Indiana University-Purdue University Indianapolis (IUPUI) / 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.