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
i3t = β0 + β1inft + ut,
(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 inft-1 as an IV for inft. How does the IV estimate of β1 compare with the OLS estimate?
(iii) Now, first difference the equation:
Δi3t = β0 + β1 Δinft + Δut,
Estimate this by OLS and compare the estimate of Bf with the previous estimates.
(iv) Can you use Δinft-1 as an IV for Δinft in the differenced equation in part (iii)? Explain.