{smcl}
{viewerjumpto "Syntax" "examplextgrangert##syntax"}{...}
{viewerjumpto "Description" "examplextgrangert##description"}{...}
{viewerjumpto "Options" "examplextgrangert##options"}{...}
{viewerjumpto "Examples" "examplextgrangert##examples"}{...}
{viewerjumpto "Stored results" "exampleproject##stored results"}{...}
{title:Title}
{phang}
{bf:[xt] xtgrangert} {hline 2} Testing for Granger non-causality in heterogeneous panel data models, using the methodology developed by Juodis, Karavias, and Sarafidis (2021).

{marker syntax}{...}
{title:Syntax}
{phang}
{p 8 16 2}{cmdab:xtgrangert} {depvar} [{indepvars}] [if] [in] 
[, lags(integer) maxlags(integer) het {ul:boot}strap[({it:options})] sum nodfc lagoverlap] 

{smcl}

{p 4 6 2}
You must {cmd:xtset} your data before using {cmd:xtgrangert}; see {helpb xtset:[XT] xtset}. 
Unbalanced panels are allowed in which case the variance for the calculation of the HPJ statistic is
bootstrapped.{p_end}

{smcl}

{marker description}{...}
{title:Description}

{pstd}
{cmd:xtgrangert} performs the Half-Panel Jackknife (HPJ) Wald-type test for Granger non-causality, developed by Juodis, Karavias, and Sarafidis (2021). 
This test offers superior size and power performance, which stems from the use of a pooled estimator with a sqrt(NT) rate of convergence. 
The test has two other useful properties; it can be used in multivariate systems and it has power against both homogeneous as well as heterogeneous alternatives.
The test allows for cross-sectional dependence and cross-sectional heteroskedasticity. 
The command also reports results for the HPJ estimator with overlapping half panels.
In the presence of cross-sectional dependence the variance of the HPJ estimator can be obtained by bootstrapping.
The bootstrap resamples across the cross-sectional dimension.
{break}
{cmd:xtgrangert} internally adds lags of the dependent variable with heterogeneous slope coefficients when calculating the HPJ test statistic and estimating the HPJ estimator.
The lags are partialled out and their estimation results are not presented in the output.
{smcl}

{marker options}{...}
{title:Options}
{dlgtab:Main}
{phang}
{opt lags():} specifies the number of lags of dependent and independent variables to be added to the regression. If {cmd:lags()} is not specified, the default is {cmd:lags(1)}.
The lags of the dependent variable are partialled out.{p_end}

{phang}
{opt maxlags:()} specifies the upper bound of lags. The BIC criterion is used to select the number of lags that provides the best model fit. {cmd:lags()} and {cmd:maxlags()} cannot be used at the same time.{p_end} 

{phang}
{opt lagoverlap} allows lags to overlap between the half panels.{p_end}

{dlgtab:SE/Robust}
{phang}
{opt het} allows for cross-sectional heteroskedasticity.

{phang}
{opt nodfc} does not apply a degrees of freedom correction in the computation of the variance-covariance matrix of the HPJ estimator. This option is mostly useful under cross-sectional heteroskedasticity.

{dlgtab:Bootstrap}
{phang}
{opt boot:strap} employs a bootstrap variance estimator in the HPJ Wald statistic, statistic, which allows for cross-sectional dependence. 100 repetitions are used based on the current seed.

{phang}
{opt boot:strap}{cmd:(}{it:#reps}{cmd:, seed({help seed}))} employs a bootstrap variance estimator in the HPJ Wald statistic, which allows for cross-sectional dependence with a custom {help seed} and {it:#reps} repetitions.

{dlgtab:Reporting}
{phang}
{opt sum} presents results on the sum of the estimated feedback coefficients. This option can be useful when the number of lags is greater than 1.


{marker results}{...}
{title:Stored results}

{pstd}
{cmd:xtgrangert} stores the following in {cmd:e()}:

{synoptset 20 tabbed}{...}
{p2col 5 20 24 2: Scalars}{p_end}
{synopt:{cmd:e(N)}}Number of individual units{p_end}
{synopt:{cmd:e(T)}}Number of time periods{p_end}
{synopt:{cmd:e(p)}}Number of lags{p_end}
{synopt:{cmd:e(BIC)}}BIC values{p_end}
{synopt:{cmd:e(W_HPJ)}}The Wald test statistic{p_end}
{synopt:{cmd:e(pvalue)}}P-value for the HPJ Wald test{p_end}

{synoptset 20 tabbed}{...}
{p2col 5 20 24 2: Matrices}{p_end}
{synopt:{cmd:e(b_HPJ)}}The HPJ coefficient estimator{p_end}
{synopt:{cmd:e(Var_HPJ)}}The variance-covariance matrix of the HPJ estimator {p_end}
{synopt:{cmd:e(b_Sum_HPJ)}}Sum of the HPJ estimates for the feedback coefficients{p_end}
{synopt:{cmd:e(Var_Sum_HPJ)}}The variance of the sum of the HPJ estimators {p_end}


{marker postestimation}{...}
{title:Postestimation commands}
{phang}
Predict can be used after {cmd:xtgrangert}. The residuals and predicted values will be stored in {newvar}.{p_end}

{phang}
{p 8 16 2}{cmd:predict} {newvar} [if] [in] 
[, {ul:res}iduals xb] 
{smcl}
{marker options}{...}
{title:Postestimation options}

{phang}
{opt res:iduals:} calculates the residuals.{p_end}

{phang}
{opt xb} calculates the linear prediction on the partialled out variables.{p_end} 


{marker examples}{...}
{title:Examples}

{phang} The dataset ``xtgrangert_example.dta'' used in this example is downloadable from
{browse "https://sites.google.com/site/yianniskaravias/files/xtgranger"}.

{pstd}xtset the data{p_end}
{phang2}{cmd:xtset cert time} 

{pstd}Dynamic model with given lags{p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, lags(2)} 

{pstd}Dynamic model with given lags, cross-sectional heteroskedasticity-robust standard errors {p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, lags(2) het}

{pstd}Dynamic model with given lags and cross-sectional heteroskedasticity-robust standard errors. It reports the sum of the lagged coefficients {p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, lags(2) het sum}

{pstd}Dynamic model with lag length selection (up to 4 lags) based on BIC, with cross-sectional heteroskedasticity-robust standard errors {p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, maxlags(4) het}{p_end}

{pstd}Dynamic model with lag length selection (up to 4 lags) based on BIC, with cross-sectional heteroskedasticity-robust standard errors, and no variance degrees-of-freedom correction {p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, maxlags(4) het nodfc}{p_end}

{pstd}Bootstrap variance of the HPJ estimator that allows for cross-sectional dependence, 
with a default of 100 repetitions{p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, bootstrap}{p_end}

{pstd}Bootstrap variance of the HPJ estimator that allows for cross-sectional dependence, 
with 200 repetitions and control of the {help seed}{p_end}
{phang2}{cmd:xtgrangert roa inefficiency quality, bootstrap(200, seed(123))}{p_end}

{title:References}
{p}
{p_end}
{pstd}

Dhaene, G., Jochmans, K., 2015. Split-panel Jackknife estimation of fixed-effect models. Rev Econ Stud, 82:991–1030

Juodis, A., Karavias, Y., and Sarafidis, V., 2021. A homogeneous approach to testing for Granger non-causality in heterogeneous panels. Empir Econ 60, 93–112. {browse "https://doi.org/10.1007/s00181-020-01970-9"}

Xiao, J., Juodis, A., Karavias, Y., Sarafidis, V., and Ditzen, J., 2022. Improved Tests for Granger Causality in Panel Data. Submitted to the Stata Journal.


{title:Acknowledgements}
{p}
{p_end}
{pstd}
{cmd:xtgrangert} is not an official Stata command. It is a free contribution to the research community. 
Please cite Xiao et al (2022) and Juodis et al (2021), as listed in the references above.
{cmd:xtgrangert} was previously called {cmd:xtgranger}.

{title:Authors}
{p}
{p_end}

{pstd}
Jiaqi Xiao{break}
University of Birmingham{break}
Birmingham, UK{break}
{browse "mailto:Jxx963@outlook.com?subject=Question/remark about -xtgrangert-&cc=Jxx963@outlook.com":Jxx963@outlook.com}

{pstd}
Arturas Juodis{break}
University of Amsterdam{break}
Amsterdam, Netherlands{break}
{browse "mailto:a.juodis@uva.nl?subject=Question/remark about -xtgrangert-&cc=i.Karavias@bham.ac.uk":a.juodis@uva.nl}

{pstd}
Yiannis Karavias{break}
University of Birmingham{break}
Birmingham, UK{break}
{browse "mailto:i.Karavias@bham.ac.uk?subject=Question/remark about -xtgrangert-&cc=i.Karavias@bham.ac.uk":i.Karavias@bham.ac.uk}

{pstd}
Vasilis Sarafidis{break}
BI Norwegian Business School{break}
Oslo, Norway{break}
{browse "mailto:vasilis.sarafidis@bi.no?subject=Question/remark about -xtgrangert-&cc=vasilis.sarafidis@bi.no":vasilis.sarafidis@bi.no}

{pstd}
Jan Ditzen{break}
Free University of Bozen-Bolzano{break}
Bozen, Italy{break}
{browse "mailto:jan.ditzen@unibz.it?subject=Question/remark about -xtgrangert-&cc=jan.ditzen@unibz.it":jan.ditzen@unibz.it}

{title:Version}

{p 4}This version 1.13 - 09.01.2023{p_end}

{p 4}{ul:Change Log}{p_end}
{p 4}Version 1.12 to 1.13{p_end}
{p 6}- added unbalanced panel support{p_end}
{p 6}- default is non overlapping panels{p_end}
{p 6}- added Option lagoverlap to allow for overlaps when using lags{p_end}