Estimation of policy effects using parametric nonlinear models: a contextual critique of the generalized method of moments

The typical empirical study in health services and outcomes research is aimed at estimating the causal effect that an exogenously imposed condition (e.g. a policy mandate) will have (or has had) on a specified outcome of interest. Controlling for unobservable confounding influences is of primary importance in such analyses. The instrumental variables (IV) method has been widely used for this purpose in the linear regression context. The present paper examines the pros and cons of alternative versions of the generalized method of moments (GMM) [of which the IV estimator is a special case] for the estimation of policy effects when endogeneity is present in a nonlinear regression setting. We show that conventional GMM is difficult to implement for policy analysis because it does not typically accommodate symmetry—similar treatment of both observable and unobservable confounders in the regression specification. Although, simple additive (nonsymmetric) regression specifications afford practical GMM estimators, they are difficult to defend from both intuitive and conceptual standpoints. Moreover, as we show via simulation, if symmetry is ignored and conventional GMM is applied based on an incorrectly specified non-symmetric model, then policy analytic estimates can be seriously biased. As a result, prospects for the development and application of intuitive consistent GMM-based policy effect estimators are dim. The problem stems from the reasonable desire on the part of the researcher to derive GMM estimators in the nonlinear framework that are based solely upon the conventional minimalist linear IV assumptions. We show, in the context of our formulation of a simple but consistent alternative to GMM in the probit case, that intuitively appealing additional assumptions about the data generating process of the policy variable will often be sufficient for the development of desirable alternatives to the GMM.