Postestimation test for cross-sectional time series FGLS regression

[Bernard Phiri]

Hi

I'm conducting a study on the determinants of bank profitability in my country. I have data from 16 of the total 18 banks (N=16) spanning over a period of 40 (T=40). Theory pointed me to 'xtgls" as opposed to 'xtreg'.

After running a pre-FGLS regression I found that autocorrelation, heteroskedasticity and cross-sectional dependence were present when I tested for them by using 'xtserial', 'xttest3' and 'xttest2' respectively.

I then ran two another FGLS regressions with all three problems specified and got the results below. Model 2 is simply a modification of model 1 as it has square terms of all the continuous variables.

Model 1:

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: common AR(1) coefficient for all panels (0.8231)

Estimated covariances = 136 Number of obs = 640
Estimated autocorrelations = 1 Number of groups = 16
Estimated coefficients = 6 Time periods = 40
Wald chi2(5) = 630.93
Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ROA | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LNTA | 3.017828 .1259643 23.96 0.000 2.770943 3.264714
CAPR | -.0089637 .0089082 -1.01 0.314 -.0264235 .0084962
LIQR | .0030467 .0016026 1.90 0.057 -.0000944 .0061878
INFL | -.0097423 .0312732 -0.31 0.755 -.0710367 .051552
GDPG | -.0421484 .126283 -0.33 0.739 -.2896584 .2053617
_cons | -41.75591 2.267979 -18.41 0.000 -46.20107 -37.31075
------------------------------------------------------------------------------

Model 2:

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: common AR(1) coefficient for all panels (0.8098)

Estimated covariances = 136 Number of obs = 640
Estimated autocorrelations = 1 Number of groups = 16
Estimated coefficients = 11 Time periods = 40
Wald chi2(10) = 645.23
Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ROA | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LNTA | 28.27193 1.988883 14.21 0.000 24.37379 32.17007
CAPR | .0968506 .0172677 5.61 0.000 .0630064 .1306947
LIQR | .020302 .0031623 6.42 0.000 .014104 .0265001
INFL | -.2763099 .1310412 -2.11 0.035 -.5331459 -.0194738
GDPG | 1.110413 .3644671 3.05 0.002 .3960706 1.824756
LNTA2 | -.9128306 .067772 -13.47 0.000 -1.045661 -.78
CAPR2 | -.0013482 .0003059 -4.41 0.000 -.0019478 -.0007487
LIQR2 | -.0000548 9.47e-06 -5.78 0.000 -.0000734 -.0000362
INFL2 | .0081777 .0044353 1.84 0.065 -.0005154 .0168707
GDPG2 | -.1538821 .0366569 -4.20 0.000 -.2257284 -.0820358
_cons | -216.4275 14.58703 -14.84 0.000 -245.0175 -187.8374
------------------------------------------------------------------------------

Question: is there a way to test between which models fits the data better seeing that AIC and the LIkelihood ratio test can't be used.

PS: I'm using an older version of STATA (14.2)

Any help is highly appreciated.

[Carlo Lazzaro]

Bernard:
welcome to this forum.
In your second model, you included square terms.
Hence, the first advice is to use the -fvvarlist- notation instead of creating those terms by hand.
As an aside, you should use the regression moded that gives a fair and true view of the data generating process you're interested in (and skimming trough the literature of your reesearch field can be a step to take in this respect).
Eventually, please do not urge people to reply to your queries privately (as recommended by the FAQ): be patient, please. We're all busy people (just like you) and could have overlooked your post and/or might not have helpful reply to give.

[Bernard Phiri]

Carlo

Thank you.

Well noted, my apologies.

[Carlo Lazzaro]

Bernard:
no problem.
Enjoy your staying with the Stata forum.

[Bernard Phiri]

Carlo:

Thank you.

Just to make a quick follow up.
I run a new FGLS regression with the 'fvvarlist' notation. My results are still the same as when I generated the variables by hand, see below.
Again, is there a way to test for which model among the ones I outlined earlier after using the AR(1) and panels(correlated) options?

Regards, Bernard

[Bernard Phiri]

Carlo:

Thank you.

Just to make a quick follow up.
I run a new FGLS regression with the 'fvvarlist' notation. My results are still the same as when I generated the variables by hand, see below.
Again, is there a way to test for which model among the ones I outlined earlier after using the AR(1) and panels(correlated) options?

Regards, Bernard

xtgls ROA LNTA CAPR    LIQR INFL GDPG c.LNTA##c.LNTA c.CAPR##c.CAPR    c.LIQR##c.LIQR c.INFL##c.INFL    c.GDPG##c.GDPG, panels(correlated) corr(ar1)

[Carlo Lazzaro]

Bernard:
there's no hard and fast rule about comparing two -xtgls- models.
As a temptative answer, you may want to consider calculating adj sq_R from -chi2- (see https://www.statalist.org/forums/for...ted-as-missing).

[Bernard Phiri]

Carlo

I've gotten past my roadblock thanks to you.
Please do have a wonderful year ahead.

Regards,
Bernard.

[Carlo Lazzaro]

Bernard:
thanks, you too.