Ample correction for sample selection in random utility models for choice experiments and other multiple-choice contexts

Abstract

Online survey panels with quota-based sampling are often used for choice experiments designed for non-market valuation of public goods. Quotas can ensure a sample of respondents that is representative in terms of its marginal distributions for a limited number of observable sociodemographic characteristics, such as age, race, gender, income brackets or geography. But economists are well aware of the additional potential for systematic selection on the basis of unobservable traits or attitudes. Systematic selection can yield an estimating sample of respondents who have different preferences than the general population. A seminal paper by Heckman (1979) demonstrates how an explicit response/non-response model can be combined with a least-squares-based outcome model based on the respondent sample, under a maintained hypothesis that the errors in the selection equation and the outcome equation are bivariate normal and potentially correlated. However, a Heckman-type approach is inappropriate for the conditional logit choice models typically used to analyze the data from choice experiments. This is because these outcome models are based on fundamentally uncorrelated Type I Extreme Value distributions which thwart reliance on the assumption of potentially correlated bivariate normal errors. We propose and demonstrate a novel method of sample selection correction for multi-alternative conditional logit models that adapts mixed logit estimation methods. (This joint paper constituted one chapter of Joe Mitchell-Nelson’s 2022 Ph.D. dissertation at the University of Oregon.)