4. (6 marks) Output for the two models y = B +Bx+Bw + e and y = B +A++ e, based

Question

4. (6 marks) Output for the two models y = B +Bx+Bw + e and y = B +A++ e, based on 35 observations, are given below. Variable Coefficient Std Error t-value Coefficient Std Error t-value 3.6356 2.763 1.316 5.8382 2.000 2.919 0.99845 1.235 0.8085 4.1072 0.338312.14 0.49785 0.1174 4.240 RESET applied to the second model yields F-values of 17.98 (for ) and 8.72 (for 2 and 9). The correlation between x and w is row-0.975. Discuss the following questions. a. (2 marks) Should w be included in the model? b. (2 marks) What can you say about omitted-variable bias? c. (2 marks) What can you say about the existence of collinearity and its possible effect?

Explanation / Answer

a) Ans: We should not include 'w' in the model because 'x' and 'w' have a high correlation.

b) Ans: Here, if you know the relation between the Y and X, you can also know the relation between the Y and W because of the high X and W correlation. So, mean of the Y =B1+B2x=B1+B2w. Hence, there is no omitted-variable bias.

c) The variables X and W have a high correlation, so, here is the existence of collinearity and its possible effect is that the variance of the coefficients (B1, B2, and B3) is so large.

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