A Simple Nonparametric Estimator for the Distribution of Random Coefficients

We propose a simple nonparametric mixtures estimator for recovering the joint distribution of parameter heterogeneity in economic models, such as the random coefficients logit. The estimator is based on linear regression subject to linear inequality constraints, and is robust, easy to program, and computationally attractive compared to alternative estimators for random coefficient models. For complex structural models, one does not need to nest a solution to the economic model during optimization. We prove consistency and provide the rate of convergence under deterministic and stochastic choices for the sieve approximating space that forms the basis of our estimator. We present a Monte Carlo study and an empirical application to dynamic programming discrete choice with a serially-correlated unobserved state variable. ∗Bajari thanks the National Science Foundation, grant SES-0720463, for generous research support. Fox thanks the National Science Foundation, the Olin Foundation, and the Stigler Center for generous funding. Thanks to helpful comments from seminar participants at the AEA meetings, Chicago, Chicago GSB, UC Davis, European Commission antitrust, Far East Econometric Society meetings, LSE, Mannheim, MIT, Northwestern, Paris I, Quantitative Marketing and Economics, Queens, Rochester, Rutgers, Stanford, Stony Brook, Toronto, UCL, USC, Virginia, and Yale. Thanks to comments from Xiaohong Chen, Andrew Chesher, Philippe Fevrier, Amit Gandhi, Han Hong, David Margolis, Andrés Musalem, Peter Reiss, Jean-Marc Robin, Andrés Santos, Azeem Shaikh and Harald Uhlig. Thanks to research assistance from Chenchuan Li.