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{title:Levin-Lin-Chu panel unit root test}

{p 8 14}{cmd:levinlin} {it:varname} 
[{cmd:if} {it:exp}] [{cmd:in} {it:range}] {cmd:,lags({it:numlist})} [ {cmdab:noc:onstant}
{cmdab:t:rend} ]

{p}{cmd:levinlin} is for use with panel data.  You must {cmd:tsset} your
data before using {cmd:levinlin}, using the panel form of {cmd:tsset}; see help {help tsset}.

{p} {it:varname} may contain time-series operators; see help {help varlist}.

{p} Users of Stata 11+ should use the official {cmd:xtunitroot llc} command.

{title:Description}

{p}{cmd:levinlin} estimates the panel unit root test developed by Levin, Lin and Chu (LLC, 2002). 
The test assumes that each individual unit in the panel shares the same AR(1) coefficient,
but allows for individual effects, time effects and possibly a time trend. Lags of the
dependent variable may be introduced to allow for serial correlation in the errors. The test may
be viewed as a pooled Dickey-Fuller test, or an Augmented Dickey-Fuller (ADF) test when lags are
included, with the null hypothesis that of nonstationarity (I(1) behavior). 
After transformation by factors provided by LLC, the t-star statistic is  
distributed standard normal under the null hypothesis of nonstationarity.

The test differs from Taylor and Sarno's (1998) multivariate ADF test, 
{help madfuller}, in that the latter is estimated using the seemingly unrelated 
regressions (SUR) estimator (that is, with an equation for each individual) under 
the same constraint of a single autoregressive parameter across individuals. 
The MADF test cannot be employed on large-N, small-T panels, since T must exceed N 
in standard SUR. This restriction does not apply to the LLC test.

{p}


{title:Options}

{p 0 4}{cmd:lags} must be specified, and may take on any non-negative value. If a single
value is provided, that lag length is used for all individuals. If a list of lags is 
provided (perhaps with a local macro), its length must match the number of individuals
in the panel.

{p 0 4}{cmd:noconstant} omits the constant term from the estimated equation (LLC case 1).

{p 0 4}{cmd:trend} includes a time trend in the estimated equation (LLC case 3).

{title:Examples}

{p 8 12}{inp:.} {stata "use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear":use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear}

{p 8 12}{inp:.} {stata levinlin rgdppc if country<11, lag(2)}

{p 8 12}{inp:.} {stata levinlin rgdppc if country<11, lag(2 2 2 3 3 3 4 4 4 4)}

{p 8 12}{inp:.} {stata levinlin D.rgdppc if country<11, lag(2) trend}

{title:References}

Banerjee, Anindya. Panel Data Unit Roots and Cointegration: An Overview.
Oxford Bulletin of Economics and Statistics, Special Issue, 607-629, 1999.

Levin, Andrew, Lin, Chien-Fu and Chia-Shang James Chu. Unit Root Tests in 
Panel Data: Asymptotic and Finite Sample Properties. Journal of Econometrics, 
108, 1-24, 2002.

Maddala, G.S. and In-Moo Kim. Unit Roots, Cointegration, and Structural Change,
Cambridge: Cambridge University Press, 1998.

Taylor, Mark P. and Lucio Sarno. The behavior of real exchange rates during
the post-Bretton Woods period. Journal of International Economics, 46,
1998, 281-312.

{title:Acknowledgements}

We are very grateful to Gene Liang for pointing out discrepancies in this
routine and providing detailed output from his routines, to J.J.A. Ewalts for 
bringing an issue with lag truncation to our attention, to Claudio E. Raddatz
for pointing out a flaw in our error-checking logic and to Lilin Liang
for detecting a problem with tempnames. Remaining errors are
ours.

{title:Authors}

Fabian Bornhorst, European University Institute, Italy, Fabian.Bornhorst@iue.it
Christopher F Baum, Boston College, USA, baum@bc.edu


{title:Also see}

{p 0 19}On-line:  help for {help est}, {help reg3}, {help dfuller}, {help madfuller} (if installed)  {p_end}