Deep Learning for the Estimation of Heterogeneous Parameters in Discrete Choice Models

Abstract

This paper studies the finite sample performance of the flexible estimation approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning for the estimation of heterogeneous parameters in economic models, in the context of discrete choice models. The approach combines the structure imposed by economic models with the flexibility of deep learning, which assures the interpretebility of results on the one hand, and allows estimating flexible functional forms of observed heterogeneity on the other hand. For inference after the estimation with deep learning, Farrell et al. (2021a) derive an influence function that can be applied to many quantities of interest. We conduct a series of Monte Carlo experiments that investigate the impact of regularization on the proposed estimation and inference procedure in the context of discrete choice models. The results show that the deep learning approach generally leads to precise estimates of the true average parameters and that regular robust standard errors lead to invalid inference results, showing the need for the influence function approach for inference. Without regularization, the influence function approach can lead to substantial bias and large estimated standard errors caused by extreme outliers. Regularization reduces this property and stabilizes the estimation procedure, but at the expense of inducing an additional bias. The bias in combination with decreasing variance associated with increasing regularization leads to the construction of invalid inferential statements in our experiments. Repeated sample splitting, unlike regularization, stabilizes the estimation approach without introducing an additional bias, thereby allowing for the construction of valid inferential statements.