1# RECORD e2cefa2df09279ce534acb1e9e0f5991e38a2e5f2# TITLE: Heterogeneous Individual Valuations of a Mild Climate3# YEAR: 2026.0 VENUE: Environmental and Resource Economics DOI: 10.1007/s10640-026-01110-44# AUTHORS: Jan K. Brueckner5# PAGES: 23 CANDIDATE TABLE PAGES (1-based): [10, 12, 13, 16, 17, 19]6# 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.789===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) =====1011Environmental and Resource Economics (2026) 89:5912https://doi.org/10.1007/s10640-026-01110-413Heterogeneous Individual Valuations of a Mild Climate14Jan Brueckner115Received: 20 January 2026 / Revised: 12 June 2026 / Accepted: 31 July 2026 / 16Published online: 17 August 202617© The Author(s) 202618Abstract19This paper explores heterogeneous individual valuations of an important amenity, climate 20mildness, using a traditional Rosen-Roback empirical framework. It does so by includ21ing interaction terms between the amenity and worker characteristics in an hedonic wage 22regression that also includes a housing-price measure. The results suggest that non-young 23workers (those in the mid-age and old groups) value a mild climate more than do young 24workers, matching the usual view that the tolerance for cold weather declines with age. 25The findings also suggest that, like their highly educated counterparts, workers with low 26education levels also highly value a mild climate, with workers in the middle range of 27education having a lower valuation. These findings, which contradict the view that only 28better-off individuals care about amenities, could reflect the lower burden in mild weather 29of the manual work done by the less educated. In addition to presenting these empirical 30findings, the paper further contributes by presenting new analytics for the Rosen-Roback 31model in a setting with individual heterogeneity.32Keywords Valuation of amenities · Climate mildness · Hedonic wage regression331 Introduction34The pioneering work of Rosen (1979) and Roback (1982) provided a theoretical framework 35for predicting the effect of amenities on wages and real-estate prices, and their approach has 36influenced all subsequent work in this area. In their framework, a city’s amenities enter both 37the worker’s indirect utility function and the firm’s cost function, both of which also depend 38on the local wage (a cost to the firm) and the price of real estate, which is an input for the 39firm as well as a consumption good for the worker. For the equilibrium requirements of 40spatially uniform utilities and production costs to be satisfied, wages and real-estate prices 41must vary with city amenity levels in a particular fashion. The required variation is ambigu42 Jan Brueckner43jkbrueck@uci.edu441 45Department of Economics, UC Irvine, Irvine, CA 92697, USA464748===== PAGE 10 (score 18, numeric-paren 0, table-words 5, var-words 5) =====49501 35159 52Page 10 of 2353J. Brueckner54ness largely dependent on region, such controls would remove much of the variation in 55mildness that identifies individual valuations of this amenity.56Table 1 shows summary statistics for the sample, with the inline-eq-IEq103 variable being de-57meaned, yielding a zero mean. As can be seen, the mean hourly wage is $15.63, with the 58minimum equal to the federal minimum wage of $5.15 and a maximum of $293.27. Slightly 59more than half the workers are male, 8.9% are black, 13.7% are hispanic, and the shares 60of the education groups decline slightly as education rises. The young and mid-age groups 61are similar in size, but only 8.5% of workers are in the old group. Being omitted from the 62regression tables, the year and marital-status variables’ statistics are not shown in Table 631, but the observations are very evenly split across the five sample years, and the most 64common marital statuses are married with civilian spouse present (54.0%), never married 65(29.0%), and divorced (10.7%).663.2 Empirical Model67To write the regression equations in compact form, let inline-eq-IEq116 and inlin e - eq -I Eq117 denote the 68three age (inline-eq-IEq118, inline-eq-IEq119, inline-eq-IEq120) and education dummies (inline-eq-IEq121, inline-eq-IEq122, inline-eq-IEq123) 69respectively. The standard unconditional wage regression includes individual characteristics 70in uninteracted form but not the housing-cost variable. Using inline-eq-IEq124 as the observation index, the 71regression equation is written 72Table 1 Summary statistics73Variable74Mean75Std. Dev.76Min77Max78Wage ($/hr)7915.638010.93815.1582293.2783Houscost (CMSA index)840.052850.25186−0.544870.78388Mildness8909012.0391−28.769221.3893Low_ed940.409950.49296097198Mid_ed990.3071000.46110101021103High_ed1040.2841050.45110601071108Young1090.4401100.49611101121113Mid_age1140.4761150.49911601171118Old1190.0851200.27912101221123Male1240.5091250.50012601271128Black1290.0891300.27913101321133Hispanic1340.1371350.34413601371138Observations = 257,478 across 219 MSAs139Variable Definitions140inline-eq-IEq320 is a CMSA-specific index equal to the intercept from a detailed hedonic housing price regression.141inline-eq-IEq321 measures annual month-level deviations from a temperature of 20 degrees Celsius at the MSA 142level.143inline-eq-IEq322 is a dummy variable indicating that the worker has a high-school degree or less.144inline-eq-IEq104 is a dummy indicating that the worker has some college or a junior-college degree.145inline-eq-IEq324 is a dummy indicating that the worker has a college degree or a post-graduate degree.146inline-eq-IEq325 is a dummy indicating that the worker’s age is less than 35 years.147inline-eq-IEq326 is a dummy indicating that the worker’s age is at least 35 but less than 55 years.148inline-eq-IEq327 is a dummy indicating that the worker’s age is at least 55 years.149150151===== PAGE 11 (score 15, numeric-paren 0, table-words 6, var-words 3) =====1521531 3154Page 11 of 23 15559156Heterogeneous Individual Valuations of a Mild Climate157 158displ159a160y - e q-Equ12161162(12)163where inline-eq-IEq125 is the error term, inli164ne-eq-IEq126 and inl165ine-eq-IEq127 are dropped to avoid collinearity, and inline-eq-IEq128 is the vec166tor of control variables (inline-eq-IEq129, inline-eq-IEq130, inline-eq-IEq131, marital status, SIC shares, and year dum167mies). The conditional form of the standard regression comes from adding inline-eq-IEq132 as a 168covariate in (12). In (12), the inline-eq-IEq133 coefficient captures the average valuation of climate 169mildness across all workers, while the inline-eq-IEq134 and inline-eq-IEq135 coefficients for i n li ne-eq-IEq136 capture the 170wage effect of education relative to inline-eq-IEq137 group and the wage effect of age relative to the 171inline-eq-IEq138 category. Since education and age are expected to raise wages, these four coefficients 172are expected to be positive and larger for i n line-eq-IEq139 than for i n line-eq-IEq140.173When interactions between inline-eq-IEq141 and the age and education variables are intro174duced, the unconditional wage regression becomes 175 176displ177a178y -eq-Equ11793180181(13)182where one of the age interactions is dropped to avoid collinearity. To get the condi183tional version of the interaction regression, inline-eq-IEq142 is added as a covariate in (13). The 184inline-e q -IEq143 interaction variables allow the wage effect of climate mildness to vary 185across all three of the education groups (i n li ne -eq-IEq144), while the inline-e q -IEq145 coefficients 186allow the mildness effect to vary across all three of the age groups. Note that, with mildness 187not appearing in uninteracted form, there is no baseline effect of inline-eq-IEq146, allowing each 188group to have its own interaction coefficient without creating multicollinearity. A nega189tive coefficient for an interaction variable, say inline-e q -IEq 1 47190, 191implies that greater climate mildness reduces the wage for members of the inline-eq-IEq148 group, 192and similarly for the other interaction coefficients. Note that this negative coefficient also 193implies that the wage gain relative to the inline-eq-IEq149 group from being in the inline-eq-IEq150 group is 194smaller when climate mildness is high than when it is low, a consequence of the depressing 195wage effect of mildness for the inline-eq-IEq151 group.1964 Empirical Results197The estimated hedonic wage regressions are shown in Tables 2–3. Table 2 shows a Rosen-198Roback wage regression with a standard treatment of amenities, where the inline-eq-IEq152 199variable appears only in level form. Table 3 adds interactions between inline-eq-IEq153 and edu200cation and between inline-eq-IEq154 and age. The various columns in the tables show a condi201tional regression (which directly gives amenity valuations) along with the corresponding 202unconditional regression (where inline-eq-IEq155 is dropped), with the theory used to motivate 203comparisons between the two regressions. All of the regressions are weighted by the CPS 204205206===== PAGE 12 (score 62, numeric-paren 36, table-words 8, var-words 6) =====2072081 320959 210Page 12 of 23211J. Brueckner212wage-representativeness variable, inline-eq-IEq156, ensuring that the observations reflect the overall 213population.8 Standard errors are clustered at the MSA level. Since no complications are 214present in the estimation, the regressions use ordinary-least-squares.2154.1 Standard Regressions216Column 1 of Table 2 shows the conditional version of a standard hedonic wage regression, 217with inline-eq-IEq169 appearing on the right-hand side. This variable’s coefficient is significantly 218positive, indicating that wages are higher in high housing-cost areas. Recall that the coef219ficient of inline-eq-IEq170, which appears only in level form, directly reveals (in absolute value) 220the average valuation of the amenity across all workers, given the presence of inline-eq-IEq171 221(see (4)). The coefficient is negative and statistically significant, as expected, indicating that 222workers will accept a lower wage to live and work in a milder climate.223Column 2 of Table 2 drops the inline-eq-IEq172 variable, yielding an unconditional wage regres224sion. While the inline-eq-IEq173 coefficient is still negative and significant, it increases in absolute 225value relative to column 1, rather than decreasing, as predicted by the theory.9 This pattern 226persists through the results below that use inline-eq-IEq174 interactions instead of the variable’s 227level, along with the CMSA-level inline-eq-IEq175. A possible explanation is that this inline-eq-IEq176 228variable is correlated with some unobserved MSA-level determinants of wages (e.g., high 2298 To be safe, these weights are still applied even though the exclusions described themselves alter the repre230sentativeness of the sample.2319 Since the coefficients come from different regressions, a formal test for equality is not possible.232VARIABLES233(1)234lwage235(2)236lwage237Mildness238−0.00202**239−0.00227**240(0.000326)241(0.000454)242Houscost2430.225**244–245(0.0229)246Mid_edx2470.215**2480.218**249(0.0106)250(0.0104)251High_edx2520.607**2530.611**254(0.0136)255(0.0134)256Mid_age2570.165**2580.166**259(0.00412)260(0.00428)261Old2620.125**2630.126**264(0.00771)265(0.00769)266Male2670.187**2680.187**269(0.0108)270(0.0107)271Black272−0.127**273−0.130**274(0.00766)275(0.00754)276Hispanic277−0.241**278−0.240**279(0.0163)280(0.0165)281Constant282−0.3852831.694284(1.035)285(1.550)286Observations287257,478288257,478289inline-eq-IEq1572900.4312910.426292Table 2 Standard Rosen-Roback 293hedonic wage regressions294Standard errors clustered at the 295metro level in parentheses296** pinline-eq-IEq1580.01, * pinline-eq-IEq1590.05297Marital-status, SIC 298employment-share, and year 299coefficients not reported300 301302303===== PAGE 13 (score 158, numeric-paren 132, table-words 3, var-words 5) =====3043051 3306Page 13 of 23 30759308Heterogeneous Individual Valuations of a Mild Climate309worker productivity in high-cost San Francisco), which prevent the expected drop of the 310inline-eq-IEq177 coefficient when inline-eq-IEq178 is removed from the regression. As will be seen 311below, the expected pattern emerges using the state-level version of inline-eq-IEq179, which may 312be less correlated with these unobservables.313Turning to the dummy control variables, inline-eq-IEq180 and inline-eq-IEq181 are dropped, so that the 314default worker is a young, female married to a civilian husband (the default marital status) 315with low education and a non-Black, non-Hispanic race. The wage effects of the dummy 316variables are as expected. More education or a non-young age raises the wage, with the 317point estimate of the age effect slightly smaller for old workers. Male wages are higher 318Table 3 Hedonic wage regressions with amenity interactions319VARIABLES320(1)321lwage322(2)323lwage324(3)325lwage326(4)327lwage328(5)329lwage330(6)331lwage332Houscost3330.223**334–3350.224**336–3370.222**338–339(0.0227)340(0.0229)341(0.0227)342Mid_ed3430.203**3440.204**3450.215**3460.218**3470.203**3480.204**349(0.00618)350(0.00611)351(0.0105)352(0.0103)353(0.00620)354(0.00612)355High_ed3560.601**3570.604**3580.607**3590.612**3600.600**3610.604**362(0.0125)363(0.0123)364(0.0136)365(0.0134)366(0.0125)367(0.0123)368Mid_age3690.165**3700.166**3710.172**3720.173**3730.172**3740.173**375(0.00412)376(0.00427)377(0.00395)378(0.00403)379(0.00396)380(0.00404)381Old3820.124**3830.125**3840.128**3850.130**3860.127**3870.128**388(0.00756)389(0.00755)390(0.00754)391(0.00752)392(0.00717)393(0.00716)394Mildness inline-eq-IEq160 low_ed395−0.00322**396−0.00358**397–398–399−0.00258**400−0.00292**401(0.000648)402(0.000684)403(0.000594)404(0.000613)405Mildness inline-eq-IEq161 mid_ed406−0.000728407−0.000902408–409–410−9.10e-05411−0.000245412(0.000426)413(0.000515)414(0.000505)415(0.000545)416Mildness inline-eq-IEq162 high_ed417−0.00181**418−0.00200**419–420–421−0.00106422−0.00123423(0.000607)424(0.000680)425(0.000699)426(0.000728)427Mildness inline-eq-IEq163 young428–429–430−0.00134**431−0.00158**432–433–434(0.000364)435(0.000440)436Mildness inline-eq-IEq164 mid_age437–438–439−0.00263**440−0.00290**441−0.00130**442−0.00134**443(0.000380)444(0.000519)445(0.000379)446(0.000378)447Mildness inline-eq-IEq165 old448–449–450−0.00198**451−0.00225**452−0.000509453−0.000539454(0.000592)455(0.000722)456(0.000585)457(0.000599)458Male4590.188**4600.187**4610.187**4620.187**4630.188**4640.187**465(0.0107)466(0.0105)467(0.0108)468(0.0106)469(0.0106)470(0.0105)471Black472−0.127**473−0.130**474−0.127**475−0.130**476−0.127**477−0.130**478(0.00747)479(0.00730)480(0.00771)481(0.00759)482(0.00752)483(0.00734)484Hispanic485−0.236**486−0.235**487−0.242**488−0.241**489−0.237**490−0.235**491(0.0137)492(0.0140)493(0.0165)494(0.0166)495(0.0138)496(0.0140)497Constant498−0.3744991.686500−0.3725011.704502−0.3595031.699504(1.031)505(1.546)506(1.040)507(1.553)508(1.036)509(1.549)510Observations511257,478512257,478513257,478514257,478515257,478516257,478517inline-eq-IEq1665180.4315190.4275200.4315210.4265220.4315230.427524Standard errors clustered at metro level in parentheses525** pinline-eq-IEq1670.01, * pinline-eq-IEq1680.05526Marital-status, SIC employment-share, and year coefficients not reported.527528529===== PAGE 14 (score 15, numeric-paren 0, table-words 4, var-words 7) =====5305311 353259 533Page 14 of 23534J. Brueckner535than those of females, and Black and Hispanic workers earn less than workers outside these 536groups. All these coefficients are strongly statistically significant.105374.2 Regressions with Amenity Interactions538Table 3 introduces amenity interactions with the three education dummies and the age dum539mies. Only education interactions are present in columns 1 and 2, with columns 3 and 4 con540taining only age interactions. Columns 5 and 6 contain both types of interactions. The first 541column within each pair shows the conditional regression, and the second column shows 542the unconditional regression. In all the regressions, the inline-eq-IEq182 variable only appears in 543interacted form, not as a level variable.544In the conditional regression in column 1, which includes inline-eq-IEq183, coefficients for two 545of the inline-eq-IEq184 interaction variables, inline-e q -IEq185 and inline-e q -IEq186, are 546negative and significant. However, the inline-e q -IEq187 coefficient, while negative, is 547insignificant and its absolute magnitude is smaller than those of the other two coefficients 548while being separately statistically unequal to each of them. The hypothesis that all three 549interaction coefficients are equal is also rejected. The results thus suggest that workers in 550both the high- and low-education groups value a mild climate, while workers in the middle 551range of education (high school with some college or an associate degree) have a lower and 552perhaps zero valuation of climate mildness.553While well-educated, and thus well-off, households are often thought to value amenities 554highly (see for example, Brueckner et al. (1999)), the presence of a similar valuation among 555the least-educated workers is noteworthy. A possible explanation is that workers with no 556more than a high-school education are frequently employed in jobs that require manual 557labor, which often occurs outside rather than indoors. As a result, climate mildness may 558make the jobs of such workers easier, accounting for their valuation of mildness. While the 559best-educated workers may have ample leisure time to enjoy outdoor activities, which could 560contribute to their valuation of climate mildness, the apparent lower valuation for workers 561in the middle range of education is somewhat puzzling. Conceivably, compared to the least-562educated, fewer of these workers may hold manual jobs, while their lower earning power 563relative to the most-educated may mean longer work hours and less time for outdoor activi564ties, thereby reducing the middle-range group’s valuation of climate mildness.565Climate-mildness valuation by the least educated workers but not by the inline-eq-IEq188 group 566also raises another issue related to the premises of the Rosen-Roback model. That model is 567based on the assumption that all workers are mobile across regions, and one may wonder 568whether this assumption is accurate for low-education workers, for whom moving costs 569may be unaffordable. While this observation may cast doubt on the applicability of the 570model to this group, it could be argued that everyone is mobile in a sufficiently long-run 571context, even workers with low resources.572Turning to the unconditional regression in column 2 of Table 3, the coefficients of the 573inline-eq-IEq189 interactions with inline-eq-IEq190 and inline-eq-IEq191 remain negative and significant. The 574coefficients are larger in absolute value than those in column 1, following the unexpected 575pattern in Table 2.57610 The omitted marital-status category is the most common one, married with civilian spouse present, and 577the dummy coefficients for the other categories are all negative, indicating higher wages in typical married 578households.579580581===== PAGE 16 (score 86, numeric-paren 36, table-words 19, var-words 8) =====5825831 358459 585Page 16 of 23586J. Brueckner587Table 4 shows the traditional wage regressions, and in the conditional version shown in 588column 1, the inline-eq-IEq229 coefficient increases in absolute value, being now larger than the 589coefficient in column 2, which is unchanged. This is the pattern predicted by the theory, with 590the required compensating decline in the wage as inline-eq-IEq230 increases being smaller when 591inline-eq-IEq231 exerts its own separate utility-equalizing force (rising with inline-eq-IEq232) rather 592being held fixed. The other estimates in Table 4 are similar to those in Table 3.593As in Table 3, the interaction regression in column 1 of Table 5 again suggests that work594ers with low and high education levels value climate mildness more than do workers with 595education in the middle range. While again larger in absolute value, the inline-e q -IEq233 596and inline-e q -IEq234 coefficients are also again both statistically different from the 597inline-eq-IEq235 interaction coefficient. The latter coefficient, however, is now also statistically sig598nificant. Note that the column-1 interaction coefficients are now larger in absolute value 599than the unconditional column-2 coefficients, as predicted by the theory.600As in Table 3, all the age interaction coefficients in column 3 of Table 5 are negative and 601significant, with the inline-eq-IEq236 and inline-eq-IEq237 interaction coefficients again larger in absolute value 602than the inline-eq-IEq238 interaction coefficient. As before, the difference is statistically significant 603only for the inline-eq-IEq239 interaction coefficient. As predicted by the theory, the column 3 604interaction coefficients are now larger in absolute value than the unconditional coefficients 605in column 4.606Turning to columns 5–6 of Table 5, the inline-e q -IEq240 coefficient in column 5 607now retains the statistical significance seen in column 1, with the inline-e q -IEq241 608coefficient losing it. That coefficient is again statistically different from the other two, 609VARIABLES610(1)611lwage612(2)613lwage614Mildness615−0.00252**616−0.00227**617(0.000436)618(0.000454)619Houscost6200.0135**621–622(0.00318)623Mid_ed6240.216**6250.218**626(0.0105)627(0.0104)628High_ed6290.611**6300.611**631(0.0134)632(0.0134)633Mid_age6340.166**6350.166**636(0.00418)637(0.00428)638Old6390.125**6400.126**641(0.00774)642(0.00769)643Male6440.187**6450.187**646(0.0107)647(0.0107)648Black649−0.126**650−0.130**651(0.00748)652(0.00754)653Hispanic654−0.241**655−0.240**656(0.0162)657(0.0165)658Constant659−1.2536601.694661(1.731)662(1.550)663Observations664257,478665257,478666inline-eq-IEq2176670.4286680.426669Table 4 Standard Rosen-Roback 670hedonic wage regressions with 671state-level housing cost672Standard errors clustered at the 673metro level in parentheses674**pinline-eq-IEq2180.01, * pinline-eq-IEq2190.05675Marital-status, SIC 676employment-share, and year 677coefficients not reported.678 679680681===== PAGE 17 (score 168, numeric-paren 134, table-words 6, var-words 7) =====6826831 3684Page 17 of 23 68559686Heterogeneous Individual Valuations of a Mild Climate687implying that workers in the middle education range have a lower mildness valuation 688than the other education groups. Column 5’s age interaction coefficients show the same 689pattern as in Table 3. Note that, while column 5’s education interaction coefficients are 690now larger than those in column 6, as predicted, that relationship does not hold for the 691age interaction coefficients.692While mostly matching the theoretical prediction regarding conditional vs. unconditional 693coefficient magnitudes, the results in Table 5 also reaffirm the conclusions from Table 3. 694They suggest that workers with high and low education levels value climate mildness by 695Table 5 Hedonic wage regressions with amenity interactions and state-level housing cost696VARIABLES697(1)698lwage699(2)700lwage701(3)702lwage703(4)704lwage705(5)706lwage707(6)708lwage709Houscost7100.0133**711–7120.0135**713–7140.0133**715–716(0.00316)717(0.00318)718(0.00316)719Mid_ed7200.203**7210.204**7220.216**7230.218**7240.203**7250.204**726(0.00618)727(0.00611)728(0.0105)729(0.0103)730(0.00619)731(0.00612)732High_ed7330.604**7340.604**7350.611**7360.612**7370.603**7380.604**739(0.0123)740(0.0123)741(0.0134)742(0.0134)743(0.0123)744(0.0123)745Mid_age7460.166**7470.166**7480.173**7490.173**7500.172**7510.173**752(0.00418)753(0.00427)754(0.00401)755(0.00403)756(0.00402)757(0.00404)758Old7590.125**7600.125**7610.129**7620.130**7630.128**7640.128**765(0.00759)766(0.00755)767(0.00761)768(0.00752)769(0.00725)770(0.00716)771Mildness inline-eq-IEq220 low_ed772−0.00378**773−0.00358**774–775–776−0.00312**777−0.00292**778(0.000706)779(0.000684)780(0.000649)781(0.000613)782Mildness inline-eq-IEq221 mid_ed783−0.00118*784−0.000902785–786–787−0.000532788−0.000245789(0.000489)790(0.000515)791(0.000545)792(0.000545)793Mildness inline-eq-IEq222 high_ed794−0.00228**795−0.00200**796–797–798−0.00152*799−0.00123800(0.000662)801(0.000680)802(0.000732)803(0.000728)804Mildness inline-eq-IEq223 young805–806–807−0.00184**808−0.00158**809–810–811(0.000448)812(0.000440)813Mildness inline-eq-IEq224 mid_age814–815–816−0.00314**817−0.00290**818−0.00132**819−0.00134**820(0.000493)821(0.000519)822(0.000378)823(0.000378)824Mildness inline-eq-IEq225 old825–826–827−0.00248**828−0.00225**829−0.000510830−0.000539831(0.000656)832(0.000722)833(0.000586)834(0.000599)835Male8360.187**8370.187**8380.187**8390.187**8400.187**8410.187**842(0.0106)843(0.0105)844(0.0107)845(0.0106)846(0.0106)847(0.0105)848Black849−0.126**850−0.130**851−0.126**852−0.130**853−0.126**854−0.130**855(0.00727)856(0.00730)857(0.00753)858(0.00759)859(0.00732)860(0.00734)861Hispanic862−0.236**863−0.235**864−0.242**865−0.241**866−0.237**867−0.235**868(0.0136)869(0.0140)870(0.0163)871(0.0166)872(0.0137)873(0.0140)874Constant875−1.2168761.686877−1.2378781.704879−1.1978801.699881(1.727)882(1.546)883(1.735)884(1.553)885(1.731)886(1.549)887Observations888257,478889257,478890257,478891257,478892257,478893257,478894inline-eq-IEq2268950.4288960.4278970.4288980.4268990.4289000.427901Standard errors clustered at metro level in parentheses902** pinline-eq-IEq2270.01, * pinline-eq-IEq2280.05903Marital-status, SIC employment-share, and year coefficients not reported.904905906===== PAGE 18 (score 36, numeric-paren 0, table-words 15, var-words 6) =====9079081 390959 910Page 18 of 23911J. Brueckner912more than workers with moderate education levels, and that young workers value climate 913mildness less than non-young workers.9144.4 Further Connections to the Theory915While Tables 4 and 5 show the predicted theoretical relationship between the coefficient 916magnitudes in the conditional and unconditional regressions, the analysis in Sect. 2 offers 917some further guidance in appraising the results. In particular, recall that the theory shows 918how differences in housing demands and amenity valuations between the two posited worker 919types can affect the magnitudes of the unconditional amenity wage effects for the types. 920Consider the unconditional regression in column 2 of Table 3, which pertains to the three 921education groups. While the regression has three groups rather than the two worker types 922in the model, pairwise comparisons can be made between the interaction coefficients using 923the theory, carrying out a inline-eq-IEq242/inline-eq-IEq243 comparison and a separate inline-eq-IEq244/inline-eq-IEq245 924comparison, relying on the effectively zero value for the inline-eq-IEq246 interaction coefficient.12925Consider first the inline-eq-IEq257/inline-eq-IEq258 comparison. Relative to the inline-eq-IEq259 group (type 2 in 926the theory), the inline-eq-IEq260 group (type 1) has a higher mildness valuation given the results of 927column 1 in Table 3, with inline-eq-IEq261928. But given its lower income, housing demand should 929also be lower for the inline-eq-IEq262 group, implying inlin e -eq-IEq263. From above, these two inequali930ties together yield a negative unconditional type-1 (inline-eq-IEq264) wage effect in eq (8) along 931with an ambiguous (possibly zero) sign for the type-2 (inline-eq-IEq265) effect in (9), matching the 932results in column 2 of Table 3.933For the inline-eq-IEq266/inline-eq-IEq267 comparison, the higher income of the inline-eq-IEq268 group (now 934type 1) should make inlin e -eq-IEq269 (type 2 is again the inline-eq-IEq270 group). The greater inline-eq-IEq271 935mildness valuation from the unconditional regression means inline-eq-IEq272936, but if the valu937ation of amenities rises faster than housing demand as income increases (the Brueckner-938Thisse-Zenou assumption), then inlin e -eq-I E q273. The conditional type-1 (inline-eq-IEq274) 939wage effect in (8) is then again negative while the type-2 (inline-eq-IEq275) effect is ambiguous and 940possibly zero, as in column 2 of Table 3.9414.5 Robustness Check: Stratified Regressions942One could argue that, if the goal is to explore the effect of education and age on the valu943ation of climate mildness, a different and possibly better approach is to estimate regres944sions stratified by worker category instead of a pooled regression with interaction variables. 945Accordingly, as a robustness check, this section replaces the regressions using inline-eq-IEq276 946interaction variables with stratified regressions. In other words, the single regression with 947inline-eq-IEq277-education interactions in column 1 of Table 3 is replaced by three separate 94812 This exercise is justifiable because deleting the inline-eq-IEq247 and alternatively inline-eq-IEq248 observations from 949the regression, leaving only two groups, yields the same coefficient pattern as seen in column 2: negative 950(zero) inline-eq-IEq249 (inline-eq-IEq250) interaction coefficients in the regression containing only inline-eq-IEq251 and inline-eq-IEq252 951observations; negative (zero) inline-eq-IEq253 (inline-eq-IEq254) interaction coefficients in the regression containing only 952inline-eq-IEq255 and inline-eq-IEq256 observations. inline-eq-IEq2247 and alternatively inline-eq-IEq2484 observations from the regression, 953leaving only two groups, yields the same coefficient pattern as seen in column 2: negative (zero) inline-eq-IEq2459954(inline-eq-IEq2550) interaction coefficients in the regression containing only inline-eq-IEq2251 and inline-eq-IEq2572 observations; 955negative (zero) inline-eq-IEq2953(inline-eq-IEq2584) interaction coefficients in the regression containing only inline-eq-IEq1255 and 956inline-eq-IEq2456 observations.957958959===== PAGE 19 (score 98, numeric-paren 72, table-words 5, var-words 8) =====9609611 3962Page 19 of 23 96359964Heterogeneous Individual Valuations of a Mild Climate965regressions, one for each education category, with inline-eq-IEq278 appearing in level form in 966each regression. A comparison of the inline-eq-IEq279 coefficients across the three regressions 967provides a different way gauging how valuation of the amenity changes across individuals 968in the different education categories. Similarly, the single regression with inline-eq-IEq280-age 969interactions in column 3 of Table 3 is replaced by three separate regressions, one for each 970age category, with inline-eq-IEq281 again appearing in level form. This approach follows Hoch 971and Drake (1974), who used the stratified approach to investigate how the effect of climate 972amenities on wages varies across occupations.973In contrast to the interaction approach, which implicitly constrains the coefficients of the 974control variables to be the same across education or age groups, the use of separate regres975sions under the stratified approach allows these coefficients to differ across groups. If the 976conclusions generated by the interaction approach also emerge under the less-restrictive 977stratified approach, then robustness is demonstrated. However, a limitation of the stratified 978approach is the inability to carry out statistical tests comparing the inline-eq-IEq282 coefficients 979across groups, which arises because the coefficients come from different regressions instead 980of common pooled regression.981The results of the stratified approach are shown in Table 6, with columns 1–3 showing 982regressions stratified by education and columns 4–6 showing regressions stratified by age.13 983The table uses the CMSA-level housing cost variable. As can be seen, all of the inline-eq-IEq283 984coefficients are significantly negative, suggesting that all the education and age groups value 98513 Note that, to conveniently evaluate education and age effects under the stratified approach, age is omitted 986from the stratified education regressions and education is omitted from the stratified age regressions. The 987alternative would be to run nine different regressions, one for each education-age combination, and to make 988comparisons across them.989Table 6 Stratified wage regressions990VARIABLES991(1)992lwage993low_ed = 1994(2)995lwage996mid_ed = 1997(3)998lwage999high_ed = 11000(4)1001lwage1002young = 11003(5)1004lwage1005mid_age = 11006(6)1007lwage1008old = 11009Houscost10100.230**10110.276**10120.275**10130.294**10140.326**10150.302**1016(0.00758)1017(0.00986)1018(0.0125)1019(0.00852)1020(0.00948)1021(0.0235)1022Mildness1023−0.00259**1024−0.00104**1025−0.000994**1026−0.00232**1027−0.00259**1028−0.00165**1029(0.000120)1030(0.000154)1031(0.000194)1032(0.000134)1033(0.000149)1034(0.000373)1035Male10360.188**10370.175**10380.244**10390.129**10400.272**10410.334**1042(0.00234)1043(0.00310)1044(0.00384)1045(0.00264)1046(0.00294)1047(0.00747)1048Black1049−0.120**1050−0.118**1051−0.133**1052−0.148**1053−0.265**1054−0.250**1055(0.00388)1056(0.00520)1057(0.00853)1058(0.00450)1059(0.00537)1060(0.0145)1061Hispanic1062−0.253**1063−0.173**1064−0.265**1065−0.325**1066−0.470**1067−0.436**1068(0.00311)1069(0.00552)1070(0.00918)1071(0.00374)1072(0.00491)1073(0.0144)1074Constant1075−1.182*1076−3.114**1077−6.871**1078−2.062**1079−3.203**1080−3.679*1081(0.500)1082(0.747)1083(1.362)1084(0.627)1085(0.746)1086(1.868)1087Observations1088105,180108979,128109073,1701091113,1651092122,466109321,8471094inline-eq-IEq28410950.22410960.22010970.15910980.22310990.21511000.2011101Standard errors clustered at metro level in parentheses1102** pinline-eq-IEq2850.01, * pinline-eq-IEq2860.051103Marital-status, SIC employment-share, and year coefficients not reported.110411051106===== PAGE 20 (score 23, numeric-paren 0, table-words 10, var-words 3) =====110711081 3110959 1110Page 20 of 231111J. Brueckner1112climate mildness. However, the patterns seen in the interaction regressions are only partly 1113evident in Table 6.1114If the education-interaction coefficient pattern were repeated in Table 6, then the 1115inline-eq-IEq287 coefficients in columns 1 and 3 would both be larger in absolute value than the 1116mildness coefficient in column 2. Instead, the inline-eq-IEq288 coefficients in the inline-eq-IEq289 and 1117inline-eq-IEq290 regressions of column 2 and 3 are almost exactly the same size, with absolute 1118values less than half that of the inline-eq-IEq291 coefficient in the inline-eq-IEq292 regression of column 11191. The implication is that workers with low education levels appear to value a mild climate 1120more than workers in the two other groups. This conclusion at least preserves the previous 1121finding that low-education workers highly value climate mildness, but it does not show 1122highly educated workers joining in this high valuation.1123As noted above, however, it is not possible to test for significant differences among the 1124estimated coefficients since they come from different regressions. Thus, for example, tests 1125for whether the inline-eq-IEq293 coefficients in the inline-eq-IEq294 and inline-eq-IEq295 regressions are statisti1126cally equal or whether they differ individually from the inline-eq-IEq296 coefficient are not possible, 1127which means that the claim above of a higher mildness valuation for the inline-eq-IEq297 group 1128cannot be rigorously justified. This inability represents a major limitation of the stratified 1129approach.1130Columns 4–6 of Table 6 show similar valuations of climate mildness in the inline-eq-IEq298 and 1131inline-eq-IEq299 groups, but a lower valuation for older workers. Therefore the previous conclu1132sion that non-young workers value climate mildness more than the young is not replicated.1133These differences in results come from not constraining the control-variable coefficients 1134to be the same across groups, the consequences of which can be seen in the variation in these 1135coefficients across the regressions in Table 6. For example, the wage effect from being male 1136is considerably larger for mid-age workers than for low-education workers (compare col1137umns 5 and 1 of Table 6). One could argue that, if the goal is to compare amenity valuations 1138across groups, then giving gender and race effects the same freedom to vary across groups 1139prevents drawing the sharp conclusions that are sought, a problem that is compounded by 1140the inability to carry out comparative tests. On the other hand, allowing flexibility in the 1141control coefficients may end up giving a truer picture of amenity valuations. For the cur1142rent exercise, however, the conclusions drawn from the amenity-interaction approach match 1143intuition better than those implied by Table 6, making them appear more credible.11444.6 Discussion1145The results in Tables 3 and 5 suggest that high- and low-education workers value climate 1146mildness more than workers with educations in the middle range, and that young workers 1147value climate mildness less than non-young workers. While the age-related valuation differ1148ences are expected, the evidence of strong valuation of climate mildness by low-education 1149workers is unexpected and novel.1150Interestingly, the paper’s results can be used to predict how the wage distributions across 1151groups within a city should differ between cities with low and high climate mildness. Focus1152ing first on the education groups, and recalling that the results show wages rising with 1153education, the larger mildness wage effect for the inline-eq-IEq300 group relative to that for the 1154inline-eq-IEq301 group implies that the wage gap between those two groups becomes larger when 1155climate mildness increases (with inline-eq-IEq302 wage falling by more). Similarly, the larger mild1156