UC Berkeley

This dissertation consists of three chapters studying microeconometric methods. The first two chapters focus on models with unobserved heterogeneity, and topics include testing shape restrictions imposed by economic theory and estimating counterfactual policy effects in duration analysis. In the last chapter, predictive methods in machine learning are adapted to study model selection within the framework of utility-maximizing binary decision-making. These proposed methods are described in greater detail below.

Causal inference on the individual treatment effect is fundamental in econometric analysis. In Chapter 1, I develop the concept of structural monotonicity, that is, monotonicity of a structural function in a treatment given any observable covariates and unobserved heterogeneity. Different from regression monotonicity, in which heterogeneous factors average out, structural monotonicity emphasizes the sign of ceteris paribus individual treatment effect. Since economic theory may neither detail enough potential heterogeneous factors nor elaborate on parametric structures, I consider a two-period panel data model with nonseparable time-invariant heterogeneity, and avoid imposing restrictions on the dimensionality of heterogeneity and functional form of the structural function. Structural monotonicity in this setup implies shape constraints on the joint cumulative distribution function (CDF) of outcome variables conditional on the observable treatments and covariates over some regions. These regions are parameterized by a nuisance parameter, which can be consistently estimated. According to the shape constraints on the conditional joint CDF over the estimated regions, I propose a test for structural monotonicity and validate the empirical bootstrap method. Some Monte Carlo experiments show that the proposed test can detect departures from structural monotonicity, which are not revealed by some existing tests for regression monotonicity.

The presence of unobserved heterogeneity is also essential for policy effects especially in duration analysis. In Chapter 2, I propose a counterfactual Kaplan-Meier estimator that incorporates time-invariant exogenous covariates and nonseparable heterogeneity in duration models with random censoring. The over-parameterization in traditional duration analysis can be avoided because distributional features of unobserved heterogeneity are unspecified. I establish the joint weak convergence of the proposed counterfactual Kaplan-Meier estimator and the traditional Kaplan-Meier estimator under some regularity conditions. Therefore, by comparing the estimated counterfactual and original unconditional distribution of the duration variable, we can evaluate the policy effects, for example the change of duration dependence in response to an exogenous manipulation of covariates.

In addition to counterfactual analysis in policy research, a better prediction may improve policy-making. In Chapter 3, I show that in a model of binary decision-making based on the prediction of a binary outcome variable, the semiparametric maximum utility estimation can be viewed as cost-sensitive binary classification. Its in-sample overfitting issue is thus similar to that of perceptron learning in the machine learning literature. To alleviate the in-sample overfitting, I apply techniques in structural risk minimization to construct a utility-maximizing prediction rule. This proposed prediction rule, in comparison to the common machine learning Lasso-logit predictor, has larger relative expected utility in some simulation results when the conditional probability of the binary outcome is misspecified. The results show that a better prediction arising from the combination of machine learning techniques and economic theory can improve policy-making.