Semiparametric Fourier-Dependent Sieve IV Estimator (SPIV) For Truncated Data

The validity of the IV estimator relies on the orthogonality with respect to the random disturbance. However, in cases of endogenously truncated data as well as in other instances (e.g., censored data) which is very frequently the nature of data used in empirical research, there exists severe contamination in the disturbance due to the endogenous selection process. Such a contamination implies that even if the instrumental variable and the random disturbance are unconditionally independent, they are yet conditionally jointly dependent given the selection variable. The rationale is that the endogenous selection process generates a comovement between the IV and the disturbance which is related to the variation in the selection equation's covariates. This contamination propagates additional bias introduced into the parameter estimates of the various covariates. Consequently, not only does the conventional IV not solve the problem it is intended to, but rather it introduces additional bias into the parameter estimates of the various covariates of the substantive equation. Our empirical implementation shows that even under mild correlation between the random disturbances, the resulting bias in the estimated parameter of the endogenous covariate in the substantive equation can amount to almost tenfold the true parameter value. We offer a semiparametric Fourier-dependent Sieve IV (SPIV) estimator correcting for both truncation as well as endogeneity biases. The Fourier estimator is a functional of the orthonormal polynomial sequence family. The most attractive feature of this estimator for our purposes is that it intrinsically prevents potential multicollinearity problems, a feature the kernel estimator does not possess. The proposed estimator removes the hurdle which prevents orthogonality under truncation or other misspecifications. Using Monte Carlo simulations attest to very high accuracy of our offered semiparametric Sieve IV estimator as well as high efficiency as reflected by √n consistency. These results have been verified by utilizing 2,000,000 different distribution functions, generating 100 million realizations to construct the various data sets