Hints to Problem Set # 2
Pablo D’Erasmo
*
January 26, 2006
1. DATA
•
Download the variables from FRED (the Federal Reserve Bank of St.
Louis
Economic Database at http://research.stlouisfed.org/fred2/
•
Construct the quarterly unemployment rate as an average of the monthly rates.
•
Timing of the variables and shocks is very important in this model. Thus, make
sure to pair GNP growth rates and unemployment data correspondingly.
2. VAR to VMA
•
The Matlab command to run a regression of y on X is “regress(y,X)”, where y
(n
×
1) is the dependent variable and X (n
×
p) is the matrix of
p
independent
variables, in this case the number of lags
p
= 8.
Run two OLS regressions (one
for Δ
y
and other for
u
to find the 32 coefficients). If the command “regress”is
not available in your version of Matlab, you can fin the coefficients by computing
(
X X
)

1
X y
for each equation.
•
As the VAR(8) process is covariance stationary (we take this as true), the lag
polynomial:
(
I
n

B
1
L

B
2
L
2

...

B
8
L
8
)
(1)
is invertible, where
B
i
are the (2
×
2) matrices representing the regression coeffi
cients. In general, the inverse is given by the following form:
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 Spring '07
 CORBAE
 Matrices, Regression Analysis, Unemployment, LTI system theory, impulse response function

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