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 \((1-t) i-\pi\), where \(i\) is the nominal interest rate, \(t\) is the tax rate, and \(\pi\) 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 \(\pi\) 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) government 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?