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Title page for ETD etd-06092008-101923


Type of Document Dissertation
Author Park, Sang Soo
Author's Email Address esesp.park@gmail.com
URN etd-06092008-101923
Title Inference on partially identified parameters: with applications to the evaluation of heterogeneous treatment effects
Degree PhD
Department Economics
Advisory Committee
Advisor Name Title
Yanqin Fan Committee Chair
Bryan Shepherd Committee Member
James Foster Committee Member
Kathryn Anderson Committee Member
Tong Li Committee Member
Keywords
  • heterogeneous treatment effects
  • partially identified parameters
  • Inference
Date of Defense 2008-05-25
Availability unrestricted
Abstract
My dissertation focuses on partial identification of the distribution function of treatment effects. When treatment effects are believed to be heterogeneous, policy evaluation often requires knowledge of the distribution function of potential treatment effects. This function cannot be point-identified unless information is available on the dependence structure between the potential outcomes with and without the treatment. At best, it can be partially identified by finding the upper and lower bounds.

This dissertation consists of four essays. The first essay develops a new approach to the inference on partially identified parameters. It presents new confidence intervals for partially identified parameters, which are asymptotically valid under plausible regularity assumptions. In later chapters, I use these confidence intervals to carry out statistical inference on the quantiles of treatment effects.

In the second essay, I explore partial identification of the distribution of treatment effects in the context of a randomized experiment. Nonparametric estimation and statistical inference on the upper and lower bounds for the distribution of treatment effects are proposed.

The third essay considers the partial identification and inference on the quantile function of treatment effects. In this essay, I apply the confidence intervals developed in the first essay and further develop them to obviate estimation of the marginal density functions.

In the fourth essay, I employ data from Project STAR, a randomized experiment designed to investigate the effects of class size reduction on students' performances. I propose a method of identifying the distribution of treatment effects conditional upon pre-treatment outcomes in order to be able to look into the heterogeneity more closely. Using this methodology, along with the theories and methods developed in the previous three essays, I find evidence that different subgroups have gained differently from class size reduction (i.e. heterogeneous treatment effects) and that the pattern of heterogeneity differs by ability level.

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