<p></p><p>Panel cointegration Test</p><p>Westerlund(2007) and&nbsp; 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：</p><p><font size="2">. xtwest loghex loggdp, westerlund constant trend lags(1 3) leads(0 3) lrwindow(3)</font></p><p><font size="2">Calculating Westerlund ECM panel cointegration tests..........</font></p><p><font size="2">Results for H0: no cointegration<br/>With 20 series and 1 covariate<br/>Average AIC selected lag length: 2.8<br/>Average AIC selected lead length: 1.65</font></p><p><br/><font size="2">Statistic&nbsp;&nbsp;&nbsp; Value&nbsp;&nbsp;&nbsp;&nbsp; Z-value&nbsp;&nbsp;&nbsp; P-value&nbsp; </font></p><p><font size="2">Gt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -4.082&nbsp;&nbsp;&nbsp;&nbsp; -9.613&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp; <br/>Ga&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -27.702&nbsp;&nbsp;&nbsp; -10.626&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp; <br/>Pt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -12.969&nbsp;&nbsp;&nbsp;&nbsp; -4.100&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp; <br/>Pa&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -22.470&nbsp;&nbsp;&nbsp; -10.119&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp; </font></p><p><br/><font size="2">. xtwest loghex loggdp, westerlund constant trend lags(1) leads(1) lrwindow(3) bootstrap(100)</font></p><p><font size="2">Bootstrapping critical values under H0..........<br/>Calculating Westerlund ECM panel cointegration tests..........</font></p><p><font size="2">Results for H0: no cointegration<br/>With 20 series and 1 covariate</font></p><p><br/><font size="2">Statistic&nbsp;&nbsp;&nbsp; Value&nbsp;&nbsp;&nbsp;&nbsp; Z-value&nbsp;&nbsp;&nbsp; P-value&nbsp;&nbsp; Robust P-value </font></p><p><font size="2">Gt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -3.150&nbsp;&nbsp;&nbsp;&nbsp; -4.424&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.050&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br/>Ga&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -31.274&nbsp;&nbsp;&nbsp; -13.027&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br/>Pt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -13.809&nbsp;&nbsp;&nbsp;&nbsp; -5.079&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.040&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br/>Pa&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -26.770&nbsp;&nbsp;&nbsp; -13.339&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </font></p><p></p><p></p><p><br/>----------------------------------------------------------------------------------------------------------------<br/>help for xtwest<br/>----------------------------------------------------------------------------------------------------------------</p><p>Westerlund error correction based panel cointegration tests</p><p><br/>&nbsp;&nbsp;&nbsp; xtwest depvar varlist [if exp] [in range] , lags(# [#]) leads(# [#]) lrwindow(#) [constant trend<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; bootstrap(#) westerlund noisily]</p><p>&nbsp;&nbsp;&nbsp; xtwest is for use with panel data.&nbsp; You must tsset your data before using xtwest; see help tsset.</p><p><br/>Description</p><p><br/>&nbsp;&nbsp;&nbsp; xtwest implements the four panel cointegration tests developed by Westerlund (2007). The underlying idea<br/>&nbsp;&nbsp;&nbsp; is to test for the absence of cointegration by determining whether there exists error correction for<br/>&nbsp;&nbsp;&nbsp; individual panel members or for the panel as a whole.&nbsp; Consider following error correction model, where<br/>&nbsp;&nbsp;&nbsp; all variables in levels are assumed to be I(1):</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D.y_it = c_i + a_i1*D.y_it-1 + a_i2*D.y_it-2 + ... +&nbsp; a_ip*D.y_it-p</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + b_i0*D.x_it + b_i1*D.x_it-1 + ... + b_ip*D.x_it-p</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + a_i(y_it-1 - b_i*x_it-1) + u_it</p><p>&nbsp;&nbsp;&nbsp; a_i provides an estimate of the speed of error-correction towards the long run equilibrium<br/>&nbsp;&nbsp;&nbsp; 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<br/>&nbsp;&nbsp;&nbsp; versus H1: a_i &lt; 0 for at least one i. These statistics start from a weighted average of the individualy<br/>&nbsp;&nbsp;&nbsp; estimated a_i's and their t-ratio's respectively. The Pa and Pt test statistics pool information over all<br/>&nbsp;&nbsp;&nbsp; the cross-sectional units to test H0: a_i = 0 for all i vs H1:&nbsp; a_i &lt; 0 for all i. Rejection of H0 should<br/>&nbsp;&nbsp;&nbsp; therefore be taken as rejection of cointegration for the panel as a whole.</p><p>&nbsp;&nbsp;&nbsp; The tests are very flexible and allow for an almost completely heterogeneous specification of both the<br/>&nbsp;&nbsp;&nbsp; long- and short-run parts of the error correction model, where the latter can be determined from the data.<br/>&nbsp;&nbsp;&nbsp; The series are allowed to be of unequal length.</p><p>&nbsp;&nbsp;&nbsp; If the cross sectional units are suspected to be correlated, robust critical values can be obtained<br/>&nbsp;&nbsp;&nbsp; through bootstrapping.</p><p><br/>Citation</p><p>&nbsp;&nbsp;&nbsp; xtwest is not an official Stata command. If you use xtwest please cite Persyn, D. and J. Westerlund. 2008.<br/>&nbsp;&nbsp;&nbsp; Error Correction Based cointegration Tests for Panel Data. Stata Journal, forthcoming.</p><p><br/>Options</p><p>&nbsp;&nbsp;&nbsp; lags(# [#]) If one number is specified, it determines a fixed number of lags pi to be included in the<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; error correction equations.&nbsp; f two numbers are specified the Akaike information criterion is used to<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; determine an optimal lag length pi for each separate time series, within the given limits.</p><p>&nbsp;&nbsp;&nbsp; leads(# [#]) Similar to the option lags it determines the number of leads to be included in the error<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; correction equations.</p><p>&nbsp;&nbsp;&nbsp; lrwindow(#) Sets the width of the Bartlett kernel window used in the semi-parametric estimation of long<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; run variances.</p><p>&nbsp;&nbsp;&nbsp; constant When given, a constant is added to the cointegration relationship.&nbsp; trend Allows for a<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; deterministic trend in the cointegration relationship.</p><p>&nbsp;&nbsp;&nbsp; trend Allows for a deterministic trend in the cointegration relationship.</p><p>&nbsp;&nbsp;&nbsp; bootstrap(#) This option shows bootstrapped p-values for all four test statistics.&nbsp; These are robust in<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the presence of common factors in the time series. The argument determines the number of bootstrap<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; replications. On Stata/IC the number of replications must be smaller than 800.</p><p>&nbsp;&nbsp;&nbsp; westerlund This option is used only to replicate the tables in Westerlund (2007).</p><p>&nbsp;&nbsp;&nbsp; noisily With this option xtwest shows the regressions for the separate series.&nbsp; If a range of lags or<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; leads is given, only the regression chosen by the AIC is shown.</p><p>References</p><p>&nbsp;&nbsp;&nbsp; Persyn, D. and J. Westerlund. 2008. Error Correction Based Cointegration Tests for Panel Data. Stata<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Journal, forthcoming.</p><p>&nbsp;&nbsp;&nbsp; Westerlund, J. 2007. Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Statistics 69(6): 709-748.</p><p><br/>&nbsp;</p><p>程序下载：</p><br/>

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