Pesaran's simple panel unit root test in presence of cross section dependence
pescadf varname [if exp] [in range] ,lags(numlist) [ trend nodemean trunoff]
pescadf is a test for panel data. You should tsset your data before using pescadf, using the panel form of tsset; see help tsset.
varname may contain time-series operators; see help varlist.
Description
pescadf runs the t-test for unit roots in heterogenous panels with cross-section dependence, proposed by Pesaran (2003). Parallel to Im, Pesaran and Shin (IPS, 2003) test, it is based on the mean of individual DF (or ADF) t-statistics of each unit in the panel. Null hypothesis assumes that all series are non-stationary. To eliminate the cross dependence, the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series (CADF statistics). Considered is also a truncated version of the CADF statistics which has finite first and second order moments. It allows to avoid size distortions, especially in the case of models with residual serial correlations and linear trends (Pesaran, 2003).
In the case where T is fixed, to ensure that the CADF statistics do not depend on the nuisance parameters the effect of the initial cross-section mean must also be eliminated, this can be achieved by applying the test to the deviations of the variable from initial crosssection mean Pesaran (2003). Lags of the dependent variable may be introduced to control for serial correlation in the errors. The order of augmentation, can be estimated using model selection criteria such as Akaike or Schwartz applied as usual to the underlying time series specification.
The exact critical values of the t-bar statistic are given by Pesaran (2003). The critical values and summary statistics of the individual t are also given in the paper, so the Z[t-bar] statistic parallel to IPS (2003) Z[t-bar] (4.10) is distributed standard normal under the null hypothesis of nonstationarity. Moreover, Pesaran (2003) suggests that generalization of the test to unbalanced panels can be made straightforwardly as IPS (2003) show. Hence in case of unbalanced panels only standarized Z[t-bar] statistics can be computed.
Analogous to IPS (2003) test, Pesaran's CADF is consistent under the alternative that only a fraction of the series are stationary.
Options
lags must be specified, and may be uqual to any non-negative integer. Provided should be or single value which determines the lag length for all units in panel, or a list of lags matching the number of units in the panel.
trend includes a time trend in the estimated equation.
nodemean neglects eliminating initial cross-section mean from the variable tested. Applying the test to such deviations is default version because it is suggested by Pesaran (2003).
trunoff As CADF statistics has no finite first and second moments, Pesaran (2003) suggest replacing extreme values of the test statistics by K1 or K2 such that Pr [-K1 < ti(N, T) < K2] is sufficiently large, namely in excess of 0.9999. Pesaran (2003) simulates K1 and K2 for 3 types of model depending on the deterministic part (no deterministics; intercept, intercept and linear trend)
Examples
. use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear
. pescadf rgdppc if country>116 & country<140, lags(2)
. pescadf rgdppc if country>116 & country<140, lags(2) trend
. pescadf rgdppc if country>116 & country<140, lags(2) trend trunoff
. pescadf D.rgdppc if country>116 & country<140, lags(1)
References
Breitung, J., Pesaran, H., (2005), Unit Roots and Cointegration in Panels, CESIFO Working Paper No. 1565
Im, K., Pesaran, H., Shin, Y., (2003), Testing for unit roots in heterogenous p > anels, Journal of Econometrics, vol. 115.
Pesaran, H., (2003), A Simple Panel Unit Root Test in the Presence of Cross Sec > tion Dependence, Cambridge Working Papers in Economics 0346, Faculty of Economics (DAE), Univers > ity of Cambridge
Acknowledgements
This routine was inspired by C. F. Baum's & F. Bornhorst's -ipshin- routine.
Author
Piotr Lewandowski, Warsaw School of Economics, Institute for Structural Researc > h, Poland, Piotr.Lewandowski@sgh.waw.pl
Also see
On-line: help for dfuller, madfuller (if installed), ipshin (if installed), levinlin (if installed)