Functional Form and the Statistical Properties of Welfare Measures

Abstract

This paper uses Monte Carlo analysis to compare the variance of consumer's surplus for several functional forms for demand. Although the semilog and linear forms fit the data well by statistical criteria, the coefficients of variation for consumer's surplus generated by these forms were substantially larger than for the double log and linear-log forms. While this paper is framed in the travel cost approach to recreational demand, there are implications for the choice of functional form whenever the measure of interest is a nonlinear transformation of the estimated parameters.Key words: benefit estimation, functional form, travel cost demand model, variance of welfare measures, welfare measures.In an influential article, Ziemer, Musser, and Hill note the importance of the choice of functional form for the magnitude of estimated measures of welfare change. In a study of the demand for a recreation site based on the travel cost model, they report nearly a fourfold difference between consumer's surplus based on a linear demand curve and surplus computed from a semilog demand. Their research emphasizes that "good" estimates of demand may not yield good estimates of welfare. The estimate of consumer's surplus is a random variable and alternative functional form specifications affect its statistical properties.'That estimates of consumer's surplus are random variables is well recognized. For example, Bockstael and Strand discuss the imWiktor L. this Journal's reviewers for helpful discussions and technical contributions.I Similar issues arise whenever the variable of interest is a nonlinear transformation of the estimated structural coefficients. For example, see Krinsky and Robb regarding the statistical properties of estimates of elasticities. pact that alternative interpretations of the error term in the demand equation have on methods of computing expected consumer's surplus. The issue of stochastic welfare measures also has received attention in the context of discrete-choice, random utility models by Hanemann.While these analyses have addressed some of the stochastic properties of welfare estimates, the influence of model specification on properties other than the mean or some other measure of central tendency has not been assessed. In this paper we focus on the variability of welfare measures across functional forms. Different functional forms imply different transformations from demand parameters to welfare measures, and these transformations map instability in parameter estimates into instability of welfare estimates in different ways.This paper shows that variability of welfare measures can alter assessments of fits of alternative specifications to the sample data. The key results are driven by the fact that the coefficient on the price variable appears in the denominator of the consumer's surplus equation. In some instances (linear and semilog) this parameter appears alone or multiplied by a constant. Hence, if the parameter is not significantly different from zero, it often will be the case (in a repeated sa...

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