New microeconometric approaches to estimating models with endogeneity

This dissertation consists of three stand-alone chapters, each of which investigates a specific endogeneity problem commonly arising in applied microeconometrics. The first chapter focuses on the multivariate probit model, a framework with a flexible structure that can be used to control for endogeneity in discrete variables. Because the likelihood function is difficult to evaluate numerically, the model is typically estimated by maximizing a simulated likelihood function. This can be a time-consuming process and in many cases the estimator does not converge. This chapter discusses an alternative estimator of the multivariate probit model in which the parameters of each equation are estimated sequentially. The estimator runs significantly faster and rarely fails to converge. The second chapter looks at the problem of endogenous control variables when estimating a treatment effect. Including the endogenous control variables leads to an endogeneity bias that affects the estimated treatment effect, but excluding the endogenous controls causes an omitted variable bias. In the absence of valid instruments, the treatment effect cannot be identified by conventional means. Focusing primarily on a simple model with a treatment variable and a single endogenous control variable, this chapter proposes assuming the endogenous variable’s parameter is a random draw from a normal distribution with a mean and variance specified by the researcher. The treatment effect can then be estimated by ordinary least squares, but the estimated variance is inflated to account for uncertainty about the endogenous variable’s parameter. As a result of this, the estimator is named variance-inflated least squares. The properties of this estimator compare favorably to those of other approaches such as ignoring the endogeneity, excluding the endogenous control variable, and using an instrumental variable. The third chapter is an applied piece that investigates the effectiveness of a public health insurance scheme in Indonesia. Noting that many people do not use medical care, this chapter assesses whether the policy has had any effect on those individuals who would not have used health care in the absence of the policy. By estimating a model that incorporates a two-stage decision for health care demand, this analysis suggests that any increase in the utilization of outpatient care due to the policy in Indonesia is highly concentrated among those who were already users of health care. While the treatment variable is endogenous, as it is not randomly allocated, economic theory is used to derive the likely direction of the bias in the estimated treatment effect. This bias does not affect the causal test conclusion about the effectiveness of the policy on non-users of medical care.