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Question 2: A key tenet of modern macroeconomic theory is that the actions taken by policy makers can have real effects on the economy. Two researchers want to determine how output and inflation behave in the wake of monetary policy actions. More precisely, they wish to identify the effects of policy shocks notdirectly dictated by current economic conditions, such as the effect of the Central Bank changing its objectives or beliefs about how the economy works, the effect of political interference, and so on. Theyestimate the following models using US monthly data from January 1970 to December 1996: Ayt = Bo + B1Dit +...+B11011t + a14fft-1 +...+2364fft-36 + vt + (1a) Apt = vo + y1Dit + ... +411D11t+814fft-1 + ... + 8364fft-36 + vt (16) + Pt Where: Yt is the logarithm of the non-seasonally-adjusted industrial production index (multiplied by 100) is the logarithm of the non-seasonally-adjusted production price index (multiplied by 100) fft is the actual value of the Fed Funds rate at timet Dmt are 11 monthly dummy variables Vt, Ut are the error terms Note: The Fed Funds rate is the main instrument of monetary policy in the US. It is the interest rate at which banks are borrowing Central Bank reserves from each other in the short-term. The Federal Reserve Open Market (FOMC) committee decides on the appropriate path of the Fed Funds rate in light of its goals for inflation and output. Although the Federal Reserve influences the Fed Funds rate by manipulating the supply of reserves available to banks, its actual level is determined as the equilibrium between the demand and supply of funds in the Fed Funds market.

a) Explain the rationale for including monthly dummy variables. b) Discuss why they include 11 monthly dummy variables. c) Why are the first differences of the Fed Funds rate, the production price index and the industrial production index used in the regression instead of their level? Explain your answer.

d) Figure 1 represents the estimated cumulative dynamic multipliers (solid line) from model 1a) and 1b) and their 95% confidence interval (dashed lines). Summarize and interpret the main results in Figure 1.

Output: estimated cumulative dynamic multipliers and 95% confidence interval Inflation: estimated cumulative dynamic multipliers and 95% confidence interval 2 0 0 Percent Percent 7- c? 0 6 12 24 30 36 13 25 31 18 7 19 37 Lags (months) Lags (months) Figure 1: Effect of a 1% increase in the Fed Funds rate (fft) on the change in output (yt) and inflation (pt)

e) The researchers suspect that using the change in the Fed Funds rate as a measure of the policy shock may lead to biased estimates of model (1): the change in the Fed Funds rate is potentially endogenous because i) the FOMC decisions are not the only sources of change in the Fed Funds rate, and ii) the decisions of the FOMC are informed by the Fed’s internal forecasts of current and future output growth and inflation prepared in advance of each meeting. State clearly the conditions that need to be satisfied for the estimates of model (1) to identify the causal effects of the Fed's actions on output and inflation. Explain why the results obtained in Figure 1 are unlikely to identify the causal effects of monetary policy if the two objections raised above are valid. f) To eliminate the source of bias identified in the previous question, the researchers use information released by the Federal Reserve around the FOMC meeting to construct a new series of monetary shocks. This new policy shock series captures the FOMC's intended change in the Fed Funds rate that is not due to changes in the Fed's forecasts of output growth and inflation. They denote this new series St. They then estimate model (1) again but substitute St for the change in the Fed Fundsrate: Ayt = BO + BiDit +...+B11D11t+alSt-1 +...+a36St-36 + vt = (3a) Apt = vo + v1Dit +...+y11D11t +81St-1 +. +836St-36 + ut (3b) Explain why this specification is more likely to identify the effect of monetary policy shocks and discuss any potential source of bias remaining.

g) Compare the results obtained using the new shock series (shown in Figure 2) to those obtained using the change in the Fed Funds rate (Figure 1). Do these results suggest that the results obtained by estimating model (1) are potentially biased? Output: estimated cumulative dynamic multipliers and 95% confidence interval Inflation: estimated cumulative dynamic multipliers and 95% confidence interval 0 Percent Percent प -4 9- 9- 0 12 24 18 Lags (months) 30 36 7 13 25 31 37 19 Lags (months) Figure 2: Effect of a 1% positive monetary shock (St) on the change in output (yt) and inflation (pt)