Ruhr Economic Papers

Ruhr Economic Papers #824

Nonparametric Estimation of the Random Coefficients Model: An Elastic Net Approach

by Florian Heiss, Stephan Hetzenecker and Maximilian Osterhaus

RGS, UDE, 09/2019, 51 S./p., 10 Euro, ISBN 978-3-86788-957-5 DOI: 10.4419/86788957



This paper investigates and extends the computationally attractive nonparametric random coefficients
estimator of Fox, Kim, Ryan, and Bajari (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it to a special case of the nonnegative elastic net. The extension improves the estimator’s recovery of the true support and allows for more accurate estimates of the random coefficients’ distribution. Our estimator is a generalization of the original estimator and therefore, is guaranteed to have a model fit at least as good as the original one. A theoretical analysis of both estimators’ properties shows that, under conditions, our generalized estimator approximates the true distribution more accurately. Two Monte Carlo experiments and an application to a travel mode data set illustrate the improved performance of the generalized estimator.

JEL-Classification: C14, C25, L

Keywords: Random coefficients; mixed logit; nonparametric estimation; elastic net