svar modeling in stata armando sánchez vargas economics research institute unam

SVAR Modeling in STATA

Armando Sánchez Vargas

Economics Research Institute UNAM

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.

I.- Motivation

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.

II.- Objectives

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.


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


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).


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.

(*)

ttt zzL 1')(


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).

t

t

t

t

t

t

t

t

ii

yy

mm

e

ii

yy

mm

e

u

u

u

u

b

b

b

baaa

*)(

*)(

)(

44

33

22

11

*)(

*)(

)(

141312

**

000

000

000

000

1000

0100

0010

1


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

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.


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 RATSGraphics yes yes yes

Autocorrelation Functions yes yes yes

Unit Root Test

yes yes yes

ADF ADF ADF

PP PP

KPSS SCP

DF-GLS Note: ADF=Augmented Dickey-Fuller Test. PP=Phillips Perron.

KPSS=Kwiatkowski-Phillips-Schmidt-Shin. SCP=Schmidt Phillips. DF-GLS=Dickey-Fuller GLS.

Stata’s capabilities: Model Specification and Estimation

Capabilities PcGiveSTAT

ARATSMalcom

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

Stata’s capabilities: Misspecificacion Tests

Capabilities PcGive STATA RATSSingle 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

Stata’s capabilities: Statistial Inferences based on the model

Capabilities PcGive STATA RATS

Maximum lag yes yes yes

Tests for trend polynomial no no yesTest for joint determination of cointegration rank and deterministic polynomial

no no yes

Trace Test in the I(1) model yes yes yesTests for r, s in the I(2)

model no no yesParameters stability:rank and cointegrating space no no yes

Roots the Model yes yes yes

Stata’s capabilities: Automatic test


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


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

Commands are appropiate for basic use.

Improvements in routines for advanced users.

Conclusions

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.

ConclusionsThe 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.

BibliographyAlan 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.

svar modeling in stata armando sánchez vargas economics research institute unam

Documents