Identification and Estimation of Polynomial Approximations to Marginal Treatment Effects

Identification and Estimation of Polynomial Approximations to Marginal Treatment Effects

Abstract: This article considers identification and estimation of polynomial approximations to the marginal treatment effect (MTE) and response (MTR) functions that maintain full dependence between observed and unobserved heterogeneity, yet are estimable in settings where the instrumental variable (IV) has as few as two empirical support points. Many approximations that would be partially identified using existing methods can be point identified by leveraging information in the second and higher moments of the outcome variable. Notably, this source of identifying information arises from core modeling assumptions within the MTE approach, but has not been previously considered. Leveraging this information requires identifying assumptions pertaining to the difference between the outcome and the value of the MTR function. Estimators based on an assumed likelihood function are proposed, and the impact of misspecification of the MTR approximation and likelihood function on the bias and variance of estimated treatment effects is explored via simulated examples.

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