Suppose you run a regression y* = ef3,where y = y* + e and x = where y and x are observed variables, V and e are their true unknown values, and e and n are measurement errors. Show that the OLS estimator of regression coefficient is biased and it does not vanish even when the sample size n tends to infinity. Indicate the magnitude and direction of bias.
(a) Using the WAGE2 data, do the OLS estimation of the linear re-gression model of log wage on education, experience, age, and IQ score along with an intercept. Explain your results. Under what assumptions OLS estimation is considered BLUE. (b) Now, do the misspecification analysis of log wage model you have con-sidered in 4(a) by implementing the data diagnostics/statistical tests for (i) linearity (ii) variables (model) selection (iii) heteroskedasticity (iv) outliers (v) normality of residuals (vi) multicollineairty and (vii) endogeneity.Write a summary of your results. (c) Calculate White’s robust standard errors (s.e) of your OLS estima-tors . Are they similar to s.e you have in 4(a)? Also, calculate GLS estimator of your regression coefficients and their s.c. Are these GLS coefficients similar to OLS estimators? Also, calculate LAD estima-tors and indicate if they are different from the OLS estimators. (d) Labor econometricians believe that the education is an endogenous variable. Is this consistent with your test of endogeneity result in 4(b)? Derive the IV estimator of coefficients of log wage regression and compare them with the corresponding OLS estimator of coeffi-cients. Do you find any differences in them?