Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 20

Suppose that you are interested in estimating the ceteris paribus relationship between y and x1. For this purpose, you can collect data on two control variables, x2 and x3. (For concreteness, you might think of y as final exam score, x1 as class attendance, x2 as GPA up through the previous semester, and x3 as SAT or ACT score.) Let be the simple regression estimate from y on x1 and let be the multiple regression estimate from y on x1,x2,x3.

(i) If x1 is highly correlated with x2 and x3 in the sample, and x2 and x3 have large partial effects on y, would you expect and to be similar or very different? Explain.

(ii) If x1 is almost uncorrelated with x2 and x3, but x2 and x3 are highly correlated, will and tend to be similar or very different? Explain.

(iii) If x1 is highly correlated with x2 and x3, and x2 and x3 have small partial effects on y, would you expect se or se to be smaller? Explain.

(iv) If x1 is almost uncorrelated with x2 and x3, x2 and x3 have large partial effects on y, and x2 and x3 are highly correlated, would you expect se or se to be smaller? Explain.

Step 1 of 8

The difference between a simple linear regression which just requires a linear relationship between two variables and in latter there has to be two or more explanatory variables. In case, one moves from multiple to a simple regression by removing a relevant variable which may be correlated with other explanatory variables then it is called an omitted variable bias.