Essays on Partial Identification in Structural Models

Open Access
Li, Lixiong
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
April 24, 2019
Committee Members:
  • Marc Albert Henry, Dissertation Advisor
  • Marc Albert Henry, Committee Chair
  • Joris Pinkse, Committee Member
  • Paul L E Grieco, Committee Member
  • Aydin Alptekinoglu, Outside Member
  • partial identification
  • structural model
My studies focus on the partial identification in structural econometric models. This dissertation includes two chapters on partial identification and one chapter on a numerical method of estimating structural discrete choice models. Chapter 1 Structural econometric models usually involve parametric distributional assumptions for unobserved heterogeneity. Although these assumptions are typically not informed by economic theory, and undermine the robustness of empirical results, they are generally thought to be necessary to simulate counterfactual predictions. In partially identified and incomplete structural models, counterfactual analysis is also hampered by the multiplicity of admissible structural parameter values and the multiplicity of counterfactual predictions for each structural parameter value. This paper shows how to construct identification conditions for both structural and counterfactual parameters in a large class of structural econometric models, including partially identified and incomplete ones, without imposing parametric distributional assumptions for unobserved variables. The identified set is characterized by moment inequalities, so that existing inferential methods can be applied, including subvector inference when only counterfactual parameters are of interest. The novelty and computational tractability of the methodology is illustrated on a class of discrete choice models and a class of entry models. Chapter 2 I investigate a model of one-to-one matching with transferable utilities, where the matching process is subject to time-consuming search frictions. I assume agents have unobserved (to economists) characteristics, which affect the matching surplus along with matching specific random shocks under a separability assumption. I show the matching surplus can be non-parametrically identified with data on matching patterns and distributions on unmatched durations across agents, given any known distribution on unobserved characteristics. In contrast to the existing literature, my identification strategy does not hinge on data on payoffs and panel data with long time series. As in frictionless matching models, I show any interior matching patterns can be rationalized by the model under some parameters. For one type of corner solution, only set identification is attained and a sharp bound has been derived. Chapter 3 This paper describes a numerical method to solve for mean product qualities which equates the real market share to the market share predicted by a discrete choice model. The method covers a general class of discrete choice model, including the pure characteristics model in \cite{berry_pure_2007} and the random coefficient logit model in \cite{berry_automobile_1995} (hereafter BLP). The method transforms the original market share inversion problem to an unconstrained convex minimization problem, so that any convex programming algorithm can be used to solve the inversion. Moreover, such results also imply that the computational complexity of inverting a demand model should be no more than that of a convex programming problem. In simulation examples, I show the method outperforms the contraction mapping algorithm in BLP. I also find the method remains robust in pure characteristics models with near-zero market shares.