Essays on Identification, Estimation and Inference of Economic Models with Testable Assumptions
Restricted (Penn State Only)
- Author:
- Liao, Moyu
- Graduate Program:
- Economics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 01, 2021
- Committee Members:
- Marc Henry, Program Head/Chair
Lingzhou Xue, Outside Unit & Field Member
Marc Henry, Chair & Dissertation Advisor
Andres Aradillas-Lopez, Major Field Member
Joris Pinkse, Major Field Member - Keywords:
- Refutability
Identification
Estimation
Hypothesis Testing
LATE - Abstract:
- I study identification, estimation, and hypothesis testing in complete and incomplete economic models with testable assumptions. Testable assumptions ($A$) give strong and interpretable empirical content to the model but they also carry the possibility that some distribution of observed outcomes may reject these assumptions. A natural way to avoid this is to find a set of relaxed assumptions ($\tilde{A}$) that cannot be rejected by any distribution of observed outcomes and such that the identified set for the parameter of interest is not changed when the original assumption holds. The main contribution of this thesis is to characterize the properties of such a relaxed assumption $\tilde{A}$ using notions of refutability and confirmability. In Chapter 1, I establish the theoretical framework for analyzing econometric structures and econometric assumptions. This framework unifies the theory of identification of complete economic structures and the theory of refutability. I propose a general method to construct such $\tilde{A}$. A general estimation and inference procedure is proposed and can be applied to a large class of incomplete economic models. I apply my methodology to the instrument monotonicity assumption in Local Average Treatment Effect (LATE) estimation and to the sector selection assumption in a binary outcome Roy model of employment sector choice. In the LATE application, I use my general method to construct a set of relaxed assumptions $\tilde{A}$ that can never be rejected, and the identified set for LATE is unchanged when $A$ holds. LATE is point identified under my extension $\tilde{A}$ in the application. I also provide an estimation and inference method on the LATE value. In Chapter 2, I generalize the framework to incomplete economic structures. I show that the general method for constructing a relaxed assumption in Chapter 1 may fail to work in incomplete economic structures. Therefore, I propose a completion procedure that is without loss of generality. With this completion procedure, we can get completed economic structures, and the method in Chapter 1 can be applied. I then look at the application to a binary outcome Roy model. I use my method to relax Roy's sector selection assumption and characterize the identified set for the binary potential outcomes as a polyhedron. In Chapter 3, I propose a dilation estimation and inference method that can be applied to a wide class of complete and incomplete economic structures. My method can easily deal with an observed variable that is of dimension greater than two.