2. This question asks you to study whether unanticipated declines in the money stock tend to raise interest rates and lead to recessions, as implied by the misperceptions theory.

a. Using quarterly data from 1960 to the present, define unanticipated money growth in each quarter to be the rate of M2 growth (expressed as an annual rate) from the preceding quarter to the current quarter, minus average M2 growth over the preceding four quarters. (Average M2 growth over the preceding four quarters is a simple approximation of expected money growth.) Graph unanticipated money growth along with the nominal three-month Treasury bill interest rate. On a separate figure, graph unanticipated money growth against the real three-month Treasury bill interest rate (the nominal rate minus the inflation rate). Are unanticipated changes in M2 associated with changes in interest rates in the theoretically predicted direction?

b. In a separate figure, graph unanticipated money growth and the unemployment rate. Are increases in the unemployment rate generally preceded by periods in which unanticipated money growth is negative? What happens to unanticipated money growth following increases in the unemployment rate? Why do you think it happens? Why should the response of this measure of unanticipated money growth to increases in unemployment make you worry about whether this measure captures the unanticipated component of money growth?