. The table
shows median expenditure shares for renters only and for the combination of renters and owners.
For renters, the median housing expenditure share averages 22.2 percent across metro areas, with
a standard deviation of 1.9 percent. Including owners in the expenditure share calculations lowers
the average share to 17.6 percent but increases the standard deviation across metro areas to 2.5
percent.
Additional specifications in the analysis make use of the aggregate expenditure share, calculated as the sum of all rental expenditures in the area divided by the sum of all incomes in the area.
The aggregate expenditure shares are lower on average than the median expenditure shares. For
renters only the average share is 19.3 percent with a standard deviation of 1.5 percent, while for
renters and owners the average share is 15.9 percent, with a standard deviation of 2.2 percent.
15
4.3
Predicted Wage Indices
The compensated regressions use an index of predicted wage differentials in order to measure the
variation in earnings potential, and thus utility levels, among residents of different metro areas. We
construct the inter-metropolitan predicted wage indices using hedonic regression methods, running
regressions of the form:
W
ln(Wij ) = αW + βX
XijW + δjW + W
ij
(16)
where Wij is the hourly wage for person i in area j (calculated as annual wage income divided by
the product of number of weeks worked and usual hours per week), XijW is a vector of personal
characteristics, and δjW is a set of area fixed effects. We take the median or mean of the β̂ W XijW
as our predicted wage indices, again subtracting the national average so that the indices may be
interpreted as the percentage deviation from the national average.16 The appendix describes the
covariates XijW in detail.
These wage indices capture the idea that observed wage differentials across metro areas reflect
both compensating differentials for workers and firms that are unrelated to the skill compositions
in those areas, and differentials that reflect the different compositions of skills and worker types
across areas. Put simply, San Jose, CA offers high wages both to compensate workers for the high
costs of living there, and because the workers there have characteristics that would predict high
wages no matter where those workers lived. The predicted wage indices are meant to capture the
latter element while omitting the former element, which is captured by the area fixed effects δjW .
Using the predicted wage indices also helps us to avoid a problem of measurement error associated
with using actual wages: the relevant income measure in the context of our static theoretical model
is permanent income, which may not be well-measured by current income. Using wages predicted
from observed worker characteristics rather than actual wages or incomes should help to alleviate
this problem. Appendix table A1 displays the predicted wage indices at the metropolitan level
using the 2000 Census 5 percent data sample.
16
Additional specifications use the average predicted values from the wage regressions.
16
5
Cross-sectional Results
Figures 3A and 3B illustrate the inter-metropolitan relationship between median expenditure shares
and relative housing costs using the Census data: 3A is for renters only; 3B, for renters and owners.
The former uses a price-index for rental units, while the latter uses a price index for all housing
units. The regression line has a slope equal to β1 = −β2 in the empirical regression (10) where it
is imposed that β3 = β4 = 0. In both cases, the relationship is positive and statistically significant,
indicating that housing demand is price-inelastic. The slope is much steeper in figure 3B, which
includes home-owners, and the fit is tighter as well.
Table 1 presents estimates using the full compensated model from (10), starting with the median
expenditure share for renters in columns 1-4. Column 1 displays the results of a simple regression
of the median housing expenditure share on the log rental price index. The geometric mean of
the median expenditure share across areas is 22.1 percent, while the implied price elasticity of
housing demand is -0.82, statistically different from unity. As predicted, the regression coefficient
on the housing price index increases as we add the non-housng price index and the predicted wage
index in column 2. The implied price elasticity of demand is -0.68, while the implied income
elasticity of demand is 0.66. The coefficients on the two price indices have opposite and roughly
equal magnitudes, so that the regression does not reject the rationality restriction of demand theory;
the p-value on the test that the coefficients on the housing and non-housing price indices sum to
zero is 0.66. The failure to reject this restriction motivates restricting the coefficients to sum to
zero in column 3, which is our preferred specification. The price and income elasticities do not
change much from column 2, while the implied elasticity of substitution between housing and nonhousing goods is 0.70, significantly less than unity. These results are consistent with Schwabe’s
Law that housing is a necessity, but are not consistent with Cobb-Douglas, quasilinear, or inelastic
preferences for housing.
These results appear largely unaffected by the inclusion of two natural amenities in column
4, distance to a coast line and the average slope of the land within a metro area. The housing
expenditure share is not statistically related to distance to the coast, but is positively related to the
17
average slope of the land. This novel result appears justified: housing on hillier terrain has better
views and is more easily seen. Households may choose to spend more on their houses to take
advantage of the better views, or to impress their neighbors.17 One limitation of including these
amenities, however is that it causes the homogeneity restriction to fail, and so we leave this issue
for further research.
Column 5 includes the expenditures of homeowners as well as renters. In this case, the homogeneity restriction continues to hold, the expenditure share is lower on average, and rises more
strongly with prices, as already seen in figure 3B. The estimates suggest a similar but lower income
elasticity, and a significantly lower price elasticity of -0.45. The elasticity of substitution is also
substantially lower at 0.42.
The preceding estimates apply to the median household. However, the market response depends on the overall amount of spending on rent, putting more weight on high-income renters.
Therefore, column 6 displays a regression with the log aggregate expenditure share on housing as
the dependent variable; this specification also uses the average rather than median of the predicted
wage index across MSAs. This specification produces an estimated price elasticity of demand
equal to -0.77, an income elasticity of 0.84, and an elasticity of substitution of 0.76. Therefore,
the results using the aggregate expenditure share are closer to being consistent with the predictions of Cobb-Douglas preferences than the results using the median expenditure share, although
Cobb-Douglas preferences can still be rejected statistically. The rationality restriction continues
to hold. Finally, column 7 presents results using the aggregate expenditure share for homeowners
and renters. These results suggest less price- and income-elastic demand and a lower elasticity
of substitution between housing and non-housing goods than results in column 6. Therefore, the
results are less consistent with Cobb-Douglas preferences. This specification rejects the rationality
restriction that the unrestricted coefficients on the housing and non-housing price indices sum to
zero.
Table 2 assesses the robustness of the results in table 1 by examining data from the 1990 and
17
This finding is complementary to that in Albouy and Ehrlich (2012) that housing is more expensive to construct
in hilly terrain.
18
1980 Censuses. It uses our preferred specification from column 3 of table 1. The results are
largely consistent across years. In both cases, the the price elasticity of housing demand is less
than one in absolute value and the income elasticity of demand is less than one, although the latter
difference is not statistically significant in the 1980 Census. However, the elasticity of substitution
is significantly less than one in both years.
Table 3 presents specifications corresponding to equation 4, which feature a more traditional
raw measure of household income. Column 1 shows results from an unrestricted regression of
the log median expenditure share on the housing and non-housing price indices and the household
income index. The three coefficients sum to -0.08, a number that is insignificantly different than
zero, passing the homogeneity restriction with a p-value of 7 percent. Unsurprisingly, the results
are similar in the restricted regression displayed in column 2. The uncompensated price elasticity
is -0.40 and the income elasticity is 0.34. However, in contrast to the compensated regressions in
tables 1 and 2, measurement error in the household income measure used in table 3 will likely lead
to division bias, causing the coefficient to be too low and underestimating the income elasticity.
Columns 4 through 6 of table 3 demonstrate that the results are relatively insensitive to alternative
specifications. However, the implied elasticity of substitution between renters and owners is higher
in the columns that include both renters and owners than in the columns that include only renters.
6
Household Demand for Housing over Time
Table 4 estimates an uncompensated housing demand using the time series data presented in Table
1. In all of the cases we use purely nominal values of prices and income. However, we include
separately the log CPI-U for shelter and the log CPI-U for all items less shelter, thereby remaining
agnostic about the proper deflator, which should be revealed by the behavior we observe.
In the bottom panel, we provide a decomposition to explain the growing share of income spent
19
on housing discussed in the introduction. Rearranging (7) and replacing Q and j with t, we have
t
t
t
t
t
t
ŝty = (1 − s¯y + H
y,p )(p̂ − ĉ ) + (y,m − 1)[(m̂ − ĉ ) − s¯y (p̂ − ĉ )] + αt t + et
(17)
The first component represents the change in the income effect due to the pure compensated price
effect. This effect is positive when the relative price of houisng increases if σ < 1, as 1−sy +H
y,p ) =
(1 − sy )(1 − σ). The second component is the income effect, making the proper adjustment for
changes in relative prices, from a parallel rise in the budget set. The third component is due to the
time trend, which could represent a change in household preferences. Indeed, number of people
in a household has fallen from 3.2 to 2.5 since 1970. Another possibility could be increasing
complementarity of housing with local amenities as households have shifted locations. The time
trend may also reflect limitations in the data and its ability to identify low-frequency responses in
housing consumption from shifting prices and income.
The first column applies to owners and renters using the BEA numbers, using nominal GDP per
household as the income measure. As required by demand theory, the three coefficients add up to
a number not significantly different from zero. In the restricted model, the implied uncompensated
own-price elasticity is -0.68, which is not significantly different from the preferred regression in
Table 1. The income elasticity is slightly smaller at 0.55. Its estimate may be confounded by
income’s collinear time trend, which is statistically significant. It suggests a secular trend towards
greater housing consumption independent of price and income movements.
In the BEA numbers, the overall increase in the housing share over the sample period was 8
percent (just under 2 percentage points). According to these estimates, the increase in the relative
price of housing raised the income share devoted to it by 7 percent, while rising incomes reduced
it by 12 percent. The positive time trend over-predicts the change at 15 percent, raising questions.
Columns 2 and 3 use average expenditure shares from the CES for renters, and for renters and
owners combined, using measures of average income. These estimates are less precise, although
the point estimates suggest elasticities closer to one, especially when owners are included. Conse-
20
quently, the decomposition suggests that changes in the expenditure share on housing were raised
somewhat by the rising price of housing, but even more by by the time trend, which ultimately
explains little. In interpreting this trend, one should bear in mind reporting issues in the CEX with
households reporting fewer and fewer of their non-housing expenditures (citation?).
In column 4 and 5, we examine the median income shares from the AHS for renters and renters
and owners. These estimates are even less precise, and suggest that demand is fairly elastic in
prices and rather less elastic in income. The decomposition reveals that the rather large increase in
housing expenditures for renters is due somewhat to increases in prices, and also to ¡i¿falling¡/i¿
median incomes. When home-owners are included, the income effect is again negative as median
incomes as a whole rose. Nevertheless, much of the change is explained by the secular time trend.
Relative to the cross-sectional point estimates, the time series estimates are slightly more elastic
with respect to prices and less with respect to incomes. If we were to apply the cross-sectional
parameters, we would find (positive) relative-price effects further from zero and (negative) income
effects closer to zero. This would explain more of the observed change, and reduce the change
attributed to the time trend.
7
7.1
Putting the Parameter Estimates into Use
Utility and Expenditure Functions
The estimates from the previous sections are sufficient to identify the utility and expenditure outlined in section 3.5. To illustrate what may be a realistic example, we take inspiration from column
3 of table 1, and use slightly rounded rational numbers for the parameters, setting σ = 2/3, δ =
7/8, γ = 3/2. Substituting in these parameter values into equations (13) and (14) yields nonhomothetic separable CES utility and expenditure functions ready for quantitative analysis:
"
U (x, y; 1) =
25 − 6y
42x
− 12
− 12
− 47
# 43
3

2
3
1
3
1
2
1
3
 7 c u +p 
, e(p, c, u; 1) = 36  23 
3
4
47u + 25
21
(18)
In the utility function, the units of x and y are as median income shares, with baseline values
at x = 0.78 and y = 0.22. Thus, a value of y = 1 would correspond to housing consumption
1/0.22 = 4.54 times that of a median renter. These functions could be applied immediately in a
number of models in urban, macro, or public economics involving the housing sector.
7.2
Cost-of-Living Indices
The price of housing varies considerably over space, and housing is a major consumption item
across households whose income varies widely. Therefore, it may be not only sensible but useful
to construct a cost-of-living index that incorporates a range of substitution and non-homothetic
consumption behaviors. Below we compare four different cost-of-living indices (COLIs) for housing and non-housing goods.
When demand is homothetic and exhibit constant elasticity of substitution the ideal cost-ofliving index is defined by fixed weight Lespeyres index in the zero-substitution case (σ = 0):
COL1 =
δcj + (1 − δ)pj
δc̄ + (1 − δ)p̄
(19)
where δ = 1 − s̄y . In the unit-elastic (σ = 1) case it is the Cobb-Douglas index:
δ
COL2 =
1−δ
(cj ) (pj )
(20)
(c̄)1−δ (p̄)1−δ
While for arbitrary values of σ, the ideal index is
"
δ σ c1−σ
+ (1 − δ)σ p1−σ
j
j
COL3 = σ 1−σ
σ
1−σ
δ c̄
+ (1 − δ) p̄
where the distribution parameter is set as δ =
1
1
s¯
1+( 1−ys¯ ) σ
y
22
1
# 1−σ
(21)
. When we allow for non-homotheticity,
we obtain an ideal cost-of-living index using the separable CES function that is remarkably similar
"
δ σ uγ(1−σ) cj1−σ + (1 − δ)σ pj1−σ
COL4 = σ γ(1−σ) 1−σ
δ u
c̄
+ (1 − δ)σ p̄1−σ
where the base utiity level is given by uγ(1−σ) =
1
# 1−σ
(22)
(1−s¯y )(1−δ)σ p̄1−σ
.
s¯y δ σ c̄1−σ
Figures 4A and 4B plot these four cost-of-living indices against the relative price of housing
(pj /cj ), with 4B adjusting for a base level of income that is one third the median represented in 4A.
In 4A, we see how the fixed housing demand measure overstates differences in cost-of-living by
ignoring households’ ability to substitute between housing and other goods according to their relative prices, while the Cobb-Douglas preference measure understates these differences by assuming
that substitution is easier than it is. Our intermediate value of substitution of σ = 2/3 more accurately reflects substitution possibilities. For example, when housing rents are double the national
average (i.e. pj /cj = 2), the fixed demand measure overstates the true cost-of-living differential
by 3.3 percentage points, while the Cobb-Douglas measure understates it by 1.4 percentage points.
In figure 4B, we see how the non-homothetic CES cost-of-living index has a much greater slope
than the one that fails to account for housing being a necessity. For poorer households, the other
COL indices understate the burden of living in expensive areas, and overstate it in poorer areas.
In other words, the correct index accounts for how high-rent cities are especially expensive for the
poor.
Of course, the regular CES function could be adapted to poorer households simply by changing its distribuiton parameter δ. The advantages of the non-homothetic CES function is that it
offers a continuous mapping of cost-of-living for any level of well-being, based on income at some
reference city at a given point in time.
23
8
Conclusion
Analyzing the cross-sectional relationship between housing rental prices and housing expenditure
shares suggests that housing demand is both price and income inelastic, albeit with elasticities
closer to one than to zero. The so-called “affordability” crisis in rental units in recent data appears
to stem somewhat from the rising relative and stagnant or declining incomes among those who
tend to rent. Nevertheless, there appears to be a secular rise in housing consumption that may be
due to shifts in household preferences, as households themselves have been changing.
For researchers interested in the role of housing, we offer a plausible ideal cost-of-living index
that improves on traditional CPI-style indices which assume fixed housing demand, may overstate
inflation or differences in housing-cost across cities, or misrepresent them for the poor. Indeed, we
find that expensive cities are even more expensive for the poor, thereby exacerbating affordability
problems. We also believe that the non-homothethic CES function may help provide economists
across fields, particularly urban and macro, with a better baseline to perform analyses and simulations.18
References
[1] Albouy, David. 2008. “Are Big Cities Really Bad Places to Live? Improving Quality-of-Life
Estimates across Cities.” NBER Working Paper No. 14981.
[2] Albouy, David, and Gabriel Ehrlich. 2012. “Land Values and Housing Productivity across
Cities.” NBER Working Paper No. 18110.
[3] Albouy, David, and Hanson Andrew. 2014. “Are Houses Too Big or in the Wrong Place?
Taxes Benefits to Housing and Inefficiencies in Location and Consumption. NBER Tax Policy
and the Economy.
[4] Albouy, David, and Lue Bert. 2014. “Driving to Opportunity: Local Rents, Wages, Commuting Costs and Sub-Metropolitan Quality of Life.” NBER Working Paper No. 19922.
[5] Albouy, David, and Bryan Stuart. 2014. “Urban Population and Amenities.” NBER Working
Paper No. 19919.
18
Our results are consistent with the assumptions made by of Albouy and Stuart (2014) and Rappaport (2008a),
should help researchers to predict population densities both within and across metropolitan areas
24
[6] Baum-Snow, Nathaniel and Ronni Pavan. 2013. ”Inequality and City Size.” Review of Economics and Statistics 95(5): 1535-1548.
[7] Black, Dan, Gates Gary, Sanders Seth, and Taylor Lowell. 2002. “Why Do Gay Men Live in
San Francisco ?” Journal of Urban Economics 51(1): 54-76
[8] Black, Daniel, Natalia Kolesnikova, and Lowell Taylor (2009) Earnings Functions When
Wages and Prices Vary by Location. Journal of Labor Economics 27(21).
[9] Blundell, Richard, Panos Pashardes and Guglielmo Weber “What do we Learn About Consumer Demand Patterns from Micro Data?” The American Economic Review 83(3): 570-597.
[10] Carrillo, Paul, Dirk Early, and Edgar Olsen. 2013. “A Panel of Interarea Price Indices for All
Areas in the United States 1982-2012” Available at SSRN: http://ssrn.com/abstract=2378028
or http://dx.doi.org/10.2139/ssrn.2378028.
[11] Cheshire, Paul, and Sheppard Stephen. 1998. “Estimating the Demand for Housing, Land,
and Neighbourhood Characteristics.” Oxford Bulletin of Economics and Statistics. Department of Economics, University of Oxford, vol. 60(3): 357-82, August.
[12] Davis, Morris A., and Jonathan Heathcote. ”The price and quantity of residential land in the
United States.” Journal of Monetary Economics 54.8 (2007): 2595-2620.
[13] Davis, Morris, and Francois Ortalo-Magne. 2011. “Household expenditures, wages, rents.”
Review of Economic Dynamics(14): 248-261.
[14] Davis, Morris and Michael Palumbo (2007) “The Price of Residential Land in Large U.S.
Cities.” Journal of Urban Economics, 63: 352-384.
[15] Deaton, Angus. 1986. “Demand Analysis” in Z. Grilliches and M.D. Intriligator Handbook
of Econometrics, 3: 1767-1839.
[16] De Leeuw, Frank. 1971. “The Demand for Housing: A Review of Cross-section Evidence.”
The Review of Economics and Statistics 53 (1): 1-10.
[17] Desmet, Klaus and Esteban Rossi-Hansberg. 2013. “Urban Accounting and Welfare.” American Economic Review 103(6): 2296-2327.
[18] Eckhout, Jan. 2004. “Gibrats law for all cities.” American Economic Review 94 (5): 14291451.
[19] Ermisch, J., J. Findlay, and K. Gibb, 1996, “The Price Elasticity of Housing Demand in
Britain: Issues of Sample Selection. Journal of Housing Economics 5(1): 64-86.
[20] Engel, E. 1857. “Die Produktions- und Consumtionsverhaltnisse des Konigreichs Sachsen.”
reprinted with Engel (1895), Anlage I, 1-54
[21] Guerreri, Veronica, Daniel Hartley, and Erik Hurst. 2013. “Endogenous Gentrification and
Housing Price Dynamics.” Journal of Public Economics 100: 45-60.
25
[22] Goodman, Allen C. 1988. “An Econometric Model of Housing Price, Permanent Income,
Tenure Choice, and Housing Demand. Journal of Urban Economics23 (May): 327353.
[23] Goodman, Allen C. 2002. “Estimating Equilibrium Housing Demand for Stayers of Housing
Price, Permanent Income, Tenure Choice, and Housing Demand. Journal of Urban Economics51: 1-24.
[24] Goodman, Allen C, and Kawai Masahiro. 1986. “Functional Form, Sample Selection, and
Housing Demand.” Journal of Urban Economics 20: 155-167.
[25] Gyourko, Joseph, Christopher Mayer, and Todd Sinai, 2013. ”Superstar Cities,” American
Economic Journal: Economic Policy 5(4): 167-99.
[26] Handbury, Jessie (2013) “Are Poor Cities Cheap for Everyone? Non-homotheticity and the
Cost-of-Living across U.S. Cities.” mimeo.
[27] Hansen, Julia L. and Formby John P. 1998. “Estimating the Income Elasticity of emand
for Housing:A Comparison of Traditional and Lorenz-Concentration Curve Methodologies.”
Journal of Housing Economics 7: 328-342.
[28] Hanushek, Eric, and Quigley John. 1980. “The Dynamics of housing market: a stock adjustment model of housing consumption.” Journal of Urban Economics 6(1), pp. 90-111.
[29] Harmon, Oskar R. 1988. “The Income Elasticity of Demand for Single-Family OwnerOccupied Housing: An Empirical Reconciliation.” Journal of Urban Economics 24: 173185.
[30] HUD PD & R Edge. “Secretary Donovan Highlights Convening on State of Americas
Rental Housing.” January 2014. http://www.huduser.org/portal/pdredge/
pdr_edge_featd_article_012714.html.
[31] Ioannides, Yannis M., and Jeffrey E. Zabel. 2003. “Neighborhood Effects and Housing Demand. Journal of Applied Econometrics 18 (Sep): 563-584.
[32] Joint Center for Housing Studies of Harvard University. 2013. “America’s Rental Housing:
Evolving Markets and Needs.” Mimeograph. Harvard University.
[33] Kau, James B., and Sirman C. F. 1979. “Urban Land Value Functions and the Price Elasticity
of Demand for Housing.” Journal of Urban Economics 6(4): 112-121.
[34] Larsen, Erling Red. 2002. “Searching for Basic Consumption Patterns:is the Engel Elasticity
of Housing Unity?”Discussion Papers No. 323, August 2002 Statistics Norway, Research
Department.
[35] Mayo, Stephen K. 1981. “Theory and Estimation in the Economics of Housing Demand.”
Journal of Urban Economics 10: 95-116.
[36] Michaels, Guy, Ferdinand Raurch, and Stephen J. Redding. 2013. ”Urbanization and Structural Transformation.” The Quarterly Journal of Economics 127(2): 535-586.
26
[37] Mills E.S. 1967. “An aggregative model of resource allocation in a metropolitan area.” American Economic Review 57: 197-210.
[38] Moretti, Enrico 2013 ”Real Wage Inequality” American Economic Journal: Applied Economics 5(1): 65-103.
[39] Muth, Richard F. 1960. “The Demand for Non-Farm Housing.” in The Demand for Durable
Goods, edited by Arnold C. Harberger, 29-96. Chicago, IL: University of Chicago Press,
1960. (Ph.D. dissertation)
[40] Piketty, Thomas. 2014. Capital in the Twenty-First Century. Cambridge, MA: Harvard University Press.
[41] Pollinsky, A. Mitchell, and Ellwood David T. 1979. “An Empirical Reconciliation of Micro
and Grouped Estimates of the Demand for Housing.” The Review of Economics and Statistics
61(2): 199-205
[42] Rappaport, Jordan. 2008a. “A Productivity Model of City Crowdedness.” Journal of Urban
Economics 65: 715-722.
[43] Rappaport, Jordan. 2008b. “Consumption Amenities and City Population Density.” Regional
Science and Urban Economics 38: 533-552.
[44] Reid, Margaret. 1962. Housing and Income. Chicago: University of Chicago Pres.
[45] Roback, Jennifer. 1982. “Wages, Rents, and the Quality of Life.” Journal of Political Economy 90: 1257-1278.
[46] Rosen, Harvey. 1985. “Housing Subsidies: Effects on Housing Decisions, Efciency, and Equity. In Handbook of Public Economics, vol. 1, edited by M. Feldstein and A. Auerbach.
Amsterdam: North-Holland.
[47] Rosen, Sherwin. 1979. “Wages-based Indexes of Urban Quality of Life.” In Current Issues in
Urban Economics, edited by P. Mieszkowski and M. Straszheim. Baltimore: John Hopkins
Univ. Press.
[48] Ruggles, Steven, Matthew Sobek, Trent Alexander, Catherine A. Fitch, Ronald Goeken, Patricia Kelly Hall, Miriam King, and Chad Ronnander. 2004. Integrated Public Use Microdata
Series: Version 3.0. Minneapolis: Minnesota Population Center.
[49] Saiz, Albert. 2010. ”The geographic determinants of housing supply.” The Quarterly Journal
of Economics 125.3: 1253-1296.
[50] Sato, Ruozo (1977) “Homothetic and Non-Homothetic CES Production Functions” American
Economic Review 67(4): 559-569.
[51] Schwabe, Hermann. 1868. ”Das Verhaltniss von Miethe und Einkom-men in Berlin,” in
Berlin und seine Entwickelung fur 1868 (Berlin, 1868): 264-67
27
[52] Stigler, George J. 1954. “The Early History of Empirical Studies of Consumer Behavior ”
Journal of Political Economy 62(2): 95-113
[53] Wright, Carroll. 1875. “Sixth Annual Report of the Bureau of Labor Statistics.”(Boston)
28
TABLE 1: COMPENSATED DEMAND FUNCTIONS - 2000 CENSUS DATA
Dependent Variable:
Regression Results:
Housing Price Index
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Aggregate
Expenditure Share
Log Aggregate
Expenditure Share
0.181
(0.013)
0.242
(0.020)
-0.274
(0.098)
-0.340
(0.081)
0.236
(0.015)
-0.236
(0.015)
-0.345
(0.080)
0.481
(0.011)
-0.481
(0.011)
-0.393
(0.062)
0.195
(0.015)
-0.195
(0.015)
-0.157
(0.081)
0.445
(0.012)
-0.445
(0.012)
-0.276
(0.065)
-1.509
(0.000)
-1.509
(0.000)
-1.509
(0.000)
0.232
(0.017)
-0.232
(0.017)
-0.413
(0.077)
-0.006
(0.088)
0.013
(0.002)
-1.509
(0.000)
-1.749
(0.000)
-1.649
(0.000)
-1.851
(0.000)
332
0.378
No
332
0.425
No
332
0.426
Yes
328
0.487
Yes
332
0.850
Yes
332
0.350
Yes
332
0.814
Yes
-0.032
(0.083)
-0.032
(0.083)
-0.204
(0.087)
-0.041
(0.103)
-0.048
(0.082)
0.388
(0.086)
0.698
0.698
0.020
0.691
0.560
0.000
Renters Only
Renters Only
Renters Only
Renters Only
Renters and Owners
Renters Only
Renters and Owners
0.221
(0.001)
-0.819
(0.013)
1.000
Restricted
0.221
(0.001)
-0.683
(0.028)
0.660
(0.081)
0.221
(0.001)
-0.687
(0.026)
0.655
(0.080)
0.697
(0.019)
0.885
(0.007)
1.459
(0.328)
0.221
(0.001)
-0.676
(0.026)
0.587
(0.077)
0.702
(0.022)
0.884
(0.008)
1.779
(0.332)
0.174
(0.001)
-0.451
(0.017)
0.607
(0.062)
0.418
(0.014)
0.985
(0.002)
0.816
(0.124)
0.192
(0.001)
-0.774
(0.023)
0.843
(0.081)
0.758
(0.018)
0.886
(0.006)
0.805
(0.409)
0.157
(0.000)
-0.511
(0.017)
0.724
(0.065)
0.472
(0.014)
0.980
(0.002)
0.619
(0.143)
Non-Housing Price Index
Predicted Wage Index
Inverse Distance to Coast
Average Slope of Land
Constant
N
Adjusted R-squared
Constrained Regression?
Unconstrained Sum of Housing and NonHousing Price Index Coefficients
P-value of Test of Homogeneity of Demand
Sample
Implied Demand Parameters:
Geometric Mean Expenditure Share
Uncompensated Own Price Elasticity of
Housing Demand
Income Elasticity of Housing Demand
Elasticity of Substitution Between Housing
and Consumption Goods
Distribution Parameter
Non-homotheticity Parameter
TABLE 2: COMPENSATED DEMAND FUNCTIONS - ADDITIONAL DATASETS
Dependent Variable:
Regression Results:
Housing Price Index
Non-Housing Price Index
Predicted Wage Index
Constant
N
Adjusted R-squared
Constrained Regression?
Unconstrained Sum of Housing and NonHousing Price Index Coefficients
P-value of Test of Homogeneity of Demand
Sample
Data Source
(1)
(2)
Log Median
Expenditure Share
Log Median
Expenditure Share
0.204
(0.014)
-0.204
(0.014)
-0.258
(0.096)
-1.510
(0.004)
0.172
(0.025)
-0.172
(0.025)
-0.150
(0.115)
-1.539
(0.005)
287
0.437
Yes
-0.238
(0.124)
288
0.144
Yes
-0.238
(0.191)
0.056
Renters Only
1990 Census
0.214
Renters Only
1980 Census
0.221
(0.001)
-0.739
(0.025)
0.742
(0.096)
0.738
(0.018)
0.871
(0.007)
1.267
(0.483)
0.215
(0.001)
-0.795
(0.034)
0.850
(0.115)
0.781
(0.032)
0.861
(0.012)
0.869
(0.690)
Implied Demand Parameters:
Geometric Mean Expenditure Share
Uncompensated Own Price Elasticity of
Housing Demand
Income Elasticity of Housing Demand
Elasticity of Substitution Between Housing and
Consumption Goods
Distribution Parameter
Non-homotheticity Parameter
TABLE 3: UNCOMPENSATED DEMAND FUNCTIONS - 2000 CENSUS DATA
Dependent Variable:
Regression Results:
Housing Price Index
Non-Housing Price Index
Household Income Index
(1)
(2)
(3)
(4)
(5)
(6)
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Median
Expenditure Share
Log Aggregate
Expenditure Share
Log Aggregate
Expenditure Share
0.617
(0.017)
-0.033
(0.054)
-0.665
(0.023)
0.604
(0.016)
0.061
(0.013)
-0.665
(0.023)
0.642
(0.011)
-0.181
(0.014)
-0.462
(0.021)
0.557
(0.016)
0.076
(0.013)
-0.634
(0.024)
0.595
(0.013)
-0.188
(0.018)
-0.407
(0.025)
-1.509
(0.002)
-1.509
(0.002)
0.583
(0.017)
0.068
(0.014)
-0.652
(0.024)
0.098
(0.051)
0.004
(0.001)
-1.509
(0.002)
-1.749
(0.002)
-1.649
(0.002)
-1.851
(0.002)
332
0.829
332
0.828
328
0.832
332
0.933
332
0.795
332
0.891
No
Yes
Yes
Yes
Yes
Yes
-0.080
(0.045)
-0.080
(0.045)
-0.183
(0.049)
0.159
(0.053)
-0.062
(0.046)
0.283
(0.064)
0.073
0.073
0.000
0.003
0.175
0.000
Renters Only
Renters Only
Renters Only
Renters and Owners
Renters Only
Renters and Owners
0.221
(0.000)
-0.383
(0.017)
0.335
(0.023)
0.221
(0.000)
-0.396
(0.016)
0.335
(0.023)
0.414
(0.015)
0.221
(0.000)
-0.417
(0.017)
0.348
(0.024)
0.436
(0.016)
0.174
(0.000)
-0.358
(0.011)
0.538
(0.021)
0.320
(0.010)
0.192
(0.000)
-0.443
(0.016)
0.366
(0.024)
0.461
(0.015)
0.157
(0.000)
-0.405
(0.013)
0.593
(0.025)
0.370
(0.013)
Inverse Distance to Coast
Average Slope of Land
Constant
N
Adjusted R-squared
Constrained Regression?
Unconstrained Sum of Housing Price, Non-Housing
Price, and Household Income Coefficients
P-value of Test of Homogeneity of Demand
Sample
Implied Demand Parameters:
Geometric Mean Expenditure Share
Uncompensated Own Price Elasticity of Housing
Demand
Income Elasticity of Housing Demand
Elasticity of Substitution Between Housing and
Consumption Goods
TABLE 4: PRICES, INCOMES, AND HOUSING EXPENDITURE SHARES - TIME SERIES DATA
Dependent Variable:
Data Source:
Unrestricted Regression Results:
Log CPI-U: Shelter
Log CPI-U: All Items Less Shelter
Log Household Income Measure
Year (Linear Time Trend)
Constant
P-value of Test of Homogeneity of Demand
Restricted Regression Results:
Log CPI-U: Shelter minus Log CPI-U: All Items Less
Shelter
Log Average Household Income minus Log CPI-U: All
Items Less Shelter
Year (Linear Time Trend)
Constant
N (years with non-missing data)
Implied Demand Parameters from Restricted Regressions:
Geometric Mean Expenditure Share
Uncompensated Own-Price Elasticity of Housing Demand
Income Elasticity of Housing Demand
(1)
(2)
(3)
(4)
(5)
Log Aggregate
Expenditure
Share
Log Average
Expenditure
Renters Only
Log Average
Expenditure
Renters &
Owners
Log Median
Expenditure
Share Renters
Log Median
Expenditure
Share Renters
and Owners
BEA
CEX
CEX
AHS
AHS
0.313
(0.082)
0.138
(0.099)
-0.449
(0.085)
0.004
(0.002)
-1.718
(0.003)
0.253
(0.294)
-0.055
(0.253)
-0.238
(0.129)
0.009
(0.004)
-1.232
(0.004)
-0.036
(0.237)
0.142
(0.210)
-0.044
(0.091)
0.005
(0.002)
-1.381
(0.003)
0.398
(0.484)
0.105
(0.608)
-0.562
(0.166)
0.007
(0.005)
-1.283
(0.010)
-0.163
(0.316)
1.022
(0.370)
-0.758
(0.224)
0.008
(0.004)
-1.605
(0.009)
0.95
0.78
0.34
0.82
0.53
0.318
(0.071)
-0.453
(0.054)
0.004
(0.001)
-1.718
(0.003)
0.249
(0.281)
-0.234
(0.122)
0.008
(0.001)
-1.232
(0.004)
0.152
(0.080)
-0.132
(0.031)
0.007
(0.001)
-1.381
(0.003)
0.262
(0.197)
-0.522
(0.127)
0.006
(0.002)
-1.283
(0.010)
0.103
(0.182)
-0.889
(0.203)
0.010
(0.001)
-1.605
(0.009)
42
28
29
21
23
0.179
(0.000)
-0.682
(0.071)
0.547
(0.054)
0.292
(0.001)
-0.751
(0.281)
0.766
(0.122)
0.251
(0.001)
-0.848
(0.080)
0.868
(0.031)
0.277
(0.003)
-0.738
(0.197)
0.478
(0.127)
0.201
(0.002)
-0.897
(0.182)
0.111
(0.203)
Decomposition of Long-run Change in Expenditure Share on Housing:
Total Change in Log Share
0.080
0.263
0.271
0.341
0.356
Change Attributed to Time Trend
0.150
0.286
0.281
0.231
0.396
Change from Compensated Relative Price Effect
0.065
0.052
0.031
0.034
-0.021
Change from Real Income Effect
-0.140
-0.018
-0.028
0.032
-0.019
Residual
0.006
-0.057
-0.013
0.043
-0.001
Homogeneity of demand requires that the coefficients on log CPI-U for shelter, log CPI-U for all items less shelter, and log real household income sum to
zero. The restricted regressions impose this constraint. Newey-West standard errors with a lag of three reported in parentheses. For non-BEA series, a
moving average with weight of 0.5 for the year after and the year before is used to deal with noise in the data.
0.8
1.0
Relative Price of Shelter
Expenditure Share on Housing
0.2
0.3
1.2
0.4
Figure 1: Expenditure Share on Housing 1970-2013
1970
1975
1980
1985
1990
1995
Year
2000
2005
2010
Aggregate Housing Share-BEA
Avg Rent Share-CEX
Avg Housing Share-CEX
Median Housing Share-AHS
Median Rent Share-AHS
Median Rent Share-Census
Relative Price of Shelter
For non BEA series, a moving average with weight of .5 for the year after and the year before is shown in the curve.
Figure 2: Housing Consumption with Production Possibility Expansions
Non-housing
E
Income
expansion
path
Constant
expenditure
share at
changing
prices
Constant
expenditure
share at
original
prices
C
B
D
Original budget
Constraint
A
Original production
possibility frontier
New production
possibility frontier
New budget
Constraint
LEGEND
A = original bundle
C = new bundle
A to B = income effect (necessity)
B to C = substitution effect (inelastic)
A to D = income effect (neutral)
D to E = substitution effect (unit)
New
Indifference
Curve
Equivalent new
budget constraint
at original relative
prices
Original
Indifference
Curve
Housing
0.25
Bloomington,
IN
Bryan-College
Station, TX
0.20
0.25
Gainesville, FL
Gainesville, FL
0.15
Median Expenditures on Housing as a Share of Income
Bloomington, IN
0.30
Figure 3B: Median Share of Income Spent on Housing
and the Relative Price of Housing, All Households 2000
Bryan-College Station, TX
0.20
Sheboygan, WI
Housing (Rental) vs. Non-Housing Price Index
METRO POP
>5 Mil
1.5-5 Mil
Non Metro
Linear fit
Slope = 0.22
0.5-1.5 Mil
<0.5 Mil
1.8
2.0
2.2
2.4
2.6
1.6
1.4
1.2
1.0
0.8
1.8
2.0
2.2
2.4
2.6
1.6
1.4
1.2
1.0
Sheboygan, WI
0.8
Median Expenditure on Gross Rent as a Share of Income
0.35
Figure 3A: Median Share of Income Spent on Rent
and the Relative Price of Housing, Renters Only 2000
Housing vs. Non-Housing Price Index
METRO POP
>5 Mil
1.5-5 Mil
Non Metro
Linear fit
Slope = 0.46
0.5-1.5 Mil
<0.5 Mil
Figure 4B: Comparison of Cost-of-living Indices
at one half of median household income
.8
.8
1
1
Cost-of-living Indices
Cost-of-living Indices
1.2
1.2
1.4
1.4
Figure 4A: Comparison of Cost-of-living Indices
at median household income
.5
1
1.5
2
2.5
.5
1
Relative Price
1.5
2
2.5
Relative Price
COL1: Fixed Demand
COL2: Cobb-Douglas
COL1: Fixed Demand
COL2: Cobb-Douglas
COL3: Homothetic CES
COL4: Separable Family of CES
COL3: Homothetic CES
COL4: Separable Family of CES
Appendix
A
Separable Family of CES
A.1
Formulation and Parameters
The simple “separable family” of CES utility function function from Sato(1977), who writes it as
U=
δ1 xρ + θ1
δ2 y ρ + θ2
αρ
where θi = − (α − δi ) ρ − δi is composed of more elementary parameters. These are δ = δ1 = 1 +
δ2 = δ =the distribution parameter, σ = 1/(1 − ρ) =the substitution parameter, and γ = 1/α=the
non-homotheticity parameter. Then using these parameters, we may rewrite the utility function as
U=
A.2
ρ
δx + θ1
(δ − 1)y ρ + θ2
γρ1
"
=
γσδx
σ−1
σ
+ 1 − γδ − σ
γσ(δ − 1)y
σ−1
σ
+ 1 − γ(δ − 1) − σ
σ
# γ(σ−1)
Marginal rate of substitution
Taking the ratio of partial derivates, the marginal rate of subtitution is then
M RSx,y
δ
=
1−δ
ρ−1 −1
− σ1
γ(1−σ)
x
δxρ + θ1
x
δ
u σ
=
ρ
y
(δ − 1)y + θ2
1−δ y
At the household optimum, we have c/p = M RSx,y ,
c
δ
=
p
1−δ
A.3
− σ1
−σ −σ
γ(1−σ)
x
x h c 1 − δ − γ(1−σ) i−σ
c
1−δ
·
u σ
=
u σ ⇒ =
uγ(1−σ)
y
y
p
δ
p
δ
Expenditure Share on Housing
To solve for the expenditure share, note that (d ln y)/d ln x = dy/dx(x/y) = −cx/py = sx /sy ,
the share spent on x relative to y is equal to
sx
d ln y
δ
=
=
sy
d ln x
1−δ
1− σ1
σ 1−σ
γ(1−σ)
x
δ
c
u σ =
uγ(1−σ)
y
1−δ
p
i
Then to solve the expenditure share for y only add one and invert
1
cx
c1−σ δ σ uγ(1−σ) + p1−σ (1 − δ)σ
=
+1=
sy
py
(1 − δ)σ p1−σ
(1 − δ)σ p1−σ
⇒ sy = σ 1−σ γ(1−σ)
δ c u
+ (1 − δ)σ p1−σ
In logarithms, we obtain an only partly linear equation
ln sy = σ ln(1 − δ) + (1 − σ) ln(p) − ln[δ σ c1−σ uU γ(1−σ) + (1 − δ)σ p1−σ ]
To complete the log-linearization, we take the total derivative we get the approximation
(1 − σ)δ σ c1−σ uγ(1−σ)b
c + γ(1 − σ)δ σ c1−σ uγ(1−σ) u
b + (1 − σ)(1 − δ)σ p1−σ pb
β σ c1−σ uγ(1−σ) + (1 − β)σ p1−σ
= (1 − sy )(1 − σ)b
p − (1 − sy )(1 − σ)b
c − γ(1 − sy )(1 − σ)b
u
sby = (1 − σ)p̂ −
This gives us that β0 = σ ln(1−δ) = ln s̄y , β1 = (1−s̄y )(1−σ), β3 = −γ(1−s̄y )(1−σ). Inverting,
the paramters can be expressed recursively as σ = 1 − β1 /(1 − eβ0 ), δ = 1 − eβ0 /σ , γ = −β3 /β1 .
A.4
Hicksian Demand and Expenditure Function
It is possible to solve for this utility function for both Hicksian demands, given by
p−σ (1 − δ)σ
y=
σ
[c1−σ δ σ uγ(1−σ) + p1−σ (1 − δ)σ ] σ−1
1 − γ(δ − 1) − σ 1 − γδ − σ γ (1−σ)
−
uσ
γσ
γσ
c−σ δ σ uγ(1−σ)
x=
σ
[c1−σ δ σ uγ(1−σ) + p1−σ (1 − δ)σ ] σ−1
1 − γ(δ − 1) − σ 1 − γδ − σ γ (1−σ)
−
uσ
γσ
γσ
σ
σ−1
σ
σ−1
as well as the expenditure function
e(p, c, u; 1) =
B


1−σ σ γ(1−σ)
1−σ
σ
 1
 1−σ
c δ u
+ p (1 − δ)
iσ

 1 γ + (1 − σ − γδ)(1 − u γ(1−σ)
σ
)
γσ
h
.
(A.1)
Data
We define cities at the Metropolitan Statistical Area (MSA) level using 1999 Office of Management
and Budget definitions of consolidated MSAs (e.g., San Francisco is combined with Oakland and
San Jose), of which there are 276. We use United States Census data from the 2000 Integrated
ii
Public-Use Microdata Series (IPUMS), from Ruggles et al. (2004), to calculate wage and housing
price differentials. The wage differentials are calculated for workers ages 25 to 55, who report
working at least 30 hours a week, 26 weeks a year. The MSA assigned to a worker is determined
by their place of residence, rather than their place of work. The wage differential of an MSA is
found by regressing log hourly wages on individual covariates and indicators for which MSA a
worker lives in, using the coefficients on these MSA indicators. The covariates consist of
• 12 indicators of educational attainment;
• a quartic in potential experience, and potential experience interacted with years of education;
• 9 indicators of industry at the one-digit level (1950 classification);
• 9 indicators of employment at the one-digit level (1950 classification);
• 4 indicators of marital status (married, divorced, widowed, separated);
• an indicator for veteran status, and veteran status interacted with age;
• 5 indicators of minority status (Black, Hispanic, Asian, Native American, and other);
• an indicator of immigrant status, years since immigration, and immigrant status interacted
with black, Hispanic, Asian, and other;
• 2 indicators for English proficiency (none or poor).
All covariates are interacted with gender.
This regression is first run using census-person weights. From the regressions a predicted
wage is calculated using individual characteristics alone, controlling for MSA, to form a new
weight equal to the predicted wage times the census-person weight. These new income-adjusted
weights are needed since workers need to be weighted by their income share. The new weights
arehttps://www.sharelatex.com/project/5338df0d5ecb36cb6b002bdb then used in a second regression, which is used to calculate the city-wage differentials from the MSA indicator variables. In
practice, this weighting procedure has only a small effect on the estimated wage differentials.
Housing price differentials are calculated using the logarithm reported gross rents and housing
values. Only housing units moved into within the last 10 years are included in the sample to ensure
that the price data are fairly accurate. The differential housing price of an MSA is calculated in
a manner similar to wages, except using a regression of the actual or imputed rent on a set of
covariates at the unit level. The covariates for the adjusted differential are
• 9 indicators of building size;
• 9 indicators for the number of rooms, 5 indicators for the number of bedrooms, number
of rooms interacted with number of bedrooms, and the number of household members per
room;
• 2 indicators for lot size;
• 7 indicators for when the building was built;
iii
• 2 indicators for complete plumbing and kitchen facilities;
• an indicator for commercial use;
• an indicator for condominium status (owned units only).
A regression of housing values on housing characteristics and MSA indicator variables is first run
using only owner-occupied units, weighting by census-housing weights. A new value-adjusted
weight is calculated by multiplying the census-housing weights by the predicted value from this
first regression using housing characteristics alone, controlling for MSA. A second regression is
run using these new weights for all units, rented and owner-occupied, on the housing characteristics
fully interacted with tenure, along with the MSA indicators, which are not interacted. The houseprice differentials are taken from the MSA indicator variables in this second regression. As with
the wage differentials, this adjusted weighting method has only a small impact on the measured
price differentials.
iv
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Abilene, TX
Akron, OH
Albany, GA
Albany-Schenectady-Troy, NY
Albuquerque, NM
Alexandria, LA
Allentown-Bethlehem, PA-NJ
Altoona, PA
Amarillo, TX
Anchorage, AK
Ann Arbor, MI
Anniston, AL
Appleton-Oshkosh, WI
Asheville, NC
Athens, GA
Atlanta, GA
Atlantic City, NJ
Auburn-Opelika, AL
Augusta, GA-SC
Austin, TX
Bakersfield, CA
Baltimore, MD
Barnstable-Yarmouth, MA
Baton Rouge, LA
Beaumont-Port Arthur-Orange, TX
Bellingham, WA
Benton Harbor, MI
Billings, MT
Biloxi-Gulfport, MS
Binghamton, NY-PA
Birmingham, AL
Bloomington, IN
Bloomington-Normal, IL
Boise City, ID
Boston, MA
Bremerton, WA
Bridgeport-Milford, CT
Brockton, MA
MSA Population
126,952
692,912
120,551
796,100
712,937
128,075
641,637
131,023
215,463
259,063
479,754
110,594
357,928
225,195
153,445
3,987,990
359,167
116,435
451,061
1,167,216
650,891
2,513,661
144,360
604,708
381,559
169,001
163,682
128,660
318,936
254,116
803,700
122,388
152,616
430,161
3,951,557
234,652
343,379
258,188
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.22
0.22
0.22
0.22
0.25
0.22
0.21
0.19
0.22
0.24
0.24
0.21
0.19
0.23
0.27
0.23
0.25
0.30
0.22
0.25
0.23
0.22
0.25
0.24
0.22
0.27
0.20
0.22
0.22
0.23
0.21
0.32
0.22
0.24
0.22
0.23
0.24
0.22
0.16
0.17
0.15
0.16
0.19
0.16
0.16
0.15
0.15
0.17
0.18
0.15
0.15
0.18
0.19
0.18
0.19
0.17
0.16
0.18
0.17
0.17
0.21
0.16
0.13
0.22
0.16
0.16
0.16
0.14
0.16
0.21
0.15
0.17
0.21
0.19
0.20
0.19
Housing Price Index
Rentals Only
Rentals & Owned
-0.21
-0.09
-0.30
0.05
0.00
-0.39
0.00
-0.37
-0.15
0.30
0.24
-0.45
-0.12
-0.11
-0.11
0.17
0.09
-0.27
-0.25
0.25
-0.11
0.05
0.11
-0.17
-0.28
0.05
-0.20
-0.22
-0.17
-0.16
-0.16
-0.02
-0.08
-0.04
0.31
0.04
0.20
0.09
-0.36
-0.08
-0.33
-0.04
0.00
-0.38
-0.04
-0.34
-0.27
0.20
0.21
-0.44
-0.14
-0.06
-0.16
0.03
0.10
-0.25
-0.28
0.12
-0.14
0.03
0.28
-0.18
-0.40
0.12
-0.20
-0.25
-0.24
-0.28
-0.16
-0.08
-0.14
-0.11
0.46
0.11
0.36
0.18
Non-Housing Price
Index
-0.03
-0.01
-0.08
0.00
-0.04
-0.06
0.01
-0.04
-0.07
0.19
0.02
-0.07
-0.03
0.00
-0.05
-0.01
0.03
-0.07
-0.05
-0.08
-0.01
0.02
0.06
0.01
-0.06
0.01
-0.03
-0.03
-0.03
-0.04
-0.05
0.01
0.05
0.01
0.12
0.01
0.05
0.06
Predicted Wage Index
Renters Only
Renters & Owners
0.01
0.01
-0.02
0.06
0.03
-0.10
-0.01
-0.02
-0.02
0.07
0.12
0.00
0.04
0.02
-0.03
-0.01
-0.13
0.04
-0.03
0.05
-0.08
0.02
0.04
-0.03
-0.05
0.04
-0.01
0.06
-0.02
0.01
0.02
0.05
0.05
0.02
0.09
0.09
-0.08
-0.02
0.00
0.03
-0.05
0.07
0.02
-0.06
0.01
-0.02
-0.02
0.05
0.13
-0.03
0.05
-0.01
0.00
0.02
-0.08
0.00
-0.02
0.06
-0.09
0.03
0.05
0.00
-0.02
0.02
0.01
0.03
-0.02
0.04
0.03
0.07
0.09
0.05
0.09
0.08
0.03
0.00
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Brownsville-Harlingen-San Benito, TX
Bryan-College Station, TX
Buffalo, NY
Canton, OH
Cedar Rapids, IA
Champaign-Urbana-Rantoul, IL
Charleston-North Charleston, SC
Charlotte-Gastonia, NC
Charlottesville, VA
Chattanooga, TN-GA
Chicago, IL
Chico, CA
Cincinnati, OH-KY-IN
Clarksville-Hopkinsville, TN-KY
Cleveland, OH
Colorado Springs, CO
Columbia, MO
Columbia, SC
Columbus, GA-AL
Columbus, OH
Corpus Christi, TX
Dalls-Fort Worth, TX
Danbury, CT
Danville, VA
Davenport-Rock Island-Moline, IA-IL
Dayton, OH
Daytona Beach, FL
Decatur, AL
Decatur, IL
Denver-Boulder, CO
Des Moines, IA
Detroit, MI
Dothan, AL
Dover, DE
Duluth-Superior, MN-WI
Dutchess County, NY
Eau Claire, WI
El Paso, TX
MSA Population
336,631
153,194
1,175,089
408,072
188,914
181,422
454,054
1,499,677
160,421
434,752
8,804,453
202,375
1,473,012
134,209
2,255,480
515,629
136,063
544,165
186,426
1,443,293
261,023
5,043,876
184,523
109,618
268,781
954,465
445,477
145,469
114,926
2,198,801
375,685
4,430,477
138,133
125,613
199,548
277,140
147,758
676,220
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.22
0.35
0.23
0.21
0.21
0.27
0.24
0.21
0.24
0.21
0.22
0.28
0.21
0.21
0.21
0.24
0.24
0.22
0.22
0.22
0.22
0.22
0.22
0.20
0.20
0.21
0.25
0.20
0.22
0.24
0.21
0.20
0.19
0.22
0.21
0.23
0.21
0.24
0.16
0.21
0.16
0.16
0.15
0.17
0.18
0.17
0.19
0.16
0.18
0.21
0.16
0.17
0.17
0.19
0.18
0.16
0.17
0.17
0.15
0.16
0.19
0.15
0.15
0.16
0.17
0.15
0.14
0.20
0.16
0.16
0.15
0.17
0.14
0.17
0.16
0.16
Housing Price Index
Rentals Only
Rentals & Owned
-0.41
-0.01
-0.11
-0.25
-0.10
-0.01
-0.01
0.01
0.07
-0.23
0.19
-0.02
-0.09
-0.18
-0.06
0.13
-0.14
-0.09
-0.23
-0.02
-0.10
0.14
0.39
-0.44
-0.17
-0.14
-0.01
-0.42
-0.29
0.23
0.00
0.02
-0.44
-0.09
-0.30
0.21
-0.20
-0.25
-0.50
-0.12
-0.16
-0.20
-0.13
-0.12
-0.01
-0.04
0.00
-0.25
0.24
0.03
-0.06
-0.30
-0.03
0.03
-0.21
-0.15
-0.25
-0.06
-0.24
-0.02
0.46
-0.41
-0.20
-0.13
-0.17
-0.34
-0.35
0.22
-0.07
0.05
-0.42
-0.14
-0.31
0.15
-0.24
-0.38
Non-Housing Price
Index
-0.03
-0.12
-0.03
-0.04
-0.04
0.03
-0.05
-0.02
-0.02
-0.02
0.04
-0.03
-0.05
-0.08
0.04
-0.06
-0.02
-0.09
-0.07
-0.02
-0.05
-0.01
0.07
-0.06
-0.05
-0.03
-0.08
-0.08
-0.05
0.03
-0.02
-0.02
-0.06
0.01
-0.02
0.05
-0.05
-0.09
Predicted Wage Index
Renters Only
Renters & Owners
-0.09
0.03
0.02
-0.01
0.05
0.08
0.00
-0.02
0.04
0.01
0.00
0.02
0.00
0.05
0.00
0.06
0.10
0.01
-0.03
0.02
0.02
0.00
0.01
-0.12
0.01
0.00
0.01
-0.04
0.02
0.03
0.04
-0.02
-0.03
0.01
0.04
0.04
0.04
-0.04
-0.16
0.04
0.04
0.00
0.06
0.06
-0.01
0.00
0.06
0.00
0.02
0.00
0.03
-0.01
0.02
0.07
0.07
0.02
-0.03
0.03
-0.01
0.01
0.14
-0.10
0.01
0.02
-0.03
0.00
0.00
0.05
0.05
0.02
-0.04
-0.02
0.06
0.06
0.02
-0.10
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Elkhart, IN
Erie, PA
Eugene-Springfield, OR
Evansville, IN-KY
Fargo-Moorhead, ND-MN
Fayetteville, NC
Fayetteville-Springdale, AR
Fitchburg-Leominster, MA
Flagstaff, AZ-UT
Flint, MI
Florence, AL
Fort Collins, CO
Fort Lauderdale-Hollywood, FL
Fort Myers-Cape Coral, FL
Fort Pierce, FL
Fort Smith, AR-OK
Fort Walton Beach, FL
Fort Wayne, IN
Fresno, CA
Gadsden, AL
Gainesville, FL
Galveston-Texas City, TX
Glens Falls, NY
Goldsboro, NC
Grand Junction, CO
Grand Rapids, MI
Greeley, CO
Green Bay, WI
Greensboro--Winston-Salem--High Point, NC
Greenville, NC
Greenville-Spartanburg, SC
Hagerstown, MD
Hamilton-Middletown, OH
Harrisburg, PA
Hartford, CT
Hattiesburg, MS
Hickory, NC
Honolulu, HI
MSA Population
182,252
279,521
324,317
252,410
121,173
299,932
309,915
141,969
117,109
240,153
142,703
235,532
1,624,272
440,333
323,090
169,401
171,551
460,349
924,612
102,183
219,795
249,853
123,609
113,118
111,922
984,107
178,872
227,296
1,252,554
134,932
796,528
128,316
334,518
629,304
708,743
111,694
342,072
876,066
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.20
0.21
0.27
0.20
0.22
0.23
0.22
0.20
0.25
0.23
0.22
0.26
0.26
0.24
0.25
0.19
0.23
0.20
0.24
0.18
0.30
0.22
0.23
0.20
0.25
0.21
0.24
0.19
0.21
0.26
0.20
0.19
0.21
0.21
0.21
0.26
0.19
0.25
0.15
0.16
0.21
0.15
0.16
0.18
0.17
0.17
0.19
0.14
0.16
0.20
0.18
0.17
0.16
0.15
0.17
0.15
0.19
0.15
0.19
0.15
0.17
0.16
0.20
0.16
0.20
0.16
0.16
0.17
0.16
0.17
0.16
0.16
0.17
0.17
0.15
0.23
Housing Price Index
Rentals Only
Rentals & Owned
-0.14
-0.25
0.01
-0.21
-0.21
-0.12
-0.19
-0.05
0.01
-0.21
-0.46
0.13
0.30
0.06
-0.03
-0.35
-0.05
-0.18
-0.06
-0.53
-0.04
-0.03
-0.05
-0.38
-0.13
-0.07
-0.07
-0.07
-0.14
-0.22
-0.21
-0.23
-0.07
-0.08
0.11
-0.29
-0.25
0.43
-0.20
-0.26
0.08
-0.21
-0.25
-0.21
-0.22
0.02
0.03
-0.32
-0.36
0.12
0.08
-0.03
-0.12
-0.36
-0.14
-0.27
-0.04
-0.45
-0.16
-0.15
-0.17
-0.30
-0.08
-0.11
-0.02
-0.07
-0.14
-0.19
-0.21
-0.14
-0.08
-0.08
0.16
-0.37
-0.23
0.65
Non-Housing Price
Index
-0.07
-0.04
0.01
-0.11
-0.01
0.01
-0.11
0.03
-0.06
-0.01
-0.07
-0.02
0.01
-0.04
-0.02
-0.11
0.00
-0.04
0.06
-0.07
-0.04
-0.03
0.04
-0.08
-0.03
0.03
0.02
-0.03
-0.06
-0.05
-0.08
-0.01
-0.01
0.00
0.04
-0.07
-0.04
0.11
Predicted Wage Index
Renters Only
Renters & Owners
-0.04
0.02
0.04
0.02
0.04
0.05
0.01
-0.03
0.06
-0.09
-0.01
0.09
-0.03
-0.04
-0.07
-0.03
0.09
0.00
-0.13
-0.01
0.07
0.02
0.00
0.01
-0.02
-0.05
-0.03
-0.01
-0.05
-0.03
-0.02
-0.02
0.03
0.03
-0.02
0.03
-0.04
0.09
-0.05
0.01
0.04
0.02
0.03
-0.03
-0.02
0.00
0.01
-0.12
0.00
0.12
-0.03
-0.05
-0.04
-0.05
0.04
0.01
-0.10
-0.01
0.07
0.02
0.00
-0.05
0.03
0.03
0.01
0.03
-0.02
-0.01
-0.01
-0.02
0.05
0.01
0.03
0.02
-0.06
0.01
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Houma-Thibodaux, LA
Houston, TX
Huntsville, AL
Indianapolis, IN
Iowa City, IA
Jackson, MI
Jackson, MS
Jackson, TN
Jacksonville, FL
Jacksonville, NC
Jamestown-Dunkirk, NY
Janesville-Beloit, WI
Johnson City-Kingsport-Bristol, TN-VA
Johnstown, PA
Joplin, MO
Kalamazoo-Portage, MI
Kankakee, IL
Kansas City, MO-KS
Kenosha, WI
Killeen-Temple, TX
Knoxville, TN
Kokomo, IN
La Crosse, WI
Lafayette, LA
Lafayette-West Lafayette, IN
Lake Charles, LA
Lakeland-Winter Haven, FL
Lancaster, PA
Lansing-East Lansing, MI
Laredo, TX
Las Cruces, NM
Las Vegas, NV
Lexington-Fayette, KY
Lima, OH
Lincoln, NE
Little Rock-North Little Rock, AR
Longview-Marshall, TX
Los Angeles-Long Beach, CA
MSA Population
103,563
4,413,414
344,491
1,603,021
108,518
160,391
438,789
107,550
1,101,766
149,091
140,116
151,640
314,402
233,942
155,401
451,406
104,042
1,682,053
148,260
313,151
576,512
100,506
105,700
247,230
181,493
183,144
482,562
464,550
445,925
190,074
173,843
1,375,174
258,129
156,274
246,945
584,977
170,557
12,400,000
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.20
0.22
0.20
0.21
0.30
0.20
0.23
0.22
0.23
0.22
0.22
0.20
0.21
0.19
0.21
0.21
0.21
0.21
0.21
0.22
0.23
0.20
0.21
0.22
0.27
0.20
0.21
0.21
0.23
0.23
0.25
0.24
0.24
0.18
0.23
0.23
0.21
0.25
0.15
0.15
0.15
0.16
0.18
0.15
0.16
0.16
0.16
0.17
0.15
0.15
0.16
0.15
0.15
0.16
0.16
0.16
0.16
0.17
0.17
0.13
0.16
0.15
0.18
0.14
0.15
0.17
0.16
0.18
0.17
0.19
0.17
0.14
0.17
0.16
0.15
0.22
Housing Price Index
Rentals Only
Rentals & Owned
-0.34
0.08
-0.24
-0.03
0.03
-0.22
-0.18
-0.33
0.01
-0.16
-0.25
-0.12
-0.38
-0.53
-0.36
-0.13
-0.13
-0.01
0.03
-0.10
-0.25
-0.20
-0.18
-0.31
-0.05
-0.33
-0.15
0.01
-0.03
-0.29
-0.31
0.18
-0.06
-0.35
-0.06
-0.15
-0.26
0.40
-0.33
-0.10
-0.26
-0.10
-0.01
-0.21
-0.26
-0.36
-0.11
-0.25
-0.39
-0.16
-0.33
-0.44
-0.42
-0.19
-0.12
-0.12
0.02
-0.25
-0.24
-0.23
-0.19
-0.27
-0.12
-0.32
-0.27
-0.03
-0.12
-0.34
-0.27
0.07
-0.11
-0.33
-0.15
-0.20
-0.36
0.53
Non-Housing Price
Index
-0.06
-0.04
-0.01
-0.07
-0.02
-0.01
-0.12
0.01
-0.05
-0.05
-0.03
-0.02
-0.13
-0.04
-0.10
-0.03
0.00
-0.02
0.02
-0.12
-0.08
-0.02
-0.04
-0.05
-0.08
-0.09
-0.06
-0.01
-0.01
-0.07
-0.09
-0.01
-0.03
-0.06
-0.02
-0.06
-0.07
0.07
Predicted Wage Index
Renters Only
Renters & Owners
-0.07
-0.04
0.01
0.00
0.09
-0.04
-0.03
-0.10
0.02
0.06
-0.01
-0.03
0.03
0.02
-0.02
-0.02
-0.08
0.02
0.01
0.05
0.02
0.00
0.04
0.02
0.05
-0.04
-0.05
-0.04
0.03
-0.09
-0.02
-0.08
0.03
0.01
0.04
0.00
0.01
-0.06
-0.07
-0.02
0.06
0.02
0.09
0.01
0.00
-0.03
0.00
-0.02
0.00
0.00
0.01
-0.01
-0.01
0.02
-0.03
0.05
0.03
-0.03
0.03
0.00
0.05
0.00
0.01
-0.03
-0.08
-0.01
0.05
-0.13
-0.08
-0.12
0.05
0.01
0.06
0.01
0.00
-0.07
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Louisville, KY-IN
Lubbock, TX
Lynchburg, VA
Macon, GA
Madison, WI
Manchester, NH
Mansfield, OH
McAllen-Pharr-Edinburg, TX
Medford, OR
Melbourne-Titusville-Cocoa, FL
Memphis, TN-AR-MS
Merced, CA
Miami, FL
Milwaukee, WI
Minneapolis-St. Paul, MN-WI
Mobile, AL
Modesto, CA
Monmouth-Ocean, NJ
Monroe, LA
Montgomery, AL
Muncie, IN
Myrtle Beach, SC
Naples, FL
Nashua, NH
Nashville-Davidson, TN
New Bedford, MA
New Haven-West Haven, CT
New Orleans, LA
New York, NY-NJ
Newburgh-Middletown, NY
Non-metropolitan AK
Non-metropolitan AL
Non-metropolitan AR
Non-metropolitan AZ
Non-metropolitan CA
Non-metropolitan CO
Non-metropolitan CT
Non-metropolitan DE
MSA Population
921,599
243,899
213,723
321,450
429,839
107,037
130,084
565,800
179,811
479,298
998,698
209,707
2,221,632
1,499,015
2,856,295
540,100
450,865
1,128,173
146,975
333,479
119,028
195,205
249,728
116,182
1,234,004
174,864
358,125
1,246,651
17,200,000
343,591
367,124
1,504,381
1,607,993
942,343
1,249,739
924,086
1,350,818
158,149
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.21
0.25
0.20
0.22
0.24
0.22
0.19
0.22
0.26
0.23
0.23
0.24
0.27
0.21
0.23
0.24
0.22
0.24
0.23
0.23
0.24
0.22
0.22
0.22
0.23
0.19
0.23
0.23
0.22
0.22
0.21
0.19
0.21
0.22
0.24
0.23
0.21
0.20
0.16
0.17
0.16
0.15
0.19
0.18
0.15
0.16
0.21
0.16
0.17
0.20
0.20
0.17
0.17
0.17
0.18
0.18
0.16
0.17
0.16
0.17
0.19
0.16
0.18
0.18
0.19
0.18
0.20
0.17
0.18
0.15
0.15
0.17
0.20
0.20
0.17
0.17
Housing Price Index
Rentals Only
Rentals & Owned
-0.18
-0.15
-0.30
-0.25
0.16
0.17
-0.32
-0.45
-0.02
0.00
-0.07
-0.13
0.20
0.04
0.18
-0.28
0.04
0.30
-0.35
-0.18
-0.24
-0.08
0.23
0.25
-0.03
-0.20
0.16
-0.11
0.34
0.23
0.17
-0.64
-0.47
-0.24
-0.03
0.03
0.17
-0.33
-0.15
-0.30
-0.30
-0.31
0.12
0.12
-0.28
-0.58
0.06
-0.17
-0.16
-0.06
0.17
0.04
0.07
-0.27
0.05
0.25
-0.32
-0.22
-0.31
-0.13
0.29
0.15
-0.05
0.04
0.20
-0.09
0.47
0.13
0.11
-0.51
-0.47
-0.20
0.13
0.13
0.17
-0.09
Non-Housing Price
Index
-0.03
-0.05
-0.07
-0.04
0.00
-0.03
-0.06
-0.09
-0.01
-0.04
-0.09
-0.02
0.00
-0.04
0.06
-0.08
0.06
0.07
-0.05
-0.04
-0.07
-0.04
0.00
0.07
-0.07
0.03
0.04
-0.03
0.07
0.04
0.19
-0.10
-0.06
-0.02
0.00
0.06
0.03
-0.02
Predicted Wage Index
Renters Only
Renters & Owners
-0.02
-0.02
-0.04
-0.03
0.11
0.02
-0.01
-0.11
0.03
0.06
-0.04
-0.15
-0.11
0.02
0.05
-0.02
-0.08
0.02
-0.05
0.02
-0.03
-0.04
-0.10
0.07
0.01
-0.09
0.01
-0.04
0.01
-0.02
0.08
-0.03
-0.05
0.00
-0.04
0.05
0.04
-0.06
0.00
-0.03
-0.02
-0.02
0.11
-0.03
-0.01
-0.19
0.03
0.04
-0.03
-0.16
-0.12
0.04
0.08
-0.01
-0.09
0.08
-0.04
0.00
0.00
-0.05
-0.06
0.07
0.01
-0.07
0.04
-0.04
0.00
0.01
0.02
-0.06
-0.06
-0.07
-0.05
0.06
0.07
-0.03
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Non-metropolitan FL
Non-metropolitan GA
Non-metropolitan HI
Non-metropolitan IA
Non-metropolitan ID
Non-metropolitan IL
Non-metropolitan IN
Non-metropolitan KS
Non-metropolitan KY
Non-metropolitan LA
Non-metropolitan MA
Non-metropolitan MD
Non-metropolitan ME
Non-metropolitan MI
Non-metropolitan MN
Non-metropolitan MO
Non-metropolitan MS
Non-metropolitan MT
Non-metropolitan NC
Non-metropolitan ND
Non-metropolitan NE
Non-metropolitan NM
Non-metropolitan NV
Non-metropolitan NY
Non-metropolitan OH
Non-metropolitan OK
Non-metropolitan OR
Non-metropolitan PA
Non-metropolitan RI
Non-metropolitan SC
Non-metropolitan SD
Non-metropolitan TN
Non-metropolitan TX
Non-metropolitan UT
Non-metropolitan VA
Non-metropolitan VT
Non-metropolitan WA
Non-metropolitan WI
MSA Population
1,222,532
2,744,802
335,651
1,863,270
863,855
2,202,549
1,791,003
1,366,517
2,828,647
1,415,540
569,691
666,998
1,033,664
2,178,963
1,565,030
1,798,819
1,869,256
774,080
2,632,956
521,239
878,760
783,050
285,196
1,744,930
2,548,986
1,862,951
1,194,699
2,023,193
258,023
1,616,255
629,811
2,123,330
4,030,376
531,967
1,640,567
608,387
1,063,531
1,866,585
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.22
0.20
0.23
0.19
0.22
0.20
0.19
0.21
0.19
0.21
0.21
0.22
0.21
0.21
0.20
0.20
0.21
0.23
0.21
0.20
0.19
0.21
0.22
0.23
0.19
0.20
0.24
0.20
0.22
0.20
0.21
0.19
0.20
0.22
0.20
0.23
0.23
0.19
0.16
0.15
0.22
0.14
0.17
0.14
0.15
0.15
0.15
0.15
0.18
0.17
0.17
0.15
0.15
0.15
0.15
0.18
0.16
0.14
0.14
0.16
0.17
0.15
0.15
0.14
0.19
0.15
0.19
0.15
0.15
0.15
0.14
0.19
0.16
0.18
0.19
0.15
Housing Price Index
Rentals Only
Rentals & Owned
-0.22
-0.40
0.12
-0.35
-0.26
-0.36
-0.31
-0.32
-0.47
-0.56
-0.03
-0.18
-0.24
-0.28
-0.34
-0.48
-0.53
-0.31
-0.37
-0.44
-0.38
-0.44
-0.04
-0.13
-0.34
-0.46
-0.11
-0.34
0.08
-0.39
-0.45
-0.50
-0.39
-0.17
-0.35
-0.02
-0.13
-0.27
-0.26
-0.35
0.35
-0.37
-0.24
-0.37
-0.30
-0.43
-0.47
-0.46
0.11
-0.11
-0.22
-0.26
-0.35
-0.47
-0.53
-0.25
-0.28
-0.51
-0.45
-0.36
-0.04
-0.26
-0.31
-0.52
-0.03
-0.34
0.21
-0.32
-0.46
-0.43
-0.47
-0.17
-0.34
-0.06
-0.03
-0.25
Non-Housing Price
Index
0.03
-0.05
0.10
-0.06
-0.03
-0.05
-0.06
-0.05
-0.05
-0.08
0.02
-0.01
-0.01
-0.05
-0.05
-0.08
-0.07
0.01
-0.03
-0.08
-0.05
-0.04
0.00
0.03
-0.03
-0.07
0.03
-0.04
0.05
0.02
0.00
-0.07
-0.11
-0.02
-0.06
0.00
0.04
-0.02
Predicted Wage Index
Renters Only
Renters & Owners
-0.08
-0.07
-0.01
0.02
0.01
0.02
-0.01
0.04
0.01
-0.05
0.04
-0.03
0.04
0.01
0.00
0.01
-0.08
0.04
-0.07
0.07
0.02
0.01
0.02
0.02
0.00
0.00
0.01
0.01
0.08
-0.05
0.05
-0.03
-0.04
0.04
-0.02
0.06
-0.01
0.01
-0.08
-0.07
-0.09
0.00
0.01
0.00
-0.02
0.01
-0.03
-0.05
0.06
0.00
0.02
0.00
0.01
-0.04
-0.08
0.03
-0.07
0.02
0.00
-0.06
-0.02
0.01
-0.02
-0.03
0.00
-0.02
0.11
-0.08
0.01
-0.06
-0.06
0.05
-0.05
0.05
0.00
0.00
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Non-metropolitan WV
Non-metropolitan WY
Non-metropolitanNH
Norfolk-Virginia Beach-Portsmouth, VA-NC
Ocala, FL
Odessa, TX
Oklahoma City, OK
Olympia, WA
Omaha, NE-IA
Orlando, FL
Panama City, FL
Pensacola, FL
Peoria, IL
Philadelphia, PA-NJ
Phoenix, AZ
Pittsburgh, PA
Portland, ME
Portland, OR-WA
Providence-Warwick-Pawtucket, RI-MA
Provo-Orem, UT
Pueblo, CO
Punta Gorda, FL
Racine, WI
Raleigh-Durham, NC
Reading, PA
Redding, CA
Reno, NV
Richland-Kennewick-Pasco, WA
Richmond, VA
Riverside-San Bernardino-Ontario, CA
Roanoke, VA
Rochester, MN
Rochester, NY
Rockford, IL
Rocky Mount, NC
Sacramento, CA
Saginaw, MI
Salem, OR
MSA Population
1,809,034
493,849
1,011,597
1,553,838
259,712
238,692
892,347
210,011
584,099
1,652,742
146,122
411,270
346,102
5,082,137
3,070,331
2,285,064
241,693
1,789,019
1,025,944
367,035
135,990
141,080
185,041
1,182,869
368,284
162,160
339,936
191,186
995,112
3,253,263
236,363
122,319
1,030,303
319,846
143,674
1,632,863
400,853
282,595
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.21
0.20
0.22
0.24
0.22
0.21
0.22
0.24
0.21
0.25
0.23
0.24
0.20
0.22
0.24
0.21
0.22
0.24
0.21
0.24
0.25
0.23
0.21
0.24
0.21
0.26
0.25
0.21
0.23
0.25
0.21
0.21
0.24
0.20
0.21
0.24
0.22
0.23
0.15
0.16
0.17
0.18
0.16
0.14
0.16
0.19
0.16
0.18
0.17
0.17
0.15
0.17
0.18
0.15
0.18
0.21
0.18
0.21
0.18
0.16
0.16
0.18
0.16
0.20
0.20
0.16
0.17
0.19
0.16
0.15
0.15
0.15
0.16
0.20
0.15
0.19
Housing Price Index
Rentals Only
Rentals & Owned
-0.43
-0.30
0.08
-0.03
-0.15
-0.22
-0.15
0.08
-0.05
0.12
-0.12
-0.15
-0.25
0.17
0.15
-0.16
0.05
0.15
-0.09
-0.01
-0.22
-0.07
-0.06
0.11
-0.05
-0.04
0.20
-0.04
-0.02
0.11
-0.21
0.02
0.08
-0.14
-0.27
0.15
-0.21
-0.03
-0.44
-0.26
0.04
-0.07
-0.33
-0.39
-0.24
0.08
-0.16
-0.05
-0.17
-0.24
-0.23
0.07
0.08
-0.19
0.07
0.21
0.04
-0.02
-0.23
-0.15
-0.07
0.05
-0.11
0.00
0.20
-0.11
-0.10
0.09
-0.22
-0.14
-0.09
-0.20
-0.24
0.19
-0.24
0.03
Non-Housing Price
Index
-0.07
-0.03
0.01
-0.05
-0.06
-0.05
-0.05
0.02
-0.08
-0.04
-0.04
-0.03
0.00
0.06
-0.06
0.00
0.03
0.03
0.02
0.00
-0.09
-0.02
-0.02
0.00
-0.01
-0.04
0.04
-0.02
-0.03
0.07
-0.09
0.01
0.01
-0.01
-0.06
0.08
0.00
0.03
Predicted Wage Index
Renters Only
Renters & Owners
0.02
0.04
0.07
0.00
-0.04
0.01
0.01
0.05
0.03
-0.01
0.00
0.03
0.03
0.02
-0.01
0.05
0.07
0.03
-0.03
0.04
-0.06
0.00
0.02
0.02
-0.02
0.01
-0.03
-0.07
0.01
-0.06
0.00
0.02
0.02
-0.02
-0.11
0.03
-0.05
-0.03
0.00
0.02
0.07
0.00
-0.08
-0.03
0.01
0.08
0.05
-0.03
-0.02
0.00
0.04
0.03
0.00
0.05
0.07
0.05
-0.01
0.08
-0.05
-0.03
0.04
0.07
-0.02
0.01
-0.03
0.00
0.03
-0.07
0.00
0.07
0.06
0.00
-0.08
0.03
0.01
-0.02
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
Salinas-Seaside-Monterey, CA
Salt Lake City-Ogden, UT
San Antonio, TX
San Diego, CA
San Francisco-Oakland, CA
San Jose, CA
San Luis Obispo-Atascadero-Paso Robles, CA
Santa Barbara-Santa Maria-Lompoc, CA
Santa Cruz, CA
Santa Fe, NM
Santa Rosa, CA
Sarasota, FL
Savannah, GA
Scranton-Wilkes-Barre, PA
Seattle-Everett, WA
Sharon, PA
Sheboygan, WI
Shreveport, LA
Sioux City, IA-NE
Sioux Falls, SD
South Bend, IN
Spokane, WA
Springfield, IL
Springfield, MO
Springfield-Chicopee-Holyoke, MA-CT
St. Cloud, MN
St. Joseph, MO
St. Louis, MO-IL
Stamford, CT
State College, PA
Stockton, CA
Sumter, SC
Syracuse, NY
Tacoma, WA
Tallahassee, FL
Tampa-St. Petersburg, FL
Terre Haute, IN
Toledo, OH-MI
MSA Population
281,166
1,331,833
1,551,396
2,807,873
4,645,830
1,688,089
246,312
400,661
258,576
148,785
459,235
587,565
232,087
624,276
2,332,682
120,147
111,021
393,700
103,140
124,076
266,264
418,375
112,222
327,829
594,643
168,856
101,442
2,602,448
354,363
134,971
562,377
104,047
731,789
706,103
286,063
2,386,781
149,397
617,883
Median Expenditure Share on Housing
Renters Only
Renters & Owners
0.24
0.23
0.22
0.25
0.23
0.23
0.28
0.27
0.27
0.24
0.24
0.24
0.24
0.20
0.24
0.19
0.17
0.22
0.21
0.21
0.21
0.25
0.20
0.23
0.22
0.20
0.22
0.21
0.23
0.29
0.23
0.21
0.23
0.23
0.30
0.23
0.22
0.21
0.24
0.19
0.15
0.23
0.23
0.25
0.24
0.25
0.27
0.20
0.24
0.18
0.18
0.17
0.22
0.15
0.15
0.16
0.15
0.16
0.15
0.18
0.15
0.17
0.18
0.15
0.16
0.15
0.22
0.19
0.19
0.15
0.15
0.19
0.18
0.17
0.15
0.16
Housing Price Index
Rentals Only
Rentals & Owned
0.40
0.08
-0.07
0.35
0.57
0.74
0.23
0.45
0.48
0.11
0.38
0.15
-0.06
-0.27
0.30
-0.32
-0.18
-0.29
-0.20
-0.10
-0.13
-0.10
-0.14
-0.25
-0.07
-0.24
-0.29
-0.07
0.57
0.04
0.07
-0.35
-0.07
0.08
-0.02
0.06
-0.34
-0.20
0.62
0.04
-0.25
0.46
0.75
0.98
0.42
0.63
0.81
0.29
0.58
0.08
-0.08
-0.21
0.40
-0.32
-0.14
-0.33
-0.27
-0.18
-0.24
-0.13
-0.21
-0.28
0.02
-0.27
-0.34
-0.11
0.85
-0.06
0.11
-0.39
-0.21
0.11
-0.10
-0.09
-0.37
-0.17
Non-Housing Price
Index
0.05
0.03
-0.08
0.06
0.14
0.11
0.04
-0.01
0.12
0.01
0.07
0.00
-0.03
-0.03
0.06
-0.05
-0.06
-0.09
-0.04
-0.03
-0.11
0.02
-0.09
-0.04
0.02
0.00
-0.08
-0.02
0.11
-0.01
0.00
-0.03
-0.01
0.02
0.04
-0.02
-0.05
-0.02
Predicted Wage Index
Renters Only
Renters & Owners
-0.06
0.02
0.00
0.02
0.09
0.10
0.04
0.01
0.04
0.11
0.04
-0.02
-0.02
0.02
0.07
0.05
0.03
-0.06
-0.04
-0.02
-0.02
0.04
0.04
0.01
0.01
0.02
0.01
0.02
0.11
0.14
-0.11
0.03
0.01
0.02
0.07
0.00
0.01
-0.01
-0.10
0.04
-0.04
0.01
0.05
0.08
0.04
-0.02
0.03
0.10
0.03
-0.01
-0.02
0.01
0.07
0.01
0.02
-0.04
-0.03
-0.01
0.01
0.04
0.05
0.00
0.02
0.01
-0.01
0.03
0.18
0.07
-0.08
-0.06
0.03
0.00
0.06
-0.01
0.00
0.01
TABLE A1: INTER-METROPOLITAN INDICES, YEAR 2000
MSA Name
MSA Population
Median Expenditure Share on Housing
Renters Only
Renters & Owners
Housing Price Index
Rentals Only
Rentals & Owned
Non-Housing Price
Index
Predicted Wage Index
Renters Only
Renters & Owners
Topeka, KS
168,994
0.21
0.15
-0.17
-0.28
-0.06
Trenton, NJ
350,093
0.21
0.17
0.27
0.23
0.04
Tucson, AZ
843,732
0.25
0.19
0.00
-0.03
-0.05
Tulsa, OK
694,760
0.22
0.15
-0.12
-0.22
-0.06
Tuscaloosa, AL
164,875
0.27
0.18
-0.20
-0.20
-0.02
Tyler, TX
174,917
0.22
0.15
-0.13
-0.25
-0.05
Utica-Rome, NY
300,337
0.22
0.15
-0.20
-0.30
-0.03
Ventura, CA
754,070
0.25
0.22
0.44
0.54
0.06
Vineland-Millville-Bridgeton, NJ
146,275
0.25
0.16
-0.05
-0.12
0.05
Visalia-Tulare-Porterville, CA
367,566
0.24
0.19
-0.16
-0.11
0.06
Waco, TX
212,313
0.23
0.16
-0.22
-0.33
-0.06
Washington, DC-MD-VA
4,733,359
0.22
0.18
0.36
0.27
0.07
Waterbury, CT
108,117
0.22
0.17
-0.04
-0.02
0.07
Waterloo-Cedar Falls, IA
124,908
0.24
0.15
-0.20
-0.27
-0.04
Wausau, WI
127,099
0.19
0.15
-0.16
-0.25
-0.02
West Palm Beach-Boca Raton, FL
1,133,519
0.25
0.18
0.23
0.09
0.05
Wichita Falls, TX
131,595
0.22
0.15
-0.19
-0.36
-0.06
Wichita, KS
543,518
0.20
0.15
-0.12
-0.25
-0.05
Williamsport, PA
121,501
0.20
0.16
-0.28
-0.26
-0.03
Wilmington, DE-NJ-MD
499,454
0.21
0.17
0.12
0.07
0.04
Wilmington, NC
233,637
0.25
0.20
-0.04
0.00
-0.02
Worcester, MA
282,673
0.21
0.18
0.02
0.10
0.05
Yakima, WA
223,726
0.25
0.19
-0.14
-0.07
0.00
Yolo, CA
170,044
0.27
0.21
0.21
0.27
0.00
York, PA
383,994
0.20
0.16
-0.09
-0.12
-0.01
Youngstown-Warren, OH
593,100
0.20
0.15
-0.29
-0.28
-0.10
Yuba City, CA
137,870
0.22
0.19
-0.15
-0.09
-0.04
Yuma, AZ
160,196
0.23
0.17
-0.14
-0.18
-0.09
Rental price indices constructed from 2000 Census 5% microdata samples. Aggregate expenditure shares constructed by dividing some of all rental expenditure by sum of all income in MSA.
0.02
0.02
-0.01
0.00
-0.01
-0.02
0.00
0.01
-0.19
-0.20
-0.03
0.07
-0.08
-0.01
0.03
-0.04
0.03
0.02
0.01
0.01
0.00
0.02
-0.12
0.04
0.00
0.00
-0.03
-0.05
0.03
0.06
0.00
0.04
-0.01
-0.02
0.01
0.02
-0.12
-0.19
-0.04
0.08
-0.12
0.02
0.02
0.00
0.00
0.04
-0.01
0.05
0.00
0.04
-0.10
0.03
0.00
0.00
-0.06
-0.12