Go to the St. Louis Federal Reserve FRED database and find data on the personal consumption expenditure price index (PCECTPI), real GDP (GDPC1), an estimate of potential GDP (GDPPOT), and the federal funds rate (DFF). For the price index, adjust the units setting to “Percent Change From Year Ago” to convert the data to the inflation rate; for the federal funds rate, change the frequency setting to “Quarterly.” Download the data into a spreadsheet. Assuming the inflation target is 2% and the equilibrium real fed funds rate is 2%, calculate the inflation gap and the output gap for each quarter, from 2000 until the most recent quarter of data available. Calculate the output gap as the percentage deviation of output from the potential level of output.

a. Use the output and inflation gaps to calculate, for each quarter, the fed funds rate predicted by the Taylor rule. Assume that the weights on inflation stabilization and output stabilization are both ½ (see the formula in the chapter). Compare the current (quarterly average) federal funds rate to the federal funds rate prescribed by the Taylor rule. Does the Taylor rule accurately predict the current rate? Briefly comment. 

b. Create a graph that compares the predicted Taylor rule values with the actual quarterly federal funds rate averages. How well, in general, does the Taylor rule prediction fit the average federal funds rate? Briefly explain. 

c. Based on the results from the 2008–2009 period, explain the limitations of the Taylor rule as a formal policy tool. How do these limitations help explain the use of nonconventional monetary policy during this period?

d. Suppose Congress changes the Fed’s mandate to a hierarchical one in which inflation stabilization takes priority over output stabilization. In this context, recalculate the predicted Taylor rule value for each quarter since 2000, assuming that the weight on inflation stabilization is ¾ and the weight on output stabilization is ¼. Create a graph showing the Taylor rule prediction calculated in part (a), the prediction using new “hierarchical” Taylor rule, and the fed funds rate. How, if at all, does changing the mandate change the predicted policy paths? How would the fed funds rate be affected by a hierarchical mandate? Briefly explain.

e. Assume again equal weights of ½ on inflation and output stabilization, and suppose instead that beginning after the end of 2008, the equilibrium real fed funds rate declines by 0.05 each quarter (i.e. 2009: Q1 is 1.95, then 1.90, etc.), and once it reaches zero, it remains at zero thereafter. How does it affect the prescribed fed funds rate? Why might this be important for policymakers to take into consideration?