Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 13

In Section 4.5, we used as an example testing the rationality of assessments of housing prices. There, we used a log-log model in price and assess [see equation (4.47)]. Here, we use a level-level formulation.
(i) In the simple regression model
price = 0 + 1 Possess + u,
the assessment is rational if 1 = 1 and 0 = 0. The estimated equation is
First, test the hypothesis that H0: 0 = 0 against the two-sided alternative. Then, test H0: 1 = 1 against the two-sided alternative. What do you conclude
(ii) To test the joint hypothesis that 0 = 0 and 1 = 1, we need the SSR in the restricted model. This amounts to computing where n = 88, since the residuals in the restricted model are just price i - assess i. (No estimation is needed for the restricted model because both parameters are specified under H 0.) This turns out to yield SSR = 209,448.99. Carry out the F test for the joint hypothesis.
(iii) Now, test H 0 : 2 = 0, 3 = 0, and 4 = 0 in the model
price = 0 + 1 assess + 2 lotsize + 3 sqrft + 4 bdrms + u.
The R-squared from estimating this model using the same 88 houses is.829.
(iv) If the variance of price changes with assess, lotsize, sqrft, or bdrms, what can you say about the F test from part (iii)