Estimating Features of a Distribution from Binomial Data

Lewbel, Arthur, Daniel McFadden, and Oliver Linton. “Estimating Features of a Distribution from Binomial Data”. Boston College Working Papers in Economics 442, 1997.

Abstract

We propose estimators of features of the distribution of an unobserved random variable W. What is observed is a sample of Y; V; X where a binary Y equals one when W exceeds a threshold V determined by experimental design, and X are covariates. Potential applications include bioassay and destructive duration analysis. Our empirical application is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values W (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers with characteristics X are asked whether they favor (with Y = 1 if yes and zero otherwise) a referendum that would provide the good at a cost V specified by experimental design. This paper provides estimators for quantiles and conditional on X moments of W under both nonparametric and semiparametric specifications.