FGLS for panel data

[Nathan Johnson]

I have a panel data N=46, T=4, with time invariant variable. Hausman test tells me I should do fixed effects, but because of the time-invariant I guess I have to do Random effects. The model is heteroscedastic and have serial correlation, based on modifed Wald test and Wooldridge. Thus, I need to use FGLS. Below is what i have done. Can anyone confirm if this looks correct? Is Wooldridge test on 1sr order autocorrelation the same one we are specifying in the xtgls by (corr AR1)? I also tried xtreg re vce (robust) and totally different results. Which one is correct and which one should i use? Any advice how do i pull off FGLS for my model? Thank you very much! I have been working on this for more than a month now...

. xtgls FDI_plus_1_ln GDP_ln TI GC CIT Edu Imp PI Yr15 Yr16 Yr17 Yr18 Yr19, panels(hetero) corr(ar1)

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: common AR(1) coefficient for all panels (0.3361)

Estimated covariances = 46 Number of obs = 276
Estimated autocorrelations = 1 Number of groups = 46
Estimated coefficients = 13 Time periods = 6
Wald chi2(12) = 1431.97
Prob > chi2 = 0.0000

------------------------------------------------------------------------------
FDI_plus_1~n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GDP_ln | 2.016305 .1019315 19.78 0.000 1.816523 2.216087
TI | -.0050162 .0075715 -0.66 0.508 -.0198561 .0098236
GC | -.2146487 .096893 -2.22 0.027 -.4045556 -.0247419
CIT | 5.900017 4.376703 1.35 0.178 -2.678164 14.4782
Edu | 14.13463 2.499647 5.65 0.000 9.235416 19.03385
Imp | 1.413051 .9549068 1.48 0.139 -.4585319 3.284634
PI | -.0000446 .0000154 -2.89 0.004 -.0000748 -.0000143
Yr15 | .0166233 .1242356 0.13 0.894 -.2268741 .2601206
Yr16 | .0279643 .1446263 0.19 0.847 -.255498 .3114266
Yr17 | -.1400918 .1546937 -0.91 0.365 -.4432858 .1631022
Yr18 | -.3144913 .1659963 -1.89 0.058 -.6398382 .0108556
Yr19 | -.789393 .175671 -4.49 0.000 -1.133702 -.4450841
_cons | -20.50538 1.113038 -18.42 0.000 -22.68689 -18.32386
------------------------------------------------------------------------------

. xtreg FDI_plus_1_ln GDP_ln TI GC CIT Edu Imp PI Yr15 Yr16 Yr17 Yr18 Yr19, re vce (robust)

Random-effects GLS regression Number of obs = 276
Group variable: ID_States Number of groups = 46

R-sq: Obs per group:
within = 0.0450 min = 6
between = 0.8504 avg = 6.0
overall = 0.7531 max = 6

Wald chi2(12) = 475.61
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. Err. adjusted for 46 clusters in ID_States)
------------------------------------------------------------------------------
| Robust
FDI_plus_1~n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GDP_ln | 2.242274 .2859811 7.84 0.000 1.681762 2.802787
TI | .0015489 .012926 0.12 0.905 -.0237856 .0268835
GC | -.2401492 .1370945 -1.75 0.080 -.5088495 .028551
CIT | 9.938618 9.922991 1.00 0.317 -9.510088 29.38732
Edu | 9.374441 6.799565 1.38 0.168 -3.952462 22.70134
Imp | -1.002315 2.87342 -0.35 0.727 -6.634114 4.629484
PI | -.0000361 .0000376 -0.96 0.337 -.0001099 .0000376
Yr15 | -.1945159 .1619585 -1.20 0.230 -.5119487 .122917
Yr16 | -.1606619 .1771356 -0.91 0.364 -.5078413 .1865175
Yr17 | -.0735213 .1829888 -0.40 0.688 -.4321728 .2851303
Yr18 | -.3672885 .2175022 -1.69 0.091 -.7935851 .059008
Yr19 | -.8331632 .2848401 -2.93 0.003 -1.39144 -.2748868
_cons | -22.47016 2.594245 -8.66 0.000 -27.55478 -17.38553
-------------+----------------------------------------------------------------
sigma_u | .81412037
sigma_e | .94769178
rho | .4246185 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Joro Kolev]

No, this does not sound correct. You have a large N small T panel, and the appropriate set of commands to deal with such data re in the -xtreg- and also in -xtgee-.

[Carlo Lazzaro]

Nathan:
as an side to Joro's helpful reply, I fail to follow how you could have run -hausman- with non-default standard errors (as they're not supported).
Hence, you shoud impose the -robust- or -cluster- options to your standard errors before running -xtreg- and then rely on the community-contributed programme -xtoverid- to test which of the two specifications fit your data better.
For the future, please use CODe delimiters to post what you typed and what Stata gave you back. Thanks.

[Nathan Johnson]

Many thanks for your responses. I will try to figure out that code delimiters - last time i was unable lol. I ran the xtoverid on both robust fixed and robust random models and still got fixed model as preferred (p<0.0000). But i don't know what to do as my model requires me to use time-invariant variable and random effect is the only way to include that? what would your suggestions? How do i justify?

Also, for the option cluster, am i correct to use the states/ my IDs? I got the same results for my xtreg re vce robust and xtreg re cluster (States1) States1 is my N, or the units. And also, do i ran xtgee just by itself with my y and x or do i need to specify anything, what would you suggest? I got similar results to the above re cluster and re vce robust. Is that all and correct what i have done to correct for first-order autocorrelation and heteroscedasticity? I was told by my supervisor to use FGLS in case of the above problems. In case i use xtgee or xtreg re vce robust, what do i say? is it the same as FGLS? I apologize in advance for stupid questions. Also, I have noticed that Woolrdridge test is for only fixed model, is that a problem?

[Carlo Lazzaro]

Nathan:
you may want to take a look at the community-contributed programme -mundlak- if you do not want to switch to -re- specification.
You're correct about clustering your standard errors on your -panelid- and, as expected, under -xtreg- -robust- and -cluster- options produce the very same output.
Basically, going FGLS means invoking options that deal with OLS disturbances such as heteroskedasticity, autocorrelation and cross-panel correlation.
Two asides:
- I increase your knowledge of econometrics studying one of the many textbooks that are reported in -xtreg- reference section (see related entry in Stata .pdf manual);
- discuss every single step of your reserach strategy with your suprevisor, just to avoid problems/issues/panic during the final trait of your approaching to dissertation drafting/discussion.

[Nathan Johnson]

Thank you. I performed Mundlak test and the preference is again for fixed effect. So I guess my main problem now is do i go ahead with random effect robust model or? Does that mean that my random model is wrong? How do i account for my time-invariant model? I saw H-T approach, but i am not sure i can figure out my endog and exog variables. Do i do hybrid model? Also, for some reason the fixed effect model brings results that are odd - education has negative effect on FDI although it should be positive and i don't know why the fixed effect is producing such result... is xtpce command not recomended for my case? Thank you!

[Nathan Johnson]

Is there an easy/ straightforward way on Stata to check all the assumptions of the fixed or random effects? e.g. i keep reading about the strict exogeneity assumption and Covariates in each time period are uncorrelated with the idiosyncratic error in each time period, etc.

[Nathan Johnson]

Dear Carlo and Joro, where can i find a reference that says xtgls is for T>N and xtgee is for N>T? i searched and couldn't find "official" reference, i need to show it to my supervisor. I have 46 states (N) observing for 6 years (2014-2019) (T). My N>T, so i should use xtgee, correct? Thank you so much!

[Carlo Lazzaro]

Nathan:
from Example 2 in Stata .pdf manual you can see that -xtgee- is uded for N>T panel dataset.
It has the advantage to be more flexible than, say, -xtreg, pa-.

[Nur Liyana]

Hello! I just read this discussion and want to confirm something. As I'm still quite new to this, I'm a bit confused. If T < N , I should use 'xtgee' or `xtreg` fe or re. If T > N, I can consider `xtgls` or `xtscc` or 'xtpcse'. My question is: if T is only 9 and N is only 8, should I still use `xtgls`, 'xtscc' or 'xtpcse'? I don't have cross-sectional dependence issues, but I do have heteroskedasticity and autocorrelation problems.

[Carlo Lazzaro]

Nur:
welcome to this forum.
Assuming you have a continuous regressand, my first move would be -xtreg,fe vce(cluster panelid)-.