Panel cointegration Test

Westerlund(2007) and  Westerlund(2008) 面板协整之误差修正技术协整检验，为网友消除面板协整之痛苦，带来迅速简洁之快乐。源程序和说明下载见后。运用下载包中的数据，可以获得如下演示结果：

. xtwest loghex loggdp, westerlund constant trend lags(1 3) leads(0 3) lrwindow(3)

Calculating Westerlund ECM panel cointegration tests..........

Results for H0: no cointegration
With 20 series and 1 covariate
Average AIC selected lag length: 2.8
Average AIC selected lead length: 1.65

Statistic    Value     Z-value    P-value 

Gt       -4.082     -9.613     0.000  
Ga      -27.702    -10.626     0.000  
Pt      -12.969     -4.100     0.000  
Pa      -22.470    -10.119     0.000  

. xtwest loghex loggdp, westerlund constant trend lags(1) leads(1) lrwindow(3) bootstrap(100)

Bootstrapping critical values under H0..........
Calculating Westerlund ECM panel cointegration tests..........

Results for H0: no cointegration
With 20 series and 1 covariate

Statistic    Value     Z-value    P-value   Robust P-value

Gt       -3.150     -4.424     0.000         0.050     
Ga      -31.274    -13.027     0.000         0.000     
Pt      -13.809     -5.079     0.000         0.040     
Pa      -26.770    -13.339     0.000         0.000     

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help for xtwest
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Westerlund error correction based panel cointegration tests

    xtwest depvar varlist [if exp] [in range] , lags(# [#]) leads(# [#]) lrwindow(#) [constant trend
        bootstrap(#) westerlund noisily]

    xtwest is for use with panel data.  You must tsset your data before using xtwest; see help tsset.

Description

    xtwest implements 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. 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 rejection 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

    xtwest is not an official Stata command. If you use xtwest please cite Persyn, D. and J. Westerlund. 2008.
    Error Correction Based cointegration Tests for Panel Data. Stata Journal, forthcoming.

Options

    lags(# [#]) If one number is specified, it determines a fixed number of lags pi 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.

    constant When given, a constant is added to the cointegration relationship.  trend Allows for a
        deterministic trend in the cointegration relationship.

    trend Allows 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.

    westerlund This option is used only to replicate the tables in Westerlund (2007).

    noisily With 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.

References

    Persyn, D. and J. Westerlund. 2008. Error Correction Based Cointegration Tests for Panel Data. Stata
        Journal, forthcoming.

    Westerlund, J. 2007. Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and
        Statistics 69(6): 709-748.

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• xtwest.ado
• xtwest.do

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