Browsing by Subject "Two-Part Model"

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    Avoiding Bad Control in Regression for Partially Qualitative Outcomes, and Correcting for Endogeneity Bias in Two-Part Models: Causal Inference from the Potential Outcomes Perspective
    (2021-05) Asfaw, Daniel Abebe; Terza, Joseph; Ottoni-Wilhelm, Mark; Tennekoon, Vidhura; Tan, Fei
    The general potential outcomes framework (GPOF) is an essential structure that facilitates clear and coherent specification, identification, and estimation of causal effects. This dissertation utilizes and extends the GPOF, to specify, identify, and estimate causally interpretable (CI) effect parameter (EP) for an outcome of interest that manifests as either a value in a specified subset of the real line or a qualitative event -- a partially qualitative outcome (PQO). The limitations of the conventional GPOF for casting a regression model for a PQO is discussed. The GPOF is only capable of delivering an EP that is subject to a bias due to bad control. The dissertation proposes an outcome measure that maintains all of the essential features of a PQO that is entirely real-valued and is not subject to the bad control critique; the P-weighted outcome – the outcome weighted by the probability that it manifests as a quantitative (real) value. I detail a regression-based estimation method for such EP and, using simulated data, demonstrate its implementation and validate its consistency for the targeted EP. The practicality of the proposed approach is demonstrated by estimating the causal effect of a fully effective policy that bans pregnant women from smoking during pregnancy on a new measure of birth weight. The dissertation also proposes a Generalized Control Function (GCF) approach for modeling and estimating a CI parameter in the context of a fully parametric two-part model (2PM) for a continuous outcome in which the causal variable of interest is continuous and endogenous. The proposed approach is cast within the GPOF. Given a fully parametric specification for the causal variable and under regular Instrumental Variables (IV) assumptions, the approach is shown to satisfy the conditional independence assumption that is often difficult to hold under alternative approaches. Using simulated data, a full information maximum likelihood (FIML) estimator is derived for estimating the “deep” parameters of the model. The Average Incremental Effect (AIE) estimator based on these deep parameter estimates is shown to outperform other conventional estimators. I apply the method for estimating the medical care cost of obesity in youth in the US.
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    Casual analysis using two-part models : a general framework for specification, estimation and inference
    (2018-06-22) Hao, Zhuang; Terza, Joseph V.; Devaraj, Srikant; Liu, Ziyue; Mak, Henry; Ottoni-Wilhelm, Mark
    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.