R January 2016  RFF DP 16-02 E P Household Location A Decisions and the P Value of Climate N Amenities O I S S Paramita Sinha and Maureen L. Cropper U C S I D 1616 P St. NW Washington, DC 20036 202-328-5000 www.rff.org Household Location Decisions and the Value of Climate Amenities Paramita Sinha and Maureen L. Cropper Abstract We value climate amenities by estimating a discrete location choice model for US households. The utility of each metropolitan statistical area (MSA) depends on location-specific amenities, earnings opportunities, housing costs, and the cost of moving to the MSA from the household head’s birthplace. We use the estimated trade-off among wages, housing costs, and climate amenities to value changes in mean winter and summer temperatures. We find that households sort among MSAs as a result of heterogeneous tastes for winter and summer temperatures. Preferences for winter and summer temperatures are negatively correlated: households that prefer milder winters, on average, prefer cooler summers, and households that prefer colder winters prefer warmer summers. Households in the Midwest region, on average, have lower marginal willingness to pay to increase winter and reduce summer temperatures than households in the Pacific and South Atlantic census divisions. We use our results to value changes in winter and summer temperatures for the period 2020 to 2050 under the B1 (climate- friendly) and A2 (more extreme) climate scenarios. On average, households are willing to pay 1 percent of income to avoid the B1 scenario and 2.4 percent of income to avoid the A2 scenario. Key Words: climate amenities, discrete choice models, taste sorting, welfare impacts of temperature changes JEL Classification Numbers: Q5, Q51 © 2016 Resources for the Future. All rights reserved. No portion of this paper may be reproduced without permission of the authors. Discussion papers are research materials circulated by their authors for purposes of information and discussion. They have not necessarily undergone formal peer review. Contents 1. Introduction ....................................................................................................................... 1 Our Approach...................................................................................................................... 2 Our Findings ....................................................................................................................... 3 2. Household Residential Location Model ............................................................................ 5 Estimation of the Model...................................................................................................... 6 3. Data ...................................................................................................................................... 8 Sample Households ............................................................................................................. 8 Climate Variables................................................................................................................ 9 Nonclimate Amenities ...................................................................................................... 10 4. Estimation Results ............................................................................................................ 11 Discrete Location Choice Models ..................................................................................... 11 Taste-Based Sorting .......................................................................................................... 13 5. Willingness to Pay for Temperature Changes................................................................ 15 The B1 and A2 SRES Scenarios ....................................................................................... 16 WTP Conditional on Current Location ............................................................................. 17 Exact Welfare Calculations............................................................................................... 18 WTP Comparison with the Literature ............................................................................... 20 6. Conclusions ........................................................................................................................ 21 References .............................................................................................................................. 22 Figures and Tables ................................................................................................................ 24 Appendix ................................................................................................................................ 34 Resources for the Future Sinha and Cropper Household Location Decisions and the Value of Climate Amenities Paramita Sinha and Maureen L. Cropper* 1. Introduction The amenity value of climate—what people are willing to pay to experience warmer winters or avoid hotter summers—is an important component of the benefits of greenhouse gas mitigation policies. Yet, with the exception of Albouy et al. (2013), the recent literature contains few estimates of the value of climate amenities for the United States. Estimating these values poses an econometric challenge: climate, by definition, changes slowly, so researchers must rely on cross-sectional variation in climate to measure its impact on household location decisions. This paper helps fill this gap by estimating a discrete location choice model in which a household’s choice of the city in which to live depends on climate amenities as well as earnings, housing costs, and other location-specific amenities. We use the model to estimate household willingness to pay (WTP) for changes in mean winter and summer temperatures and use these values to assess the welfare effects of temperature changes in cities throughout the United States. Traditionally, economists have used hedonic wage and property value functions to value climate amenities (Cragg and Kahn 1999; Gyourko and Tracy 1991; Blomquist et al. 1988; Smith 1983). In a world in which households can migrate costlessly across cities, location- specific amenities should be capitalized into wages and property values. In equilibrium, each household will select a city (i.e., a vector of amenities) so that the marginal cost of obtaining each amenity, measured in terms of wages and housing costs, just equals the value it places on the amenity (Roback 1982).1 This approach has been followed most recently by Albouy et al. (2013), who regress a quality of life (QOL) index—a weighted sum of wage and price indices— for each public-use microdata area (PUMA) on a vector of location-specific amenities, including climate amenities. *Paramita Sinha, RTI International, [email protected]; Maureen Cropper, University of Maryland and Resources for the Future, [email protected]. We thank the US Environmental Protection Agency, RTI International, and Resources for the Future for funding. This paper would not have been possible without the excellent research assistance of Martha Caulkins and GIS support from RTI. 1 Formally, marginal WTP for an amenity equals the sum of the slope of the hedonic wage function with respect to the amenity plus the slope of the hedonic property value function, weighted by the share of income spent on housing, evaluated at the chosen amenity vector (Roback 1982). 1 Resources for the Future Sinha and Cropper An alternate approach to valuing amenities that vary by location is to estimate a discrete choice model of household location decisions (Bayer et al. 2004; Bayer and Timmins 2007; Bayer et al. 2009; Cragg and Kahn 1997; Klaiber and Phaneuf 2010). Households choose among locations based on the utility they receive from each location, which depends on wages, housing costs, and location-specific amenities. Variations in wages, housing costs, and amenities across locations permit identification of the parameters of the household’s utility function. The discrete choice approach, which we follow here, offers several advantages over the traditional hedonic approach. Most important, it allows the researcher to more easily incorporate 2 market frictions, including the psychological and informational costs of moving. The hedonic approach assumes that consumers are perfectly mobile and hence that the weighted sum of wage and housing price gradients will equal the consumer’s marginal willingness to pay (MWTP) for an amenity. Bayer et al. (2009) demonstrate that this equality fails to hold in the presence of moving costs, and they incorporate the psychological and informational costs of leaving one’s birthplace into an equilibrium model of household location choice. We also incorporate moving costs from birthplace in our model of location choice and demonstrate that their omission significantly understates the value consumers place on temperature and precipitation. The discrete choice approach allows us to obtain exact welfare measures for changes in temperature throughout the United States based on two climate scenarios. These welfare measures incorporate both taste sorting based on climate and the opportunity for households to move in response to changes in temperature. Our Approach In this paper, we value climate amenities by estimating a model of residential location choice among metropolitan statistical areas (MSAs) for US households in 2000. We model the choice among MSAs based on potential earnings, housing costs, moving costs, climate amenities, and other location-specific amenities. The model is estimated as a mixed logit model, which allows the coefficients on climate amenities to vary among households. We compute the means of these coefficients for each household, conditional on choice of MSA, and then examine 2 Barriers to mobility prevent the sum of wage and housing price gradients from equaling marginal willingness to pay, and they imply that the assumption of national labor and housing markets, which underlies the hedonic approach, may not accurately capture wage and housing costs in different cities. 2 Resources for the Future Sinha and Cropper how the average conditional means for climate amenities vary across MSAs to describe taste sorting. We use the conditional means in two ways to value future changes in temperature. We compute the value of changes in temperature assuming that each household does not move. This is analogous to the value of temperature changes computed by Albouy et al. (2013) based on local linear estimates of the hedonic price function. We also compute exact welfare measures (i.e., expected compensating variation) using each household’s conditional distribution of taste coefficients. These measures implicitly allow households to move in response to temperature changes. Our paper builds on the work of Cragg and Kahn (1997), who were the first to use a discrete choice approach to value climate amenities.3 We extend their work, following Bayer et al. (2009), by including moving costs and modeling choices across MSAs. Unlike Bayer et al., however, we cannot use multiple cross sections to difference out unobserved amenities within cities. Historical data indicate that climate changes slowly, forcing us to rely on a single cross section of data rather than data over consecutive decades.4 We attempt to allay concerns about omitted variable bias by controlling for a wide variety of location-specific amenities other than temperature, especially those that are correlated with temperature. Our Findings Our results indicate that households are willing to pay to avoid cold winter temperatures and hot summer temperatures; however, these values vary significantly by residential location. We find a strong positive correlation between MWTP for winter temperature and the temperature of the city in which the household lives: households with the highest MWTP for warmer winters live in Florida, while those with the lowest MWTP live in the Midwest. Preferences for summer temperature and winter temperature are, however, negatively correlated (ρ = –0.83). This implies that households that prefer milder winters, on average, also prefer milder summers, while households that prefer colder winters have a lower MWTP to reduce summer temperatures. MWTP to avoid hotter summers is, on average, higher in the South Atlantic and Pacific regions than in the Midwest. At the level of census regions, households in the Midwest and Northeast 3 Cragg and Khan (1997) value climate amenities by estimating a model of the choice of state in which to live for households that moved between 1985 and 1990. 4 This is also true of the literature that examines the impact of climate on agriculture (Schlenker and Roberts 2009). 3 Resources for the Future Sinha and Cropper have lower MWTPs to increase winter and reduce summer temperatures than households in the South and West. We use these estimates to value changes in mean summer and winter temperatures over the period 2020 to 2050 for 284 US cities that contained over 80 percent of the US population in 2000. The Hadley model projects that, under the B1 climate scenario from the Special Report on Emissions Scenarios (SRES),5 mean summer temperature (population weighted) will increase, on average, by 3.3°F in these cities and mean winter temperature by 3.4°F. Cities in the New England and Middle Atlantic states will experience larger increases in winter temperature than in summer temperature, although the reverse is true for the East South Central and West South Central census divisions, and also the Pacific and Mountain states. Ignoring sorting overstates the WTP of households in the New England and Middle Atlantic states for the B1 scenario and greatly understates the value of avoiding the B1 scenario to households in the Midwest. On net, allowing for taste sorting increases the average household WTP to avoid the B1 scenario compared with a world in which sorting is ignored. Allowing for sorting actually decreases the average household WTP to avoid the more severe A2 scenario. The A2 scenario results in very large increases in summer temperature in the East and West South Central divisions and the Midwest region. Ignoring sorting overstates the disamenity of the A2 scenario in the Midwest and South census regions. Taking sorting into account, the mean household WTP to avoid the B1 scenario in the 2020–2050 timeframe is about 1 percent of income; it is about 2.4 percent of income for avoiding the A2 scenario. We note that the latter value is within the range reported by Albouy et al. (2013) for a much more drastic climate scenario in the period 2090–2099.6 One possible reason for the difference in estimates is that we base our estimates on all households, whereas Albouy et al. (2013) focus on prime-aged households. Our results suggest that the value attached to climate amenities varies with the age of the household head: on average, households with heads over the age of 55 have a MWTP for higher winter temperature and a MWTP to avoid 5 To represent a range of driving forces for emissions, such as demographic development, socioeconomic development, and technological change, the Intergovernmental Panel on Climate Change (IPCC) developed a set of emissions scenarios. In the SRES, IPCC (2000) describes these scenarios in more detail. We use projections from a climate-friendly scenario (B1) and a more extreme scenario (A2). 6 Albouy et al. (2013) focus on the A2 scenario in the period 2090–2099, when it is expected to raise mean temperature in the United States by 8.3˚F compared with the 1970–2000 period. 4 Resources for the Future Sinha and Cropper increased summer temperature that is about twice as high as households with heads between 25 and 55 years old. For policy purposes, we focus on results based on all households. The paper is organized as follows. Section 2 presents the household’s location decision and the econometric models we estimate. Section 3 describes the data used in our analysis. Estimation results are presented in Section 4. Section 5 uses these results to evaluate the value of temperature changes projected by the B1 and A2 SRES scenarios. Section 6 concludes the paper. 2. Household Residential Location Model We model household location in 2000 assuming that each household selected its preferred MSA from the set of MSAs in the United States in 2000. Household utility depends on income minus the cost of housing, location-specific amenities, and moving costs from the birthplace of the household head. Specifically, we assume that the utility that household i receives from city j is given by 𝑈 = 𝛼(𝑌 −𝑃 )+𝑨 𝜷 +𝑀𝐶 (1) 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑗 𝑖 𝑖𝑗 where Y is household i’s income and P its housing expenditure in city j. MC represents the ij ij ij costs—psychological and other—of moving from the head of household’s birthplace to city j. A j is a vector of location-specific amenities. We allow the coefficients on temperature amenities to vary across households. Household income is the sum of the wages of all workers in the household, W , plus nonwage income, which is assumed not to vary by residential location. To ij predict the earnings of household workers in locations not chosen, we estimate hedonic wage and housing price equations for each MSA, as described below. Moving costs capture the psychological, search, and out-of-pocket costs of leaving a household’s place of origin. Seventy-three percent of households in our sample (see Table 1, full sample) live in the census region in which the head was born; 67 percent live in the same census division. Although households have been moving to warmer weather since the Second World War (Rappaport 2007), family ties and informational constraints may have prevented this from occurring more completely. As shown below, failure to account for these costs significantly alters the value attached to winter and summer temperatures. Following Bayer et al. (2009), we represent moving costs as a series of dummy variables that reflect whether city j is outside of the state, census division, and/or census region in which household i’s head was born. Formally, 𝑀𝐶 = 𝜋 𝑑𝑆𝑡𝑎𝑡𝑒 +𝜋 𝑑𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 +𝜋 𝑑𝑅𝑒𝑔𝑖𝑜𝑛 (2) 𝑖𝑗 0 𝑖𝑗 1 𝑖𝑗 2 𝑖𝑗 5 Resources for the Future Sinha and Cropper where d State denotes a dummy variable that equals one if j is in a state that is different from the ij one in which household head i was born, d Division equals 1 if location j is outside of the census ij division in which the household head was born, and d Region equals 1 if location j lies outside of ij the census region in which the household head was born. Estimation of the Model Estimating the location choice model requires information on the wages that a household would earn and the cost of housing in all MSAs. Because wages are observed only in the household’s chosen location, we estimate a hedonic wage equation for each MSA and use it to predict Wij. The hedonic wage equation for MSA j regresses the logarithm of the hourly wage rate for worker m in MSA j on variables (𝑿𝑤 ) measuring the demographic characteristics— 𝑚𝑗 education, experience, and industry and occupation—of worker m: ln𝑤 = 𝛾2+𝑿𝑤 𝜞𝑋,2 +𝜈2 ∀ 𝑗 = 1,…,𝐽 (3) 𝑚𝑗 𝑗 𝑚𝑗 𝑚𝑗 Equation (3) is estimated using data on full-time workers in the public use microdata sample (PUMS).7 The coefficients of equation (3) are used to calculate the earnings of each worker in the sample used to estimate the discrete choice model (see Table 1), under the assumption that individuals work the same number of hours and weeks in all locations. Summing earnings over all individuals in each household, we obtain predicted household wages for household i in location j (Wˆ ). Predicted income in city j, 𝑌̂ equals predicted wage income plus non-wage ij 𝑖𝑗 income of household i which is assumed not to vay by MSA. The cost of housing in each location is estimated based on hedonic property value equations for each MSA, ln𝑃 = 𝛿2 +𝑿𝑃𝜟𝑋,2 +𝜔2 ∀ 𝑗 = 1,…,𝐽 (4) 𝑖𝑗 𝑗 𝑖𝑗 𝑚𝑗 𝑃 is the annual cost of owning house i in city j, computed as the sum of the monthly mortgage 𝑖𝑗 payment or rent and the cost of utilities, property taxes, and property insurance. 𝑿𝑃 contains a 𝑖𝑗 dummy variable indicating whether the house was owned or rented, as well as a vector of dwelling characteristics. Utility costs are added both to the costs of owning a home and to rents 7 The equation is estimated using data on all persons working at least 40 weeks per year and between 30 and 60 hours per week. Persons who are self-employed, in the military, or in farming, fishing, or forestry are excluded from the sample. 6 Resources for the Future Sinha and Cropper because heating and cooling requirements vary with climate. We wish to separate these costs from climate amenities. Equation (4) is estimated separately for each MSA in our dataset. We predict housing expenditures for household i in city j (𝑃̂ ) assuming that the household 𝑖𝑗 purchases the same bundle of housing characteristics in city j as it purchases in its chosen city. The results of estimating the hedonic wage and housing market equations for all cities are summarized in Appendix Tables A-1 and A-2. We find, as do Cragg and Kahn (1997), that the coefficients in both sets of hedonic equations vary significantly across MSAs, suggesting that the assumption of national labor and housing markets made in hedonic studies is inappropriate. We estimate the discrete location choice model in two stages. The first is a mixed logit model in which the indirect utility function incorporates unobserved heterogeneity in preferences for winter and summer temperature, and MSA fixed effects (δ): j 𝑉 = 𝛼(𝑌̂ −𝑃̂ )+𝑊𝑇𝛽 +𝑆𝑇𝛽 +𝑀𝐶 +𝛿 +𝜀 (5) 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑗 𝑊𝑇 𝑗 𝑆𝑇 𝑖𝑗 𝑗 𝑖𝑗 We assume that the coefficients (β and β ) are jointly normally distributed, with zero mean WT ST vector and variance-covariance matrix Σ. The household’s utility function is observed with error term ε ; that is, V = U + ε . The error term ε combines the error in predicting household i’s ij ij ij ij ij wages and housing expenditures in city j with household i’s unmeasured preferences for city j. Assuming that the idiosyncratic errors are independently and identically distributed Type I extreme value, the probability of household i selecting city j is given by the mixed logit model. In the second stage, city-specific fixed effects are regressed on the vector of amenities to estimate the means of the temperature coefficients and the coefficients on other amenities: 𝛿 = 𝑨 Γ+𝑢 (6) 𝑗 𝒋 𝑗 The parameters of equation (5) are estimated via simulated maximum likelihood techniques, using a choice set equal to the household’s chosen alternative and a random sample of 59 alternatives from the set of 284 MSAs.8 8 The validity of the McFadden sampling procedure (McFadden 1978) hinges on the independence of irrelevant alternatives, which does not hold in the mixed logit model. We do, however, face computational trade-offs in estimating the mixed logit model using all 284 elements of the universal choice set and a sample large enough to estimate 284 fixed effects with precision. Experiments with the size of the choice set indicated that increasing the size of the choice set beyond 60 MSAs did not significantly alter parameter estimates. In estimating equation (5) the means of β and β are constrained to be zero. WT ST 7