PhD Candidate
in Economics

This study addresses a longstanding practical difficulty in nested-logit demand estimation: assigning products to nests. Current implementations treat nest membership as known — an assumption this paper relaxes. Misspecified nests lead to a different model and therefore misleading conclusions. We propose a fully data-driven, two-stage procedure. First, we recover the matrix of cross-price elasticities nonparametrically, exploiting a control-function identification that allows for endogenous prices, using sparse deep neural networks suited to nonlinear and high-dimensional settings. Second, we cluster products with the k-medoids algorithm, using the fact that within-nest cross-product price elasticities are identical in the nested logit. We establish consistency and convergence rates for both the elasticity estimator and the subsequent classification. A Monte Carlo study demonstrates the accuracy of the proposed algorithm.

Elasticities are fundamental objects in empirical economics, yet their nonparametric identification under endogenous regressors remains largely unexplored. This paper develops a general framework for identifying conditional average elasticities using a control-function approach, without imposing parametric restrictions on the structural outcome equation. We propose an estimation procedure based on a sparse multi-output deep neural network suited to nonlinear and high-dimensional demand systems. Extending existing results to the multi-output setting, we derive an L² convergence rate of O_p(m^−1/8) for the elasticity functional. Monte Carlo simulations show that the estimator recovers elasticity matrices accurately across a range of data-generating processes — including log-log, random utility models, and nonlinear generic specifications — particularly in large samples.