Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 15

Use the data in INTDEF.RAW for this exercise. A simple equation relating the three-month T-bill rate to the inflation rate (constructed from the Consumer Price Index) is
i3 t = 0 + 1 inf + u t.
(i) Estimate this equation by OLS, omitting the first time period for later comparisons. Report the results in the usual form.
(ii) Some economists feel that the Consumer Price Index mismeasures the true rate of inflation, so that the OLS from part (i) suffers from measurement error bias. Reestimate the equation from part (i), using inf t-1 as an IV for inf t. How does the IV estimate of 1 compare with the OLS estimate
(iii) Now, first difference the equation:
i3 t = 0 + l inf t + u t.
Estimate this by OLS and compare the estimate of 1 with the previous estimates.
(iv) Can you use inft-1 as an IV for inf t in the differenced equation in part (iii) Explain. (Hint: Are inf t and inf t-1 sufficiently correlated )