{smcl}
{* *! version 1.0.0  28may2026}{...}
{cmd:help xtcsnardl_postestimation}{right:also see:  {help xtcsnardl}  {help xtcsnardl_methodology}  {help xtcsnardl_examples}  {help xtcsnardl_graph}}
{hline}

{title:Post-estimation tools  {hline 2}  CS-NARDL}

{title:Contents}

{p 8 12 2}
{help xtcsnardl_postestimation##return:1.}  {cmd:e()} returns{break}
{help xtcsnardl_postestimation##testing:2.} Custom Wald tests with {cmd:test} / {cmd:lincom} / {cmd:nlcom}{break}
{help xtcsnardl_postestimation##predict:3.} Fitted values, residuals and the EC term{break}
{help xtcsnardl_postestimation##multipliers:4.} Recovering long-run and dynamic multipliers manually{break}
{help xtcsnardl_postestimation##cd:5.}     Independent CD diagnostics{break}
{help xtcsnardl_postestimation##estout:6.}  Exporting tables (estout / esttab){break}
{help xtcsnardl_postestimation##stability:7.} CUSUM, CUSUMSQ and stability diagnostics


{marker return}{...}
{title:1. e() returns}

{pstd}
{cmd:xtcsnardl} stores everything {cmd:xtpmg} stores, plus the CS-NARDL-specific entries
documented in {help xtcsnardl##return:the main help}.  Most useful:

{synoptset 28 tabbed}{...}
{synopthdr:Macros}
{synoptline}
{synopt:{cmd:e(cmd)}}always {cmd:xtcsnardl}{p_end}
{synopt:{cmd:e(estimator)}}{cmd:cs_nardl_pmg}, {cmd:cs_nardl_mg}, or {cmd:cs_nardl_dfe}{p_end}
{synopt:{cmd:e(depvar)}}dependent variable{p_end}
{synopt:{cmd:e(asymmetric)}}variables decomposed asymmetrically{p_end}
{synopt:{cmd:e(pos_vars)}}generated positive partial-sum variable names{p_end}
{synopt:{cmd:e(neg_vars)}}generated negative partial-sum variable names{p_end}
{synopt:{cmd:e(csa_vars)}}variables whose CSA was added as proxies{p_end}
{synopt:{cmd:e(ec_name)}}name of the EC equation (default {bf:ECT}){p_end}
{synopt:{cmd:e(ivar)}, {cmd:e(tvar)}}panel/time identifiers{p_end}
{synoptline}

{synopthdr:Scalars}
{synoptline}
{synopt:{cmd:e(npanels)}}N{p_end}
{synopt:{cmd:e(avg_T)}}average T{p_end}
{synopt:{cmd:e(cr_lags)}}CSA lag length used{p_end}
{synopt:{cmd:e(n_csa_orig)}}number of base CSA variables{p_end}
{synopt:{cmd:e(level)}}confidence level{p_end}
{synoptline}

{pstd}
{cmd:e(b)} and {cmd:e(V)} hold the full vector of coefficients (xtpmg layout):

{p 4 6 2}
{c 149} {bf:[ECT]varname} {hline 2} long-run coefficients (the cointegrating vector){p_end}
{p 4 6 2}
{c 149} {bf:[SR]D.varname} {hline 2} short-run differences (PMG/MG mean group){p_end}
{p 4 6 2}
{c 149} {bf:[SR]ECT} or {bf:[ec]ECT} {hline 2} pooled speed of adjustment{p_end}
{p 4 6 2}
{c 149} {bf:[ivar_i:.]} {hline 2} panel-specific coefficients (PMG/MG only){p_end}

{pstd}
Inspect with:

{phang2}{cmd:. ereturn list}{p_end}
{phang2}{cmd:. matrix list e(b)}{p_end}


{marker testing}{...}
{title:2. Custom Wald tests, lincom and nlcom}

{pstd}
The default Table 5 reports H{sub:0}: {&beta}{sup:+} = {&beta}{sup:-} for every variable in
{opt asymmetric()}.  You can run any linear or non-linear hypothesis using the standard Stata
tools.

{pstd}
{bf:(a) Long-run asymmetry on a single variable}

{phang2}{cmd:. test [ECT]x_pos = [ECT]x_neg}{p_end}

{pstd}
{bf:(b) Joint long-run asymmetry across several variables}

{phang2}{cmd:. test ([ECT]x_pos = [ECT]x_neg) ([ECT]z_pos = [ECT]z_neg)}{p_end}

{pstd}
{bf:(c) Test of additive long-run elasticity}

{phang2}{cmd:. lincom [ECT]x_pos + [ECT]x_neg}{p_end}

{pstd}
gives the net symmetric long-run elasticity (zero under symmetry by construction).

{pstd}
{bf:(d) Test of a specific magnitude}

{phang2}{cmd:. test [ECT]x_pos = -0.10}{p_end}

{pstd}
{bf:(e) Half-life as a non-linear function of phi}

{phang2}{cmd:. nlcom (HL: ln(2) / abs(_b[SR:ECT]))}{p_end}

{pstd}
{bf:(f) Sum of short-run coefficients (cumulative impact effect)}

{phang2}{cmd:. lincom [SR]D.x_pos + [SR]LD.x_pos + [SR]L2D.x_pos}{p_end}


{marker predict}{...}
{title:3. Fitted values, residuals and the error-correction term}

{pstd}
{cmd:xtpmg} provides a {cmd:predict} method that {cmd:xtcsnardl} inherits.

{phang2}{cmd:. predict yhat,  xb}             {hline 2} fitted {&Delta}y{p_end}
{phang2}{cmd:. predict uhat,  residuals}      {hline 2} idiosyncratic residual{p_end}
{phang2}{cmd:. predict ec,    ec}             {hline 2} cointegrating residual (long-run){p_end}

{pstd}
The {bf:ec} option requires that {opt ec(name)} was specified in estimation; the variable
{it:name} is generated by xtpmg during estimation and persists after.  Plot the panel
trajectories of the EC term to check cointegration visually:

{phang2}{cmd:. tsline ECT if country == 1}{p_end}
{phang2}{cmd:. xtline ECT}{p_end}


{marker multipliers}{...}
{title:4. Recovering long-run and dynamic multipliers manually}

{pstd}
The asymmetric long-run multipliers are just the cointegrating coefficients:

{phang2}{cmd:. lincom [ECT]x_pos}      {hline 2} m+(infty){p_end}
{phang2}{cmd:. lincom [ECT]x_neg}      {hline 2} m-(infty){p_end}
{phang2}{cmd:. lincom [ECT]x_pos - [ECT]x_neg}      {hline 2} asymmetry{p_end}

{pstd}
For the cumulative dynamic multipliers, the option {opt multip(#)} computes them automatically
(Table 8).  To export them to a dataset for custom plotting:

{cmd}
* re-run with multip and capture
qui xtcsnardl D.y L.y D.x, lr(L.y x) asymmetric(x) multip(20)

* manual recursion using e() returns
local phi = _b[SR:ECT]
local bp  = _b[ECT:x_pos]
local bn  = _b[ECT:x_neg]
local h   = 20
clear
qui set obs `=`h'+1'
gen h = _n - 1
gen mp = 0
gen mn = 0
local gp = 1
local gn = -1
forvalues k = 1/`h' {
    local gp = `gp' + `phi'*(`gp' - `bp')
    local gn = `gn' + `phi'*(`gn' - `bn')
    qui replace mp = `gp' in `=`k'+1'
    qui replace mn = `gn' in `=`k'+1'
}
gen asym = mp - mn
list h mp mn asym
{txt}


{marker cd}{...}
{title:5. Independent CD diagnostics}

{pstd}
{cmd:xtcsnardl} runs the Pesaran CD test by default (Table 10).  For confirmation with
external tools:

{phang2}{cmd:. predict uhat, residuals}{p_end}
{phang2}{cmd:. xtcd2 uhat}                {hline 2} Ditzen-Reese implementation{p_end}
{phang2}{cmd:. xtcd uhat}                 {hline 2} alternative{p_end}
{phang2}{cmd:. xtcse2 uhat}               {hline 2} Pesaran-Tosetti exponent of CSD{p_end}

{pstd}
The {help xtcse2:xtcse2} command additionally estimates the {ul:exponent of cross-sectional
dependence}; values in [0, 0.5] correspond to weak CSD (CSA augmentation is sufficient),
values in (0.5, 1] correspond to strong CSD and indicate residual factor structure.


{marker estout}{...}
{title:6. Exporting tables (estout / esttab)}

{pstd}
After estimation, the e(b)/e(V) layout is compatible with {help estout:estout} and esttab.
A typical export workflow:

{cmd}
qui xtcsnardl D.y L.y D.x, lr(L.y x) asymmetric(x) pmg
estimates store cs_pmg

qui xtcsnardl D.y L.y D.x, lr(L.y x) asymmetric(x) mg
estimates store cs_mg

* Print to clipboard / LaTeX
esttab cs_pmg cs_mg, ///
    keep([ECT]x_pos [ECT]x_neg [SR]ECT) ///
    star(* 0.10 ** 0.05 *** 0.01) ///
    se(%6.4f) b(%7.4f) ///
    label collabels(none) ///
    mtitles("PMG" "MG") ///
    addnotes("Long-run asymmetric coefficients reported." ///
              "Asterisks denote significance.")
{txt}


{marker stability}{...}
{title:7. CUSUM, CUSUMSQ and stability diagnostics}

{pstd}
Mehta & Derbeneva (2024) report CUSUM and CUSUMSQ for the pooled residuals.  Reconstruct them
as follows:

{cmd}
qui xtcsnardl D.y L.y D.x, lr(L.y x) asymmetric(x)
predict uhat, residuals

* Pool residuals into a single time series
collapse (mean) uhat, by(year)
tsset year

* CUSUM and CUSUMSQ
estat sbcusum                     // requires Stata 15+ regress fit
* Or manually:
gen cs  = sum(uhat)
gen css = sum(uhat^2)
tsline cs                         // CUSUM
tsline css                        // CUSUMSQ
{txt}

{pstd}
Within the 5% confidence bands, the model is stable.  In top-journal practice the bands are
{&plusmn} 2 SE for CUSUM and {&plusmn} 1 standard error for the squared variant.  See Brown,
Durbin and Evans (1975) for the original derivation.


{title:Tips for top-journal reporting}

{phang}
1. Always report Table 1 (long-run), Table 2 (ECT + half-life), Table 5 (asymmetry tests) and
Table 10 (CD residual diagnostic).  These four tables are the minimum required by most
applied-econometrics referees.

{phang}
2. Report {opt panelcoef} (Table 7) when panels differ in characteristics (country-by-country
comparison expected).  Suppress when N is large.

{phang}
3. Report multipliers (Table 8) {ul:and} the corresponding graph ({bf:csn_multip_1}) {hline 2}
journals like to see both the numerical and visual evidence.

{phang}
4. Test {ul:nested specifications}: linear ARDL (no {opt asymmetric}), Panel NARDL ({opt nocsa}),
CS-NARDL (default), and use Hausman / information criteria for selection.

{phang}
5. Always run {help xtcd2:xtcd2} on the dependent variable {ul:before} estimation and on the
residuals {ul:after}.  Report both p-values in the same table.


{title:Author}

{pstd}
{bf:Dr Merwan Roudane}{break}
{bf:merwanroudane920@gmail.com}{break}
{cmd:xtcsnardl} v1.0.0, 28 May 2026{p_end}


{title:Also see}

{psee}
Online: {help xtcsnardl},  {help xtcsnardl_methodology},  {help xtcsnardl_examples},  {help xtcsnardl_graph}{p_end}
{psee}
Related: {help xtpmg},  {help xtpmg_postestimation},  {help xtcd2},  {help xtcse2},  {help estout},  {help estat}{p_end}