A Switching Regressions Framework for Models with Count-Valued Omni-Dispersed Outcomes: Specification, Estimation and Causal Inference

Abstract

In this dissertation, I develop a regression-based approach to the specification and estimation of the effect of a presumed causal variable on a count-valued outcome of interest. Statistics for relevant causal inference are also derived. As an illustration and as a basis for comparing alternative parametric specifications with respect to ease of implementation, computational efficiency and statistical performance, the proposed models and estimation methods are used to analyze household fertility decisions. I estimate the effect of a counterfactually imposed additional year of wife’s education on actual family size (AFS) and desired family size (DFS) [count-valued variables]. In order to ensure the causal interpretability of the effect parameter as I define it, the underlying regression model is cast in a potential outcomes (PO) framework. The specification of the relevant data generating process (DGP) is also derived. The regression-based approach developed in the dissertation, in addition to taking explicit account of the fact that the outcome of interest is count-valued, is designed to account for potential sample selection bias due to a particular data deficiency in the count data context and to accommodate the possibility that some structural aspects of the model may vary with the value of a binary switching variable. Moreover, my approach loosens the equi-dispersion constraint [conditional mean (CM) equals conditional variance (CV)] that plagues conventional (poisson) count-outcome regression models. This is a particularly important feature of my model and method because in most contexts in empirical economics the data are either over-dispersed (CM < CV) or under-dispersed (CM > CV) – fertility models are usually characterized by the latter. Alternative count data models were discussed and compared using simulated and real data. The simulation results and estimation results using real data suggest that the estimated effects from my proposed models (models that loosen the equi-dispersion constraint, account for the sample selection, and accommodate variability in structural aspect of the models due to a switching variable) substantively differ from estimates from a conventional linear and count regression specifications.