The value of climate amenities: A comparison of hedonic and discrete choice approaches

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Abstract

Amenities that vary across cities are typically valued using either a hedonic model, in which amenities are capitalized into wages and housing prices, or a discrete model of household location choice. In this paper, we use the 2000 Public Use Microdata Sample (PUMS) to value climate amenities using both methods. We compare estimates of marginal willingness to pay (MWTP), allowing preferences for climate amenities to vary by location. We find that mean MWTP for warmer winters is about twice as large using the discrete choice approach as with the hedonic approach; mean MWTP for cooler summers is approximately the same. The two approaches differ, however, in their estimates of MWTP by location. These disparities lead to significant differences in estimates of willingness to pay to avoid the A2 and B1 SRES scenarios in 2020–2050 using the two approaches.

Introduction

To value amenities that vary across cities, researchers have typically followed one of two approaches. They have used either hedonic models of wages and housing prices (Roback 1982; Blomquist et al., 1988; Albouy et al., 2016) or discrete models of location choice (Cragg and Kahn 1997; Bayer et al., 2009; Fan et al., 2016; Sinha et al., 2018b). The former approach infers willingness to pay for amenities by estimating hedonic price functions for wages and housing costs as a function of location-specific attributes; the second, by estimating the probability that consumers choose a city in which to live as a function of wages, housing prices, and location-specific attributes.

Cragg and Kahn (1997), Bayer et al. (2009), and Sinha et al. (2018b) note that the discrete choice approach typically produces estimates of amenity values that are very different from estimates produced by the continuous hedonic approach. In a discrete choice model where households choose the US state in which to reside, Cragg and Kahn (1997) find the marginal willingness to pay for July and February temperatures exceeds the marginal prices implied by hedonic price functions. Bayer et al. (2009) estimate marginal willingness to pay (MWTP) to reduce air pollution using a discrete choice approach and find MWTP is three times greater than values capitalized into per capita incomes and property values. In their discrete choice model, Sinha et al. (2018b) estimate higher damages associated with projected climate changes in US cities under the A2 scenario in the Special Report on Emissions Scenarios than comparable estimates from Albouy et al. (2016) hedonic model.1

In this paper, we use the same dataset to value climate amenities—specifically, winter and summer temperature—using hedonic and discrete choice methods. We compare estimates from each approach, allowing preferences for climate amenities to vary by location. Similar to Albouy (2012), our hedonic models regress the weighted sum of wage and housing price indices on climate amenities and various city characteristics using metropolitan statistical areas (MSAs) as the geographic unit. Wage and housing price indices are estimated, following Albouy et al. (2016), assuming national labor and housing markets. We construct a weighted sum of wage and housing price indices for each MSA using the same weights as in Albouy et al. (2016) and, alternately, using a traditional set of weights (Roback 1982). We capture preference heterogeneity by allowing the marginal price of climate amenities to vary by city using local linear regressions, in the spirit of Bajari and Benkard (2005) and Bajari and Kahn (2005).

In discrete location choice models, consumers choose among MSAs based on predicted wages and housing costs, moving costs from birthplace, and the same set of location-specific amenities as used in the hedonic models. To capture heterogeneity in preferences, we estimate random parameter logit models and calculate the distribution of each household's tastes for climate conditional on the city in which they live. This allows us to estimate mean MWTP for climate amenities by city.

We focus on prime-aged households when comparing the two approaches. Because the hedonic approach assumes that amenities are capitalized into wages, and because a significant fraction of older households have no wage income, Albouy et al. (2016) focus on workers aged 25–55. We have estimated discrete location choice models for various age groups (Sinha et al., 2018b) and find that preferences for climate amenities vary by the age of the household head; however, we focus on households with heads between 25 and 55 when comparing discrete choice with hedonic estimates.

We find that the two approaches produce different estimates of mean MWTP for winter and summer temperature and different estimates of MWTP by location when we allow preferences to vary across cities. Although both approaches find that households have positive MWTP for warmer winters and cooler summers, mean estimates of MWTP for winter temperature produced by the discrete choice approach are about twice as large as estimates produced by the hedonic approach. Moreover, the two approaches produce different variation in MWTP by city. The discrete choice model finds that households living in warmer areas have a higher MWTP for winter temperature: there is a strong positive correlation between winter temperature and MWTP for warmer winters. The discrete choice model thus projects that under most climate scenarios, the parts of the country that will benefit from warmer winters (the Northeast and Midwest) value this less than the average US household. When we use the two sets of MWTP estimates to value the A2 and B1 SRES climate scenarios in 2020–2050 we find that the value of avoiding each scenario is about twice as high using the hedonic than using the discrete choice approach.

We also explore why estimates produced by the two approaches vary. One reason is that the hedonic and discrete choice models as typically applied differ in their underlying assumptions about consumer mobility. The hedonic approach as characterized by Roback (1982) assumes perfect mobility, whereas moving costs are more easily incorporated in discrete models of location choice. As Bayer et al. (2009) note, moving costs—both psychological and out-of-pocket—may prevent amenities from being fully capitalized into wages and housing values. When we estimate the discrete choice model without moving costs, the value of climate amenities falls significantly. It is also the case that moving costs, which vary by household and city, help identify variation in MWTP across cities in the discrete choice model (Berry and Haile 2010). When they are removed, the ordering of MWTP by city is (incorrectly) reversed.

A related reason for differences in the two sets of estimates is the way in which data on wages and housing prices are used. The hedonic model assumes a single national labor market and a single housing market. The data are used to estimate price indices for each MSA, assuming that the returns to human capital and marginal prices of housing characteristics are the same everywhere. The discrete choice model assumes that each MSA constitutes a separate labor and a separate housing market. It is the variation in wage income and housing costs across MSAs, as well as the variation in moving costs across MSAs, that identifies household preferences in the discrete choice model. This suggests that differences in how the two models use information on housing and labor markets may account in part for the difference in estimates.

The paper is organized as follows. Section 2 describes the hedonic model of amenity valuation as originally developed by Roback (1982) and modified by Albouy (2012) and Albouy et al. (2016). We present the discrete location choice model that we estimate in Section 3 and discuss similarities and differences between the two approaches at the end of this section. In Section 4 we describe our data and empirical specifications. Section 5 presents the results of both modeling approaches. Section 6 concludes.

Section snippets

The Roback and Albouy models

The hedonic approach to valuing location-specific amenities dates from Jennifer Roback's (1982) seminal article “Wages, Rents, and the Quality of Life,” which built on Rosen's (1979) model of the value of location-specific amenities. Roback posited that in a world of perfectly mobile individuals, wages and land prices would adjust to equalize utility in all locations. Consider a world of homogeneous individuals who receive utility from housing, H, a traded good, C, and a location-specific

A discrete choice approach to valuing climate amenities

The discrete choice approach to amenity valuation, like the hedonic approach, assumes that households choose among geographic locations based on the utility they receive from each location, which depends on wages, housing costs, and location-specific amenities. Variation in wages, housing costs, and amenities across locations permits identification of the parameters of the household's indirect utility function.

One advantage of the discrete choice approach is that it allows the researcher to

Data and empirical specifications

The data used to estimate our discrete choice and hedonic models come from the 5 percent PUMS of the 2000 census as well as other publicly available data sources.

Estimation results

In the spirit of Cragg and Kahn (1997) and Bayer et al. (2009), we compare estimates of mean MWTP from the discrete choice and hedonic models to see whether the discrete choice approach yields similar mean estimates of amenity values. We are, however, also interested in how MWTP varies across cities. From the perspective of valuing climate, it matters how MWTP for temperature changes varies geographically: Are households living in areas where temperatures are likely to increase under future

Conclusions

The goal of this paper is to compare the continuous hedonic and discrete choice approaches to valuing climate amenities—in particular, summer and winter temperatures. While previous comparisons of the two methods have focused on comparing mean MWTP (Cragg and Kahn 1997; Bayer et al., 2009) we have focused on comparing how MWTP for small changes in winter and summer temperatures vary with a household's current location. Preferences for temperature vary across cities due to sorting or adaptation,

Credit author statement

Sinha – Designed and conducted the research

Caulkins – Conducted the research

Cropper – Designed the research and wrote the paper

Acknowledgments

We dedicate this paper to Martha L. Caulkins, who died on February 24, 2019. We thank the US Environmental Protection Agency and RTI International for funding. This paper would not have been possible without GIS support from RTI. We thank David Albouy, Nick Kuminoff, Chris Timmins, two anonymous referees and an Editor of this Journal for their comments. Ingmar Prucha and Hao Bo provided valuable help with model estimation. Any errors are ours.

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