Incorporating observed choice into the construction of welfare measures from random utility models

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Abstract

This paper develops an approach to welfare measurement from random utility models that incorporates the implications of an individual's observed choice. The economic and statistical properties of the proposed approach are discussed, and its empirical implications are illustrated with an application to outdoor recreation demand. Welfare estimates for two policy scenarios and four alternative repeated discrete choice specifications—a conditional logit, a quasi-nested logit, a random marginal utility of income logit, and a full random coefficients logit—are constructed for a subsample of the 1994 National Survey of Recreation and the Environment.

Introduction

This paper develops an approach to welfare measurement from random utility models (RUMs) that conditions on an individual's observed choice. The economic and statistical properties of the proposed conditional approach to welfare measurement are compared with the unconditional approaches developed by Small and Rosen [35] and Hanemann [16], and a subsample of the 1994 National Survey of Recreation and the Environment (NSRE) is used to illustrate its empirical implications. Conditional and unconditional welfare estimates for two policy scenarios and four repeated discrete choice specifications (e.g. [10], [28]) are presented. These estimates suggest that: (1) sample means of conditional and unconditional welfare estimates are qualitatively similar but often diverge by more than what a correctly specified model would predict; (2) the conditional estimates appear to be more robust across alternative model specifications; and (3) the distribution of benefits implied by the conditional and unconditional estimates are qualitatively different.

The conditional approach to welfare measurement has some precedence in both the non-market valuation and marketing literatures. The notion that alternative interpretations of the factors that give rise to randomness in applied demand analysis imply different welfare estimators was first argued by Bockstael and Strand [6] in the context of single-equation demand models. Smith [36] later criticized their work because it failed to account for the fact that every demand model is in some sense misspecified. His criticism is particularly relevant in the context of RUMs because misspecification can cause sample means of conditional and unconditional consumer surplus estimates to diverge significantly. Similarly in the marketing literature, Allenby and Rossi [2] and Train and Revelt [43] have recently proposed estimating an individual's “partworth” (i.e., marginal utility) for a commodity characteristic by conditioning on her observed choice(s). These authors argue that a comparison of sample means of individual unconditional and conditional partworths can serve as an informal specification test. Both of these insights have close parallels with the conditional approach to welfare measurement developed in this paper.

The paper is organized as follows. Section 2 develops the theory of the conditional approach to welfare measurement and discusses its economic and statistical properties. Section 3 details the recreation data set used in the empirical analysis, and Section 4 reports parameter estimates from four repeated discrete choice specifications—a standard conditional logit, a quasi-nested logit proposed by Train [40] and Herriges and Phaneuf [18], a random marginal utility of income (RMUI) logit, and a full random coefficients logit model—used to model consumer choice. Section 5 then describes the two welfare scenarios considered, and Section 6 discusses the procedures used to construct unconditional and conditional Hicksian welfare estimates. Section 7 presents and interprets these estimates for the alternative policy scenarios and model specifications, and Section 8 concludes.

Section snippets

Theory

This section discusses the theoretical foundation of the conditional approach to welfare measurement and its relationship to the unconditional approach developed by Small and Rosen [35] and Hanemann [16]. Although both approaches can be applied to all choice models employing the random utility hypothesis, this section uses the repeated discrete choice model of recreation demand (e.g. [10], [28]) to structure the discussion. In addition to simplifying exposition, focusing on this model is

Data

This section describes the recreation data from the 1994 National Survey of Recreation and the Environment (NSRE) used to empirically assess the proposed conditional approach to welfare measurement. A collaborative effort of several federal agencies, the 1994 NSRE consisted of two survey modules that attempted to determine the impact of the natural environment on current participation in water-based outdoor recreation. The Economic Research Service (ERS) at the Department of Agriculture

Model specification and parameter estimates

Four parametric specifications of the repeated discrete choice model are employed in the empirical application. For all four, the recreation season consists of 100 separable choice occasions,15, 16

Welfare scenarios

In the recreation literature, two generic types of policy scenarios are often considered. One type evaluates the benefits arising from the improvement of water quality conditions in a watershed, river basin, or other large geographic region (e.g. [31]), while a second considers the addition or loss of one or a small set of sites arising from more acute, geographically concentrated environmental impacts [32]. This section uses policy scenarios from each of these broad categories to demonstrate

Procedures for constructing Hicksian welfare measures

This section outlines the procedures used to construct conditional Hicksian welfare measures for the four repeated discrete choice specifications. As noted in Section 2, the standard procedure for constructing an individual's seasonal willingness to pay from the repeated discrete choice framework involves first constructing Hicksian consumer surplus estimates separately for each choice occasion and then aggregating these estimates across choice occasions. Both unconditional and conditional

Welfare estimates

Table 3, Table 4 report sample welfare statistics for both policy scenarios and all four specifications. Although unconditional and conditional estimates can be compared along several dimensions, the discussion here focuses on three: (1) a within-specification comparison; (2) an across-specification comparison; and (3) a comparison of distributional impacts.

Beginning with a pairwise comparison of unconditional and conditional sample mean welfare estimates for each policy scenario and

Conclusion

This paper has proposed an approach to welfare measurement from random utility models that incorporates the implications of an individual's observed choice. The conditional approach to welfare measurement was motivated in the context of the repeated discrete choice model of recreation demand but is applicable to any choice model where the unobserved determinants of choice are given a behavioral interpretation. If the researcher has correctly specified the data generating process, the theory

Acknowledgements

I thank my dissertation advisor, V. Kerry Smith, for many helpful comments and suggestions. Holger Sieg, Bill Desvousges, Randy Kramer, Dan Graham, and three anonymous referees were also instrumental in the development of this paper. Peter Feather and Daniel Hellerstein generously provided the data used in the empirical application. My former employer, the US Bureau of Labor Statistics, provided a pleasant and supportive working environment while I completed this paper. I take full

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      Another commonly used approach to estimate water quality benefits is recreation demand estimation using random utility models (RUMs). We identified 11 papers in the literature that use these models to value water quality changes (Mullen and Menz, 1985; Smith et al., 1986; Bockstael et al., 1987; Bockstael et al., 1989; Phaneuf et al., 2000; Phaneuf, 2002; von Haefen, 2003; Phaneuf et al., 2008; Egan et al., 2009; Abidoye et al., 2012; Abidoye and Herriges, 2012). Similar to the hedonic literature, all but one of these studies finds that water quality improvements increase recreational visitation and willingness to pay, but omitted variables bias is a concern for interpreting these results (Moeltner and von Haefen, 2011; Phaneuf, 2013).

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