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

Exercise 16

Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6:

You would like to test the null hypothesis H0: ?1 — ?2 = 1.

(i) Let 1 and 2 denote the OLS estimators of ?1 and ?2. Find Var(1 — 32) in terms of the variances of ji1 and J52 and the covariance between them. What is the standard error of 1 — 3 2?

(ii) Write the t statistic for testing H0: 1 — 3 2=1

(iii) Define . Write a regression equation involving ?0, ?1 ?1 and ?3 that allows you to directly obtain 1 and its standard error.

Step 1 of 5

Consider the multiple linear regression model with three independent variables:

In order to test the null hypothesis.