Robust Structural Estimation under Misspecified Latent-State Dynamics

TL;DR

This paper introduces a method to assess how sensitive scalar parameters in dynamic structural models are to potential misspecifications in latent-state dynamics, providing bounds and computational tools for robust analysis.

Contribution

It develops a framework to quantify the sensitivity of parameters to latent process misspecification, with tractable optimization and asymptotic properties.

Findings

Perturbed elasticities deviate up to 15.24% from reference.

Consumer surplus estimates vary by up to 102.75%.

Labor elasticity deviations reach 76.83% for weekday drivers.

Abstract

Estimation and counterfactual analysis in dynamic structural models rely on assumptions about the dynamic process of latent variables, which may be misspecified. We propose a framework to quantify the sensitivity of scalar parameters of interest (e.g., welfare, elasticity) to such assumptions. We derive bounds on the scalar parameter by perturbing a reference dynamic process, while imposing a stationarity condition for time-homogeneous models or a Markovian condition for time-inhomogeneous models. The bounds are the solutions to optimization problems, for which we derive a computationally tractable dual formulation. We establish consistency, convergence rate, and asymptotic distribution for the estimator of the bounds. We demonstrate the approach with two applications: an infinite-horizon dynamic demand model for new cars in the United Kingdom, Germany, and France, and a finite-horizon dynamic labor supply model for taxi drivers in New York City. In the car application, perturbed price elasticities deviate by at most 15.24% from the reference elasticities, while perturbed estimates of consumer surplus from an additional $3,000 electric vehicle subsidy vary by up to 102.75%. In the labor supply application, the perturbed Frisch labor supply elasticity deviates by at most 76.83% for weekday drivers and 42.84% for weekend drivers.