Title: Three Essays on Identification in Microeconometrics
Description: My dissertation consists of three chapters that concern identification in microeconometrics. The first two chapters discuss partial identification of distributional treatment effects in the causal inference models. The third chapter, which is joint work with Pierre-Andre Chiappori, studies identification of structural parameters in collective consumption models in labor economics. In the first chapter, I consider partial identification of the distribution of treatment effects when the marginal distributions of potential outcomes are fixed and restrictions are imposed on the support of potential outcomes. Examples of such support restrictions include monotone treatment response, concave or convex treatment response, and the Roy model of self-selection. Establishing informative bounds on the DTE is difficult because it involves constrained optimization over the space of joint distributions. I formulate the problem as an optimal transportation linear program and develop a new dual representation to characterize the general identification region with respect to the marginal distributions.

I use this result to derive informative bounds for economic examples. I also propose an estimation procedure and illustrate the usefulness of my approach in the context of an empirical analysis of the effects of smoking on infant birth weight. The empirical results show that monotone treatment response has substantial identifying power for the DTE when the marginal distributions are given. In the second chapter, I study partial identification of distributional parameters in nonparametric triangular systems. The model consists of an outcome equation and a selection equation. It allows for general unobserved heterogeneity and selection on unobservables. The distributional parameters that I consider are the marginal distributions of potential outcomes, their joint distribution, and the distribution of treatment effects. I explore different types of plausible restrictions to tighten existing bounds on these parameters. My identification applies to the whole population without a full support condition on instrumental variables and does not rely on parametric specifications or rank similarity.

I also provide numerical examples to illustrate identifying power of each restriction. The third chapter is joint work with Pierre-Andre Chiappori. In it, we identify the heterogeneous sharing rule in collective models. In such models, agents have their own preferences, and make Pareto efficient decisions. The econometrician can observe the household's (aggregate) demand, but not individual consumptions. We consider identification of `cross sectional' collective models, in which prices are constant over the sample. We allow for unobserved heterogeneity in the sharing rule and measurement errors in the household demand of each good. We show that nonparametric identification obtains except for particular cases (typically, when some of the individual Engel curves are linear). The existence of two exclusive goods is sufficient to identify the sharing rule, irrespective of the total number of commodities.