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

TL;DR

This paper extends a nonparametric random coefficients estimator by linking it to the elastic net, improving support recovery and distribution estimation accuracy, with theoretical guarantees and empirical validation.

Contribution

It introduces a generalized estimator based on the elastic net, enhancing the original sparse estimator's ability to recover true support and estimate distributions more accurately.

Findings

The generalized estimator outperforms the original in support recovery.

The estimator provides more accurate distribution estimates.

Empirical tests confirm improved performance in real data.

Abstract

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.