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SVAR Modeling in STATA Armando Sánchez Vargas Economics Research Institute UNAM

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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

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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

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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 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).

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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. (*)

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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 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.

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The model selection strategy

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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

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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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Stata’s capabilities: Univariate Analysis CapabilitiesPcGiveSTATARATS Graphicsyes Autocorrelation Functionsyes Unit Root Test yes ADF PP KPSSSCP DF-GLS Note: ADF=Augmented Dickey-Fuller Test. PP=Phillips Perron. KPSS=Kwiatkowski-Phillips-Schmidt-Shin. SCP=Schmidt Phillips. DF- GLS=Dickey-Fuller GLS.

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Stata’s capabilities: Model Specification and Estimation CapabilitiesPcGiveSTATA RATS Malcom Automatic Seasonal Dummiesyesnoyes Maximum lagyes Trend polynomialyes Cointegration ranksyes Exogenous variablesyes VAR estimationyes

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Stata’s capabilities: Misspecificacion Tests CapabilitiesPcGiveSTATARATS Single TestJoint TestSingle TestJoint TestSingle TestJoint Test Normalityyes noyes Homoskedasticityyes no No Autocorrelationyes noyes no Parameters Stabilityyes no yes Linearityno

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Stata’s capabilities: Statistial Inferences based on the model CapabilitiesPcGiveSTATARATS Maximum lagyes Tests for trend polynomialno yes Test for joint determination of cointegration rank and deterministic polynomial no yes Trace Test in the I(1) modelyes Tests for r, s in the I(2) modelno yes Parameters stability:rank and cointegrating spaceno yes Roots the Modelyes

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Stata’s capabilities: Automatic test CapabilitiesPcGiveSTATARATS Weak exogeneity testno yes Indentificationno yes Granger causalitynoyes Tests on α y βyes

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Stata’s capabilities: Structural VAR analysis whit stationary and non stationary variables CapabilitiesPcGiveSTATARATS Stationary Non stationaryStationary Non stationaryStationary Non stationary Estimationno yesnoyes Simulationno yesnoyes Graphicsno yesnoyes

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

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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

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Conclusions What might be refined: I.It should automatically include seasonals. II.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.

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