Count-Regression-Based Empirical Causal Analysis from a Potential Outcomes Perspective: Accounting for Boundedness, Discreteness, Dispersion and Unobservable Confounding

Abstract

Empirical economic research is primarily driven by the desire to offer scientific evidence that serves to inform the study of cause-and-effect. In this dissertation, I developed new models for count-regression-model-based (CRM-based) causal effect estimation in which the value for the outcome of interest is restricted to the non-negative integers. I implement first-order two-stage residual inclusion (FO-2SRI) methods, in the context of the general potential outcomes framework, that accommodate nonlinearities due to the intrinsic characteristics of count-valued outcomes such as boundedness (outcome nonnegative), discreteness (outcome has countable support) and dispersion (conditional variance and other higher order conditional moments of the outcome not necessarily equal to its conditional mean) of count data, and unobservable confounding. The focus here is on the case in which the causal variable is continuous. The newly proposed causal effect estimators are compared with extant FO-2SRI estimators based on conventional control function methods and the linear instrumental variables (LIV) estimator. A series of simulation studies are performed to investigate the accuracy of the proposed estimators and compare the results with the extant estimators. In the simulation studies, the robustness of the fully nonlinear CRM-based FO-2SRI methods are investigated with attention to an important type of misspecification error. The models are also applied to a real-world data from Nigeria to investigate the effect of female education on their fertility decisions in a developing country. The results of the simulation studies reveal that estimates obtained via the newly proposed estimators are very accurate and widely diverge from the results from the extant control function and LIV methods. Moreover, one of the new estimators, which allows dispersion flexibility, dominated all other estimators (aside from a few extreme dispersion cases) with regard to avoidance of misspecification bias. Finally, the results showed that same estimator to be quite accurate for a wide range of values of the dispersion parameter (which measures mean/variance divergence). Similar results were obtained via the real data analysis which indicates that increasing women’s education decreases childbearing.