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Re: st: fixed effect, autocorrelation heteroskedasticity


From   ghislain dutheil <gdutheil@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: fixed effect, autocorrelation heteroskedasticity
Date   Mon, 25 Aug 2008 15:59:56 +0200

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 écrit :
> 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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