In this question, we are  going dig deeper into the Taylor Rule and it variants  (modifications).

Effective Federal Funds Rate

As Taylor assumed, we assume the equilibrium real rate of interest, r* = 2% and the optimal inflation rate, the target inflation rate is also equal to 2%.

a) Using the 'standard' Taylor rule with Inflation PCE (not the core), and using end of 2011 data (2011-10-01) what is the federal funds rate implied by the 'standard' Taylor Rule? According to the actual federal funds rate (use the Effective Federal Funds Rate), is the Fed being hawkish or dovish? Explain. 

b) Repeat part a) using the modified version of the Taylor using the unemployment gap instead of the GDP gap just like we did in the lectures. Also, use the PCE core rate of inflation instead of overall inflation like you used above - the Fed arguably cares more about core inflation than overall inflation. According to the actual federal funds rate (use the Effective Federal Funds Rate), is the Fed being hawkish or dovish? Which "Taylor" rule explains Fed behavior better, the original or the modified Taylor Rule? Explain. 

c) Let's go back in time to the fourth quarter of 1965 (1965-10-01) when the "We are all Keynesians" was featured in Time magazine. We argued that this was heyday of Keynesian economics so we would expect to get dovish results. Using the original Taylor Rule that you used in part a) and the modified Taylor Rule that you used in part b), prove that the Fed was dovish according to both versions of the Taylor Rule.

d) We now go back to the Volcker period where he was known as being a hawk on inflation. Using the data from the second quarter of 1982 (1982-04-01), prove that the Volcker Fed was hawkish according to both versions of the Taylor Rule