UC San Diego

When a sample of data does not fully reveal the "true" data generating structure (or parameter) but gives information that bounds the set of observationally equivalent structures, an economic model is said to be partially identified. This dissertation develops and applies estimation and inference methods for economic models whose population features are only partially identified. In Chapter 1 (co-authored with Halbert White), I apply econometric techniques from the partial identification literature to address a fundamental problem in asset pricing theory. Namely, that the market price of risk is only identified as a set under incomplete markets. I construct a set estimator and confidence regions for the set of market risk prices. I further show that it is possible to test hypotheses of economic interest without fully identifying the market price of risk. The econometric techniques used in Chapter 1 are developed by Chapter 2 (co-authored with Halbert White). When the dimension of the parameter space is large, this is a particular challenge for set-valued estimators, as high dimensionality can create computational difficulties and seriously hamper the interpretation of estimation results. We study how the use of a natural two-stage extension of the Chernozhukov, Hong, and Tamer's (2007) (CHT) framework can exploit a priori knowledge about the data generating process to mitigate the problems otherwise associated with set estimation in high-dimensional parameter spaces. Chapter 3 unifies two general approaches recently proposed in the literature, the criterion function approach and support function approach. CHT develop a theory of set estimation and inference for the set [Theta]/I of parameter values that minimize a criterion function. The support function approach provides an alternative characterization of CHT's level-set estimator by its supporting hyperplanes. This results in an estimation and inference method that has the wide applicability of the criterion function approach and the computational tractability of the support function approach. By establishing the asymptotic distribution of the properly normalized support function of the level set estimator, I provide Wald-type inference tools to conduct tests regarding the identified set [Theta]/I and a point [Theta]₀ in the identified set