3. This problem asks you to calculate the actual (as opposed to the expected) real after-tax interest rate using annual data from 1961 to the present. The formula for the actual real after-tax interest rate is

( )

t i

− −

π

1 , where i is the nominal interest rate, t is the tax rate, and π is the inflation rate.

Use the average for each year of the three-month Treasury bill interest rate for the nominal interest rate i and measure annual inflation π by the CPI inflation rate from December to December. Take the tax rate t to be the ratio of total (Federal plus state and local) gov ernment receipts to nominal GDP in the fourth quarter of each year. In what periods was the real after-tax interest rate positive? In what periods was it negative?