Question 1
Suppose that you have 150 observations on production (yt) and investment (it), and you have estimated the following ADL(3,2) model:
(1 – 0.5L – 0.1L2 – 0.05L3)yt = 0.7 + (0.2 + 0.1L +0.05L2)it (1)
a. Use this model to describe the dynamic effects of investment on production. Your answer should include a calculation of the impact multiplier and the long-run multiplier.
b. Suppose that you can obtain other output associated with the above regression (eg., the residuals et, the R2, the sum of squared residuals, etc.). Carefully explain how you would test each of the null hypotheses given below.
[Hints: In each case your answer should state the extra output you would need from regression of equation (1), the extra regression(s) that you would need to run, an explanation of how you would construct the test statistic, a statement on the distribution of the test statistic under the null hypothesis, and a brief description of your critical region.]
i. H0: investment has no long run effect on production.
ii. H0: there is no third order serial correlation in the errors.