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Re: st: fixed effect, autocorrelation heteroskedasticity
Thanks David, thanks Clive,
I give more information :
My data : units are countries, my T runs from 1955 to 2006 (52 years),
data is balanced, response variable is normally distributed.
Here my results :
. xtgls y x1 x2 new_* if obs>1954,p(h) corr(ar1)
note: new_pays_14 dropped due to collinearity
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: common AR(1) coefficient for all panels (0.9210)
Estimated covariances = 14 Number of obs = 728
Estimated autocorrelations = 1 Number of groups = 14
Estimated coefficients = 16 Time periods = 52
Wald chi2(15) = 4919.00
Log likelihood = 952.8368 Prob > chi2 =
0.0000
y Coef. Std. Err. z P>z [95% Conf. Interval]
x1 .3798278 .0294945 12.88 0.000 .3220197 .4376359
x2 .1726235 .0468473 3.68 *0.000 * .0808044 .2644425
new_pays_1 -3.460705 .1801701 -19.21 0.000 -3.813832 -3.107579
new_pays_2 -2.841054 .1648916 -17.23 0.000 -3.164236 -2.517872
new_pays_3 -3.757751 .1864565 -20.15 0.000 -4.123199 -3.392303
new_pays_4 -1.881691 .1400781 -13.43 0.000 -2.156239 -1.607143
new_pays_5 -2.138633 .1837457 -11.64 0.000 -2.498768 -1.778498
new_pays_6 -3.408386 .2389035 -14.27 0.000 -3.876628 -2.940143
new_pays_7 -2.590972 .1518792 -17.06 0.000 -2.88865 -2.293294
new_pays_8 -6.032898 .3024923 -19.94 0.000 -6.625772 -5.440024
new_pays_9 -3.028034 .1719979 -17.61 0.000 -3.365143 -2.690924
new_pays_10 -3.71647 .197751 -18.79 0.000 -4.104055
-3.328885
new_pays_11 -3.792297 .2487666 -15.24 0.000 -4.279871
-3.304724
new_pays_12 -3.284582 .2416106 -13.59 0.000 -3.75813
-2.811034
new_pays_13 -1.64241 .1429002 -11.49 0.000 -1.922489 -1.36233
_cons 4.764067 .5989794 7.95 0.000 3.590089 5.938045
xtpcse y x1 x2 new_* if obs>1954, correlation(ar1)
(note: estimates of rho outside [-1,1] bounded to be in the range [-1,1])
Prais-Winsten regression, correlated panels corrected standard errors
(PCSEs)
Group variable: newid Number of obs
= 728
Time variable: obs Number of groups
= 14
Panels: correlated (balanced) Obs per group: min
= 52
Autocorrelation: common AR(1) avg
= 52
max = 52
Estimated covariances = 105 R-squared =
0.9620
Estimated autocorrelations = 1 Wald chi2(15) =
5937.36
Estimated coefficients = 16 Prob > chi2 =
0.0000
Panel-corrected
Coef. Std. Err. z P>z [95% Conf. Interval]
x1 .4503796 .0454639 9.91 0.000 .361272 .5394873
x2 .122018 .0775376 1.57 *0.116 * -.029953 .273989
new_pays_1 2.368664 .2301929 10.29 0.000 1.917494 2.819833
new_pays_2 2.913281 .2588473 11.25 0.000 2.40595 3.420613
new_pays_3 2.095312 .2180982 9.61 0.000 1.667848 2.522777
new_pays_4 3.825269 .2940457 13.01 0.000 3.24895 4.401587
new_pays_5 3.552052 .3126555 11.36 0.000 2.939259 4.164846
new_pays_6 2.481951 .2716012 9.14 0.000 1.949623 3.01428
new_pays_7 3.141937 .2687181 11.69 0.000 2.615259 3.668614
new_pays_8 (dropped)
new_pays_9 2.771673 .2540433 10.91 0.000 2.273758 3.269589
new_pays_10 2.157031 .2128672 10.13 0.000 1.739819 2.574243
new_pays_11 2.112108 .2568422 8.22 0.000 1.608707 2.615509
new_pays_12 2.572271 .2679651 9.60 0.000 2.047069 3.097473
new_pays_13 4.04784 .2898361 13.97 0.000 3.479771 4.615908
new_pays_14 5.499673 .4054914 13.56 0.000 4.704925 6.294422
_cons -1.236201 .9730438 -1.27 0.204 -3.143331 .6709301
rho .9190896
As you see X1 is significant in the two case, but X2 is not. My
theoretical economical question is X2 is or is not explicative of Y ?
So if i take one model i have one answer if i take the other i have an
other one, i have to choose very carrefully.
Clive said " Much depends on how much contemporaneous correlation of the
errors there is in your data. If you have lots, and T > N by a factor of
3 or more (which you have), then FGLS estimates should be okay. If you
don't have much by way of CCEs, then OLS-PCSE is to be preferred"
I don't how to know if there is a lots or a few CCE ?
Can you help me
Thanks
Ghislain
Clive Nicholas a �crit :
> Ghislain Dutheil replied:
>
>
>> the two model give results quite different : in one case (FGLS) an
>> explonary variable is significative in the other, PCSE, it is not, and i
>> have only two explonary variables... so the difference is sensible . So
>> excuse me but why cross-sectional GLS estimates is pretty unreliable
>> compare to OLS-PCSE ?
>>
>
> Since you neither show us any output from your models nor explain what
> these models seek to explain theoretically, there really is no way of
> judging how 'sensible' your results are. Only you will know.
>
> Much depends on how much contemporaneous correlation of the errors
> there is in your data. If you have lots, and T > N by a factor of 3 or
> more (which you have), then FGLS estimates should be okay. If you
> don't have much by way of CCEs, then OLS-PCSE is to be preferred; see
> the whole of Beck and Katz (1995). In most panel data (T > 50 is not
> typical), the paramter estimates are inefficient under FGLS: "The FGLS
> standard errors underestimate sampling variability because FGLS
> assumes that \sigma [the N x N matrix of contemporaneous covariances]
> is known, not estimated. Our conclusion is that the Parks-Kmenta
> [FGLS] estimator simply should not be used" (Beck, 2001).
>
> However, you _still_ haven't really told us about your data. We're
> still left to assume that your units are countries (which would rule
> out -bootstrap-ping or -simulate-ing your way out of any
> difficulties), that your Ts are equidistantly spaced, and that your
> response variable is normally distributed. If your RV isn't, then none
> of the modelling approaches mentioned in this thread may be useful for
> fitting to your data.
>
>
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