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Title

xtwest-- Westerlund error-correction-based panel cointegration tests

Syntax

xtwestdepvarvarlist[ifexp] [inrange],lags(# [#])leads(# [#])lrwindow(#)[constanttrendbootstrap(#)westerlundnoisilymg]

xtwestis for use with panel data. You musttssetyour data before usingxtwest; see help tsset.

Description

xtwestimplements the four panel cointegration tests developed by Westerlund (2007). The underlying idea is to test for the absence of cointegration by determining whether there exists error correction for individual panel members or for the panel as a whole. Consider following error correction model, where all variables in levels are assumed to be I(1):D.y_it = c_i + a_i1*D.y_it-1 + a_i2*D.y_it-2 + ... + a_ip*D.y_it-p

+ b_i0*D.x_it + b_i1*D.x_it-1 + ... + b_ip*D.x_it-p

+ a_i(y_it-1 - b_i*x_it-1) + u_it

a_i provides an estimate of the speed of error-correction towards the long run equilibrium y_it = - (b_i/a_i) * x_it for that series i. The Ga and Gt test statistics test H0: a_i = 0 for all i versus H1: a_i < 0 for at least one i. These statistics start from a weighted average of the individualy estimated a_i's and their t-ratio's respectively. Rejection of H0 should therefore be taken as evidence of cointegration of at least one of the cross-sectional units. The Pa and Pt test statistics pool information over all the cross-sectional units to test H0: a_i = 0 for all i vs H1: a_i < 0 for all i. Rejection of H0 should therefore be taken as evidence of cointegration for the panel as a whole.

The tests are very flexible and allow for an almost completely heterogeneous specification of both the long- and short-run parts of the error correction model, where the latter can be determined from the data. The series are allowed to be of unequal length.

If the cross sectional units are suspected to be correlated, robust critical values can be obtained through bootstrapping.

Citation

xtwestis not an official Stata command. If you usextwestplease cite Persyn, D. and J. Westerlund. 2008. Error Correction Based cointegration Tests for Panel Data.Stata Journal8 (2), 232-241.

Options

lags(#[#])If one number is specified, it determines a fixed number of lags p to be included in the error correction equations. f two numbers are specified the Akaike information criterion is used to determine an optimal lag length pi for each separate time series, within the given limits.

leads(#[#])Similar to the option lags it determines the number of leads to be included in the error correction equations.

lrwindow(#)Sets the width of the Bartlett kernel window used in the semi-parametric estimation of long run variances.

constantWhen given, a constant is added to the cointegration relationship.

trendAllows for a deterministic trend in the cointegration relationship.

bootstrap(#)This option shows bootstrapped p-values for all four test statistics. These are robust in the presence of common factors in the time series. The argument determines the number of bootstrap replications. On Stata/IC the number of replications must be smaller than 800.

westerlundThis option should be used only to replicate the tables in Westerlund (2007).

noisilyWith this option xtwest shows the regressions for the separate series. If a range of lags or leads is given, only the regression chosen by the AIC is shown.

mgIf specified, xtwest reports the mean group error-correction model, averaging coefficients of the error-correction equation over all cross-sectional units, together with the implied long-run relationship. This is much like the output ofxtpmgwith the "mg" option, but allowing for different lag and lead lengths in the different cross-sectional units.

Examplesuse http://fmwww.bc.edu/repec/bocode/x/xtwestdata.dta

In many applications at least a constant term is added to the cointegration equation xtwest loghex loggdp, constant lags(1 3) leads(0 3) lrwindow(3)

Bootstrapping takes a long time unless the lead and lag lengths are fixed xtwest loghex loggdp, constant trend lags(1) leads(1) lrwindow(3) bootstrap(100)

The westerlund option should only be used to replicate the results of Westerlund (2007) xtwest loghex loggdp, westerlund constant trend lags(1 3) leads(0 3) lrwindow(3) xtwest loghex loggdp, westerlund constant trend lags(1) leads(1) lrwindow(3) bootstrap(100)

ReferencesPersyn, D. and J. Westerlund. 2008. Error Correction Based Cointegration Tests for Panel Data.

Stata Journal8 (2), 232-241.Westerlund, J. 2007. Testing for Error Correction in Panel Data.

OxfordBulletin of Economics and Statistics69(6): 709-748.

AuthorsDamiaan Persyn (corresponding author) LICOS, Centre for Institutions and Economic Performance Katholieke Universiteit Leuven Leuven, Belgium damiaan.persyn@econ.kuleuven.be

Joakim Westerlund Department of Economics Lund University Lund, Sweden joakim.westerlund@nek.lu.se

Also seeArticle:

Stata Journal, volume 8, number 2: st0146

Online:

ipshin,hadrilm,xtfisher,xtpmg(if installed)