Casual analysis using two-part models : a general framework for specification, estimation and inference

Abstract

The two-part model (2PM) is the most widely applied modeling and estimation framework in empirical health economics. By design, the two-part model allows the process governing observation at zero to systematically differ from that which determines non-zero observations. The former is commonly referred to as the extensive margin (EM) and the latter is called the intensive margin (IM). The analytic focus of my dissertation is on the development of a general framework for specifying, estimating and drawing inference regarding causally interpretable (CI) effect parameters in the 2PM context. Our proposed fully parametric 2PM (FP2PM) framework comprises very flexible versions of the EM and IM for both continuous and count-valued outcome models and encompasses all implementations of the 2PM found in the literature. Because our modeling approach is potential outcomes (PO) based, it provides a context for clear definition of targeted counterfactual CI parameters of interest. This PO basis also provides a context for identifying the conditions under which such parameters can be consistently estimated using the observable data (via the appropriately specified data generating process). These conditions also ensure that the estimation results are CI. There is substantial literature on statistical testing for model selection in the 2PM context, yet there has been virtually no attention paid to testing the “one-part” null hypothesis. Within our general modeling and estimation framework, we devise a relatively simple test of that null for both continuous and count-valued outcomes. We illustrate our proposed model, method and testing protocol in the context of estimating price effects on the demand for alcohol.