{smcl}
{com}{sf}{ul off}{txt}{.-}
      name:  {res}<unnamed>
       {txt}log:  {res}C:\STATADAT\cs_egranger.smcl
  {txt}log type:  {res}smcl
 {txt}opened on:  {res} 2 Dec 2010, 22:11:47
{txt}
{com}. which egranger
{txt}c:\ado\personal\egranger.ado
{res}*! egranger version 1.0.3  2Dec2010
*! author Mark Schaffer
{txt}
{com}. version
{txt}version 11.1

{com}. 
. * average per-capita disposable personal income dataset
. use http://www.stata-press.com/data/r9/rdinc, clear
{txt}
{com}. 
. * T is zero in the first period (lost in 2nd step and test regressions)
. gen t=_n-1
{txt}
{com}. gen tsq=t^2
{txt}
{com}. 
. * Cointegration test
. 
. egranger ln_ne ln_se, regress

{txt}Engle-Granger test for cointegration{col 55}N (1st step)  ={res}       55
{col 55}{txt}N (test)      ={res}       54
{txt}{hline 78}
{col 19}Test{col 32}1% Critical{col 50}5% Critical{col 67}10% Critical
{col 16}Statistic{col 36}Value{col 54}Value{col 72}Value
{hline 78}
 Z(t){col 15}{res}    -0.469{col 33}    -3.558{col 51}    -2.917{col 69}    -2.596

{txt}Critical values from MacKinnon (1990, 2010)
{hline 78}
{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}Engle-Granger test regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}  D._egresid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.0184894{col 26}{space 2} .0394634{col 37}{space 1}   -0.47{col 46}{space 3}0.641{col 54}{space 4}-.0976428{col 67}{space 3} .0606641
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. scalar Zt=e(Zt)
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  1,    53) ={res}25842.40
    {txt}   Model {char |} {res} 59.2458578     1  59.2458578           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .121506903    53  .002292583           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04788

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.resid L.resid, nocons

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      54
{txt}{hline 13}{char +}{hline 30}           F(  1,    53) ={res}    0.22
    {txt}   Model {char |} {res} .000039678     1  .000039678           {txt}Prob > F      = {res} 0.6413
    {txt}Residual {char |} {res} .009580086    53  .000180756           {txt}R-squared     = {res} 0.0041
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res}-0.0147
    {txt}   Total {char |} {res} .009619764    54  .000178144           {txt}Root MSE      = {res} .01344

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.resid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.0184894{col 26}{space 2} .0394634{col 37}{space 1}   -0.47{col 46}{space 3}0.641{col 54}{space 4}-.0976428{col 67}{space 3} .0606641
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. qui test L.resid
{txt}
{com}. assert reldif(abs(Zt),sqrt(r(F))) < 1e-8
{txt}
{com}. 
. egranger ln_ne ln_se, lags(2) regress
{res}Replacing variable _egresid...

{txt}Augmented Engle-Granger test for cointegration{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 2{col 55}{txt}N (test)      ={res}       52
{txt}{hline 78}
{col 19}Test{col 32}1% Critical{col 50}5% Critical{col 67}10% Critical
{col 16}Statistic{col 36}Value{col 54}Value{col 72}Value
{hline 78}
 Z(t){col 15}{res}    -1.336{col 33}    -3.558{col 51}    -2.917{col 69}    -2.596

{txt}Critical values from MacKinnon (1990, 2010)
{hline 78}
{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}Engle-Granger test regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}  D._egresid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.050771{col 26}{space 2} .0379952{col 37}{space 1}   -1.34{col 46}{space 3}0.188{col 54}{space 4}-.1271252{col 67}{space 3} .0255831
{txt}{space 9}LD. {c |}{col 14}{res}{space 2}  .358361{col 26}{space 2} .1367238{col 37}{space 1}    2.62{col 46}{space 3}0.012{col 54}{space 4} .0836042{col 67}{space 3} .6331178
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0658113{col 26}{space 2} .1399569{col 37}{space 1}    0.47{col 46}{space 3}0.640{col 54}{space 4}-.2154426{col 67}{space 3} .3470653
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. scalar Zt=e(Zt)
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  1,    53) ={res}25842.40
    {txt}   Model {char |} {res} 59.2458578     1  59.2458578           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .121506903    53  .002292583           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04788

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.resid L.resid L(1/2)D.resid, nocons

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      52
{txt}{hline 13}{char +}{hline 30}           F(  3,    49) ={res}    3.12
    {txt}   Model {char |} {res} .001407853     3  .000469284           {txt}Prob > F      = {res} 0.0345
    {txt}Residual {char |} {res} .007381708    49  .000150647           {txt}R-squared     = {res} 0.1602
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.1088
    {txt}   Total {char |} {res} .008789561    52   .00016903           {txt}Root MSE      = {res} .01227

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.resid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.050771{col 26}{space 2} .0379952{col 37}{space 1}   -1.34{col 46}{space 3}0.188{col 54}{space 4}-.1271252{col 67}{space 3} .0255831
{txt}{space 9}LD. {c |}{col 14}{res}{space 2}  .358361{col 26}{space 2} .1367238{col 37}{space 1}    2.62{col 46}{space 3}0.012{col 54}{space 4} .0836042{col 67}{space 3} .6331178
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0658113{col 26}{space 2} .1399569{col 37}{space 1}    0.47{col 46}{space 3}0.640{col 54}{space 4}-.2154426{col 67}{space 3} .3470653
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. qui test L.resid
{txt}
{com}. assert reldif(abs(Zt),sqrt(r(F))) < 1e-8
{txt}
{com}. 
. egranger ln_ne ln_se ln_me, lags(2) regress
{res}Replacing variable _egresid...

{txt}Augmented Engle-Granger test for cointegration{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 2{col 55}{txt}N (test)      ={res}       52
{txt}{hline 78}
{col 19}Test{col 32}1% Critical{col 50}5% Critical{col 67}10% Critical
{col 16}Statistic{col 36}Value{col 54}Value{col 72}Value
{hline 78}
 Z(t){col 15}{res}    -3.294{col 33}    -4.107{col 51}    -3.452{col 69}    -3.124

{txt}Critical values from MacKinnon (1990, 2010)
{hline 78}
{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.2213408{col 26}{space 2}  .052206{col 37}{space 1}   -4.24{col 46}{space 3}0.000{col 54}{space 4}-.3260998{col 67}{space 3}-.1165818
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.271222{col 26}{space 2} .0567175{col 37}{space 1}   22.41{col 46}{space 3}0.000{col 54}{space 4}  1.15741{col 67}{space 3} 1.385034
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.5177237{col 26}{space 2} .0572861{col 37}{space 1}   -9.04{col 46}{space 3}0.000{col 54}{space 4}-.6326767{col 67}{space 3}-.4027706
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}Engle-Granger test regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}  D._egresid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.3233623{col 26}{space 2} .0981799{col 37}{space 1}   -3.29{col 46}{space 3}0.002{col 54}{space 4}-.5206623{col 67}{space 3}-.1260624
{txt}{space 9}LD. {c |}{col 14}{res}{space 2}    .3137{col 26}{space 2} .1233709{col 37}{space 1}    2.54{col 46}{space 3}0.014{col 54}{space 4} .0657768{col 67}{space 3} .5616231
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.1488599{col 26}{space 2} .1303368{col 37}{space 1}   -1.14{col 46}{space 3}0.259{col 54}{space 4}-.4107814{col 67}{space 3} .1130616
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. scalar Zt=e(Zt)
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se ln_me

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  2,    52) ={res}       .
    {txt}   Model {char |} {res}  59.355967     2  29.6779835           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .011397736    52  .000219187           {txt}R-squared     = {res} 0.9998
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9998
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res}  .0148

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.2213408{col 26}{space 2}  .052206{col 37}{space 1}   -4.24{col 46}{space 3}0.000{col 54}{space 4}-.3260998{col 67}{space 3}-.1165818
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.271222{col 26}{space 2} .0567175{col 37}{space 1}   22.41{col 46}{space 3}0.000{col 54}{space 4}  1.15741{col 67}{space 3} 1.385034
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.5177237{col 26}{space 2} .0572861{col 37}{space 1}   -9.04{col 46}{space 3}0.000{col 54}{space 4}-.6326767{col 67}{space 3}-.4027706
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.resid L.resid L(1/2)D.resid, nocons

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      52
{txt}{hline 13}{char +}{hline 30}           F(  3,    49) ={res}    6.87
    {txt}   Model {char |} {res} .001424504     3  .000474835           {txt}Prob > F      = {res} 0.0006
    {txt}Residual {char |} {res} .003387013    49  .000069123           {txt}R-squared     = {res} 0.2961
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.2530
    {txt}   Total {char |} {res} .004811517    52  .000092529           {txt}Root MSE      = {res} .00831

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.resid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.3233623{col 26}{space 2} .0981799{col 37}{space 1}   -3.29{col 46}{space 3}0.002{col 54}{space 4}-.5206623{col 67}{space 3}-.1260624
{txt}{space 9}LD. {c |}{col 14}{res}{space 2}    .3137{col 26}{space 2} .1233709{col 37}{space 1}    2.54{col 46}{space 3}0.014{col 54}{space 4} .0657768{col 67}{space 3} .5616231
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.1488599{col 26}{space 2} .1303368{col 37}{space 1}   -1.14{col 46}{space 3}0.259{col 54}{space 4}-.4107814{col 67}{space 3} .1130616
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. qui test L.resid
{txt}
{com}. assert reldif(abs(Zt),sqrt(r(F))) < 1e-8
{txt}
{com}. 
. egranger ln_ne ln_se, lags(3) regress trend
{res}Replacing variable _egresid...

{txt}Augmented Engle-Granger test for cointegration{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 3{col 55}{txt}N (test)      ={res}       51
{txt}1st step includes linear trend
{hline 78}
{col 19}Test{col 32}1% Critical{col 50}5% Critical{col 67}10% Critical
{col 16}Statistic{col 36}Value{col 54}Value{col 72}Value
{hline 78}
 Z(t){col 15}{res}    -1.559{col 33}    -4.137{col 51}    -3.495{col 69}    -3.176

{txt}Critical values from MacKinnon (1990, 2010)
{hline 78}
{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9179047{col 26}{space 2} .0491845{col 37}{space 1}   18.66{col 46}{space 3}0.000{col 54}{space 4} .8192089{col 67}{space 3} 1.016601
{txt}{space 6}_trend {c |}{col 14}{res}{space 2} .0020942{col 26}{space 2} .0033919{col 37}{space 1}    0.62{col 46}{space 3}0.540{col 54}{space 4}-.0047122{col 67}{space 3} .0089005
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .9166857{col 26}{space 2} .3259759{col 37}{space 1}    2.81{col 46}{space 3}0.007{col 54}{space 4} .2625672{col 67}{space 3} 1.570804
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}Engle-Granger test regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}  D._egresid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.058504{col 26}{space 2} .0375381{col 37}{space 1}   -1.56{col 46}{space 3}0.126{col 54}{space 4} -.134021{col 67}{space 3} .0170129
{txt}{space 9}LD. {c |}{col 14}{res}{space 2} .4161955{col 26}{space 2} .1367298{col 37}{space 1}    3.04{col 46}{space 3}0.004{col 54}{space 4} .1411307{col 67}{space 3} .6912603
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0098615{col 26}{space 2} .1413458{col 37}{space 1}    0.07{col 46}{space 3}0.945{col 54}{space 4}-.2744895{col 67}{space 3} .2942126
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1797595{col 26}{space 2} .1374333{col 37}{space 1}    1.31{col 46}{space 3}0.197{col 54}{space 4}-.0967206{col 67}{space 3} .4562395
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. scalar Zt=e(Zt)
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se t

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  2,    52) ={res}12770.53
    {txt}   Model {char |} {res}  59.246742     2   29.623371           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .120622693    52  .002319667           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04816

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9179047{col 26}{space 2} .0491845{col 37}{space 1}   18.66{col 46}{space 3}0.000{col 54}{space 4} .8192089{col 67}{space 3} 1.016601
{txt}{space 11}t {c |}{col 14}{res}{space 2} .0020942{col 26}{space 2} .0033919{col 37}{space 1}    0.62{col 46}{space 3}0.540{col 54}{space 4}-.0047122{col 67}{space 3} .0089005
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .9166857{col 26}{space 2} .3259759{col 37}{space 1}    2.81{col 46}{space 3}0.007{col 54}{space 4} .2625672{col 67}{space 3} 1.570804
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.resid L.resid L(1/3)D.resid, nocons

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      51
{txt}{hline 13}{char +}{hline 30}           F(  4,    47) ={res}    3.50
    {txt}   Model {char |} {res} .001952309     4  .000488077           {txt}Prob > F      = {res} 0.0139
    {txt}Residual {char |} {res} .006550765    47  .000139378           {txt}R-squared     = {res} 0.2296
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.1640
    {txt}   Total {char |} {res} .008503074    51  .000166727           {txt}Root MSE      = {res} .01181

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.resid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.058504{col 26}{space 2} .0375381{col 37}{space 1}   -1.56{col 46}{space 3}0.126{col 54}{space 4} -.134021{col 67}{space 3} .0170129
{txt}{space 9}LD. {c |}{col 14}{res}{space 2} .4161955{col 26}{space 2} .1367298{col 37}{space 1}    3.04{col 46}{space 3}0.004{col 54}{space 4} .1411307{col 67}{space 3} .6912603
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0098615{col 26}{space 2} .1413458{col 37}{space 1}    0.07{col 46}{space 3}0.945{col 54}{space 4}-.2744895{col 67}{space 3} .2942126
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1797595{col 26}{space 2} .1374333{col 37}{space 1}    1.31{col 46}{space 3}0.197{col 54}{space 4}-.0967206{col 67}{space 3} .4562395
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. qui test L.resid
{txt}
{com}. assert reldif(abs(Zt),sqrt(r(F))) < 1e-8
{txt}
{com}. 
. egranger ln_ne ln_se ln_me, lags(4) regress qtrend
{res}Replacing variable _egresid...

{txt}Augmented Engle-Granger test for cointegration{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 4{col 55}{txt}N (test)      ={res}       50
{txt}1st step includes quadratic trend
{hline 78}
{col 19}Test{col 32}1% Critical{col 50}5% Critical{col 67}10% Critical
{col 16}Statistic{col 36}Value{col 54}Value{col 72}Value
{hline 78}
 Z(t){col 15}{res}    -3.655{col 33}    -5.089{col 51}    -4.410{col 69}    -4.073

{txt}Critical values from MacKinnon (1990, 2010)
{hline 78}
{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.4853195{col 26}{space 2} .0829014{col 37}{space 1}   -5.85{col 46}{space 3}0.000{col 54}{space 4}-.6518318{col 67}{space 3}-.3188071
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.532462{col 26}{space 2} .0900714{col 37}{space 1}   17.01{col 46}{space 3}0.000{col 54}{space 4} 1.351548{col 67}{space 3} 1.713375
{txt}{space 6}_trend {c |}{col 14}{res}{space 2} .0043097{col 26}{space 2} .0011442{col 37}{space 1}    3.77{col 46}{space 3}0.000{col 54}{space 4} .0020114{col 67}{space 3} .0066079
{txt}{space 4}_trend^2 {c |}{col 14}{res}{space 2}-.0000493{col 26}{space 2} .0000141{col 37}{space 1}   -3.50{col 46}{space 3}0.001{col 54}{space 4}-.0000776{col 67}{space 3} -.000021
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.6391797{col 26}{space 2} .1337661{col 37}{space 1}   -4.78{col 46}{space 3}0.000{col 54}{space 4}-.9078567{col 67}{space 3}-.3705026
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}Engle-Granger test regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}  D._egresid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.605947{col 26}{space 2} .1657767{col 37}{space 1}   -3.66{col 46}{space 3}0.001{col 54}{space 4}-.9398383{col 67}{space 3}-.2720556
{txt}{space 9}LD. {c |}{col 14}{res}{space 2} .3424608{col 26}{space 2} .1665914{col 37}{space 1}    2.06{col 46}{space 3}0.046{col 54}{space 4} .0069285{col 67}{space 3} .6779931
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0629834{col 26}{space 2} .1552987{col 37}{space 1}    0.41{col 46}{space 3}0.687{col 54}{space 4}-.2498043{col 67}{space 3} .3757711
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1640868{col 26}{space 2} .1299853{col 37}{space 1}    1.26{col 46}{space 3}0.213{col 54}{space 4}-.0977171{col 67}{space 3} .4258907
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .2312064{col 26}{space 2} .1299288{col 37}{space 1}    1.78{col 46}{space 3}0.082{col 54}{space 4}-.0304836{col 67}{space 3} .4928965
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. scalar Zt=e(Zt)
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se ln_me t tsq

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  4,    50) ={res}86783.30
    {txt}   Model {char |} {res} 59.3588148     4  14.8397037           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .008549861    50  .000170997           {txt}R-squared     = {res} 0.9999
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9998
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .01308

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.4853195{col 26}{space 2} .0829014{col 37}{space 1}   -5.85{col 46}{space 3}0.000{col 54}{space 4}-.6518318{col 67}{space 3}-.3188071
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.532462{col 26}{space 2} .0900714{col 37}{space 1}   17.01{col 46}{space 3}0.000{col 54}{space 4} 1.351548{col 67}{space 3} 1.713375
{txt}{space 11}t {c |}{col 14}{res}{space 2} .0043097{col 26}{space 2} .0011442{col 37}{space 1}    3.77{col 46}{space 3}0.000{col 54}{space 4} .0020114{col 67}{space 3} .0066079
{txt}{space 9}tsq {c |}{col 14}{res}{space 2}-.0000493{col 26}{space 2} .0000141{col 37}{space 1}   -3.50{col 46}{space 3}0.001{col 54}{space 4}-.0000776{col 67}{space 3} -.000021
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.6391797{col 26}{space 2} .1337661{col 37}{space 1}   -4.78{col 46}{space 3}0.000{col 54}{space 4}-.9078567{col 67}{space 3}-.3705026
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.resid L.resid L(1/4)D.resid, nocons

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      50
{txt}{hline 13}{char +}{hline 30}           F(  5,    45) ={res}    4.35
    {txt}   Model {char |} {res} .001723709     5  .000344742           {txt}Prob > F      = {res} 0.0026
    {txt}Residual {char |} {res} .003568661    45  .000079304           {txt}R-squared     = {res} 0.3257
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.2508
    {txt}   Total {char |} {res} .005292371    50  .000105847           {txt}Root MSE      = {res} .00891

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.resid{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2} -.605947{col 26}{space 2} .1657767{col 37}{space 1}   -3.66{col 46}{space 3}0.001{col 54}{space 4}-.9398383{col 67}{space 3}-.2720556
{txt}{space 9}LD. {c |}{col 14}{res}{space 2} .3424608{col 26}{space 2} .1665914{col 37}{space 1}    2.06{col 46}{space 3}0.046{col 54}{space 4} .0069285{col 67}{space 3} .6779931
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .0629834{col 26}{space 2} .1552987{col 37}{space 1}    0.41{col 46}{space 3}0.687{col 54}{space 4}-.2498043{col 67}{space 3} .3757711
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1640868{col 26}{space 2} .1299853{col 37}{space 1}    1.26{col 46}{space 3}0.213{col 54}{space 4}-.0977171{col 67}{space 3} .4258907
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .2312064{col 26}{space 2} .1299288{col 37}{space 1}    1.78{col 46}{space 3}0.082{col 54}{space 4}-.0304836{col 67}{space 3} .4928965
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. qui test L.resid
{txt}
{com}. assert reldif(abs(Zt),sqrt(r(F))) < 1e-8
{txt}
{com}. 
. * 2-step ECM
. 
. egranger ln_ne ln_se, regress ecm
{res}Replacing variable _egresid...

{txt}Engle-Granger 2-step ECM estimation{col 55}N (1st step)  ={res}       55
{col 55}{txt}N (2nd step)  ={res}       54

Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{res}Engle-Granger 2-step ECM
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.0853794{col 26}{space 2} .0504812{col 37}{space 1}   -1.69{col 46}{space 3}0.097{col 54}{space 4}-.1867246{col 67}{space 3} .0159659
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .7795017{col 26}{space 2} .0813571{col 37}{space 1}    9.58{col 46}{space 3}0.000{col 54}{space 4} .6161706{col 67}{space 3} .9428328
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0112707{col 26}{space 2} .0052036{col 37}{space 1}    2.17{col 46}{space 3}0.035{col 54}{space 4}  .000824{col 67}{space 3} .0217174
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. savedresults save eg e()
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  1,    53) ={res}25842.40
    {txt}   Model {char |} {res} 59.2458578     1  59.2458578           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .121506903    53  .002292583           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04788

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.ln_ne L.resid D.ln_se

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      54
{txt}{hline 13}{char +}{hline 30}           F(  2,    51) ={res}   99.33
    {txt}   Model {char |} {res} .034166643     2  .017083322           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .008771225    51  .000171985           {txt}R-squared     = {res} 0.7957
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.7877
    {txt}   Total {char |} {res} .042937868    53  .000810148           {txt}Root MSE      = {res} .01311

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.0853794{col 26}{space 2} .0504812{col 37}{space 1}   -1.69{col 46}{space 3}0.097{col 54}{space 4}-.1867246{col 67}{space 3} .0159659
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .7795017{col 26}{space 2} .0813571{col 37}{space 1}    9.58{col 46}{space 3}0.000{col 54}{space 4} .6161706{col 67}{space 3} .9428328
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0112707{col 26}{space 2} .0052036{col 37}{space 1}    2.17{col 46}{space 3}0.035{col 54}{space 4}  .000824{col 67}{space 3} .0217174
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. savedresults comp eg e(), include(macros: depvar scalar: ll matrix: b V) tol(1e-7) verbose
{txt}comparing macro  e(depvar)
comparing scalar e(ll)
comparing matrix e(b)
comparing matrix e(V)

{com}. 
. egranger ln_ne ln_se, lags(2) regress ecm
{res}Replacing variable _egresid...

{txt}Engle-Granger 2-step ECM estimation{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 2{col 55}{txt}N (2nd step)  ={res}       52

Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{res}Engle-Granger 2-step ECM
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2276234{col 26}{space 2} .0682977{col 37}{space 1}   -3.33{col 46}{space 3}0.002{col 54}{space 4}-.3651821{col 67}{space 3}-.0900648
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .6542194{col 26}{space 2} .0890734{col 37}{space 1}    7.34{col 46}{space 3}0.000{col 54}{space 4} .4748164{col 67}{space 3} .8336224
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .3925555{col 26}{space 2} .1270397{col 37}{space 1}    3.09{col 46}{space 3}0.003{col 54}{space 4} .1366844{col 67}{space 3} .6484266
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .2123833{col 26}{space 2} .1381692{col 37}{space 1}    1.54{col 46}{space 3}0.131{col 54}{space 4}-.0659037{col 67}{space 3} .4906703
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.4358891{col 26}{space 2} .1420771{col 37}{space 1}   -3.07{col 46}{space 3}0.004{col 54}{space 4}-.7220471{col 67}{space 3}-.1497312
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.2481128{col 26}{space 2} .1557079{col 37}{space 1}   -1.59{col 46}{space 3}0.118{col 54}{space 4}-.5617246{col 67}{space 3}  .065499
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0246004{col 26}{space 2} .0083166{col 37}{space 1}    2.96{col 46}{space 3}0.005{col 54}{space 4} .0078499{col 67}{space 3}  .041351
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. savedresults save eg e()
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  1,    53) ={res}25842.40
    {txt}   Model {char |} {res} 59.2458578     1  59.2458578           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .121506903    53  .002292583           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04788

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9480494{col 26}{space 2} .0058975{col 37}{space 1}  160.76{col 46}{space 3}0.000{col 54}{space 4} .9362206{col 67}{space 3} .9598782
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .7178752{col 26}{space 2} .0503722{col 37}{space 1}   14.25{col 46}{space 3}0.000{col 54}{space 4} .6168413{col 67}{space 3} .8189091
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.ln_ne L.resid D.ln_se L(1/2)D.(ln_ne ln_se)

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      52
{txt}{hline 13}{char +}{hline 30}           F(  6,    45) ={res}   40.57
    {txt}   Model {char |} {res} .030682635     6  .005113773           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .005672325    45  .000126052           {txt}R-squared     = {res} 0.8440
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.8232
    {txt}   Total {char |} {res} .036354961    51  .000712842           {txt}Root MSE      = {res} .01123

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2276234{col 26}{space 2} .0682977{col 37}{space 1}   -3.33{col 46}{space 3}0.002{col 54}{space 4}-.3651821{col 67}{space 3}-.0900648
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .6542194{col 26}{space 2} .0890734{col 37}{space 1}    7.34{col 46}{space 3}0.000{col 54}{space 4} .4748164{col 67}{space 3} .8336224
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .3925555{col 26}{space 2} .1270397{col 37}{space 1}    3.09{col 46}{space 3}0.003{col 54}{space 4} .1366844{col 67}{space 3} .6484266
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .2123833{col 26}{space 2} .1381692{col 37}{space 1}    1.54{col 46}{space 3}0.131{col 54}{space 4}-.0659037{col 67}{space 3} .4906703
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.4358891{col 26}{space 2} .1420771{col 37}{space 1}   -3.07{col 46}{space 3}0.004{col 54}{space 4}-.7220471{col 67}{space 3}-.1497312
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.2481128{col 26}{space 2} .1557079{col 37}{space 1}   -1.59{col 46}{space 3}0.118{col 54}{space 4}-.5617246{col 67}{space 3}  .065499
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0246004{col 26}{space 2} .0083166{col 37}{space 1}    2.96{col 46}{space 3}0.005{col 54}{space 4} .0078499{col 67}{space 3}  .041351
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. savedresults comp eg e(), include(macros: depvar scalar: ll matrix: b V) tol(1e-7) verbose
{txt}comparing macro  e(depvar)
comparing scalar e(ll)
comparing matrix e(b)
comparing matrix e(V)

{com}. 
. egranger ln_ne ln_se ln_me, lags(2) regress ecm
{res}Replacing variable _egresid...

{txt}Engle-Granger 2-step ECM estimation{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 2{col 55}{txt}N (2nd step)  ={res}       52

Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.2213408{col 26}{space 2}  .052206{col 37}{space 1}   -4.24{col 46}{space 3}0.000{col 54}{space 4}-.3260998{col 67}{space 3}-.1165818
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.271222{col 26}{space 2} .0567175{col 37}{space 1}   22.41{col 46}{space 3}0.000{col 54}{space 4}  1.15741{col 67}{space 3} 1.385034
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.5177237{col 26}{space 2} .0572861{col 37}{space 1}   -9.04{col 46}{space 3}0.000{col 54}{space 4}-.6326767{col 67}{space 3}-.4027706
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{res}Engle-Granger 2-step ECM
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2709819{col 26}{space 2}  .088889{col 37}{space 1}   -3.05{col 46}{space 3}0.004{col 54}{space 4}-.4503671{col 67}{space 3}-.0915966
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .0640645{col 26}{space 2}   .08965{col 37}{space 1}    0.71{col 46}{space 3}0.479{col 54}{space 4}-.1168565{col 67}{space 3} .2449855
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .9618695{col 26}{space 2} .1001312{col 37}{space 1}    9.61{col 46}{space 3}0.000{col 54}{space 4} .7597966{col 67}{space 3} 1.163942
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .4622649{col 26}{space 2} .1376253{col 37}{space 1}    3.36{col 46}{space 3}0.002{col 54}{space 4} .1845257{col 67}{space 3}  .740004
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.0662137{col 26}{space 2} .1517664{col 37}{space 1}   -0.44{col 46}{space 3}0.665{col 54}{space 4}-.3724906{col 67}{space 3} .2400633
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.1895303{col 26}{space 2} .0875705{col 37}{space 1}   -2.16{col 46}{space 3}0.036{col 54}{space 4}-.3662547{col 67}{space 3}-.0128058
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.0924367{col 26}{space 2} .0886593{col 37}{space 1}   -1.04{col 46}{space 3}0.303{col 54}{space 4}-.2713583{col 67}{space 3}  .086485
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.2893808{col 26}{space 2} .1454555{col 37}{space 1}   -1.99{col 46}{space 3}0.053{col 54}{space 4}-.5829219{col 67}{space 3} .0041603
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .1327842{col 26}{space 2} .1607832{col 37}{space 1}    0.83{col 46}{space 3}0.414{col 54}{space 4}-.1916893{col 67}{space 3} .4572578
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0036678{col 26}{space 2} .0028481{col 37}{space 1}    1.29{col 46}{space 3}0.205{col 54}{space 4}-.0020799{col 67}{space 3} .0094156
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. savedresults save eg e()
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se ln_me

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  2,    52) ={res}       .
    {txt}   Model {char |} {res}  59.355967     2  29.6779835           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .011397736    52  .000219187           {txt}R-squared     = {res} 0.9998
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9998
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res}  .0148

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.2213408{col 26}{space 2}  .052206{col 37}{space 1}   -4.24{col 46}{space 3}0.000{col 54}{space 4}-.3260998{col 67}{space 3}-.1165818
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.271222{col 26}{space 2} .0567175{col 37}{space 1}   22.41{col 46}{space 3}0.000{col 54}{space 4}  1.15741{col 67}{space 3} 1.385034
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.5177237{col 26}{space 2} .0572861{col 37}{space 1}   -9.04{col 46}{space 3}0.000{col 54}{space 4}-.6326767{col 67}{space 3}-.4027706
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.ln_ne L.resid D.(ln_se ln_me) L(1/2)D.(ln_ne ln_se ln_me)

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      52
{txt}{hline 13}{char +}{hline 30}           F(  9,    42) ={res}   78.74
    {txt}   Model {char |} {res} .034320966     9  .003813441           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .002033995    42  .000048428           {txt}R-squared     = {res} 0.9441
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9321
    {txt}   Total {char |} {res} .036354961    51  .000712842           {txt}Root MSE      = {res} .00696

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2709819{col 26}{space 2}  .088889{col 37}{space 1}   -3.05{col 46}{space 3}0.004{col 54}{space 4}-.4503671{col 67}{space 3}-.0915966
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .0640645{col 26}{space 2}   .08965{col 37}{space 1}    0.71{col 46}{space 3}0.479{col 54}{space 4}-.1168565{col 67}{space 3} .2449855
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .9618695{col 26}{space 2} .1001312{col 37}{space 1}    9.61{col 46}{space 3}0.000{col 54}{space 4} .7597966{col 67}{space 3} 1.163942
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .4622649{col 26}{space 2} .1376253{col 37}{space 1}    3.36{col 46}{space 3}0.002{col 54}{space 4} .1845257{col 67}{space 3}  .740004
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.0662137{col 26}{space 2} .1517664{col 37}{space 1}   -0.44{col 46}{space 3}0.665{col 54}{space 4}-.3724906{col 67}{space 3} .2400633
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.1895303{col 26}{space 2} .0875705{col 37}{space 1}   -2.16{col 46}{space 3}0.036{col 54}{space 4}-.3662547{col 67}{space 3}-.0128058
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.0924367{col 26}{space 2} .0886593{col 37}{space 1}   -1.04{col 46}{space 3}0.303{col 54}{space 4}-.2713583{col 67}{space 3}  .086485
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.2893808{col 26}{space 2} .1454555{col 37}{space 1}   -1.99{col 46}{space 3}0.053{col 54}{space 4}-.5829219{col 67}{space 3} .0041603
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .1327842{col 26}{space 2} .1607832{col 37}{space 1}    0.83{col 46}{space 3}0.414{col 54}{space 4}-.1916893{col 67}{space 3} .4572578
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0036678{col 26}{space 2} .0028481{col 37}{space 1}    1.29{col 46}{space 3}0.205{col 54}{space 4}-.0020799{col 67}{space 3} .0094156
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. savedresults comp eg e(), include(macros: depvar scalar: ll matrix: b V) tol(1e-7) verbose
{txt}comparing macro  e(depvar)
comparing scalar e(ll)
comparing matrix e(b)
comparing matrix e(V)

{com}. 
. egranger ln_ne ln_se, lags(3) regress trend ecm
{res}Replacing variable _egresid...

{txt}Engle-Granger 2-step ECM estimation{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 3{col 55}{txt}N (2nd step)  ={res}       51
{txt}1st step includes linear trend

{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9179047{col 26}{space 2} .0491845{col 37}{space 1}   18.66{col 46}{space 3}0.000{col 54}{space 4} .8192089{col 67}{space 3} 1.016601
{txt}{space 6}_trend {c |}{col 14}{res}{space 2} .0020942{col 26}{space 2} .0033919{col 37}{space 1}    0.62{col 46}{space 3}0.540{col 54}{space 4}-.0047122{col 67}{space 3} .0089005
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .9166857{col 26}{space 2} .3259759{col 37}{space 1}    2.81{col 46}{space 3}0.007{col 54}{space 4} .2625672{col 67}{space 3} 1.570804
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{res}Engle-Granger 2-step ECM
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2658499{col 26}{space 2} .0818016{col 37}{space 1}   -3.25{col 46}{space 3}0.002{col 54}{space 4}-.4309323{col 67}{space 3}-.1007675
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .7003052{col 26}{space 2} .0989823{col 37}{space 1}    7.08{col 46}{space 3}0.000{col 54}{space 4} .5005508{col 67}{space 3} .9000595
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .4340785{col 26}{space 2} .1338002{col 37}{space 1}    3.24{col 46}{space 3}0.002{col 54}{space 4} .1640588{col 67}{space 3} .7040982
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .1530296{col 26}{space 2} .1455307{col 37}{space 1}    1.05{col 46}{space 3}0.299{col 54}{space 4}-.1406631{col 67}{space 3} .4467223
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .2807848{col 26}{space 2} .1474322{col 37}{space 1}    1.90{col 46}{space 3}0.064{col 54}{space 4}-.0167454{col 67}{space 3} .5783149
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.4932871{col 26}{space 2} .1493358{col 37}{space 1}   -3.30{col 46}{space 3}0.002{col 54}{space 4}-.7946589{col 67}{space 3}-.1919154
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} -.266764{col 26}{space 2} .1585255{col 37}{space 1}   -1.68{col 46}{space 3}0.100{col 54}{space 4}-.5866814{col 67}{space 3} .0531533
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2}-.2714892{col 26}{space 2} .1641429{col 37}{space 1}   -1.65{col 46}{space 3}0.106{col 54}{space 4} -.602743{col 67}{space 3} .0597645
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2}  .027822{col 26}{space 2} .0095982{col 37}{space 1}    2.90{col 46}{space 3}0.006{col 54}{space 4} .0084521{col 67}{space 3} .0471919
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. savedresults save eg e()
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se t

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  2,    52) ={res}12770.53
    {txt}   Model {char |} {res}  59.246742     2   29.623371           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .120622693    52  .002319667           {txt}R-squared     = {res} 0.9980
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9979
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .04816

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2} .9179047{col 26}{space 2} .0491845{col 37}{space 1}   18.66{col 46}{space 3}0.000{col 54}{space 4} .8192089{col 67}{space 3} 1.016601
{txt}{space 11}t {c |}{col 14}{res}{space 2} .0020942{col 26}{space 2} .0033919{col 37}{space 1}    0.62{col 46}{space 3}0.540{col 54}{space 4}-.0047122{col 67}{space 3} .0089005
{txt}{space 7}_cons {c |}{col 14}{res}{space 2} .9166857{col 26}{space 2} .3259759{col 37}{space 1}    2.81{col 46}{space 3}0.007{col 54}{space 4} .2625672{col 67}{space 3} 1.570804
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.ln_ne L.resid D.ln_se L(1/3)D.(ln_ne ln_se)

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      51
{txt}{hline 13}{char +}{hline 30}           F(  8,    42) ={res}   30.52
    {txt}   Model {char |} {res} .030609646     8  .003826206           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .005264878    42  .000125354           {txt}R-squared     = {res} 0.8532
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.8253
    {txt}   Total {char |} {res} .035874524    50   .00071749           {txt}Root MSE      = {res}  .0112

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.2658499{col 26}{space 2} .0818016{col 37}{space 1}   -3.25{col 46}{space 3}0.002{col 54}{space 4}-.4309323{col 67}{space 3}-.1007675
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .7003052{col 26}{space 2} .0989823{col 37}{space 1}    7.08{col 46}{space 3}0.000{col 54}{space 4} .5005508{col 67}{space 3} .9000595
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2} .4340785{col 26}{space 2} .1338002{col 37}{space 1}    3.24{col 46}{space 3}0.002{col 54}{space 4} .1640588{col 67}{space 3} .7040982
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .1530296{col 26}{space 2} .1455307{col 37}{space 1}    1.05{col 46}{space 3}0.299{col 54}{space 4}-.1406631{col 67}{space 3} .4467223
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .2807848{col 26}{space 2} .1474322{col 37}{space 1}    1.90{col 46}{space 3}0.064{col 54}{space 4}-.0167454{col 67}{space 3} .5783149
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.4932871{col 26}{space 2} .1493358{col 37}{space 1}   -3.30{col 46}{space 3}0.002{col 54}{space 4}-.7946589{col 67}{space 3}-.1919154
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} -.266764{col 26}{space 2} .1585255{col 37}{space 1}   -1.68{col 46}{space 3}0.100{col 54}{space 4}-.5866814{col 67}{space 3} .0531533
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2}-.2714892{col 26}{space 2} .1641429{col 37}{space 1}   -1.65{col 46}{space 3}0.106{col 54}{space 4} -.602743{col 67}{space 3} .0597645
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2}  .027822{col 26}{space 2} .0095982{col 37}{space 1}    2.90{col 46}{space 3}0.006{col 54}{space 4} .0084521{col 67}{space 3} .0471919
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. savedresults comp eg e(), include(macros: depvar scalar: ll matrix: b V) tol(1e-7) verbose
{txt}comparing macro  e(depvar)
comparing scalar e(ll)
comparing matrix e(b)
comparing matrix e(V)

{com}. 
. egranger ln_ne ln_se ln_me, lags(4) regress qtrend ecm
{res}Replacing variable _egresid...

{txt}Engle-Granger 2-step ECM estimation{col 55}N (1st step)  ={res}       55
{txt}Number of lags   = {res} 4{col 55}{txt}N (2nd step)  ={res}       50
{txt}1st step includes quadratic trend

{res}Engle-Granger 1st-step regression
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.4853195{col 26}{space 2} .0829014{col 37}{space 1}   -5.85{col 46}{space 3}0.000{col 54}{space 4}-.6518318{col 67}{space 3}-.3188071
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.532462{col 26}{space 2} .0900714{col 37}{space 1}   17.01{col 46}{space 3}0.000{col 54}{space 4} 1.351548{col 67}{space 3} 1.713375
{txt}{space 6}_trend {c |}{col 14}{res}{space 2} .0043097{col 26}{space 2} .0011442{col 37}{space 1}    3.77{col 46}{space 3}0.000{col 54}{space 4} .0020114{col 67}{space 3} .0066079
{txt}{space 4}_trend^2 {c |}{col 14}{res}{space 2}-.0000493{col 26}{space 2} .0000141{col 37}{space 1}   -3.50{col 46}{space 3}0.001{col 54}{space 4}-.0000776{col 67}{space 3} -.000021
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.6391797{col 26}{space 2} .1337661{col 37}{space 1}   -4.78{col 46}{space 3}0.000{col 54}{space 4}-.9078567{col 67}{space 3}-.3705026
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{res}Engle-Granger 2-step ECM
{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 4}_egresid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.5210037{col 26}{space 2} .1859011{col 37}{space 1}   -2.80{col 46}{space 3}0.008{col 54}{space 4}-.8988003{col 67}{space 3}-.1432072
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2}-.0103413{col 26}{space 2} .1188278{col 37}{space 1}   -0.09{col 46}{space 3}0.931{col 54}{space 4}-.2518283{col 67}{space 3} .2311458
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .9902381{col 26}{space 2} .1339257{col 37}{space 1}    7.39{col 46}{space 3}0.000{col 54}{space 4} .7180683{col 67}{space 3} 1.262408
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}   .73665{col 26}{space 2} .2025554{col 37}{space 1}    3.64{col 46}{space 3}0.001{col 54}{space 4} .3250079{col 67}{space 3} 1.148292
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .2364299{col 26}{space 2} .2045024{col 37}{space 1}    1.16{col 46}{space 3}0.256{col 54}{space 4} -.179169{col 67}{space 3} .6520288
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .0756895{col 26}{space 2} .1879246{col 37}{space 1}    0.40{col 46}{space 3}0.690{col 54}{space 4}-.3062192{col 67}{space 3} .4575981
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .2736581{col 26}{space 2} .1849599{col 37}{space 1}    1.48{col 46}{space 3}0.148{col 54}{space 4}-.1022256{col 67}{space 3} .6495418
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.0205804{col 26}{space 2} .1366553{col 37}{space 1}   -0.15{col 46}{space 3}0.881{col 54}{space 4}-.2982975{col 67}{space 3} .2571367
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} -.036329{col 26}{space 2}   .09952{col 37}{space 1}   -0.37{col 46}{space 3}0.717{col 54}{space 4} -.238578{col 67}{space 3} .1659199
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1892732{col 26}{space 2} .1050514{col 37}{space 1}    1.80{col 46}{space 3}0.080{col 54}{space 4} -.024217{col 67}{space 3} .4027633
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .0322983{col 26}{space 2} .1041928{col 37}{space 1}    0.31{col 46}{space 3}0.758{col 54}{space 4}-.1794469{col 67}{space 3} .2440435
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.7510835{col 26}{space 2}  .267965{col 37}{space 1}   -2.80{col 46}{space 3}0.008{col 54}{space 4}-1.295654{col 67}{space 3} -.206513
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.2488536{col 26}{space 2} .2178504{col 37}{space 1}   -1.14{col 46}{space 3}0.261{col 54}{space 4}-.6915789{col 67}{space 3} .1938717
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2}-.2578413{col 26}{space 2} .1849592{col 37}{space 1}   -1.39{col 46}{space 3}0.172{col 54}{space 4}-.6337236{col 67}{space 3} .1180409
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2}  -.24145{col 26}{space 2}  .187394{col 37}{space 1}   -1.29{col 46}{space 3}0.206{col 54}{space 4}-.6222804{col 67}{space 3} .1393804
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0005089{col 26}{space 2} .0030577{col 37}{space 1}    0.17{col 46}{space 3}0.869{col 54}{space 4}-.0057051{col 67}{space 3}  .006723
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}

{com}. savedresults save eg e()
{txt}
{com}. capture drop resid
{txt}
{com}. regress ln_ne ln_se ln_me t tsq

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      55
{txt}{hline 13}{char +}{hline 30}           F(  4,    50) ={res}86783.30
    {txt}   Model {char |} {res} 59.3588148     4  14.8397037           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} .008549861    50  .000170997           {txt}R-squared     = {res} 0.9999
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9998
    {txt}   Total {char |} {res} 59.3673647    54  1.09939564           {txt}Root MSE      = {res} .01308

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}       ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}ln_se {c |}{col 14}{res}{space 2}-.4853195{col 26}{space 2} .0829014{col 37}{space 1}   -5.85{col 46}{space 3}0.000{col 54}{space 4}-.6518318{col 67}{space 3}-.3188071
{txt}{space 7}ln_me {c |}{col 14}{res}{space 2} 1.532462{col 26}{space 2} .0900714{col 37}{space 1}   17.01{col 46}{space 3}0.000{col 54}{space 4} 1.351548{col 67}{space 3} 1.713375
{txt}{space 11}t {c |}{col 14}{res}{space 2} .0043097{col 26}{space 2} .0011442{col 37}{space 1}    3.77{col 46}{space 3}0.000{col 54}{space 4} .0020114{col 67}{space 3} .0066079
{txt}{space 9}tsq {c |}{col 14}{res}{space 2}-.0000493{col 26}{space 2} .0000141{col 37}{space 1}   -3.50{col 46}{space 3}0.001{col 54}{space 4}-.0000776{col 67}{space 3} -.000021
{txt}{space 7}_cons {c |}{col 14}{res}{space 2}-.6391797{col 26}{space 2} .1337661{col 37}{space 1}   -4.78{col 46}{space 3}0.000{col 54}{space 4}-.9078567{col 67}{space 3}-.3705026
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. predict double resid, res
{txt}
{com}. regress D.ln_ne L.resid D.(ln_se ln_me) L(1/4)D.(ln_ne ln_se ln_me)

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}      50
{txt}{hline 13}{char +}{hline 30}           F( 15,    34) ={res}   46.19
    {txt}   Model {char |} {res}   .0335319    15   .00223546           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res}  .00164552    34  .000048398           {txt}R-squared     = {res} 0.9532
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.9326
    {txt}   Total {char |} {res}  .03517742    49  .000717907           {txt}Root MSE      = {res} .00696

{txt}{hline 13}{c TT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{col 1}     D.ln_ne{col 14}{c |}      Coef.{col 26}   Std. Err.{col 38}      t{col 46}   P>|t|{col 54}     [95% Con{col 67}f. Interval]
{hline 13}{c +}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{space 7}resid {c |}
{space 9}L1. {c |}{col 14}{res}{space 2}-.5210037{col 26}{space 2} .1859011{col 37}{space 1}   -2.80{col 46}{space 3}0.008{col 54}{space 4}-.8988003{col 67}{space 3}-.1432072
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}D1. {c |}{col 14}{res}{space 2}-.0103413{col 26}{space 2} .1188278{col 37}{space 1}   -0.09{col 46}{space 3}0.931{col 54}{space 4}-.2518283{col 67}{space 3} .2311458
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}D1. {c |}{col 14}{res}{space 2} .9902381{col 26}{space 2} .1339257{col 37}{space 1}    7.39{col 46}{space 3}0.000{col 54}{space 4} .7180683{col 67}{space 3} 1.262408
{txt}{space 12} {c |}
{space 7}ln_ne {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}   .73665{col 26}{space 2} .2025554{col 37}{space 1}    3.64{col 46}{space 3}0.001{col 54}{space 4} .3250079{col 67}{space 3} 1.148292
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} .2364299{col 26}{space 2} .2045024{col 37}{space 1}    1.16{col 46}{space 3}0.256{col 54}{space 4} -.179169{col 67}{space 3} .6520288
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .0756895{col 26}{space 2} .1879246{col 37}{space 1}    0.40{col 46}{space 3}0.690{col 54}{space 4}-.3062192{col 67}{space 3} .4575981
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .2736581{col 26}{space 2} .1849599{col 37}{space 1}    1.48{col 46}{space 3}0.148{col 54}{space 4}-.1022256{col 67}{space 3} .6495418
{txt}{space 12} {c |}
{space 7}ln_se {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.0205804{col 26}{space 2} .1366553{col 37}{space 1}   -0.15{col 46}{space 3}0.881{col 54}{space 4}-.2982975{col 67}{space 3} .2571367
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2} -.036329{col 26}{space 2}   .09952{col 37}{space 1}   -0.37{col 46}{space 3}0.717{col 54}{space 4} -.238578{col 67}{space 3} .1659199
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2} .1892732{col 26}{space 2} .1050514{col 37}{space 1}    1.80{col 46}{space 3}0.080{col 54}{space 4} -.024217{col 67}{space 3} .4027633
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2} .0322983{col 26}{space 2} .1041928{col 37}{space 1}    0.31{col 46}{space 3}0.758{col 54}{space 4}-.1794469{col 67}{space 3} .2440435
{txt}{space 12} {c |}
{space 7}ln_me {c |}
{space 9}LD. {c |}{col 14}{res}{space 2}-.7510835{col 26}{space 2}  .267965{col 37}{space 1}   -2.80{col 46}{space 3}0.008{col 54}{space 4}-1.295654{col 67}{space 3} -.206513
{txt}{space 8}L2D. {c |}{col 14}{res}{space 2}-.2488536{col 26}{space 2} .2178504{col 37}{space 1}   -1.14{col 46}{space 3}0.261{col 54}{space 4}-.6915789{col 67}{space 3} .1938717
{txt}{space 8}L3D. {c |}{col 14}{res}{space 2}-.2578413{col 26}{space 2} .1849592{col 37}{space 1}   -1.39{col 46}{space 3}0.172{col 54}{space 4}-.6337236{col 67}{space 3} .1180409
{txt}{space 8}L4D. {c |}{col 14}{res}{space 2}  -.24145{col 26}{space 2}  .187394{col 37}{space 1}   -1.29{col 46}{space 3}0.206{col 54}{space 4}-.6222804{col 67}{space 3} .1393804
{txt}{space 12} {c |}
{space 7}_cons {c |}{col 14}{res}{space 2} .0005089{col 26}{space 2} .0030577{col 37}{space 1}    0.17{col 46}{space 3}0.869{col 54}{space 4}-.0057051{col 67}{space 3}  .006723
{txt}{hline 13}{c BT}{hline 11}{hline 11}{hline 9}{hline 8}{hline 13}{hline 12}
{res}{txt}
{com}. savedresults comp eg e(), include(macros: depvar scalar: ll matrix: b V) tol(1e-7) verbose
{txt}comparing macro  e(depvar)
comparing scalar e(ll)
comparing matrix e(b)
comparing matrix e(V)

{com}. 
. log close
      {txt}name:  {res}<unnamed>
       {txt}log:  {res}C:\STATADAT\cs_egranger.smcl
  {txt}log type:  {res}smcl
 {txt}closed on:  {res} 2 Dec 2010, 22:11:50
{txt}{.-}
{smcl}
{txt}{sf}{ul off}