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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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