Partial Identi?cation and Inference for Dynamic Models and Counterfactuals

We provide a general framework for investigating partial identi?cation of structural dynamic discrete choice models and their counterfactuals, along with uniformly valid inference procedures. In doing so, we derive sharp bounds for the model parameters, counterfactual behavior, and low-dimensional outcomes of interest, such as the average welfare e?ects of hypothetical policy interventions. We characterize the properties of the sets analytically and show that when the target outcome of interest is a scalar, its identi?ed set is an interval whose endpoints can be calculated by solving well-behaved constrained optimization problems via standard algorithms. We obtain a uniformly valid inference procedure by an appropriate application of subsampling. To illustrate the performance and computational feasibility of the method, we consider both a Monte Carlo study of ?rm entry/exit, and an empirical model of export decisions applied to plant-level data from Colombian manufacturing industries. In these applications, we demonstrate how the identi?ed sets shrink as we incorporate alternative model restrictions, providing intuition regarding the source and strength of identi?cation.