New Estimates of Climate Demand: Evidence from Location Choice

JOURNAL OF URBAN ECONOMICS ARTICLE NO.

42, 261]284 Ž1997.

UE962027

New Estimates of Climate Demand: Evidence from Location Choice Michael Cragg and Matthew Kahn1 Department of Economics and SIPA, Columbia Uni¨ ersity, 420 West 118th Street, New York, New York 10027 Received December 15, 1995; revised October 17, 1996

We develop and apply to Census data a new method for estimating climate demand. The method is useful for ranking quality of life based upon a willingness to pay criterion. Our two major findings are that the willingness to pay quality of life index is correlated with the hedonic approach’s ranking but that the migration approach generates much larger estimates of willingness to pay for a more moderate climate. This finding is relevant for evaluating the economic impact of global warming. Q 1997 Academic Press

1. INTRODUCTION Estimates of climate demand are needed to measure the impact of global warming and to project the spatial distribution of people across climatologically different regions. This paper develops and applies a discrete choice model for estimating the demand for local public goods such as climate. Our method uses migrants’ state location choices to reveal their willingness to tradeoff private consumption for local public goods. We present a discrete choice utility maximization framework that has embedded in it hedonic wage and rental regressions. These hedonic regressions identify the implicit prices people pay for amenities while estimates of the utility index provide measures of marginal utility from amenity increases. Thus, in one integrated framework we address two key questions in environmental economics: how much do people pay for non-market environmental goods? and how much would they be willing to pay? 1

We thank the editor and two anonymous reviewers and Jacob Mincer, David Bloom, Jeff Pliskin, Joe Tracy, and other participants at the Columbia University Labor Seminar and the ColgaterHamilton College Seminar for helpful comments. The Spencer Foundation provided valuable funding. We are especially grateful to Mr. Mahler and Mr. Crunch for diligently performing all calculations. 261 0094-1190r97 $25.00 Copyright Q 1997 by Academic Press All rights of reproduction in any form reserved.

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Migration data offers a revealed preference methodology to quantify the incomeramenities tradeoff.2 Migrants are attractive because they are ‘‘small’’ and take equilibrium prices as exogenous when choosing their utility-maximizing state. We model each state as representing a bundle of human capital factor prices, land and housing attribute prices, and a vector of local public goods. Some states offer a high return to education and a low price per room of a housing unit but cold winter temperatures. Other states offer a low return to human capital but have excellent amenities. Assuming that people live and work in the same state, people must simultaneously choose the local labor market where they will supply their skills and the set of local public goods they will consume. Estimating a 48-dimensional conditional logit model, we identify individual willingness to tradeoff income for amenities. Our conditional logit model has the structural interpretation of identifying the willingness to tradeoff private consumption for public goods consumption. After estimating the model, we simulate the migration probabilities. Finally, we measure preference intensities by calculating willingness to pay for changes in a location’s amenities vector. This paper builds on Graves’ w18, 19x migration research on climate demand and on Rosen’s w39x research agenda of identifying structural demand parameters for capitalized non-market amenities. Graves w18, 19x and Mueser and Graves w34x have used aggregated migration net flow data to quantify migratory elasticities with respect to local amenities. Our research extends this earlier migration research along two dimensions. First, the opportunity cost of location choice can be further disaggregated.3 Second, earlier reduced form research’s coefficient estimates could not be used for calculating consumer surplus from amenities. Our research also adds to the hedonic quality of life literature. Migration data offers an additional source of information that has not been exploited in equilibrium hedonic studies. In the 1980’s, several studies pointed out the inherent difficulties of conducting the hedonic two-stage identification procedure. In the absence of available instruments, willingness to pay could not be identified ŽMcDonnell and Phillips w31x, Epple w13x, Palmquist w36x, Brown and Rosen w9x.. In the aftermath of this 2

Recent migration studies that have focused on quality of life pursuit include Berger and Blomquist w4x, Greenwood and Hunt w20x, Douglas and Wall w12x, and Mueser and Graves w34x. A separate line of migration research has focused on migration’s role in bringing about regional labor market adjustment as individuals arbitrage spatial variation in employment and income opportunities ŽDavanzo w10x, Gabriel, Marquez and Wascher w17x, Blanchard and Katz w5x, and Hughes and McCormick w26x.. 3 Some migration studies have proxied for economic opportunity using mean per capita state income ŽBarro and Sala-I-Martin w2x.. By working with micro data, we estimate hedonic wage and rental regressions to impute each person’s wage and rental across space.

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critique, the empirical literature of the late 1980’s and 1990’s has focused on the more modest goal of simply estimating environmental goods’ implicit prices ŽRoback w38x, Blomquist et al. w7x, Gyourko and Tracy w24x.. The hedonic literature has ranked locations based on index weights generated by how much people pay for each attribute. Our paper offers an alternative method for ranking locations based on how much people are willing to pay for each attribute. This paper is organized as follows. Section 2 presents our migration methodology. Section 3 presents our estimated models, and Section 4 demonstrates how the quality of life rankings change based upon a willingness to pay versus amount paid criteria. Finally, Section 5 concludes. 2. A MIGRATION METHOD FOR VALUING ENVIRONMENTAL QUALITY The hedonic ‘‘equilibrium’’ approach for estimating demand for nonmarket goods makes no use of migration data. The methods we present are based upon the characteristics approach to demand theory ŽLancaster w28, 29x.. Similar to a product differentiation model in industrial organization, we model each geographical location as a bundle of attributes. Utility-maximizing consumers will maximize a random utility function by making a discrete choice from a high dimensional choice set ŽMcFadden w33x.. For each person, each location represents a bundle of income opportunities, rental prices for a quality-adjusted housing unit, and a fixed set of exogenous environmental amenities. Our basic idea for measuring climate demand is to use the income]amenities tradeoff implicit in the discrete choice of location by migrants. We exploit two sources of spatial variation in wages and rents to identify climate demand. First, we explicitly incorporate that migrants pay for non-market local public goods through lower wages and higher rents in nonlinear wage and rental equations.4 These compensating differentials will adjust to equalize utilities ‘‘on average’’ across locations, but individual consumers will still find some locations preferable to others, and this will be revealed in their migration decisions. The second source of spatial variation in wages and rents is shocks to local labor and land markets.5 As a local labor market experiences demand shocks Žmanufacturing plant 4 Analogous to Quigley’s w37x methodology, we exploit the non-linearity of the migrant’s budget constraint arising from the log]wage and log]rent specifications to identify the parameters in the utility function. 5 Davis et al. w11x examine the unemployment consequences of local labor market demand shocks arising from military defense contracts, manufacturing plant openings, or natural resource price fluctuation. Blanchard and Katz w5x find that an initial negative shock of 1% to state employment increases the state unemployment rate by up to 0.37% after two years and decreases state wages by up to 0.4% after about six years.

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closings. or supply shocks Žan influx of immigrants., wages and rents will slowly adjust such that the ‘‘price’’ of migrating to this location has changed. For example, if Indiana experiences a sharp increase in labor demand relative to Florida, wages will rise in Indiana yielding a growing wage differential Žin addition to the pre-shock compensating differential . between the states. If large numbers of migrants continue to choose Florida over Indiana then this indicates a high willingness to pay for Florida’s climate. Allowing for heterogenous local public goods preferences across demographics groups, we identify each group’s preferences exploiting the spatial variation in wages and rents and climate. If all demographic groups had the same preferences and the national economy had achieved a long-run equilibrium, then the hedonic gradient would sketch out the representative agent’s indifference curve.6 In this case, migration data would not be needed for quantifying climate demand. We model a migrant’s choice of location in a classic utility-maximizing framework: location choice is a function of consumption Žincome net of the cost of amenities and housing costs. and the local climate levels. Location choice is also a function of a random taste shock. This yields stochastic location demand functions which are a function of hedonic prices and local quality of life. By measuring demand for amenities, we are able to measure the consumer surplus associated with a change in local amenities. The demand analysis is based upon migrants’ rather than the population’s choice of location for two reasons. First, the data demands for modeling location choice are onerous. A complete history of location choice, family structure, and household earnings is required.7 This would not be a problem if amenities, rents, income, and the distribution of the population did not change. Second, because equilibrium hedonic prices are a function of the supply and demand for public goods, land, and labor, the hedonic prices are therefore endogenous to the location choice of the entire population invalidating their inclusion as regressors in a structural model of environmental demand. We overcome this endogeneity problem and avoid the problem of jointly modeling both hedonic prices and location choice by assuming that migrants are ‘‘small.’’ Thus, they have no impact on equilibrium prices. It is this assumption that allows us to model and measure the demand for environmental quality separately from a hedonic equilibrium model. 6

In equilibrium, no individual or firm could raise their utility or profit by migrating. Linneman and Graves w30x use the PSID to study an individual’s joint decision to switch jobs and to migrate. 7

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By using the revealed state location choice of migrants as a method for measuring the demand for environmental goods, we make a number of implicit assumptions. First, we implicitly assume that migration is a sequential decision. Households choose to move locally or out-of-state, and conditional on moving out-of-state they choose a new location.8 Second, the model implicitly assumes that expected average consumption and climate is similar across cities within a state. It would be unreasonable to study the demand for education and other localized public goods by examining state-level choice. 2.1 Model We focus on the location choice for the set of people who have chosen to switch states. This group has overcome any migration cost barrier and now must choose which state to live in. The basic assumption underlying our estimation of the amenities demand system is that every location offers a bundled set of amenities of whose characteristics, Zi , both the household and econometrician are fully aware. Each household h within an age]education strata maximizes the common random utility function by choosing a state i, max U Ž Zi , c h i N X h . q e i h

Ž 1.

c h i s Ž 1 y Ti . ) yi Ž X h , Zi . )Wi Ž X h . y ri Ž X h , Zi . ,

Ž 2.

i , c hi

subject to

where c h i is expected composite consumption valued in dollars for household h in location i, X h is a vector of household characteristics such as the head of household’s age and education, Zi is the bundle of amenities in location i, and yi Ž X h , Zi . and ri Ž X h , Zi . are the expected weekly incomes and rents for a household with attributes X h that chooses location i. Note that income and rents are a function of the local public goods vector Zi , indicating that the attributes are capitalized into local wages and rents. Wi Ž X h . is a household’s expected annual weeks worked in location i. If unemployment is high in a given state, the annual weeks worked will be low. Ti stands for state taxes. The error term represents any idiosyncratic variation in preferences across households such as a change in marital status or a change in one’s health after controlling for life cycle and education differences. See Berger and Blomquist w4x for a study that explicitly models the initial move decision. Unlike our work, they choose to collapse the second-stage migration decision for the set of people who do choose to move into a choice between moving to a top-ranked ‘‘quality of life’’ area or not. Bartik et al. w1x estimate amenities demand as revealed by the initial decision of whether to move. 8

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Substituting the maximal value for c h i yields the indirect utility function Vi h q e i h s max Ui h s V Ž z i , yi , ri , Wi , Ti N X h . q e i h , c hi

Ž 3.

then the utility-maximizing discrete choice problem involves choosing the location j such that Vjh y Vi h ) e jh y e i h; i

Ž 4.

McFadden w32x has shown that if the residuals have a type-I extreme-value ŽWeibull. distribution then the probability that location j is chosen is the conditional multinomial logit n

P j Ž p, Z, X h . s exp Ž Vjh .

Ý exp Ž Vk h . ,

Ž 5.

ks1

where Z is the vector Ž Z1 , . . . , Zn .. The n equations specified in Ž5. are a system of probabilistic demand functions for choosing each of the possible locations of the individual with characteristics X h . McFadden w33x and Small and Rosen w40x show that the P j Ž p, Z, X h . are well-behaved demand equations satisfying the usual properties. In our empirical work we adopt two specifications for the utility function, Vi h s b c h i q f 9Zi q c cities i

Ž 6.

Vi h s b 1 c h i q b 2 c h2 i q f 9Zi q c cities i .

Ž 7.

Eq. Ž6. presents a linear index utility function while Eq. Ž7. includes a quadratic term in private consumption. This allows a given agereducation group’s marginal rate of substitution between private and public goods to vary. Note that the utility functions in Eqs. Ž6. and Ž7. include the number of cities in a state as a regressor Žlabeled cities in Eqs. Ž6. and Ž7... Controlling for a state’s climate and its wages and rents, we predict that people are more likely to move to a state with more cities. Including the cities variable allows us to nest our climate demand model with a ‘‘dartboard’’ model of random location choice.9 9

The dartboard model assumes that population is uniformly distributed across states and hence large states will attract more migrants. However, because people move to cities it is more appropriate to label large states as those with many cities. Although we only present estimates with cities as the regressor, we have also experimented with including state land area. These are available upon request. We do not include state population as a‘‘dartboard’’ regressor because it is endogenous. A state’s number of cities is highly correlated with lagged population.

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NEW ESTIMATES OF CLIMATE DEMAND TABLE 1 Summary Statistics on Census Data Movers

Age Years of schooling Weeks in year Average hours per week Annual household income Dropout High school graduate College educated Post-college schooling Married Number of observations

Stayers

Mean

S.E.

Mean

S.E.

Minimum

Maximum

40.42 12.11 46.05 44.27 34,974 0.09 0.48 0.35 0.08 0.81 30,236

8.09 2.71 13.20 14.10 32,573 0.29 0.50 0.48 0.27 0.39 30,236

40.20 11.14 46.81 43.25 30,403 0.16 0.56 0.23 0.05 0.79 122,071

8.00 2.81 12.37 12.97 28,501 0.36 0.50 0.42 0.21 0.41 122,071

30 1 0 0 0 0 0 0 0 0

60 17 52 99 197,869 1 1 1 1 1

Note. Data are a one percent sample of the 1990 PUMS Census of Population and Housing Data. Sample includes male heads of household who were between 30 and 60.

2.2 Empirical Implementation This paper uses micro data to study individual state location choice. Any discrete choice research project must tradeoff tractability for realism. States are both a convenient geographical unit of observation and also a reasonable unit of analysis for studying climate demand. To implement the proposed model, data on regional migration, regional environmental goods, regional wages and rentals, and hedonic prices must be collected and constructed. We use the 1% PUMS samples of the 1990 Census of Population and Housing to measure individual state-to-state migration. The PUMS indicates a household’s location at the time of interview and five years previously. If the previous state of residence is different from the current state and the head of household is a male between 30 and 60, we include this family in our data. While the PUMS provides data on the age of the family members, their marital status, the household size, educational attainment of family members, we simply describe a family by the head of household’s age and education.10 Table 1 provides summary statistics on our sample. We use the Census because it is the largest available data set which provides a geographically representative data set on migrants. Since we will be focusing on the location choice of the set of people who chose to move, it is relevant to compare this group to the set of people who 10 This data selection rule is adopted because we do not know the migrant’s marital status in 1985, the base year.

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chose not to switch states between 1985 and 1990. Table 1 presents the summary statistics for the two groups. Movers are younger and have roughly 1 more year of education. Movers have a much higher probability of having finished college than non-movers, but weeks worked, hours worked, and marital status are quite comparable across the two groups. Between 1985 and 1990, 19% of college graduates age 30]39 switched states, 11% of college graduates age 40]49 moved between states, and 7.9% of college graduates age 50]59 moved. For high school graduates, 9.2% age 30]39 moved, 6.6% age 40]49 moved, and, 4.9% age 50]59 switched states. Our primary focus is on environmental attributes which are nonpurchased pure public goods Žthe climate.. These are distinct from other public goods which may be rivalrous or purchased Žpollution, crime, schooling, and infrastructure .. Our Z’s in Eqs. Ž6. and Ž7. include environmental variables such as summer and winter temperature, yearly rainfall, possible sunshine, humidity, and state adjacency to the coast. This climate specification allows us to closely match the climate specification adopted in the hedonic valuation literature ŽBlomquist et al. w7x, Roback w38x, Gyourko and Tracy w24x.. Our data sources are the Statistical Abstract of the United States and the National Oceanic Administration’s climate CD ROM which covers all monitoring stations from 1900 to 1989. The summary statistics are presented in Table 2. The model, Eqs. Ž1. ] Ž5., indicates that utility-maximizing individuals know what their wages, rents, weeks worked, and environmental bundle

TABLE 2 Summary Statistics on Cross-State Variation in Data

High school graduate age 30]40 High school graduate age 40]50 High school graduate age 50]60 College educated age 30]40 College educated age 40]50 College educated age 50]60 Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity

Mean

S.E.

Minimum

Maximum

$13,266 $15,858 $15,681 $20,935 $24,524 $25,298 35.9 33.7 74.2 0.5 57 80

$1,545 $1,797 $1,701 $2,556 $3,039 $3,162 13.3 10.4 5.2 0.5 8 10

$9,954 $12,566 $12,265 $15,904 $18,880 $19,345 9.5 15.2 64.1 0.0 38 44

$17,753 $20,781 $19,824 $28,046 $32,307 $33,241 58.5 62.5 83.0 1.0 81 94

Note. Means, S.E., minimum, and maximum are the summary statistics computed across states.

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would be in all 48 states. To reconstruct the information available to each of our movers, we must impute expected private consumption in each state. As shown in Eq. Ž2., we need estimates of each individual’s wage, weeks worked, and rent in each state. We start with our wage estimates. To impute wage rates for each individual in the migration data set, we use coefficient estimates of the regression, n

log Ž g jh . s

Ý d jh g 0 q g 1 j ) HSh q g 2 j ) BA h q g 3 j )GBAh js1

qg4 j ) EXP q g 5 j ) EXP 2 q pw Z j 4 q e h , Ž 8 . where d jh is equal to one if household h lives in state j, HS, BA, and GBA are dummy variables indicating high school completion, college education, and graduate education, respectively, EXP measures potential labor market experience, and Z j is the vector of environmental amenities data. The wage regression in Eq. Ž8. is a standard ‘‘Mincer’’ wage regression except for the fact that we allow the returns to human capital and experience to vary from state to state. Note that we do not allow the constant to vary across states.11 The hedonic wage regression presented in Eq. Ž8. is different from the typical hedonic wage regression because it recognizes that there is significant variation in returns to education and work experience across regions. An individual’s wage can be high to compensate for low levels of local amenities or because his human capital has a higher marginal product in that geographical location. Thus, unlike Blomquist et al. w7x and Gyourko and Tracy w24x, we allow factor prices to vary across states.12 To estimate this regression we use the 1% PUMS from the Census of Population and Housing. Our sample consists of men ages 30]60 who worked at least 30 hours per week and were neither self-employed nor handicapped and earned between $2.00 and $500 per hour. We assume that the econometrician calculates wages exactly as individuals do. People assume that their wage will be the average wage for an individual with the same simple set of characteristics.13 This implicitly assumes that people 11

The hedonic prices for climate would not be identified if we included state dummies. Beeson w3x and Kahn w27x present evidence on how the returns to human capital vary across cities. 13 Thus, we are implicitly assuming that there is no spatial selection on unobservables. Intuitively, this means that controlling for observables, the average man in Iowa’s wages are representative of what the average man in New York would earn if he moves to Iowa. Given the set of variables in the Census, it is extremely difficult to implement an interesting selection correction. Borjas et al. w8x use panel data from the National Longitudinal Survey of Youth to explore spatial selection and report some evidence that high-ability individuals are moving to more dispersed wage distributions. 12

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have myopic expectations about the wage process rather than rational expectations. Thus, we are following the Freeman w14, 15x myopic occupational choice methodology and not attempting to estimate a rational expectations model of location choice based on discounted expected present value. Table 3 presents our estimates of environmental capitalization into wages ŽOLS estimates of Eq. Ž8... We present two sets of wage regression results. The right-hand column presents results where we have included state-specific factor prices while in the left-hand column we impose that factor prices are equal across states. Estimation of Eq. Ž8. yields 247 coefficients which are presented in the second column. We simplify the presentation by presenting only the average and standard deviation across the 48 states when the coefficient was differentiated by state. For example, we allowed the high school graduate dummy to vary across the 48 states. The average of the 48 coefficients was 0.2763 and the standard deviation was 0.0570. Thus the approximate range in the estimated coefficients is 0.2763 qry 2*0.0570. Therefore, the range on the return to a high school diploma ranges from 16 to 39% over being a dropout. This represents large spatial differences in the returns to human capital. The two log]wage specifications presented in Table 3 yield very different estimates of the implicit price of climate. The coefficient estimates pw Žsee Eq. Ž8.. represent the price of amenities that are capitalized into wages. The key difference between the two specifications is that when we allow human capital’s price to vary across space, the climate coefficients estimates are individually insignificant. Imposing the ‘‘law-of-one price,’’ the amenity t-statistics soar but the temperature variable still has the ‘‘wrong sign.’’ For example, July temperature and humidity lower wages while sunshine raises wages. A compensating differentials model would predict the opposite finding. We do find that increased February temperature lowers wages.14 As indicated in Eq. Ž2., we recognize the importance of quantifying not only the mean wages in each state for a given agereducation group but also expected employment. One method for controlling for state unemployment is to create agereducation group cell means of unemployment rates based on the CPS question ‘‘are you currently unemployed.’’ Since this question only measures an instantaneous concept of unemployment rather than an accumulated annual measure, we control for spatial variation in unemployment by using information on annual weeks worked in the

14 Henderson w25x provides theoretical insights on the relevant factors that affect whether amenities are capitalized into rents rather than wages.

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TABLE 3 Wage and Rental Hedonic Regressions Law-of-one price for human capital

Log]wage regressions Intercept Age Age squared High school graduate College graduate More than college Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity Number of observations R-squared

Coefficient

t-statistics

Coefficient

S.D.

1.2840 0.0553 y0.0005 0.3079 0.5985 0.7488 0.0009 y0.0028 y0.0094 0.0594 0.0042 y0.0003 170,498 0.218

30.29 37.75 y31.18 86.73 145.66 170.25 5.93 y15.13 y26.70 20.46 18.10 y1.53 170,498 0.218

0.9372 0.0559* 0.0005* 0.2763* 0.5462* 0.6807* 0.0086 0.0017 0.0110 0.0368 0.0080 0.0021 170,498 0.238

0.7850 0.0075** 0.0003** 0.0570** 0.0878** 0.1125** 0.0043 0.0051 0.0096 0.0792 0.0064 0.0056 170,498 0.238

Law-of-one price for housing attributes Log]rent regression Intercept Dummy s 1 if unit is a house Number of rooms Number of bedrooms Built in 1985]1989 Built in 1980]1984 Built in 1970]1979 Built in 1960]1969 Built in 1950]1959 Built in 1940]1949 Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity Number of observations R-squared

Human capital prices vary by state

6.8248 0.0163 0.0876 0.0458 0.2415 0.0492 0.0214 0.0583 0.0126 y0.0339 0.0033 0.0025 y0.0316 0.1562 0.0154 y0.0014 122,909 0.186

185.45 4.20 42.00 13.71 40.64 8.68 4.69 12.04 2.36 y5.80 15.86 10.40 y70.99 40.04 53.05 y5.65 122,909 0.186

Housing attribute prices vary by state 7.3461 0.0812* 0.0657* 0.0785* 0.2621* 0.0136* y0.0026* 0.0288* 0.0090* y0.0715* 0.0061 0.0011 y0.0461 0.1782 0.0192 0.0013 122,909 0.264

0.1333 0.0763** 0.0642** 0.0800** 0.1409** 0.1507** 0.1384** 0.1395** 0.1239** 0.1097** 0.0008 0.0009 0.0017 0.0143 0.0010 0.0010 122,909 0.264

Note. Two specifications of the log]wage and log]rental regression are presented. The first specification is a standard hedonic wage and rental regression, and hence the standard errors have the traditional interpretation. The second specification is a non-standard hedonic regression where we allow the ‘‘price’’ of human capital and housing attributes to differ by state. To simplify the presentation of the non-standard hedonic regressions we do not present the 48 state estimates for each human capital or housing attribute. Instead, we present the average of the 48 coefficient estimates and the standard deviation across the 48 estimates. A * indicates that we are presenting the average of the 48 state-specific coefficients in that category and a ** indicates the standard deviation across the 48 estimates. The data source for the rental regression is the 1990 PUMS household file while for the wage regressions, the data source is the 1990 PUMS individual file.

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previous year. We impute expected annual weeks worked in each state i for each household h using Eq. Ž9.: Wi Ž X h . s 52) Pr Ž work G 50 weeks . q Ž 1 y Pr Ž work - 50 weeks . . ) E Ž Weeks N work - 50 weeks . . Ž 9. For each state, we calculate the probability of working less than 50 weeks from estimates of a logit model for whether an individual worked less than 50 weeks where the regressor included age and dummy variables for being a high school graduate, a college graduate, or gaining post-college schooling. For each state, we estimate an OLS regression of weeks worked on age and dummy variables for being a high school graduate, a college graduate, or gaining post-college schooling for the set of individuals who worked less than 50 weeks in the year. These estimates are used to calculate EŽWeeks N worked - 50 weeks.. For both the logit and weeks worked regressions we use the sample of men between 30 and 59 from the 1% PUMS sample. These estimates are used to compute expected annual weeks worked for each state using Eq. Ž9., which controls for state unemployment differences. We have now summarized how we impute wages and weeks worked. To simplify our imputation of private consumption, we abstract from modeling housing. We assume that the minimum level of housing consumption for every household is a new rented home with four rooms and two bedrooms. To impute the cost of housing in each state, we use coefficient estimates of the rental regression n

log Ž r jh . s

Ý d jh a 0 q a 1 j ) HOUSEh q a 2 j ) ROOMSh js1

qa 3 j ) BROOMSh q a 4 j YIh q ??? qa 10 j Y 7h q pr Z j 4 q j h , Ž 10 . where d jh is equal to one if household h lives in state j, HOUSE indicates whether the rental unit was a house, ROOMS indicates the number of rooms in the unit, BROOMS indicates the number of bedrooms, Y 1, . . . , Y 7 are a set of dummy variables corresponding to the year interval when the unit was built, and Z j is the vector of environmental amenities. Note that analogous to the wage regression ŽEq. Ž8.., factor prices vary across states but the constant and the price of local public goods do not. This housing rental regression is different from the typical hedonic regression because the price of housing varies spatially. It is important to allow the price of rental units to vary across space because this controls for the ‘‘cost of

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living.’’ Cities where land is cheap will feature lower prices for a four room house. Our methodology controls for this.15 Our sample consists of the set of all rental units in the 1990 1% PUMS data set. The dependent variable is gross rent. We find significant evidence that environmental attributes are capitalized into rentals. The lower part of Table 3 presents our estimates. Similar to our wage regressions, we present two specifications. The right-hand rental column presents our estimates with state-specific housing prices while the left-hand rental column does not. The key point is that, unlike our wage estimates presented in Table 3, we estimate very similar coefficient values for both specifications. Unlike the wage regressions, our coefficient estimates are much more intuitive. February temperature, proximity to the beach, and sunshine raise rents and July temperature, humidity, and lower rainfall lowers rents. In this section we have shown how we created each component of Eq. Ž2.. The final variable is state average income taxes Ti excluding federal taxes based upon data from the ‘‘Statistical Abstract of the United States.’’ We assume that taxes are used to purchase local public goods and that people who pay different taxes get different services. For each income level, the disutility of foregone private consumption paid in taxes is offset by the utility gain from purchased public goods. This assumption nets out the impact of local produced public services such as education, crime, and safety.16 Our final data set of state-to-state movers contains 26,988 men. For each person in each of their 47 potential destination states, we have imputed person-specific predicted annual weeks worked, weekly wages, and rentals. These variables are inserted into Eq. Ž2., which yields the private annual consumption for each potential destination. Note that in specifying the net composite consumption we calculate it net of state taxes and net of the cost of environmental goods implicitly priced in wages and rentals Žsee Eqs. Ž8. and Ž9... 15 Gabriel et al. w16x document that migrant locational choice is sensitive to spatial variation in home prices. If demand for labor is growing in areas where housing is inelastically supplied, then regional adjustment may be slowed because migrants pursue both higher wages and lower rents. 16 See Gyourko and Tracy w21, 22, 23, 24x for an analysis of the capitalization of local services and taxes into wages and rents and also for a model which allows for differences in efficiency and rent seeking in local governments. Blank w6x suggests that women eligible for welfare are less likely to leave more generous states. Our approach does not allow for migration to be explained by arbitraging spatial variation in transfer payments. If this was a major cause of migration, then our model should have predictive power for the movement of less educated people. Walker w42x finds little evidence that generous states are welfare magnets.

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3. ESTIMATED MODELS Two specifications of the migration model of environmental demand are estimated. The first model imposes that utility is linear in private consumption and environmental amenities ŽEq. Ž6... The second model allows the marginal utility of income to vary with income ŽEq. Ž7... The model is estimated via maximum likelihood for six sub-groups of the population, three age groups 30]39 years, 40]49 years, and 50]60 years of age for both high school and college graduates separately. The estimates from the twelve separate conditional logit estimates are presented in Table 4. In all specifications, we find that holding environmental attributes constant people are moving to states that offer higher private consumption.17 Interestingly, we find that for each human capital group the magnitude of the coefficient on private consumption Žthe marginal utility of private consumption. falls across age cohorts. In addition, college graduates have a higher marginal utility of consumption than high school graduates. The model yields mostly intuitive signs with respect to the environmental variables. Note that for both education groups, we find that the marginal utility from increased February temperature increases with age and that marginal disutility from summer temperature sharply rises for those aged 50]60.18 We find that the summer and winter temperature, humidity, and rain variables have the expected signs. We find mixed results for the coast variable. It has the right sign for younger migrants but the wrong sign for older migrants. To judge the explanatory power of our model, for each of the six age]education cells, we simply graph the actual and the predicted probabilities of moving to each state.19 These goodness of fit graphs are presented in Figs. 1 and 2. These figures present some simple facts for where migrants actually move versus where our model predicted they would go. An excellent model would feature a simple 458 line. This would indicate that the predictions of the model just match the actual probabilities. Given that we have placed our model’s predictions on the vertical axis and the actual migration probabilities on the horizontal axis, any data points that lie above the 458 line indicate that our model has overpredicted 17 Note that for men aged 50]60 who did not complete college we find in the linear private consumption model that increased private consumption does increase one’s probability of moving to that state, but in the model that includes consumption and consumption squared we find a counter intuitive sign. However, an F-test shows that a quadratic term adds no additional explanatory power. 18 It is also relevant to note that our estimates of the marginal utility from environmental attributes do not appear to be sensitive to the inclusion of the square of private consumption. 19 These predictions are based on the linear private consumption models presented in Table 4.

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TABLE 4 Coefficient Estimates 30]40 years

40]50 years

50]60 years

Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic At least a college degree Composite consumption Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity Number of cities Number of observations Log likelihood Composite consumption Consumption squared Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity Number of cities Number of observations Log likelihood

1.14E-04 0.007 0.013

19.7 4.1 5.7

y0.022 y5.9 0.320 9.8 0.013 5.3 y0.009 y4.3 0.083 34.2 6,836 6,836 y24,039 y24,039 2.99E-04 y3.94E-09 0.007 0.015

y0.024 y6.4 0.292 8.8 0.012 5.1 y0.010 y4.6 0.081 33.6 6,836 6,836 y24,027 y24,027

1.53E-04 y3.71E-09 0.006 0.033

16.0 1.4 13.4

3.63E-05 0.012 0.038

3.3 3.1 7.8

y0.036 y7.8 y0.084 y17.4 0.004 1.5 y0.009 y3.2 0.082 25.6 3,823 3,823 y13,367 y13,367

y0.040 y0.095 0.008 y0.014 0.091 1,363 y4,752

y5.2 y11.6 1.6 y3.0 17.2 1,363 y4,752

5.5 y1.09E-04 y3.4 2.731E-09 1.7 0.011 13.7 0.037

y1.4 1.9 2.9 7.5

7.6 2.87E-04 y4.7 y3.35E-09 4.3 0.004 6.4 0.040

Completed high school but did not complete college Composite consumption 5.05E-05 5.2 Average rainfall in 1980’s 0.005 3.6 Average February 0.032 16.6 temperature Average July temperature y0.021 y6.2 Significant coastal beach 0.212 6.6 Sunshine 0.004 1.9 Humidity y0.014 y7.5 Number of cities 0.072 32.3 Number of observations 8,190 8,190 y29,351 y29,351 Log likelihood Composite consumption Consumption squared Average rainfall in 1980’s Average February temperature Average July temperature Significant coastal beach Sunshine Humidity Number of cities Number of observations Log likelihood

1.07E-04 0.003 0.038

y0.037 y8.1 y0.082 y16.9 0.004 1.4 y0.010 y3.7 0.081 25.1 3,823 3,823 y13,361 y13,361

y0.039 y0.098 0.009 y0.012 0.092 1,363 y4,751

y5.0 y11.6 1.8 y2.7 17.3 1,363 y4,751

4.2 3.3 18.0

8.84E-06 0.008 0.057

0.6 2.8 14.8

y0.026 y6.0 y0.095 y22.7 0.002 0.6 y0.010 y4.2 0.075 26.2 4,513 4,513 y15,895 y15,895

y0.037 y0.079 y0.007 y0.016 0.072 2,263 y7,896

y5.9 y14.2 y1.7 y4.5 18.3 2,263 y7,896

3.6 y3.97E-06 y2.7 4.064E-10 3.6 0.008 18.1 0.057

y0.1 0.2 2.8 14.8

4.63E-05 0.007 0.048

4.2 1.75E-04 y2.9 y3.91E-09 3.8 0.007 16.8 0.048

y0.022 y6.3 0.206 6.4 0.004 2.1 y0.014 y7.7 0.072 32.4 8,190 8,190 y29,347 y29,347

y0.026 y6.1 y0.096 y22.8 0.002 0.6 y0.011 y4.6 0.076 26.4 4,513 4,513 y15,892 y15,892

y0.036 y0.079 y0.007 y0.016 0.072 2,263 y7,896

y5.9 y14.2 y1.7 y4.5 18.0 2,263 y7,896

Notes. Estimates are based upon the PUMS migrant data merged with the PUMS wages and weeks worked imputations together with state tax and amenitites data. The estimation equation is presented in eq. Ž5 ., and the specifications are presented in eq. 6 and eq. 7.

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FIG. 1. College graduate mobility rates.

migration to that state. To improve our reader’s understanding of our data, we graph the data by the initial of each destination state. Thus, Texas is represented as TX. The correlation of the ranks between the actual migration propensities and those predicted for college graduates age 30 to 39 is 0.86 and for high school graduates is 0.78.

FIG. 2. High school graduate mobility rates.

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NEW ESTIMATES OF CLIMATE DEMAND TABLE 5 Willingness to Pay Willingness to pay

Hedonic payment

S.D. Age 30]40 Age 40]50 Age 50]60 Rent Consumption College Average rainfall in 1980’s 13.3 Average February 10.4 temperature Average July temperature 5.2 Significant coastal beach 0.5 Sunshine 8.1 Humidity 10.3 Non-college Average rainfall in 1980’s 13.3 Average February 10.4 temperature Average July temperature 5.2 Significant coastal beach 0.5 Sunshine 8.1 Humidity 10.3

$839 $1,182

$407 $3,746

y$984 $1,414 $913 y$846

y$1,747 y$396 $338 y$847

$1,434 $6,704

$1,975 $10,774

y$2,160 $2,117 $643 y$2,785

y$2,898 y$1,036 $280 y$2,323

$206 $122

y$59 $739

y$5,788 y$705 y$1,322 $777 $1,885 $610 y$3,906 y$68

$303 y$507 y$120 $0

$4,360 $10,860

$206 $122

y$59 $739

y$21,490 y$705 y$4,488 $777 y$5,956 $610 y$18,400 y$68

y$303 y$507 y$120 $0

$12,676 $67,297

Note. Willingness to pay imputations are based upon the estimates from the linear specification presented in Table 4. Willingness to pay is defined as the value in dollars an individual is willing to pay for a one standard deviation increase in the amenities variable. Annualized hedonic payments are computed using the wage and rental estimates from Table 3 and Eq. Ž2. assuming someone works 2,000 hours a year.

To simulate the magnitudes of our parameters we introduce the simple concept of the iso-probability, which is analogous to an indifference curve. We use the logit specification in Eq. Ž5. and ask, ‘‘if an environmental good’s quantity increased by one standard deviation, how much private consumption could we take away from that person such that his probability of moving to a given state is left unchanged?’’ Table 5 presents these quantities for all of our environmental amenities. This table translates Table 4’s utility estimates into ‘‘marginal rates of substitution’’ which may be compared across amenities and age]education categories. Table 5 shows that households place a high value on climate and that the relative valuation for college and noncollege graduates is very similar. The attribute most valued by households is February temperature. College graduates age 30]40 are willing to pay almost twelve hundred dollars for a standard deviation Ž10.48. increase in February temperature while people aged 50]60 are willing to pay over $10,000 for the same increase. This growth in willingness to pay may reflect increased demand for health inputs over the life cycle and that climate is a normal good. Another

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reason for the increasing premium for warm winters with age might be that older movers are moving in anticipation of retirement. Surprisingly, our estimate of willingness to pay for February temperature is even larger for non-college graduates. Older non-college graduates are willing to pay over $60,000 for the increase. This tremendous estimate is caused by the low estimate of non-college graduate age 50]59 marginal utility of private consumption presented in Table 4. College graduates, age 50]59, are willing to pay $4,360 for 1 standard deviation less rainfall, $5,788 for 1 standard deviation less July temperature, $1,885 for 1 standard deviation more sunshine, and $3,906 for 1 standard deviation less humidity. As an indicator of such a group’s consumer surplus, it is interesting to compare this willingness to pay with the amount they actually do pay as reflected by lower wages and higher rents as discussed in Eqs. Ž8. and Ž10.. The last two columns of Table 5 show how much people actually pay in higher rents and lower consumption for a standard deviation increase in the amenity.20 The second, third, and fourth columns indicate how much people are willing to pay for the standard deviation increase. What is immediately apparent is that people are willing to pay much more than they actually pay for a more moderate climate. This difference between the willingness-to-pay and the hedonic measures is important from a policy perspective. Nordhaus w35x argues that models measuring the impact of climate change have not incorporated the value people place on consuming climate. Instead, the global warming literature has stressed the impact of temperature change on agriculture and forestry. Nordaus w35x estimates hedonic wage regressions to incorporate climate valuation into the total costs of climate change. Our findings suggest that hedonic valuation estimates greatly understate willingness to pay for a more temperate climate and lower annual variability in temperature. 4. CONTRASTING REVEALED PREFERENCE VS HEDONIC QUALITY OF LIFE RANKINGS Estimates from our conditional logit specifications of state location choice can be used to rank state quality of life. These rankings can be compared to the equilibrium hedonic approach for ranking quality of life. Each method recognizes that a state is a Lancastrian bundle. To rank a state, we need to compute index weights of how to collapse the vector of environmental attributes into a scalar index. The hedonic quality of life 20 In Table 5, we present two sets of implicit payments estimates based on the hedonic methodology. The rental column is based on capitalization into rents. Here we find mostly intuitive coefficient estimates. The consumption column is generated as the full price of attributes. Unlike Gyourko and Tracy w24x, we find many unintuitive climate full-price estimates. These estimates are being generated from statistically insignificant coefficients from the hedonic wage regression in Table 3.

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ranking is based upon the concept of how much you implicitly pay for amenities as indicated from hedonic wage and rental regressions. In contrast, our method uses index weights based upon willingness to pay. Table 6, part a, constructs the migration quality of life ranking by taking our estimates in Table 4 and creating a willingness to pay based on how much money a person would have to be compensated to not move if the attributes of the state were changed to the national average.21 Note that for all 6 agereducation categories, Florida is the top ranked state and that Arizona and California are typically ranked in the top three. For example, Florida is ranked first for college graduates aged 50]60 at $22,957. This indicates that for the probability of moving to Florida to remain unchanged when Florida’s attributes are changed to the national average, the typical person in this age]education strata needs to be given $22,957 a year. Note that we are not simply discovering a ‘‘big state effect;’’ Arizona is the second-best state and Pennsylvania, New York, and Illinois are ranked very low. Table 6, part b, constructs the hedonic quality of life ranking based on the full prices of amenities as reported in Table 5. Unlike the migration approach, this table reports how much private consumption a person would receive if a state’s attributes were moved to the national average. At the bottom of Table 6, we report the Spearman and Pearson correlations of the indices. They average over 0.5. Although they are correlated, several interesting anomalies appear. California is no longer ranked in the top three but instead is now ranked 25th! Florida and Arizona are still ranked very high, but Georgia and New Mexico are no longer in the top ten and Oregon and Washington are ranked in the low thirties. The reason for the differences in ranking across the two methods is that the hedonic index weights place more importance on July over February temperature Žsee Table 5. while the willingness to pay index weights place more importance on February than on July temperature. The migration approach yields a quality of life ranking roughly similar to the equilibrium approach. To understand the contribution of using migration data, it is important to return to the assumptions that are the basis for the hedonic approach. In both models, amenities are assumed to be fixed over time. To interpret the hedonic wage and rental regressions as tracing out the representative agent’s indifference curve for local public goods, one must assume there is a common set of preferences and no barriers to mobility. Through geographic arbitrage, implicit prices arise such that people are exactly indifferent over location choice. Once the long-run equilibrium is reached, observed migration is idiosyncratic and unexplain21 Based on Eq. Ž6., we calculate f Ž Zi y z ..rb , where z is the national average of the amenity Zi .

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

FL 17,330 AZ 13,553 CA 10,347 LA 9,729 TX 9,079 GA 8,343 AL 7,930 SC 7,010 MS 6,681 NM 5,978 NC 5,925 OR 5,847 WA 5,773 VA 4,114 NV 3,129 MD 2,954 ID 2,941 MA 2,696 UT 2,233 NJ 1,724 TN 911 AR 229 RI y292 OK y478

30]40 FL 24,935 AZ 17,682 LA 13,298 CA 11,832 TX 10,628 GA 10,557 AL 10,022 MS 9,013 SC 8,438 NM 8,214 AR 6,296 TN 6,293 NC 5,970 OR 5,856 WA 5,719 NV 5,175 OK 3,586 ID 3,045 RI 2,646 DE 2,258 KY 2,088 VA 2,044 UT 1,880 MD y93

40]50

High school graduates

FL 146,255 AZ 93,054 LA 73,523 WA 61,666 OR 61,014 CA 60,668 GA 59,586 TX 55,463 AL 54,757 MS 47,327 SC 45,506 NM 38,995 NC 33,461 TN 32,052 ID 30,027 AR 27,633 NV 24,686 RI 19,897 UT 15,632 DE 12,914 VA 12,880 KY 11,500 OK 8,753 CT 2,402

50]60 FL 4,093 CA 3,974 AZ 3,061 LA 2,802 AL 2,665 MA 2,542 GA 2,363 SC 2,298 NC 2,290 MS 2,155 TX 2,019 VA 2,007 MD 1,911 NM 1,856 ME 1,542 NJ 1,506 WA 1,284 OR 1,263 NH 1,100 ID 549 NY 514 NV 182 UT 18 OH y36

30]40 FL 7,238 AZ 6,262 CA 5,070 NM 4,111 LA 3,028 WA 2,822 OR 2,801 NV 2,793 TX 2,751 ID 2,576 GA 2,562 AL 2,241 SC 1,943 MS 1,686 UT 1,514 TN 1,446 NC 1,383 RI 1,099 AR 1,061 CO 778 VA 404 OK 371 DE 215 KY y8

40]50

college graduates

Ža. Willingness to pay for the deviation in state’s attributes from the average

TABLE 6 Quality of Life Rankings

FL 22,957 AZ 19,528 CA 12,908 NM 12,122 LA 11,590 AL 9,203 GA 8,452 ID 7,982 MS 7,089 TN 6,923 SC 6,849 WA 6,670 RI 6,441 OR 6,402 NV 5,604 NC 5,509 TX 5,442 AR 4,654 UT 3,881 CT 2,332 VA 2,122 MA 2,040 DE 2,004 CO 1,098

50]60

FL 1,820 AZ 1,810 AR 1,352 OK 1,289 TX 1,115 LA 1,003 TN 1,001 NE 890 KY 820 DE 739 GA 731 NV 689 KS 675 MS 673 MO 650 AL 591 NM 541 SC 507 WV 464 IL 305 IN 298 UT 259 RI 136 NC 131

Žb. Amount paid for the deviation in state’s attributes from the average

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CO y139 MI y207 RI y301 WI y433 TN y524 WY y1,021 PA y1,059 CT y1,072 AR y1,083 OK y1,268 DE y1,345 KY y1,796 MN y1,803 MO y1,897 MT y2,066 KS y2,277 WV y2,636 VT y2,690 IL y2,865 IN y2,973 NE y2,999 IA y3,220 SD y3,816 ND y4,470 0.12 0.46

WV y948 MD y1,248 MA y4,943 NJ y6,539 PA y9,294 MO y18,896 CO y19,258 MT y24,014 NE y25,663 OH y30,791 IN y31,707 KS y33,627 IL y35,080 VT y38,398 NY y42,060 WY y45,881 ME y54,015 NH y59,295 MI y60,493 IA y70,514 WI y85,528 SD y89,342 MN y118,284 ND y123,833 0.69 0.63

0.67 0.60

CT y214 PA y291 MD y358 WV y504 MA y529 MT y724 WY y773 NJ y800 NE y1,192 MO y1,295 KS y1,743 IN y2,215 OH y2,408 IL y2,501 VT y2,565 ME y2,664 NY y2,728 NH y2,972 MI y3,629 IA y3,967 SD y4,380 WI y4,857 ND y6,042 MN y6,795 0.65 0.56

KY 1,014 PA 888 OK 870 MD 192 NJ y1,166 WV y2,191 MO y3,100 WY y4,284 MT y4,853 ME y5,671 VT y6,540 KS y6,799 IN y7,073 NH y7,442 NY y7,589 IL y7,615 NE y7,784 OH y8,214 MI y11,958 IA y12,681 WI y15,566 SD y16,843 ND y22,223 MN y23,174

CA 119 CT 45 PA y61 IA y153 ID y203 SD y296 VA y297 CO y387 MD y449 MT y457 NJ y562 OR y584 VT y641 WA y668 WY y713 OH y790 ND y939 MA y1,236 NY y1,428 MI y1,475 WI y1,651 NH y1,815 MN y1,829 ME y1,944

Note. In Table 6 part a, willingness to pay quality of life rankings are based upon the linear-in-consumption estimates in Table 4. They are defined as how much money a person would have to be compensated to not move if the attribute of the state were changed to the national average. In Table 6b, the hedonic quality of life rankings are based upon the law-of-one price estimates in Table 3. They are defined as how much private consumption a person would receive if a state’s attributes were moved to the national average.

25 DE y1,236 CT y477 26 CO y2,002 WV y769 27 OH y2,024 NJ y1,326 28 KY y2,197 PA y1,723 29 CT y2,574 MO y1,743 30 NY y2,739 MA y2,310 31 ME y2,881 CO y2,462 32 PA y3,304 NE y2,691 33 NH y3,789 KS y3,789 34 MO y4,273 IN y5,182 35 WV y4,706 IL y5,737 36 MT y4,748 MT y5,882 37 MI y4,753 OH y6,274 38 KS y5,002 WY y7,221 39 WY y5,231 VT y8,555 40 NE y5,301 NY y8,738 41 WI y6,805 ME y10,099 42 IL y6,808 NH y10,602 43 IN y7,062 IA y11,061 44 VT y8,025 MI y11,564 45 IA y9,946 SD y13,801 46 MN y10,869 WI y15,005 47 SD y11,778 ND y19,896 48 ND y15,635 MN y20,477 Correlation with hedonic quality of life ranking Pearson 0.51 0.77 Spearman 0.45 0.72

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able by consumption differentials across locations. The migration approach presented above allows different demographic groups to have different preferences for amenities and allows the price of a state’s local public goods to differ. Unlike the existing hedonic literature, our model assumes state-by-state ‘‘island economies’’ Žfactor prices differ for human capital in Eq. Ž8. and land in Eq. Ž10...22 The year-to-year productivity shocks change the full price of public goods consumption, thereby generating migration. That the economy is in tatonnement allows us to measure revealed choice demand for public goods. To reconcile the two models, shocks would have to stop; the migration process would continue until the national economy achieves a steady state where people are indifferent about their location. 5. CONCLUSION In this paper, we develop an alternative to the hedonic method for ranking quality of life which implicitly measures the demand for public goods. Our revealed preference method is based upon migrants’ location choice. Although the method is computationally intensive, through our state-level climate model, we have found that the models are tractable and the results are consistent with economic intuition. Focusing on valuing climate}a pure public good which varies across states but far less so within a state}allowed us to estimate a 48-dimensional problem. Our research yields two findings important to policy. First, the ensuing quality of life rankings are intuitively plausible and correlated with the more standard hedonic rankings. There are some important differences such as California, which is ranked much higher in our index than in the hedonic index.23 Second, our willingness-to-pay valuations of climate yield measures much larger than the traditional hedonic valuations. This finding has important implications for research using hedonic measures as inputs into evaluating the costs of global warming since it suggests that the calculated costs will be understated. While our state-level analysis is too spatially aggregated to tackle valuation problems of local public goods such as air quality, proximity to Superfund sites, crimes, and school quality, our paper is suggestive that such estimation is feasible. A city-level set of migration estimates would predict willingness to pay for local public goods. Future work developing methods to estimate what consumers are willing to pay for environmental 22 The standard hedonic price regression imposes factor price equalization thereby ruling out local labor market shocks. 23 The literature valuing technological innovation is currently struggling with whether hedonic methods or willingness to pay methods should be used for ranking brand quality for such goods as computers, stereo equipment, medical equipment, pharmaceuticals, televisions, and VCRs Žsee Trajtenberg w41x for a discussion..

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goods is critical to undertaking cost]benefit analysis of legislation geared toward increased provision of local public goods like the Clean Air or Clean Water Act.

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