SEMIPARAMETRIC FOURIER-DEPENDENT SIEVE IV ESTIMATOR
Instrumental variables are intended to correct for misspecifications largely stemming from endogeneity problems or omission of relevant important covariates correlated with some of the other included covariates. 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. The endogenous selection process generates a co-movement 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 that the conventional IV does not solve the problem it is intended to but rather 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 10 times the true parameter value for 500 observations and can amount to 5 times the true parameter value in a sample of 10,000 observations. We offer a semi-parametric Fourier-dependent Sieve IV (SPIV ) estimator correcting for both truncation as well as endogeneity biases. The proposed estimator removes the hurdle which prevents orthogonality under truncation or other misspecifications. Using Monte Carlo simulations attest to the high accuracy of our offered semi-parametric Sieve IV estimator as expressed by the √ n consistency. These results have been verified by utilizing 2,000,000 different distribution functions, practically generating 100 millions realizations to generate the various data sets.