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st: AR1 and xtgls


From   Bryon Balint <[email protected]>
To   "'[email protected]'" <[email protected]>
Subject   st: AR1 and xtgls
Date   Thu, 2 Jan 2014 20:05:03 +0000

Hello, I am using -xtgls- in Stata 13.0. My data has 2050 observations across 114 panels, which are set monthly. I also have an independent variable for a time trend, which is incremented monthly (one of the things I'm investigating is performance improvement over time). This time trend variable is also interacted with other variables.

The -xtserial- test indicates that I have autocorrelation, so I reran xtgls using the c(ar1) option. My understanding of AR1 correction was that it changes the standard errors but not the coefficient estimates. The coefficients have changed, but most of them remain statistically significant. However, the coefficients on the time trend variable and all of the interactions with the time trend variable are no longer significant after using the c(ar1) option. I am trying to understand why this is the case. Is it because my time trend variable uses the same intervals (monthly) that the AR1 correction uses?

Some examples below: Example 1 is without AR1 correction, Example 2 is with AR1 correction. The time trend variable is c_px_tss and its interactions are the variables following it.

EXAMPLE 1

. xtgls actualval structure_yes i_structure_cost2    c_p1syn  c_p1syn_cost c_variationspertask_to
> tal i_c_vt_cost2  c_variationspertask_total_syn i_c_vt_syn_cost2 i_struc_c_vt i3_struc_c_vt_cos
> t2  c_px_tss i_px_tss_cost2  c_px_tss_syn c_px_tss_syn_cost i_px_tss_c_vt i3_px_tss_c_vt_cost2 
> i_px_tss_c_vt_syn i_px_tss_c_vt_syn_cost group2_cost newbl* monthcounter i_monthcounter_cost2, 
> p(h)

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   no autocorrelation

Estimated covariances      =       114          Number of obs      =      2050
Estimated autocorrelations =         0          Number of groups   =       114
Estimated coefficients     =        29          Obs per group: min =         5
                                                               avg =  17.98246
                                                               max =        25
                                                Wald chi2(28)      =    897.26
                                                Prob > chi2        =    0.0000

-----------------------------------------------------------------------------------------------
                    actualval |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------+----------------------------------------------------------------
                structure_yes |   .6757174   .2999774     2.25   0.024     .0877725    1.263662
            i_structure_cost2 |   .7171097   2.130786     0.34   0.736    -3.459154    4.893373
                      c_p1syn |  -.2386655   .0818019    -2.92   0.004    -.3989943   -.0783366
                 c_p1syn_cost |   .8814414   .5280493     1.67   0.095    -.1535163    1.916399
    c_variationspertask_total |  -.3886945   .1226349    -3.17   0.002    -.6290544   -.1483345
                 i_c_vt_cost2 |   -.462433   .7868393    -0.59   0.557     -2.00461    1.079744
c_variationspertask_total_syn |  -.1170541   .0399244    -2.93   0.003    -.1953044   -.0388038
             i_c_vt_syn_cost2 |   .6831517   .2708621     2.52   0.012     .1522717    1.214032
                 i_struc_c_vt |   .1888914   .1344301     1.41   0.160    -.0745866    .4523695
          i3_struc_c_vt_cost2 |  -1.154606   .7110748    -1.62   0.104    -2.548287    .2390747
                     c_px_tss |   .0407651   .0279762     1.46   0.145    -.0140672    .0955974
               i_px_tss_cost2 |   .4496724   .1982409     2.27   0.023     .0611274    .8382175
                 c_px_tss_syn |     .02902   .0105108     2.76   0.006     .0084192    .0496208
            c_px_tss_syn_cost |   .0559958   .0795014     0.70   0.481    -.0998241    .2118157
                i_px_tss_c_vt |   .0212492   .0065342     3.25   0.001     .0084424    .0340559
         i3_px_tss_c_vt_cost2 |   .1660515   .0621026     2.67   0.007     .0443327    .2877703
            i_px_tss_c_vt_syn |   .0156071   .0049837     3.13   0.002     .0058391    .0253751
       i_px_tss_c_vt_syn_cost |   .0759115   .0424666     1.79   0.074    -.0073215    .1591445
                        _cons |   97.60483   .7827861   124.69   0.000      96.0706    99.13906
-----------------------------------------------------------------------------------------------

EXAMPLE 2 


. xtgls actualval structure_yes i_structure_cost2    c_p1syn  c_p1syn_cost c_variationspertask_to
> tal i_c_vt_cost2  c_variationspertask_total_syn i_c_vt_syn_cost2 i_struc_c_vt i3_struc_c_vt_cos
> t2  c_px_tss i_px_tss_cost2  c_px_tss_syn c_px_tss_syn_cost i_px_tss_c_vt i3_px_tss_c_vt_cost2 
> i_px_tss_c_vt_syn i_px_tss_c_vt_syn_cost group2_cost newbl* monthcounter i_monthcounter_cost2, 
> p(h) c(ar1) force

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   common AR(1) coefficient for all panels  (0.6421)

Estimated covariances      =       114          Number of obs      =      2050
Estimated autocorrelations =         1          Number of groups   =       114
Estimated coefficients     =        29          Obs per group: min =         5
                                                               avg =  17.98246
                                                               max =        25
                                                Wald chi2(28)      =    350.42
                                                Prob > chi2        =    0.0000

-----------------------------------------------------------------------------------------------
                    actualval |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------+----------------------------------------------------------------
                structure_yes |    .290638   .2755976     1.05   0.292    -.2495233    .8307993
            i_structure_cost2 |  -.7768766   1.751299    -0.44   0.657     -4.20936    2.655607
                      c_p1syn |  -.0112962    .114967    -0.10   0.922    -.2366273     .214035
                 c_p1syn_cost |   1.510317   .7128032     2.12   0.034     .1132483    2.907386
    c_variationspertask_total |  -.2019513   .1342058    -1.50   0.132    -.4649898    .0610871
                 i_c_vt_cost2 |  -1.024145    .797939    -1.28   0.199    -2.588077    .5397867
c_variationspertask_total_syn |  -.0028495    .055857    -0.05   0.959    -.1123272    .1066283
             i_c_vt_syn_cost2 |   .3885293   .3908295     0.99   0.320    -.3774824    1.154541
                 i_struc_c_vt |   .0365023   .1241229     0.29   0.769    -.2067742    .2797787
          i3_struc_c_vt_cost2 |  -.7389062   .6054729    -1.22   0.222    -1.925611    .4477989
                     c_px_tss |   .0058479   .0399997     0.15   0.884    -.0725501    .0842458
               i_px_tss_cost2 |    .419579   .2525058     1.66   0.097    -.0753234    .9144813
                 c_px_tss_syn |   .0117767   .0150597     0.78   0.434    -.0177397    .0412931
            c_px_tss_syn_cost |   .0067606   .1046975     0.06   0.949    -.1984427    .2119639
                i_px_tss_c_vt |   .0101954   .0092202     1.11   0.269    -.0078757    .0282666
         i3_px_tss_c_vt_cost2 |   .1195411   .0802724     1.49   0.136    -.0377898     .276872
            i_px_tss_c_vt_syn |   .0043021   .0071224     0.60   0.546    -.0096574    .0182617
       i_px_tss_c_vt_syn_cost |   .1194113   .0559825     2.13   0.033     .0096876     .229135
                 monthcounter |     .02217   .0344892     0.64   0.520    -.0454275    .0897675
         i_monthcounter_cost2 |  -.0533212    .170076    -0.31   0.754     -.386664    .2800215
                        _cons |   98.67921   .9634511   102.42   0.000     96.79088    100.5675
-----------------------------------------------------------------------------------------------

Thanks,
Dr. Bryon Balint


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