Question: Consider the following model:
Yt = B1 + B2Xt + ut
where Y = monthly changes in the AAA bond rate, X = monthly change In the three month Treasury bill rate (TB3), and it = stochastic error term. Obtain monthly data on these variables from any reliable source (e.g. the Federal Reserve Bank of St. Louis) for the past 30 years.
(a) Estimate Eq. (I) by OLS. Show the necessary output.
(b) Since general economic conditions affect changes in both AAA and TB3, we cannot treat TB3 as purely exogenous. These general economic factors may very well be hidden in the error term, ur So TB3 and the error term are likely to be correlated. How would you use IV estimation to obtain an IV estimator of .82? Which IV would you use to instrument TB3?
(c) Using the Instrument you have chosen, obtain the IV estimate of B2 and compare this estimate with the OLS estimate of B2 obtained in (a).
(d) Someone suggests to you that you can use past changes in TB3 as an instrument (or current TB3. What may be the logic behind this suggestion? Sup-pose you use TB3 lagged one month as the instrument. Using this instrument, estimate Eq. (1) above and comment on the results.