In a 2018 speech, St. Louis Federal Reserve Bank President James Bullard spoke about modernizing monetary policy rules, such as the Taylor Rule. He suggested the modernized Taylor Rule should take the form: i_t=*i_(t-1)+(1-)*[r_t^*+^*+*(_t-_t^e )+*(u_t-u_t^n )] i_t: policy (fed funds) rate r_t^*: natural real interest rate ^*: inflation target _t^e: expected inflation rate u_t: unemployment rate u_t^n: natural rate of unemployment Bullard suggested the following parameters were appropriate: =0.85 =1.5 =0.1 This Taylor rule relies on computing expected inflation. Bullard makes the following calculation of inflation expectations: _t^e=5 year Treasury bond yield-(5 year Treasury inflation protected bond yield) This measure of inflation expectations is calculated as the 5-Year Breakeven Inflation Rate on the Federal Reserve Economic Data website. Bullard subtracts 0.3 percentage points from the rate to account for the likely overestimate of inflation by the consumer price index, which is used to determine the inflation rate protected by the TIPS bond. Please add quarterly-frequency inflation expectations to the dataset for the homework on Canvas. Compute the unemployment rate gap: u_t-u_t^n based on the data provided for the assignment. (10 points) Please compute the new Taylor rule interest rate for all possible quarters in the dataset provided for the assignment, assuming that the real interest rate is constant at 2% and the inflation target is 2%. Plot this Taylor rule interest rate over time with the original Taylor rule rate and the fed funds rate on a line graph. Which Taylor rule is more consistent with actual Federal Reserve policy? (20 points)

In a 2018 speech, St. Louis Federal Reserve Bank President James Bullard spoke about modernizing monetary policy rules, such as the Taylor Rule. He suggested the modernized Taylor Rule should take the form: it = p*it-1 + (1 -p) * [ri* + 1* + a * (Tlt ) + B * (ut - u)] it: policy (fed funds) rate r: natural real interest rate A*: inflation target The expected inflation rate ut: unemployment rate ur: natural rate of unemployment Bullard suggested the following parameters were appropriate: P = 0.85 a = 1.5 B = 0.1 d. This Taylor rule relies on computing expected inflation. Bullard makes the following calculation of inflation expectations: = 5 year Treasury bond yield - (5 year Treasury inflation protected bond yield) This measure of inflation expectations is calculated the "5-Year Breakeven Inflation Rate on the Federal Reserve Economic Data website. Bullard subtracts 0.3 percentage points from the rate to account for the likely overestimate of inflation by the consumer price index, which is used to determine the inflation rate protected by the TIPS bond. Please add quarterly-frequency inflation expectations to the dataset for the homework on Canvas. e. Compute the unemployment rate gap: Ut u based on the data provided for the assignment. (10 points) f. Please compute the new Taylor rule interest rate for all possible quarters in the dataset provided for the assignment, assuming that the real interest rate is constant at 2% and the inflation target is 2%. Plot this Taylor rule interest rate over time with the original Taylor rule rate and the fed funds rate on a line graph. Which Taylor rule is more consistent with actual Federal Reserve policy? (20 points) In a 2018 speech, St. Louis Federal Reserve Bank President James Bullard spoke about modernizing monetary policy rules, such as the Taylor Rule. He suggested the modernized Taylor Rule should take the form: it = p*it-1 + (1 -p) * [ri* + 1* + a * (Tlt ) + B * (ut - u)] it: policy (fed funds) rate r: natural real interest rate A*: inflation target The expected inflation rate ut: unemployment rate ur: natural rate of unemployment Bullard suggested the following parameters were appropriate: P = 0.85 a = 1.5 B = 0.1 d. This Taylor rule relies on computing expected inflation. Bullard makes the following calculation of inflation expectations: = 5 year Treasury bond yield - (5 year Treasury inflation protected bond yield) This measure of inflation expectations is calculated the "5-Year Breakeven Inflation Rate on the Federal Reserve Economic Data website. Bullard subtracts 0.3 percentage points from the rate to account for the likely overestimate of inflation by the consumer price index, which is used to determine the inflation rate protected by the TIPS bond. Please add quarterly-frequency inflation expectations to the dataset for the homework on Canvas. e. Compute the unemployment rate gap: Ut u based on the data provided for the assignment. (10 points) f. Please compute the new Taylor rule interest rate for all possible quarters in the dataset provided for the assignment, assuming that the real interest rate is constant at 2% and the inflation target is 2%. Plot this Taylor rule interest rate over time with the original Taylor rule rate and the fed funds rate on a line graph. Which Taylor rule is more consistent with actual Federal Reserve policy? (20 points)