Semiparametric Instrumental Variable Method

Abstract

Endogeneity can be caused by omitted variables, errors in variables and many other sources. In the existing literature, endogeneity issues are often addressed under an instrumental variables regression setting, assuming the availability and validity of instrumental variables (IVs).

As revealed and experienced in many empirical problems, there are difficulties finding available and valid IVs in practice. In order to avoid such difficulty finding valid IVs and offer a simple alternative to address endogeneity issues, we propose to project the original model under study and subtract possible omitted regressors (covariates) left in the error term of the original model before we construct an exogenous regression model. As the projection and construction procedure itself is semiparametric, we define it as a semiparametric instrumental variable (SIV) method. We then employ the proposed SIV method to fully identify and then estimate the parameters and functions of interest involved in the original model consistently and unbiasedly.

One advantage is that the proposed SIV method offers a valid and closed--form IV function based on the data under consideration. Another advantage is that the proposed SIV method is a unified approach to addressing endogeneity issues and also invariant to the degree of endogeneity, covering a wide range of weak endogeneity, involved in many classes of linear, nonlinear, and non--separable models. An additional advantage is that the proposed SIV method is easily computable and implementable.

This paper establishes an asymptotic theory for the proposed SIV estimation method, and then propose a simple LASSO approach coupled with a generalized cross--validation method to examine the finite--sample performance of both the proposed method and the established theory by simulated and real data examples.