MACRO Econometrics

Problem 1: Consider the following simple two-variable VAR model.

yttttt zyzaay εγγ +++−= −− 1121111210

zttttt zyyaaz εγγ +++−= −− 1221212120

Here ytε and ztε are normally distributed with mean zero and variance 2 yσ and

2 zσ respectively.

Assume that ytε and ztε are also mutually uncorrelated.

(a) Explain why you cannot estimate these equations directly. (b) Find a reduced-from version of these equations. (c) Find the variance-covariance matrix of the reduced-from residuals. (d) Derive the moving-average representation of ty and tz . Using this representation, show

the effect of a one-unit shock in ytε on z at time t+3.

Problem 2: For this set of exercises use annualized macroeconomic data for the U.S. or other country to estimate a monetary VAR. This allows us to study the dynamic interrelationships among the inflation rate (π), the real GDP growth (Δy), and the federal funds rate (i). In class we created the inflation rate series as the logarithmic change in the GDP deflator as π=(ln(gdpdefl)- ln(gdpdefl(t-1)))*400 and real GDP growth series as Δy=(ln(y)-ln(y(t-1)))*400.

1. Create series for the inflation rate and GDP growth, and obtain a series for the short term interest rate (federal funds rate for the United States) for:

a. A specific meaningful period of the monetary history of the United States, or another country. Include a brief (half page summary) on the conduction of monetary policy during such period.

b. Plot the data.

2. Estimate a three-variable monetary VAR using 4 lags of each variable and a constant. Use the ordering such that the Δy, is causally prior to π, and that π is causally prior to i.

a. Present your EViews output for this three variable monetary VAR. b. What are the potential advantages of using the variables π and Δy instead of the

raw data for the gdp deflator or real gdp?

3. Obtain the impulse response functions for the monetary VAR model estimated in 2. Plots must include the responses up to 40 periods.

a. Describe the dynamics of a shock to monetary policy and its effects on inflation and GDP growth. Include plots.

4. Now estimate the forecast variance decomposition for the 3 variable VAR up to 40 periods. Interpret your results, and include the EViews output.

5. Repeat 2a. switching the order so that π, is causally prior to Δy, and that Δy is causally prior to i.

a. Does switching the order of π and Δy have any effects on the impulse responses to a monetary policy shock?

6. Repeat 2a. under the same Cholseki ordering of the variables but using the SVAR feature (structural factorization) in EViews. Present the EViews output and impulse response functions. Are there any differences between 3a. and the impulse response functions for the present set-up?