SVAR Modeling in STATA
Armando Sánchez Vargas
Economics Research Institute
UNAM
I.- Motivation
 Stata is a powerful and flexible statistical
package for modeling time series.
 Prospective and advanced users would want
to know:
I.
SVAR modeling facilities the package offers.
II.
The main advantages of Stata compared with other
time series packages.
III. What is still needed and what might be refined to
implement the whole SVAR methodology in Stata.
II.- Objectives
 The main purpose of this presentation is to
discuss STATA´s capability to implement the
entire SVAR methodology with non-stationary
series.
 A second objective is to discuss what is
needed to improve the implementation of
SVAR models in STATA.
III.- SVAR Methodology
 The main objective of SVAR models is
to find out the dynamic responses of
economic variables to disturbances by
combining time series analysis and
economic theory.
III.- SVAR Methodology
In the presence of unit roots the
structuralisation of a VAR model can take
place at three distinct stages:
III.- SVAR Methodology
I.
The first step consists of specifying an
appropriate VAR representation for the set of
variables.*
*
Which implies to choose the lag order, the cointegration rank and the kind
of associated deterministic polynomial and a sensible identification of
the space spanned by the cointegrating vectors (Johansen, 1995).
III.- SVAR Methodology
II. In the second step, the “structuralisation” stage, we use
the VAR model in its error correction form to identify the
short run associations between the variables and their
determinants, which are hidden in the covariance
matrix of the residuals of such multivariate model. In
order to recover the short run model coefficients we can
use the variance covariance matrix of the VAR in its
error correction form (*) and impose theoretical
restrictions.
(*)
( L)zt     zt 1   t
'
III.- SVAR Methodology
Then, we start with an exactly-identified structure given
by the lower triangular decomposition of the variancecovariance matrix of the estimated VAR disturbances
and restrict the non-significant parameters to zero
moving to a situation of over-identification (i.e).
1
0

0

0
a12 a13 a14    et  b11

 

1 0 0   ( mm* )t   0

0 1 0    ( y y*)t   0
 

0 0 1    (ii*)t   0
0   uet 
u


b22 0 0   ( mm* )t 
0 b33 0   u( y y*)t 


0 0 b44   u(ii*)t 
0
0
III.- SVAR Methodology
III. Finally, the short and medium run validity
of the model can also be verified by
plausible modeling of the instantaneous
correlations via impulse response
functions.
The model selection strategy
IV.- SVAR Estimation
 First, we must do misspecification test over
VAR, this guarantee a good model; because is
very important to have the correctly VAR then to
have a good SVAR.
 After the reduced from VAR representation has
been aptly estimated, the researcher is allowed
to specify a set of constraints on the A and B
matrices.
IV.- SVAR Estimation
 The SVAR procedure verifies whether the restrictions
comply with the rank condition for local identification.
This check is carried out numerically by randomly
drawing A and B matrices satisfying the restrictions
being imposed.
 At this stage, of the identification condition is met, the
procedure SVAR carries out maximum likelihood
estimation of the structural VAR parameters by using the
score algorithm. In the case of over-identification, the LR
test for checking the validity of the over-indentifying
restrictions is computed.
IV.- SVAR Estimation
Starting from the estimate of the SVAR
representation, the procedure VMA
estimates the structural VMA and the
FEVD parameters, together with their
respective asymptotic standard errors.
The results of this analysis are then
available for being displayed, saved and
graphed.
Stata’s capabilities:
Univariate Analysis
Capabilities
PcGive
STATA
RATS
Graphics
yes
yes
yes
Autocorrelation Functions
yes
yes
yes
yes
yes
yes
ADF
ADF
ADF
PP
PP
KPSS
SCP
Unit Root Test
DF-GLS
Note: ADF=Augmented Dickey-Fuller Test. PP=Phillips Perron.
KPSS=Kwiatkowski-Phillips-Schmidt-Shin. SCP=Schmidt Phillips. DFGLS=Dickey-Fuller GLS.
Stata’s capabilities: Model
Specification and Estimation
Capabilities
Automatic Seasonal Dummies
Maximum lag
Trend polynomial
Cointegration ranks
Exogenous variables
VAR estimation
RATS
PcGive STATA Malcom
yes
yes
yes
yes
yes
yes
no
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
Stata’s capabilities:
Misspecificacion Tests
Capabilities
PcGive
STATA
RATS
Single Test
Joint Test
Single Test
Joint Test
Single Test
Joint Test
Normality
yes
yes
yes
no
yes
yes
Homoskedasticity
yes
yes
no
no
no
no
No Autocorrelation
Parameters Stability
yes
yes
yes
yes
no
no
yes
no
yes
no
no
yes
Linearity
no
no
no
no
no
no
Stata’s capabilities: Statistial
Inferences based on the model
Capabilities
Maximum lag
Tests for trend polynomial
Test for joint determination
of cointegration rank and
deterministic polynomial
Trace Test in the I(1) model
Tests for r, s in the I(2)
model
Parameters stability:rank
and cointegrating space
Roots the Model
PcGive
yes
no
STATA
yes
no
RATS
yes
yes
no
no
yes
yes
yes
yes
no
no
yes
no
yes
no
yes
yes
yes
Stata’s capabilities:
Automatic test
Capabilities
PcGive
STATA
RATS
Weak exogeneity test
no
no
yes
Indentification
no
no
yes
Granger causality
no
yes
yes
Tests on α y β
yes
yes
yes
Stata’s capabilities: Structural VAR
analysis whit stationary and non
stationary variables
Capabilities
PcGive
Non
Stationary stationary
STATA
RATS
Stationary
Non
stationary
Stationary
Non
stationary
Estimation
no
no
yes
no
yes
yes
Simulation
no
no
yes
no
yes
yes
Graphics
no
no
yes
no
yes
yes
Conclusions
 Commands are appropiate for basic use.
 Improvements in routines for advanced users.
Conclusions
 What is needed:
I.
Addition of some other Unit Roots Tests.
II. The VAR capabilities could benefit by the addition of
single and joint misspecification tests.
III. Adding a few tests and graphs as automatic output:
Tests for trend polynomial, Test for joint determination
of cointegration rank and deterministic polynomial,
Tests for r, s in the I(2) model, Parameters
stability:rank and cointegrating space.
IV. Considered the cointegrated SVAR model
Conclusions
 What might be refined:
I. It should automatically include seasonals.
II. It should automatic include tests in the
I(1) model.
Conclusions
The VAR, SVAR and VECM commands deal with
non stationarity through the prior differencing or
the incorporation of deterministic trend or
cointegration.
Stata needs more flexibility for dealing with non
stationary series.
In general, Stata is powerful, versatile and well
designed program which maybe improved by
adding some features and refinements.
Bibliography
Alan Yaffe, Robert (2007): Stata 10 (Time series and Forecasting), Journal of
Statistical Software, December 2007, volume 23, software review 1, New York.
Gottschalk, J. (2001): An Introduction into the SVAR Methodology: Identification,
Interpretation and Limitations of SVAR Models, Kiel Institute of World Economics.
Amisano & C Gianni (1997): Topics in Structural VAR Econometrics, New York.
Dwyer, M. (1998): Impulse Response Priors for Discriminating Structural Vector
Autoregressions,
UCLA
Department
of
Economics.
Krolzig, H. (2003): General to Specific Model Selection Procedures for Structural
Vector Auto Regressions. Department of Economics and Nuffield College. No 2003W15.
Sarte, P.D. (1997): On the Identification of Structural Vector Auto Regressions.
Federal Reserve Bank of Richmond, Canada, Sum: 45-68.