Estimating a VAR
• After making the necessary data transformations, you
must define the equations to use in the VAR. Typically,
you will use the following five instructions to set up a
VAR:
SYSTEM(model=modelname)
or SYSTEM 1 to number of equations in the system
VARIABLES list of dependent variables
LAGS 1 to lag length
DETERMINISTIC list of deterministic (constant,
seasonals) and exogenous variables
END(SYSTEM)
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Example for estimating a VAR
As illustrated in the Programming Manual, you can set up a 3-variable
VAR for the variables dlrgdp, dlrm2, and drs using:
system(model=var1)
var dlrgdp dlrm2 drs
lags 1 to 12
det constant
end(system)
The SYSTEM and VARIABLES (i.e., var) instructions set us a system of VAR
equations called var1. Here the lag length is 12 and each regression equation
includes a constant.
Next, use ESTIMATE to obtain the results, save the residuals in the series
resids12, and to save the variance/covariance matrix in V
estimate(residuals=resids12,outsigma=V)
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Creating Seasonals
ENTRY
1972:01
cal 1972 1 12
1972:02
all 1999:10
1972:03
open data f:\classes\413\2000\cars.txt 1972:04
1972:05
data(format=prn,org=obs) /
1972:06
1972:07
seasonal december
1972:08
pri / december
1972:09
1972:10
1972:11
lin cars
1972:12
# constant december{0 to –10}
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DECEMBER
0
0
0
0
0
0
0
0
0
0
0
1
3
estimate(OUTSIGMA=V,other options) start end residuals
where: start end
The range of entries to use.
residuals
The residuals from the first equation are stored in the series given by
residuals, the residuals from the second equation are stored in series number
residuals+1, and so forth. The appropriate number of series should be
declared on the ALLOCATE instruction.
OUTSIGMA=
The name of the variance/covariance matrix. This option
computes and saves the covariance matrix of the residuals. You must use this
option if you want to perform innovation accounting or hypothesis tests
The other principal options are:
NOPRINT By default, RATS prints out the results of the OLS estimation of
each equation. Use NOPRINT to suppress the output.
NOFTESTS By default, RATS prints the results of all Granger causality
tests. Use to supress this output.
SIGMA This option computes and displays (but does not save) the covariance
matrix of the residuals. Use both OUTSIGMA= and SIGMA if you want to
compute, save, and print the variance/covariance matrix.
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Impulse Responses and Variance
Decompositions
errors(IMPULSES) equations steps name
where: equations
Number of equations in the VAR.
steps
The forecast horizon and the number
of impulse responses.
name
The name of the covariance matrix
used on the ESTIMATE instruction.
The principal option is IMPULSES. If you exclude
IMPULSES, RATS calculates and prints only the variance
decompositions.
There is a supplementary card for each equation
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Hypothesis Testing in RATS
ratio(degrees=df ,mcorr=c,other options) start end
# 1 2 ... n
# n+1 n+2 ... 2n
where: start end The range over which the test is to be performed.
degrees=
The number of degrees of freedom (equal to the number
of restrictions in the system).
mcorr=
Sims= small sample correction for likelihood ratio tests
(i.e., the value of c). Set mcorr equal to the largest number of parameters
estimated in any one of the equations (usually equal to the number of parameters
estimated in each of the unrestricted equations).
NOPRINT, supresses the printing of the covariance matrices and the marginal
significance level of the test. It is possible to obtain the marginal significance level
with the instruction:
display %signif
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Example of a Cross Equation Restriction
Example: Suppose, a two-variable VAR using 12 lags of
each variable is estimated and the residuals are saved in
series 1 and 2. The estimation is over the sample period
63:2 to 91:4. Next, the same sample period is used to
estimate a model with a lag length of 8 and the residuals are
saved in series 3 and 4. The lag length test is conducted
using:
ratio(degrees=16,mcorr=28) 63:2 91:4
#12
#34
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Multivariate AIC and SBC
When you use the OUTSIGMA= option on the ESTIMATE statement,
RATS computes the covariance matrix of the residuals. You can fetch
the logarithmic determinant of this covariance matrix using
%LOGDET.
compute aic = %nobs*%logdet + 2*N
compute sbc = %nobs*%logdet + N*log(%nobs)
display ‘aic =‘ aic ‘sbc =‘ sbc
where you must set N equal to the number of parameters estimated in
the entire system
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Seemingly Unrelated Regressions
Different lag lengths
yt = a11(1)yt-1 + a11(2)yt-2 + a12zt-1 + e1t
zt = a21yt-1 + a22zt-1 + e2t
Non-Causality
yt = a11yt-1 + e1t
zt = a21yt-1 + a22zt-1 + e2t
Effects of a third variable
yt = a11yt-1 + a12zt-1 + e1t
zt = a21yt-1 + a22zt-1 + a23wt + e2t
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Estimating a Near-VAR
Step 1: As in Step 1 of a VAR estimation, use the ALLOCATE instruction to
reserve room for each of the residual series.
Step 2: You must define the equations to use in the near-VAR. The simplest
way is to use the DEFINE= option of the LINREG instruction.
To set up the first near-VAR system above, use:
linreg(define=1) y
# y{1 to 2} z{1}
linreg(define=2) z
# y{1} z{1}
To set up the third near-VAR system above, use:
linreg(define=1) y
# y{1} z{1}
linreg(define=2) z
# y{1} z{1} w
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Near-VAR II
Step 3 The typical syntax of SUR is:
sur(options) equations start end
# equation resids
where: equations
The number of equations in the system
start end
The range of entries to use.
equation The number of the equation.
resids
The series in which to store the residuals.
There is 1 supplementary instruction for each equation.
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