Problem Set: Macro Simulation Project

Purpose: to gain an understanding of how the economy described by the AS/AD model responds to various shocks under various assumed parameter values.

General Instructions-

• Your answers must be exceeding neat and well organized.
• Your graphs must be completely labeled and easy to read.
• Do not include print outs of your EXCEL spreadsheet.

Simulation Experiments-

Below is a list of simulation exercises that you are to complete for this project using the AS/AD model, which incorporates the following monetary policy rule:

R_t - r^- = m^-(π_t - π^-) + n^-Y˜_t

Assume initially that the central bank is equally concerned with the keeping inflation near its target and output near potential, which implies equal weights:  n = .5; m = .5

Provide the following information for each experiment:

a. the assumed parameter values.

b. the completely labeled exceedingly neat easily readable impulse response graphs.

c. the completely labeled, exceedingly neat, and easily readable AS/AD graphs.

d. a concise, precise and well-articulated explanation of the economic responses going on in the experiment.

For experiments 1 through 4 assume the standard form of the consumption function:

????  = ??¯_????¯_??

Experiment 1a:  positive oil price shock lasting 3 periods.

Experiment 1b: Redo 1a assuming the Fed is more concerned with inflation than the output gap.  Explain the differences in your results for 1a and 1b.

Experiment 2a:  negative aggregate demand shock lasting 8 periods.

Experiment 2b: redo 2a assuming the Fed is more concerned with the output gap than inflation.

Experiment 3a: Fed permanently increases the inflation target.

Experiment 3b:  redo 3a assuming the Phillips curve is steeper.

Experiment 3c: redo 3a assuming expectations adjust instantly and completely to the new inflation target.

For experiment 4 you will use the policy loss function:

L = .5_t=0Σ^NY˜_t² +.5_t=0Σ^N(π_t - π^-)²

The policy loss function measures the disutility that a policymaker experiences when inflation deviates from its target and output deviates from potential (which means that the gap is non zero).  N represents the number of periods in your simulation.

The Fed's objective is to conduct monetary policy (by choosing m^- and n^-) in order to minimize L.

Also for experiment 4 you will want to generate a series of random number between -.5 and .5. The series should be of length N (the number of periods in your simulation). Call your series of random numbers v_t. Then use this series of random numbers to create a series of aggregate demand shocks:

a^-_t = .7a^-_t-1+v_t

Assume a₀ = 0.

Once you have generated your series of random numbers and your aggregate demand shocks it is best to copy and paste special (choose "paste values") in order to stabilize the random number series. If you do not do this the random numbers will change every time you change something else on your spreadsheet.

Experiment 4a. Simulate the effect of this random aggregate demand shock. Calculate the loss (L) due to this aggregate demand shock.

Experiment 4b. play around with different values for the parameters in the Fed's monetary policy rule (m and n ) to see whether it is possible to reduce the loss experienced in 4a.  Explain your results.

Experiments 5a and 5b:  assume consumption takes the form:

??_??/ Y^-?? = ??¯_c +????~_?? where 0 < ?? < 1 is the marginal propensity to consume out of current income.

Experiment 5a: negative aggregate demand shock lasting 8 periods, assume ??=.90

Experiment 5b:  negative aggregate demand shock lasting 8 periods, assume ??=.10

Explain the differences in your results.