# RECORD e2cefa2df09279ce534acb1e9e0f5991e38a2e5f
# TITLE: Heterogeneous Individual Valuations of a Mild Climate
# YEAR: 2026.0  VENUE: Environmental and Resource Economics  DOI: 10.1007/s10640-026-01110-4
# AUTHORS: Jan K. Brueckner
# PAGES: 23  CANDIDATE TABLE PAGES (1-based): [10, 12, 13, 16, 17, 19]
# ABSTRACT: This paper explores heterogeneous individual valuations of an important amenity, climate mildness, using a traditional Rosen-Roback empirical framework. It does so by including interaction terms between the amenity and worker characteristics in an hedonic wage regression that also includes a housing-price measure. The results suggest that non-young workers (those in the mid-age and old groups) value a mild climate more than do young workers, matching the usual view that the tolerance for cold weather declines with age. The findings also suggest that, like their highly educated counterparts, workers with low education levels also highly value a mild climate, with workers in the middle range of education having a lower valuation. These findings, which contradict the view that only better-off individuals care about amenities, could reflect the lower burden in mild weather of the manual work done by the less educated. In addition to presenting these empirical findings, the paper further contributes by presenting new analytics for the Rosen-Roback model in a setting with individual heterogeneity.


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Environmental and Resource Economics (2026) 89:59
https://doi.org/10.1007/s10640-026-01110-4
Heterogeneous Individual Valuations of a Mild Climate
Jan Brueckner1
Received: 20 January 2026 / Revised: 12 June 2026 / Accepted: 31 July 2026 / 
Published online: 17 August 2026
© The Author(s) 2026
Abstract
This paper explores heterogeneous individual valuations of an important amenity, climate 
mildness, using a traditional Rosen-Roback empirical framework. It does so by includ­
ing interaction terms between the amenity and worker characteristics in an hedonic wage 
regression that also includes a housing-price measure. The results suggest that non-young 
workers (those in the mid-age and old groups) value a mild climate more than do young 
workers, matching the usual view that the tolerance for cold weather declines with age. 
The findings also suggest that, like their highly educated counterparts, workers with low 
education levels also highly value a mild climate, with workers in the middle range of 
education having a lower valuation. These findings, which contradict the view that only 
better-off individuals care about amenities, could reflect the lower burden in mild weather 
of the manual work done by the less educated. In addition to presenting these empirical 
findings, the paper further contributes by presenting new analytics for the Rosen-Roback 
model in a setting with individual heterogeneity.
Keywords  Valuation of amenities · Climate mildness · Hedonic wage regression
1  Introduction
The pioneering work of Rosen (1979) and Roback (1982) provided a theoretical framework 
for predicting the effect of amenities on wages and real-estate prices, and their approach has 
influenced all subsequent work in this area. In their framework, a city’s amenities enter both 
the worker’s indirect utility function and the firm’s cost function, both of which also depend 
on the local wage (a cost to the firm) and the price of real estate, which is an input for the 
firm as well as a consumption good for the worker. For the equilibrium requirements of 
spatially uniform utilities and production costs to be satisfied, wages and real-estate prices 
must vary with city amenity levels in a particular fashion. The required variation is ambigu­
	 Jan Brueckner
jkbrueck@uci.edu
1	
Department of Economics, UC Irvine, Irvine, CA 92697, USA


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J. Brueckner
ness largely dependent on region, such controls would remove much of the variation in 
mildness that identifies individual valuations of this amenity.
Table 1 shows summary statistics for the sample, with the inline-eq-IEq103 variable being de-
meaned, yielding a zero mean. As can be seen, the mean hourly wage is $15.63, with the 
minimum equal to the federal minimum wage of $5.15 and a maximum of $293.27. Slightly 
more than half the workers are male, 8.9% are black, 13.7% are hispanic, and the shares 
of the education groups decline slightly as education rises. The young and mid-age groups 
are similar in size, but only 8.5% of workers are in the old group. Being omitted from the 
regression tables, the year and marital-status variables’ statistics are not shown in Table 
1, but the observations are very evenly split across the five sample years, and the most 
common marital statuses are married with civilian spouse present (54.0%), never married 
(29.0%), and divorced (10.7%).
3.2  Empirical Model
To write the regression equations in compact form, let inline-eq-IEq116 and inlin e - eq -I Eq117 denote the 
three age (inline-eq-IEq118, inline-eq-IEq119, inline-eq-IEq120) and education dummies (inline-eq-IEq121, inline-eq-IEq122, inline-eq-IEq123) 
respectively. The standard unconditional wage regression includes individual characteristics 
in uninteracted form but not the housing-cost variable. Using inline-eq-IEq124 as the observation index, the 
regression equation is written 
Table 1  Summary statistics
Variable
Mean
Std. Dev.
Min
Max
Wage ($/hr)
15.63
10.93
5.15
293.27
Houscost (CMSA index)
0.052
0.251
−0.544
0.783
Mildness
0
12.03
−28.76
21.38
Low_ed
0.409
0.492
0
1
Mid_ed
0.307
0.461
0
1
High_ed
0.284
0.451
0
1
Young
0.440
0.496
0
1
Mid_age
0.476
0.499
0
1
Old
0.085
0.279
0
1
Male
0.509
0.500
0
1
Black
0.089
0.279
0
1
Hispanic
0.137
0.344
0
1
Observations = 257,478 across 219 MSAs
Variable Definitions
inline-eq-IEq320 is a CMSA-specific index equal to the intercept from a detailed hedonic housing price regression.
inline-eq-IEq321 measures annual month-level deviations from a temperature of 20 degrees Celsius at the MSA 
level.
inline-eq-IEq322 is a dummy variable indicating that the worker has a high-school degree or less.
inline-eq-IEq104 is a dummy indicating that the worker has some college or a junior-college degree.
inline-eq-IEq324 is a dummy indicating that the worker has a college degree or a post-graduate degree.
inline-eq-IEq325 is a dummy indicating that the worker’s age is less than 35 years.
inline-eq-IEq326 is a dummy indicating that the worker’s age is at least 35 but less than 55 years.
inline-eq-IEq327 is a dummy indicating that the worker’s age is at least 55 years.


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Heterogeneous Individual Valuations of a Mild Climate
	
displ
a
y - e q-Equ12

(12)
where inline-eq-IEq125 is the error term, inli
ne-eq-IEq126  and inl
ine-eq-IEq127  are dropped to avoid collinearity, and inline-eq-IEq128 is the vec­
tor of control variables (inline-eq-IEq129, inline-eq-IEq130, inline-eq-IEq131, marital status, SIC shares, and year dum­
mies). The conditional form of the standard regression comes from adding inline-eq-IEq132 as a 
covariate in (12). In (12), the inline-eq-IEq133 coefficient captures the average valuation of climate 
mildness across all workers, while the inline-eq-IEq134 and inline-eq-IEq135 coefficients for i n li ne-eq-IEq136 capture the 
wage effect of education relative to inline-eq-IEq137 group and the wage effect of age relative to the 
inline-eq-IEq138 category. Since education and age are expected to raise wages, these four coefficients 
are expected to be positive and larger for i n line-eq-IEq139 than for i n line-eq-IEq140.
When interactions between inline-eq-IEq141 and the age and education variables are intro­
duced, the unconditional wage regression becomes 
	
displ
a
y -eq-Equ1
3

(13)
where one of the age interactions is dropped to avoid collinearity. To get the condi­
tional version of the interaction regression, inline-eq-IEq142 is added as a covariate in (13). The 
inline-e q -IEq143 interaction variables allow the wage effect of climate mildness to vary 
across all three of the education groups (i n li ne -eq-IEq144), while the inline-e q -IEq145 coefficients 
allow the mildness effect to vary across all three of the age groups. Note that, with mildness 
not appearing in uninteracted form, there is no baseline effect of inline-eq-IEq146, allowing each 
group to have its own interaction coefficient without creating multicollinearity. A nega­
tive coefficient for an interaction variable, say inline-e q -IEq 1 47
, 
implies that greater climate mildness reduces the wage for members of the inline-eq-IEq148 group, 
and similarly for the other interaction coefficients. Note that this negative coefficient also 
implies that the wage gain relative to the inline-eq-IEq149 group from being in the inline-eq-IEq150 group is 
smaller when climate mildness is high than when it is low, a consequence of the depressing 
wage effect of mildness for the inline-eq-IEq151 group.
4  Empirical Results
The estimated hedonic wage regressions are shown in Tables 2–3. Table 2 shows a Rosen-
Roback wage regression with a standard treatment of amenities, where the inline-eq-IEq152 
variable appears only in level form. Table 3 adds interactions between inline-eq-IEq153 and edu­
cation and between inline-eq-IEq154 and age. The various columns in the tables show a condi­
tional regression (which directly gives amenity valuations) along with the corresponding 
unconditional regression (where inline-eq-IEq155 is dropped), with the theory used to motivate 
comparisons between the two regressions. All of the regressions are weighted by the CPS 


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J. Brueckner
wage-representativeness variable, inline-eq-IEq156, ensuring that the observations reflect the overall 
population.8 Standard errors are clustered at the MSA level. Since no complications are 
present in the estimation, the regressions use ordinary-least-squares.
4.1  Standard Regressions
Column 1 of Table 2 shows the conditional version of a standard hedonic wage regression, 
with inline-eq-IEq169 appearing on the right-hand side. This variable’s coefficient is significantly 
positive, indicating that wages are higher in high housing-cost areas. Recall that the coef­
ficient of inline-eq-IEq170, which appears only in level form, directly reveals (in absolute value) 
the average valuation of the amenity across all workers, given the presence of inline-eq-IEq171 
(see (4)). The coefficient is negative and statistically significant, as expected, indicating that 
workers will accept a lower wage to live and work in a milder climate.
Column 2 of Table 2 drops the inline-eq-IEq172 variable, yielding an unconditional wage regres­
sion. While the inline-eq-IEq173 coefficient is still negative and significant, it increases in absolute 
value relative to column 1, rather than decreasing, as predicted by the theory.9 This pattern 
persists through the results below that use inline-eq-IEq174 interactions instead of the variable’s 
level, along with the CMSA-level inline-eq-IEq175. A possible explanation is that this inline-eq-IEq176 
variable is correlated with some unobserved MSA-level determinants of wages (e.g., high 
8 To be safe, these weights are still applied even though the exclusions described themselves alter the repre­
sentativeness of the sample.
9 Since the coefficients come from different regressions, a formal test for equality is not possible.
VARIABLES
(1)
lwage
(2)
lwage
Mildness
−0.00202**
−0.00227**
(0.000326)
(0.000454)
Houscost
0.225**
–
(0.0229)
Mid_edx
0.215**
0.218**
(0.0106)
(0.0104)
High_edx
0.607**
0.611**
(0.0136)
(0.0134)
Mid_age
0.165**
0.166**
(0.00412)
(0.00428)
Old
0.125**
0.126**
(0.00771)
(0.00769)
Male
0.187**
0.187**
(0.0108)
(0.0107)
Black
−0.127**
−0.130**
(0.00766)
(0.00754)
Hispanic
−0.241**
−0.240**
(0.0163)
(0.0165)
Constant
−0.385
1.694
(1.035)
(1.550)
Observations
257,478
257,478
inline-eq-IEq157
0.431
0.426
Table 2  Standard Rosen-Roback 
hedonic wage regressions
Standard errors clustered at the 
metro level in parentheses
** pinline-eq-IEq1580.01, * pinline-eq-IEq1590.05
Marital-status, SIC 
employment-share, and year 
coefficients not reported
 


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Heterogeneous Individual Valuations of a Mild Climate
worker productivity in high-cost San Francisco), which prevent the expected drop of the 
inline-eq-IEq177 coefficient when inline-eq-IEq178 is removed from the regression. As will be seen 
below, the expected pattern emerges using the state-level version of inline-eq-IEq179, which may 
be less correlated with these unobservables.
Turning to the dummy control variables, inline-eq-IEq180 and inline-eq-IEq181 are dropped, so that the 
default worker is a young, female married to a civilian husband (the default marital status) 
with low education and a non-Black, non-Hispanic race. The wage effects of the dummy 
variables are as expected. More education or a non-young age raises the wage, with the 
point estimate of the age effect slightly smaller for old workers. Male wages are higher 
Table 3  Hedonic wage regressions with amenity interactions
VARIABLES
(1)
lwage
(2)
lwage
(3)
lwage
(4)
lwage
(5)
lwage
(6)
lwage
Houscost
0.223**
–
0.224**
–
0.222**
–
(0.0227)
(0.0229)
(0.0227)
Mid_ed
0.203**
0.204**
0.215**
0.218**
0.203**
0.204**
(0.00618)
(0.00611)
(0.0105)
(0.0103)
(0.00620)
(0.00612)
High_ed
0.601**
0.604**
0.607**
0.612**
0.600**
0.604**
(0.0125)
(0.0123)
(0.0136)
(0.0134)
(0.0125)
(0.0123)
Mid_age
0.165**
0.166**
0.172**
0.173**
0.172**
0.173**
(0.00412)
(0.00427)
(0.00395)
(0.00403)
(0.00396)
(0.00404)
Old
0.124**
0.125**
0.128**
0.130**
0.127**
0.128**
(0.00756)
(0.00755)
(0.00754)
(0.00752)
(0.00717)
(0.00716)
Mildness inline-eq-IEq160 low_ed
−0.00322**
−0.00358**
–
–
−0.00258**
−0.00292**
(0.000648)
(0.000684)
(0.000594)
(0.000613)
Mildness inline-eq-IEq161 mid_ed
−0.000728
−0.000902
–
–
−9.10e-05
−0.000245
(0.000426)
(0.000515)
(0.000505)
(0.000545)
Mildness inline-eq-IEq162 high_ed
−0.00181**
−0.00200**
–
–
−0.00106
−0.00123
(0.000607)
(0.000680)
(0.000699)
(0.000728)
Mildness inline-eq-IEq163 young
–
–
−0.00134**
−0.00158**
–
–
(0.000364)
(0.000440)
Mildness inline-eq-IEq164 mid_age
–
–
−0.00263**
−0.00290**
−0.00130**
−0.00134**
(0.000380)
(0.000519)
(0.000379)
(0.000378)
Mildness inline-eq-IEq165 old
–
–
−0.00198**
−0.00225**
−0.000509
−0.000539
(0.000592)
(0.000722)
(0.000585)
(0.000599)
Male
0.188**
0.187**
0.187**
0.187**
0.188**
0.187**
(0.0107)
(0.0105)
(0.0108)
(0.0106)
(0.0106)
(0.0105)
Black
−0.127**
−0.130**
−0.127**
−0.130**
−0.127**
−0.130**
(0.00747)
(0.00730)
(0.00771)
(0.00759)
(0.00752)
(0.00734)
Hispanic
−0.236**
−0.235**
−0.242**
−0.241**
−0.237**
−0.235**
(0.0137)
(0.0140)
(0.0165)
(0.0166)
(0.0138)
(0.0140)
Constant
−0.374
1.686
−0.372
1.704
−0.359
1.699
(1.031)
(1.546)
(1.040)
(1.553)
(1.036)
(1.549)
Observations
257,478
257,478
257,478
257,478
257,478
257,478
inline-eq-IEq166
0.431
0.427
0.431
0.426
0.431
0.427
Standard errors clustered at metro level in parentheses
** pinline-eq-IEq1670.01, * pinline-eq-IEq1680.05
Marital-status, SIC employment-share, and year coefficients not reported.


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than those of females, and Black and Hispanic workers earn less than workers outside these 
groups. All these coefficients are strongly statistically significant.10
4.2  Regressions with Amenity Interactions
Table 3 introduces amenity interactions with the three education dummies and the age dum­
mies. Only education interactions are present in columns 1 and 2, with columns 3 and 4 con­
taining only age interactions. Columns 5 and 6 contain both types of interactions. The first 
column within each pair shows the conditional regression, and the second column shows 
the unconditional regression. In all the regressions, the inline-eq-IEq182 variable only appears in 
interacted form, not as a level variable.
In the conditional regression in column 1, which includes inline-eq-IEq183, coefficients for two 
of the inline-eq-IEq184 interaction variables, inline-e q -IEq185 and inline-e q -IEq186, are 
negative and significant. However, the inline-e q -IEq187 coefficient, while negative, is 
insignificant and its absolute magnitude is smaller than those of the other two coefficients 
while being separately statistically unequal to each of them. The hypothesis that all three 
interaction coefficients are equal is also rejected. The results thus suggest that workers in 
both the high- and low-education groups value a mild climate, while workers in the middle 
range of education (high school with some college or an associate degree) have a lower and 
perhaps zero valuation of climate mildness.
While well-educated, and thus well-off, households are often thought to value amenities 
highly (see for example, Brueckner et al. (1999)), the presence of a similar valuation among 
the least-educated workers is noteworthy. A possible explanation is that workers with no 
more than a high-school education are frequently employed in jobs that require manual 
labor, which often occurs outside rather than indoors. As a result, climate mildness may 
make the jobs of such workers easier, accounting for their valuation of mildness. While the 
best-educated workers may have ample leisure time to enjoy outdoor activities, which could 
contribute to their valuation of climate mildness, the apparent lower valuation for workers 
in the middle range of education is somewhat puzzling. Conceivably, compared to the least-
educated, fewer of these workers may hold manual jobs, while their lower earning power 
relative to the most-educated may mean longer work hours and less time for outdoor activi­
ties, thereby reducing the middle-range group’s valuation of climate mildness.
Climate-mildness valuation by the least educated workers but not by the inline-eq-IEq188 group 
also raises another issue related to the premises of the Rosen-Roback model. That model is 
based on the assumption that all workers are mobile across regions, and one may wonder 
whether this assumption is accurate for low-education workers, for whom moving costs 
may be unaffordable. While this observation may cast doubt on the applicability of the 
model to this group, it could be argued that everyone is mobile in a sufficiently long-run 
context, even workers with low resources.
Turning to the unconditional regression in column 2 of Table 3, the coefficients of the 
inline-eq-IEq189 interactions with inline-eq-IEq190 and inline-eq-IEq191 remain negative and significant. The 
coefficients are larger in absolute value than those in column 1, following the unexpected 
pattern in Table 2.
10 The omitted marital-status category is the most common one, married with civilian spouse present, and 
the dummy coefficients for the other categories are all negative, indicating higher wages in typical married 
households.


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Table 4 shows the traditional wage regressions, and in the conditional version shown in 
column 1, the inline-eq-IEq229 coefficient increases in absolute value, being now larger than the 
coefficient in column 2, which is unchanged. This is the pattern predicted by the theory, with 
the required compensating decline in the wage as inline-eq-IEq230 increases being smaller when 
inline-eq-IEq231 exerts its own separate utility-equalizing force (rising with inline-eq-IEq232) rather 
being held fixed. The other estimates in Table 4 are similar to those in Table 3.
As in Table 3, the interaction regression in column 1 of Table 5 again suggests that work­
ers with low and high education levels value climate mildness more than do workers with 
education in the middle range. While again larger in absolute value, the inline-e q -IEq233 
and inline-e q -IEq234 coefficients are also again both statistically different from the 
inline-eq-IEq235 interaction coefficient. The latter coefficient, however, is now also statistically sig­
nificant. Note that the column-1 interaction coefficients are now larger in absolute value 
than the unconditional column-2 coefficients, as predicted by the theory.
As in Table 3, all the age interaction coefficients in column 3 of Table 5 are negative and 
significant, with the inline-eq-IEq236 and inline-eq-IEq237 interaction coefficients again larger in absolute value 
than the inline-eq-IEq238 interaction coefficient. As before, the difference is statistically significant 
only for the inline-eq-IEq239 interaction coefficient. As predicted by the theory, the column 3 
interaction coefficients are now larger in absolute value than the unconditional coefficients 
in column 4.
Turning to columns 5–6 of Table 5, the inline-e q -IEq240 coefficient in column 5 
now retains the statistical significance seen in column 1, with the inline-e q -IEq241 
coefficient losing it. That coefficient is again statistically different from the other two, 
VARIABLES
(1)
lwage
(2)
lwage
Mildness
−0.00252**
−0.00227**
(0.000436)
(0.000454)
Houscost
0.0135**
–
(0.00318)
Mid_ed
0.216**
0.218**
(0.0105)
(0.0104)
High_ed
0.611**
0.611**
(0.0134)
(0.0134)
Mid_age
0.166**
0.166**
(0.00418)
(0.00428)
Old
0.125**
0.126**
(0.00774)
(0.00769)
Male
0.187**
0.187**
(0.0107)
(0.0107)
Black
−0.126**
−0.130**
(0.00748)
(0.00754)
Hispanic
−0.241**
−0.240**
(0.0162)
(0.0165)
Constant
−1.253
1.694
(1.731)
(1.550)
Observations
257,478
257,478
inline-eq-IEq217
0.428
0.426
Table 4  Standard Rosen-Roback 
hedonic wage regressions with 
state-level housing cost
Standard errors clustered at the 
metro level in parentheses
**pinline-eq-IEq2180.01, * pinline-eq-IEq2190.05
Marital-status, SIC 
employment-share, and year 
coefficients not reported.
 


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Heterogeneous Individual Valuations of a Mild Climate
implying that workers in the middle education range have a lower mildness valuation 
than the other education groups. Column 5’s age interaction coefficients show the same 
pattern as in Table 3. Note that, while column 5’s education interaction coefficients are 
now larger than those in column 6, as predicted, that relationship does not hold for the 
age interaction coefficients.
While mostly matching the theoretical prediction regarding conditional vs. unconditional 
coefficient magnitudes, the results in Table 5 also reaffirm the conclusions from Table 3. 
They suggest that workers with high and low education levels value climate mildness by 
Table 5  Hedonic wage regressions with amenity interactions and state-level housing cost
VARIABLES
(1)
lwage
(2)
lwage
(3)
lwage
(4)
lwage
(5)
lwage
(6)
lwage
Houscost
0.0133**
–
0.0135**
–
0.0133**
–
(0.00316)
(0.00318)
(0.00316)
Mid_ed
0.203**
0.204**
0.216**
0.218**
0.203**
0.204**
(0.00618)
(0.00611)
(0.0105)
(0.0103)
(0.00619)
(0.00612)
High_ed
0.604**
0.604**
0.611**
0.612**
0.603**
0.604**
(0.0123)
(0.0123)
(0.0134)
(0.0134)
(0.0123)
(0.0123)
Mid_age
0.166**
0.166**
0.173**
0.173**
0.172**
0.173**
(0.00418)
(0.00427)
(0.00401)
(0.00403)
(0.00402)
(0.00404)
Old
0.125**
0.125**
0.129**
0.130**
0.128**
0.128**
(0.00759)
(0.00755)
(0.00761)
(0.00752)
(0.00725)
(0.00716)
Mildness inline-eq-IEq220 low_ed
−0.00378**
−0.00358**
–
–
−0.00312**
−0.00292**
(0.000706)
(0.000684)
(0.000649)
(0.000613)
Mildness inline-eq-IEq221 mid_ed
−0.00118*
−0.000902
–
–
−0.000532
−0.000245
(0.000489)
(0.000515)
(0.000545)
(0.000545)
Mildness inline-eq-IEq222 high_ed
−0.00228**
−0.00200**
–
–
−0.00152*
−0.00123
(0.000662)
(0.000680)
(0.000732)
(0.000728)
Mildness inline-eq-IEq223 young
–
–
−0.00184**
−0.00158**
–
–
(0.000448)
(0.000440)
Mildness inline-eq-IEq224 mid_age
–
–
−0.00314**
−0.00290**
−0.00132**
−0.00134**
(0.000493)
(0.000519)
(0.000378)
(0.000378)
Mildness inline-eq-IEq225 old
–
–
−0.00248**
−0.00225**
−0.000510
−0.000539
(0.000656)
(0.000722)
(0.000586)
(0.000599)
Male
0.187**
0.187**
0.187**
0.187**
0.187**
0.187**
(0.0106)
(0.0105)
(0.0107)
(0.0106)
(0.0106)
(0.0105)
Black
−0.126**
−0.130**
−0.126**
−0.130**
−0.126**
−0.130**
(0.00727)
(0.00730)
(0.00753)
(0.00759)
(0.00732)
(0.00734)
Hispanic
−0.236**
−0.235**
−0.242**
−0.241**
−0.237**
−0.235**
(0.0136)
(0.0140)
(0.0163)
(0.0166)
(0.0137)
(0.0140)
Constant
−1.216
1.686
−1.237
1.704
−1.197
1.699
(1.727)
(1.546)
(1.735)
(1.553)
(1.731)
(1.549)
Observations
257,478
257,478
257,478
257,478
257,478
257,478
inline-eq-IEq226
0.428
0.427
0.428
0.426
0.428
0.427
Standard errors clustered at metro level in parentheses
** pinline-eq-IEq2270.01, * pinline-eq-IEq2280.05
Marital-status, SIC employment-share, and year coefficients not reported.


===== PAGE 18 (score 36, numeric-paren 0, table-words 15, var-words 6) =====

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J. Brueckner
more than workers with moderate education levels, and that young workers value climate 
mildness less than non-young workers.
4.4  Further Connections to the Theory
While Tables 4 and 5 show the predicted theoretical relationship between the coefficient 
magnitudes in the conditional and unconditional regressions, the analysis in Sect. 2 offers 
some further guidance in appraising the results. In particular, recall that the theory shows 
how differences in housing demands and amenity valuations between the two posited worker 
types can affect the magnitudes of the unconditional amenity wage effects for the types. 
Consider the unconditional regression in column 2 of Table 3, which pertains to the three 
education groups. While the regression has three groups rather than the two worker types 
in the model, pairwise comparisons can be made between the interaction coefficients using 
the theory, carrying out a inline-eq-IEq242/inline-eq-IEq243 comparison and a separate inline-eq-IEq244/inline-eq-IEq245 
comparison, relying on the effectively zero value for the inline-eq-IEq246 interaction coefficient.12
Consider first the inline-eq-IEq257/inline-eq-IEq258 comparison. Relative to the inline-eq-IEq259 group (type 2 in 
the theory), the inline-eq-IEq260 group (type 1) has a higher mildness valuation given the results of 
column 1 in Table 3, with inline-eq-IEq261
. But given its lower income, housing demand should 
also be lower for the inline-eq-IEq262 group, implying inlin e -eq-IEq263. From above, these two inequali­
ties together yield a negative unconditional type-1 (inline-eq-IEq264) wage effect in eq (8) along 
with an ambiguous (possibly zero) sign for the type-2 (inline-eq-IEq265) effect in (9), matching the 
results in column 2 of Table 3.
For the inline-eq-IEq266/inline-eq-IEq267 comparison, the higher income of the inline-eq-IEq268 group (now 
type 1) should make inlin e -eq-IEq269 (type 2 is again the inline-eq-IEq270 group). The greater inline-eq-IEq271 
mildness valuation from the unconditional regression means inline-eq-IEq272
, but if the valu­
ation of amenities rises faster than housing demand as income increases (the Brueckner-
Thisse-Zenou assumption), then inlin e -eq-I E q273. The conditional type-1 (inline-eq-IEq274) 
wage effect in (8) is then again negative while the type-2 (inline-eq-IEq275) effect is ambiguous and 
possibly zero, as in column 2 of Table 3.
4.5  Robustness Check: Stratified Regressions
One could argue that, if the goal is to explore the effect of education and age on the valu­
ation of climate mildness, a different and possibly better approach is to estimate regres­
sions stratified by worker category instead of a pooled regression with interaction variables. 
Accordingly, as a robustness check, this section replaces the regressions using inline-eq-IEq276 
interaction variables with stratified regressions. In other words, the single regression with 
inline-eq-IEq277-education interactions in column 1 of Table 3 is replaced by three separate 
12 This exercise is justifiable because deleting the inline-eq-IEq247 and alternatively inline-eq-IEq248 observations from 
the regression, leaving only two groups, yields the same coefficient pattern as seen in column 2: negative 
(zero) inline-eq-IEq249 (inline-eq-IEq250) interaction coefficients in the regression containing only inline-eq-IEq251 and inline-eq-IEq252 
observations; negative (zero) inline-eq-IEq253 (inline-eq-IEq254) interaction coefficients in the regression containing only 
inline-eq-IEq255 and inline-eq-IEq256 observations. inline-eq-IEq2247 and alternatively inline-eq-IEq2484 observations from the regression, 
leaving only two groups, yields the same coefficient pattern as seen in column 2: negative (zero) inline-eq-IEq2459
(inline-eq-IEq2550) interaction coefficients in the regression containing only inline-eq-IEq2251 and inline-eq-IEq2572 observations; 
negative (zero) inline-eq-IEq2953(inline-eq-IEq2584) interaction coefficients in the regression containing only inline-eq-IEq1255 and 
inline-eq-IEq2456 observations.


===== PAGE 19 (score 98, numeric-paren 72, table-words 5, var-words 8) =====

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59
Heterogeneous Individual Valuations of a Mild Climate
regressions, one for each education category, with inline-eq-IEq278 appearing in level form in 
each regression. A comparison of the inline-eq-IEq279 coefficients across the three regressions 
provides a different way gauging how valuation of the amenity changes across individuals 
in the different education categories. Similarly, the single regression with inline-eq-IEq280-age 
interactions in column 3 of Table 3 is replaced by three separate regressions, one for each 
age category, with inline-eq-IEq281 again appearing in level form. This approach follows Hoch 
and Drake (1974), who used the stratified approach to investigate how the effect of climate 
amenities on wages varies across occupations.
In contrast to the interaction approach, which implicitly constrains the coefficients of the 
control variables to be the same across education or age groups, the use of separate regres­
sions under the stratified approach allows these coefficients to differ across groups. If the 
conclusions generated by the interaction approach also emerge under the less-restrictive 
stratified approach, then robustness is demonstrated. However, a limitation of the stratified 
approach is the inability to carry out statistical tests comparing the inline-eq-IEq282 coefficients 
across groups, which arises because the coefficients come from different regressions instead 
of common pooled regression.
The results of the stratified approach are shown in Table 6, with columns 1–3 showing 
regressions stratified by education and columns 4–6 showing regressions stratified by age.13 
The table uses the CMSA-level housing cost variable. As can be seen, all of the inline-eq-IEq283 
coefficients are significantly negative, suggesting that all the education and age groups value 
13 Note that, to conveniently evaluate education and age effects under the stratified approach, age is omitted 
from the stratified education regressions and education is omitted from the stratified age regressions. The 
alternative would be to run nine different regressions, one for each education-age combination, and to make 
comparisons across them.
Table 6  Stratified wage regressions
VARIABLES
(1)
lwage
low_ed = 1
(2)
lwage
mid_ed = 1
(3)
lwage
high_ed = 1
(4)
lwage
young = 1
(5)
lwage
mid_age = 1
(6)
lwage
old = 1
Houscost
0.230**
0.276**
0.275**
0.294**
0.326**
0.302**
(0.00758)
(0.00986)
(0.0125)
(0.00852)
(0.00948)
(0.0235)
Mildness
−0.00259**
−0.00104**
−0.000994**
−0.00232**
−0.00259**
−0.00165**
(0.000120)
(0.000154)
(0.000194)
(0.000134)
(0.000149)
(0.000373)
Male
0.188**
0.175**
0.244**
0.129**
0.272**
0.334**
(0.00234)
(0.00310)
(0.00384)
(0.00264)
(0.00294)
(0.00747)
Black
−0.120**
−0.118**
−0.133**
−0.148**
−0.265**
−0.250**
(0.00388)
(0.00520)
(0.00853)
(0.00450)
(0.00537)
(0.0145)
Hispanic
−0.253**
−0.173**
−0.265**
−0.325**
−0.470**
−0.436**
(0.00311)
(0.00552)
(0.00918)
(0.00374)
(0.00491)
(0.0144)
Constant
−1.182*
−3.114**
−6.871**
−2.062**
−3.203**
−3.679*
(0.500)
(0.747)
(1.362)
(0.627)
(0.746)
(1.868)
Observations
105,180
79,128
73,170
113,165
122,466
21,847
inline-eq-IEq284
0.224
0.220
0.159
0.223
0.215
0.201
Standard errors clustered at metro level in parentheses
** pinline-eq-IEq2850.01, * pinline-eq-IEq2860.05
Marital-status, SIC employment-share, and year coefficients not reported.


===== PAGE 20 (score 23, numeric-paren 0, table-words 10, var-words 3) =====

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J. Brueckner
climate mildness. However, the patterns seen in the interaction regressions are only partly 
evident in Table 6.
If the education-interaction coefficient pattern were repeated in Table 6, then the 
inline-eq-IEq287 coefficients in columns 1 and 3 would both be larger in absolute value than the 
mildness coefficient in column 2. Instead, the inline-eq-IEq288 coefficients in the inline-eq-IEq289 and 
inline-eq-IEq290 regressions of column 2 and 3 are almost exactly the same size, with absolute 
values less than half that of the inline-eq-IEq291 coefficient in the inline-eq-IEq292 regression of column 
1. The implication is that workers with low education levels appear to value a mild climate 
more than workers in the two other groups. This conclusion at least preserves the previous 
finding that low-education workers highly value climate mildness, but it does not show 
highly educated workers joining in this high valuation.
As noted above, however, it is not possible to test for significant differences among the 
estimated coefficients since they come from different regressions. Thus, for example, tests 
for whether the inline-eq-IEq293 coefficients in the inline-eq-IEq294 and inline-eq-IEq295 regressions are statisti­
cally equal or whether they differ individually from the inline-eq-IEq296 coefficient are not possible, 
which means that the claim above of a higher mildness valuation for the inline-eq-IEq297 group 
cannot be rigorously justified. This inability represents a major limitation of the stratified 
approach.
Columns 4–6 of Table 6 show similar valuations of climate mildness in the inline-eq-IEq298 and 
inline-eq-IEq299 groups, but a lower valuation for older workers. Therefore the previous conclu­
sion that non-young workers value climate mildness more than the young is not replicated.
These differences in results come from not constraining the control-variable coefficients 
to be the same across groups, the consequences of which can be seen in the variation in these 
coefficients across the regressions in Table 6. For example, the wage effect from being male 
is considerably larger for mid-age workers than for low-education workers (compare col­
umns 5 and 1 of Table 6). One could argue that, if the goal is to compare amenity valuations 
across groups, then giving gender and race effects the same freedom to vary across groups 
prevents drawing the sharp conclusions that are sought, a problem that is compounded by 
the inability to carry out comparative tests. On the other hand, allowing flexibility in the 
control coefficients may end up giving a truer picture of amenity valuations. For the cur­
rent exercise, however, the conclusions drawn from the amenity-interaction approach match 
intuition better than those implied by Table 6, making them appear more credible.
4.6  Discussion
The results in Tables 3 and 5 suggest that high- and low-education workers value climate 
mildness more than workers with educations in the middle range, and that young workers 
value climate mildness less than non-young workers. While the age-related valuation differ­
ences are expected, the evidence of strong valuation of climate mildness by low-education 
workers is unexpected and novel.
Interestingly, the paper’s results can be used to predict how the wage distributions across 
groups within a city should differ between cities with low and high climate mildness. Focus­
ing first on the education groups, and recalling that the results show wages rising with 
education, the larger mildness wage effect for the inline-eq-IEq300 group relative to that for the 
inline-eq-IEq301 group implies that the wage gap between those two groups becomes larger when 
climate mildness increases (with inline-eq-IEq302 wage falling by more). Similarly, the larger mild­