2.13 (E Section 2.3.1)

Consider the data generating process defined in terms of Assumptions 1–7 with the following specifications.

In Assumption 1 take n ¼ 10 and xi ¼ 100 þ i for i ¼ 1,    , 10, in Assumption 3 take s2 ¼ 1, and in Assumption 6 take a ¼ 100 and b ¼ 1. Note that we happen to know the parameters of this DGP, but we will simulate the situation where the modeller knows only a set of data generated by the DGP, and not the parameters of the DGP.

a. Simulate one data set from this model and determine the least squares estimates a and

b, the standard errors of a and

b, and the t-values of a and b.

b. Determine 95% interval estimates for a and b.

c. Repeat steps a and b 100 times. Compare the resulting variances in the 100 estimates a and b with the theoretical variances. How many of the 100 computed interval estimates contain the true values of a and b?

d. Now combine the data into one large data set with 1000 observations. Estimate a and b by using all 1000 observations simultaneously and construct 95% interval estimates for a and b.

Discuss the resulting outcomes.