Question

please ve as detail as possible at explaining it

1. (HGL 6.7 ] Table 1 below contains output for the two models y = B1 + B2x + B3w+e y = B1 + B2x + e obtained using N=35 observations. RESET applied to the second model yields F-values of 17.98 (for y2) and 8.72 (for y2 and 9'). Table 1 Unrestricted Model Restricted Model Coefficient coefficient (Standard Error) (Standard Error) Variable [t-Statistic] [t-Statistic) -0.99845 4.1072 (1.2350)SE (0.3383) (-0.8085]r-sle+ [12.14] 0.49785 (0.1174) SE [4.24] T-slat Constant 3.6356 (2.7630) SE (1.316) T-4 -5.8382 (2.0000) [-2.919) The correlation between x and w is rw = 0.975. Discuss the following questions: (a) Should w be included in the model? (b) What can you say about omitted-variable bias? (c) What can you say about the existence of collinearity and its possible effect?

Answer 1

a) No, ‘w’ should not be included in the model. Since r_XW is very high, near exact multi-collinearity will be present and our estimation will be faulty.

b) Omitted Variable Bias when one of the regressors/explainatory variables in the model is correlated with an unobserved factor. It violates the OLS assumption of endogenity.

c) Multi-Collinearity arises when 2 or more regressors/explainatory variables in the model are correlated with each other. It leads to the violation of the Full Rank Condition and results in inflated OLS estimators. Also, the variance of OLS estimators will have an upward bias, and they will no longer be efficient.