SVAR Modeling in STATA

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SVAR Modeling in STATA

• Armando Sánchez Vargas
• Economics Research Institute UNAM

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I.- Motivation

• Stata is a powerful and flexible statistical
  package for modeling time series.
• Prospective and advanced users would want to
  know
• SVAR modeling facilities the package offers.
• The main advantages of Stata compared with other
  time series packages.
• What is still needed and what might be refined
  to implement the whole SVAR methodology in Stata.

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II.- Objectives

• The main purpose of this presentation is to
  discuss STATAs 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.

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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.

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III.- SVAR Methodology

• In the presence of unit roots the
  structuralisation of a VAR model can take place
  at three distinct stages

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III.- SVAR Methodology

• 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).

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III.- SVAR Methodology

• 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.
• ()

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III.- SVAR Methodology

• Then, we start with an exactly-identified
  structure given by the lower triangular
  decomposition of the variance-covariance matrix
  of the estimated VAR disturbances and restrict
  the non-significant parameters to zero moving to
  a situation of over-identification (i.e).

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III.- SVAR Methodology

1. 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.

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The model selection strategy
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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.

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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.

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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.

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Statas capabilities Univariate Analysis
Capabilities PcGive STATA RATS
Graphics yes yes yes
Autocorrelation Functions yes yes yes
Unit Root Test yes yes yes
Unit Root Test ADF ADF ADF
Unit Root Test PP PP
Unit Root Test KPSS SCP
Unit Root Test   DF-GLS  
Note ADFAugmented Dickey-Fuller Test. PPPhillips Perron. KPSSKwiatkowski-Phillips-Schmidt-Shin. SCPSchmidt Phillips. DF-GLSDickey-Fuller GLS. Note ADFAugmented Dickey-Fuller Test. PPPhillips Perron. KPSSKwiatkowski-Phillips-Schmidt-Shin. SCPSchmidt Phillips. DF-GLSDickey-Fuller GLS. Note ADFAugmented Dickey-Fuller Test. PPPhillips Perron. KPSSKwiatkowski-Phillips-Schmidt-Shin. SCPSchmidt Phillips. DF-GLSDickey-Fuller GLS. Note ADFAugmented Dickey-Fuller Test. PPPhillips Perron. KPSSKwiatkowski-Phillips-Schmidt-Shin. SCPSchmidt Phillips. DF-GLSDickey-Fuller GLS.
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Statas capabilities Model Specification and
Estimation
Capabilities PcGive STATA RATS Malcom
Automatic Seasonal Dummies yes no yes
Maximum lag yes yes yes
Trend polynomial yes yes yes
Cointegration ranks yes yes yes
Exogenous variables yes yes yes
VAR estimation yes yes yes
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Statas capabilities Misspecificacion Tests
Capabilities PcGive PcGive STATA STATA RATS 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 yes yes no yes yes no
Parameters Stability yes yes no no no yes
Linearity no no no no no no
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Statas capabilities Statistial Inferences based
on the model
Capabilities PcGive STATA RATS
Maximum lag yes yes yes
Tests for trend polynomial no no yes
Test for joint determination of cointegration rank and deterministic polynomial no no yes
Trace Test in the I(1) model yes yes yes
Tests for r, s in the I(2) model no no yes
Parameters stabilityrank and cointegrating space no no yes
Roots the Model yes yes yes
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Statas capabilities Automatic test
Capabilities PcGive STATA RATS
Weak exogeneity test no no yes
Indentification no no yes
Granger causality no yes yes
Tests on a y ß yes yes yes
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Statas capabilities Structural VAR analysis
whit stationary and non stationary variables
Capabilities PcGive PcGive STATA STATA RATS RATS
  Stationary Non stationary 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
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Conclusions

• Commands are appropiate for basic use.
• Improvements in routines for advanced users.

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Conclusions

• What is needed
• Addition of some other Unit Roots Tests.
• The VAR capabilities could benefit by the
  addition of single and joint misspecification
  tests.
• 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 stabilityrank and
  cointegrating space.
• Considered the cointegrated SVAR model

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Conclusions

• What might be refined
• It should automatically include seasonals.
• It should automatic include tests in the I(1)
  model.

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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.

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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 2003-W15.
• Sarte, P.D. (1997) On the Identification of
  Structural Vector Auto Regressions. Federal
  Reserve Bank of Richmond, Canada, Sum 45-68.