Moment Restrictions for Nonlinear Panel Data Models with Feedback

TL;DR

This paper characterizes feedback-robust moment conditions for nonlinear panel data models, enabling more flexible modeling of dynamic economic systems with unobserved heterogeneity and providing methods for efficient estimation.

Contribution

It offers a comprehensive framework to derive feedback-robust moments and compute efficiency bounds, improving upon existing models that restrict feedback in dynamic panel data analysis.

Findings

Characterization of all feedback-robust moment conditions

Construction of feasible estimators for specific models

Calculation of semiparametric efficiency bounds

Abstract

Many panel data methods, while allowing for general dependence between covariates and time-invariant agent-specific heterogeneity, place strong a priori restrictions on feedback: how past outcomes, covariates, and heterogeneity map into future covariate levels. Ruling out feedback entirely, as often occurs in practice, is unattractive in many dynamic economic settings. We provide a general characterization of all feedback and heterogeneity robust (FHR) moment conditions for nonlinear panel data models and present constructive methods to derive feasible moment-based estimators for specific models. We also use our moment characterization to compute semiparametric efficiency bounds, allowing for a quantification of the information loss associated with accommodating feedback, as well as providing insight into how to construct estimators with good efficiency properties in practice. Our results apply both to the finite dimensional parameter indexing the parametric part of the model as well as to estimands that involve averages over the distribution of unobserved heterogeneity. We illustrate our methods by providing a complete characterization of all FHR moment functions in the multi-spell mixed proportional hazards model. We compute efficient moment functions for both model parameters and average effects in this setting.