Specification, estimation and testing of treatment effects in multinomial outcome models : accommodating endogeneity and inter-category covariance

Abstract

In this dissertation, a potential outcomes (PO) based framework is developed for causally interpretable treatment effect parameters in the multinomial dependent variable regression framework. The specification of the relevant data generating process (DGP) is also derived. This new framework simultaneously accounts for the potential endogeneity of the treatment and loosens inter-category covariance restrictions on the multinomial outcome model (e.g., the independence from irrelevant alternatives restriction). Corresponding consistent estimators for the “deep parameters” of the DGP and the treatment effect parameters are developed and implemented (in Stata). A novel approach is proposed for assessing the inter-category covariance flexibility afforded by a particular multinomial modeling specification [e.g. multinomial logit (MNL), multinomial probit (MNP), and nested multinomial logit (NMNL)] in the context of our general framework. This assessment technique can serve as a useful tool for model selection. The new modeling/estimation approach developed in this dissertation is quite general. I focus here, however, on the NMNL model because, among the three modeling specifications under consideration (MNL, MNP and NMNL), it is the only one that is both computationally feasible and is relatively unrestrictive with regard to inter-category covariance. Moreover, as a logical starting point, I restrict my analyses to the simplest version of the model – the trinomial (three-category) NMNL with an endogenous treatment (ET) variable conditioned on individual-specific covariates only. To identify potential computational issues and to assess the statistical accuracy of my proposed NMNL-ET estimator and its implementation (in Stata), I conducted a thorough simulation analysis. I found that conventional optimization techniques are, in this context, generally fraught with convergence problems. To overcome this, I implement a systematic line search algorithm that successfully resolves this issue. The simulation results suggest that it is important to accommodate both endogeneity and inter-category covariance simultaneously in model design and estimation. 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 model and estimation method are used to analyze the impact of substance abuse/dependence on the employment status using the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) data.