[Carlo Lazzaro]

Radhika:
1) -regress- and -xtreg,fe- implies different estimators; therefore, what you experienced may happen. In addition, you don't tell whether or not you run an OLS with or without fixed effect specification (that is, with -i.panelid- in the right-hand side of your regression equation;
2) and ) heteroskedasticity and autocorrelation of the systematic error can both be dealt with -robust- or -vce(cluster panelid)- standard errors (they do the very same job under -xtreg-);
3) the -xtrest0- outcome highlights the evidence of a panel-wise effect, but do not tell that -re- is necessarily the way to (as -fe- may be a better estimator for your dataset),
4) I'd also test the functional form of the regressand via a procedure = -linktest-, but that you should code by hand, as it is not supported by -xtreg-.

[Radhika Channanamchery]

Radhika:
1) -regress- and -xtreg,fe- implies different estimators; therefore, what you experienced may happen. In addition, you don't tell whether or not you run an OLS with or without fixed effect specification (that is, with -i.panelid- in the right-hand side of your regression equation;
2) and ) heteroskedasticity and autocorrelation of the systematic error can both be dealt with -robust- or -vce(cluster panelid)- standard errors (they do the very same job under -xtreg-);
3) the -xtrest0- outcome highlights the evidence of a panel-wise effect, but do not tell that -re- is necessarily the way to (as -fe- may be a better estimator for your dataset),
4) I'd also test the functional form of the regressand via a procedure = -linktest-, but that you should code by hand, as it is not supported by -xtreg-.

Dear Carlo,

Thank you for your helpful reply.

I have finally selected the FE model based on my xtoverid test result.

1) An important variable called the Agro-Ecological Zone dummy is omitted in the model due to collinearity as it is the same AEZ code for a particular district over all four time periods.

How can I include it if I want to? Can I cluster it? In my RE model, when I have used- i.AEZ- command, I have obtained significant p values for all the 10 AEZ categories. What should I do If I want to include them in my FE model?(My RE model is rejected by xtoverid test)

2) Can I use- i. year- in my RE model also, as it is known as time fixed effect.? I have checked -testparm i.year - after running an RE model with i.year at RHS of my RE model. P value is 0.02.Is it correct?

Expecting your kind reply.

Thank you

Radhika

[Carlo Lazzaro]

Radhika:
the main issue here is that the -re- coefficients are not consistent (because -fe-) is the way to go, as per -xtoverid- outcome. Therefore, the staitical signicance that you got is meaningless, as it is based on a flawed methodological ground.
Obviously, you can insist with -re-, at your own risk, though.

[Radhika Channanamchery]

Radhika:
the main issue here is that the -re- coefficients are not consistent (because -fe-) is the way to go, as per -xtoverid- outcome. Therefore, the staitical signicance that you got is meaningless, as it is based on a flawed methodological ground.
Obviously, you can insist with -re-, at your own risk, though.

Dear Carlo,

This is also a related question w.r.t. to the test using-xtoverid - command. I have a problem with comparing the FE and RE, after I have detected heteroskedasticity ( and autocorr) I am trying to use xtoverid insead of hausman.

As I have used the crop diversification index as my dependent variable instead of the area under horticulture crops, using the same independent variables, I cannot get any results with xtoverid . It showed the following error message . When I run I got ,

xtoverid
Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS
r(198);

In my RE model RHO value is Zero(sigma _u =0). What is the meaning of this?

I have also run BPLM test which shows the following results


xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

HI[districtid,t] = Xb + u[districtid] + e[districtid,t]

Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
HI | .0090133 .0949384
e | .0089344 .0945221
u | 0 0

Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000



Should I choose pooled OLS ?

What is the right model here?

Please kindly suggest.

Thank you
Radhika

[Carlo Lazzaro]

Radhika:
the resultys you mention are consitent in highlighting the absence of evidence of a panel-wise effect in your dataset.
That's why -xroverid- outocome points you toward a pooled OLS.

[Radhika Channanamchery]

Radhika:
the resultys you mention are consitent in highlighting the absence of evidence of a panel-wise effect in your dataset.
That's why -xroverid- outocome points you toward a pooled OLS.

Thank you, Carlo, for your kind reply.

I have chosen Pooled OLS in this case. Still, I have a few confusions
1. In its specification, can I use i.panelid and i.year as district and time dummies?
2. Can I cluster the SE with the cluster(panelid) option in the RHS of the model? What is the meaning here? Is it the same as robust SE after detecting the problem of Heteroscedasticity or autocorrelation in the FE model? I have tested for heteroscedasticity and multicollinearity after running the Pooled OLS. The results are as follows.

reg HI meantemperature rainfall populationdensitypersqkm gddppercapitaRS numberofbanksper1000sqkm averagelandsize_ha shareofnonagriareainga shareofirr_final sharemarginal shareofscandst Share_urbanpop i.year


.hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of HI

chi2(1) = 2.72
Prob > chi2 = 0.0992

. imtest,white

White's test for Ho: homoskedasticity
against Ha: unrestricted heteroskedasticity

chi2(107) = 108.00
Prob > chi2 = 0.4547

Cameron & Trivedi's decomposition of IM-test

---------------------------------------------------
Source | chi2 df p
---------------------+-----------------------------
Heteroskedasticity | 108.00 107 0.4547
Skewness | 18.70 14 0.1766
Kurtosis | 0.00 1 0.9846
---------------------+-----------------------------
Total | 126.70 122 0.3670


vif

Variable | VIF 1/VIF
-------------+----------------------
meantemper~e | 1.29 0.773142
rainfall | 2.27 0.441055
population~m | 13.83 0.072300
gddppercap~S | 6.81 0.146893
numberofba~m | 3.85 0.259482
averagelan~a | 9.47 0.105559
shareofnon~a | 16.64 0.060086
shareofirr~l | 1.31 0.763926
sharemargi~l | 9.44 0.105927
shareofsca~t | 1.74 0.574333
Share_urba~p | 1.42 0.702147
year |
2006 | 1.71 0.586477
2011 | 3.88 0.257576
2016 | 6.58 0.152052
-------------+----------------------
Mean VIF | 5.73

. estat vce,corr

Correlation matrix of coefficients of regress model

| 2006.
e(V) | meante~e rainfall popula~m gddppe~S number~m averag~a shareo~a sh~final sharem~l shar~dst Share_~p year
-------------+------------------------------------------------------------------------------------------------------------------------
meantemper~e | 1.0000
rainfall | -0.3070 1.0000
population~m | -0.1446 0.1906 1.0000
gddppercap~S | 0.0052 -0.3333 -0.0569 1.0000
numberofba~m | 0.0178 -0.1683 -0.0068 -0.0636 1.0000
averagelan~a | -0.0009 0.3043 -0.2987 -0.2667 -0.1166 1.0000
shareofnon~a | 0.1356 -0.0218 -0.8975 -0.1740 -0.2192 0.3292 1.0000
shareofirr~l | -0.2896 0.2231 0.1119 0.0017 -0.0086 -0.1852 -0.0619 1.0000
sharemargi~l | -0.0203 0.2317 -0.0914 -0.2591 -0.2430 0.8783 0.1104 -0.1323 1.0000
shareofsca~t | -0.3109 0.4215 0.0760 0.0550 0.1718 0.2309 -0.1260 0.0298 0.2264 1.0000
Share_urba~p | -0.1424 0.2682 0.1297 -0.1238 -0.4563 0.0934 0.0298 0.1174 0.1327 0.0673 1.0000
2006.year | 0.1040 0.0136 -0.0530 -0.2912 0.0317 0.1858 0.1003 -0.1167 0.1627 -0.0616 -0.0144 1.0000
2011.year | 0.0813 0.2174 -0.0528 -0.7562 -0.0445 0.3242 0.2344 -0.1164 0.2909 -0.0956 0.0835 0.5429
2016.year | -0.0388 0.3833 -0.0082 -0.8446 -0.1338 0.3281 0.2493 -0.0200 0.2837 -0.0554 0.1693 0.4735
_cons | -0.6979 -0.0974 0.2905 0.2134 0.0402 -0.6721 -0.3207 0.2602 -0.5913 -0.0882 -0.0583 -0.2575

| 2011. 2016.
e(V) | year year _cons
-------------+------------------------------
2011.year | 1.0000
2016.year | 0.8177 1.0000
_cons | -0.3269 -0.2481 1.0000


As per heteroscedasticity tests, there is no heteroscedasticity problem.

In the case of Multicollinearity, population, and share of the non-agricultural area shows vif value of more than 10. Is it needs to be corrected? How to correct it?

I would appreciate your kind help with this.

Thank you, and looking forward to your kind reply.
Radhika

[Carlo Lazzaro]

Radhica:
1) yes, you can I use i.panelid and i.year as district and time dummies in pooled OLS;
2) you should cluster your standard errors at -panelid- level, as your panel-specific observations are not independent;
3) multicollinearity is not an issue in your case; a VIF=10 should not be a source of concern;
4) I would give -linktest- a shot.

[Radhika Channanamchery]

Radhica:
1) yes, you can I use i.panelid and i.year as district and time dummies in pooled OLS;
2) you should cluster your standard errors at -panelid- level, as your panel-specific observations are not independent;
3) multicollinearity is not an issue in your case; a VIF=10 should not be a source of concern;
4) I would give -linktest- a shot.

Thank you Carlo for your reply.

I have included i.year and i.panelid in the model.

reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sq
> km gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid,cluster(districtid)


The P value of the model is not shown in the results. Is it any error?

Linear regression Number of obs = 108
F( 13, 26) = .
Prob > F = .
R-squared = 0.3793
Root MSE = .09452

(Std. Err. adjusted for 27 clusters in districtid)
------------------------------------------------------------------------------------------
| Robust
SI_all | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
shareofscandst | -.0125334 .0080951 -1.55 0.134 -.029173 .0041062
shareofnonagriareainga | .0091163 .0058625 1.56 0.132 -.0029342 .0211668
Share_urbanpop | -.0012651 .0070174 -0.18 0.858 -.0156897 .0131594
shareofirr_final | -.0006138 .0003033 -2.02 0.053 -.0012373 9.64e-06
sharemarginal | .0033908 .0026645 1.27 0.214 -.0020862 .0088677
averagelandsize_ha | .0539845 .1078722 0.50 0.621 -.16775 .2757191
numberofbanksper1000sqkm | -.000725 .0004749 -1.53 0.139 -.0017013 .0002512
gddppercapitaRS | -1.34e-07 5.84e-07 -0.23 0.820 -1.33e-06 1.07e-06
populationdensitypersqkm | -.0002481 .0000826 -3.00 0.006 -.0004179 -.0000784
rainfall | .0000667 .0000514 1.30 0.206 -.000039 .0001725
meantemperature | -.0095323 .0157201 -0.61 0.550 -.0418453 .0227808
|
year |
2006 | -.0064564 .0378465 -0.17 0.866 -.0842509 .0713381
2011 | .0366481 .0775858 0.47 0.641 -.1228319 .1961281
2016 | .0657914 .1136645 0.58 0.568 -.1678493 .2994321
|
districtid |
2 | -.0302375 .3964734 -0.08 0.940 -.8452003 .7847253
3 | .3173174 .1926224 1.65 0.112 -.0786235 .7132584
4 | -.0109322 .0390729 -0.28 0.782 -.0912478 .0693834
5 | .1399038 .1347675 1.04 0.309 -.1371147 .4169223


My second query is on model specification test you have mentioned in your previous reply.

.linktest

Source | SS df MS Number of obs = 108
-------------+------------------------------ F( 2, 105) = 32.12
Model | .366060296 2 .183030148 Prob > F = 0.0000
Residual | .598362316 105 .005698689 R-squared = 0.3796
-------------+------------------------------ Adj R-squared = 0.3677
Total | .964422612 107 .009013295 Root MSE = .07549

------------------------------------------------------------------------------
SI_all | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_hat | 1.394775 1.910719 0.73 0.467 -2.393828 5.183377
_hatsq | -.3193171 1.542202 -0.21 0.836 -3.37722 2.738585
_cons | -.1208546 .5890733 -0.21 0.838 -1.288878 1.047169
------------------------------------------------------------------------------


As the P value is not significant and it accepts the H0 of No omitted variable problem. Am I right?

I have tried ovtest too. What is the difference bw the two?


. ovtest

Ramsey RESET test using powers of the fitted values of SI_all
Ho: model has no omitted variables
F(3, 64) = 3.14
Prob > F = 0.0311
This test rejects the H0 of no omitted variables. Which test is to be followed, and why is it so?

Share your kind reply in this regard.

Thank you
Radhika

[Carlo Lazzaro]

Radhika:
1) see -help j_robustsingular- about the missing F statistic (and related stuff);
2) as per -linktest- outcome, the functional form specification of the regressand seems correct;
3) did you run -estat ovtest- after -reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid,cluster(districtid)- or after -linktest-?

[Radhika Channanamchery]

Radhika:
1) see -help j_robustsingular- about the missing F statistic (and related stuff);
2) as per -linktest- outcome, the functional form specification of the regressand seems correct;
3) did you run -estat ovtest- after -reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid,cluster(districtid)- or after -linktest-?

Dear Carlo,
Thank you for your kind reply. The following details were given in the help file when I have checked -help j_robustsingular-

The F or chi2 model statistic has been reported as missing.

Your estimation results show an F or chi2 model statistic reported to be
missing. Stata has done that so as not to be misleading, not because there
is something necessarily wrong with your model.

1. should I proceed with the model or not?

2. I have run it after running the Pooled OLS regression with the following specification:

reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid,cluster(districtid)
estate ovtest
result as follows

sey RESET test using powers of the fitted values of SI_all
Ho: model has no omitted variables
F(3, 64) = 3.14
Prob > F = 0.0311

But the result from the link test contradicts this result. Which one is to be followed?

linktest

Source | SS df MS Number of obs = 108
-------------+------------------------------ F( 2, 105) = 32.12
Model | .366060296 2 .183030148 Prob > F = 0.0000
Residual | .598362316 105 .005698689 R-squared = 0.3796
-------------+------------------------------ Adj R-squared = 0.3677
Total | .964422612 107 .009013295 Root MSE = .07549

------------------------------------------------------------------------------
SI_all | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_hat | 1.394775 1.910719 0.73 0.467 -2.393828 5.183377
_hatsq | -.3193171 1.542202 -0.21 0.836 -3.37722 2.738585
_cons | -.1208546 .5890733 -0.21 0.838 -1.288878 1.047169
------------------------------------------------------------------------------

Please share your kind reply.

Thank you very much

Radhika

[Carlo Lazzaro]

Radhika:
1) you should proceed with your model;
2) you may try an augemented regression to test wether the difference with -estat ovtest- persisits:

reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid fitted sq_fitted,cluster(districtid)

[Radhika Channanamchery]

Radhika:
1) you should proceed with your model;
2) you may try an augemented regression to test wether the difference with -estat ovtest- persisits:

reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm gddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid fitted sq_fitted,cluster(districtid)

Dear Carlo,

Thank you for your kind suggestions and help.

I have tried augmented regression using fitted and sq_fitted as predictors in the model.
The following result shows that the p-value of the sq_fitted is not significant (0.846). So my model is not misspecified. So I will get the support from both link test (which showed insignificant values for _hat, _hatsq and -cons) and augmented regression results to support the claim of the right model specification here.

1. Is it the right interpretation?

2. If possible, please help with why an insignificant p-value of the sq_fitted variable implies the right specification of a model.



Augmented Regression results are as follows.



/
reg SI_all shareofscandst shareofnonagriareainga Share_urbanpop shareofirr_final sharemarginal averagelandsize_ha numberofbanksper1000sqkm g
> ddppercapitaRS populationdensitypersqkm rainfall meantemperature i.year i.districtid fitted sq_fitted,cluster(districtid)
note: fitted omitted because of collinearity

Linear regression Number of obs = 108
F( 14, 26) = .
Prob > F = .
R-squared = 0.3799
Root MSE = .09519

(Std. Err. adjusted for 27 clusters in districtid)
------------------------------------------------------------------------------------------
| Robust
SI_all | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
shareofscandst | -.0230668 .0550701 -0.42 0.679 -.136265 .0901314
shareofnonagriareainga | .0164226 .0358774 0.46 0.651 -.0573244 .0901696
Share_urbanpop | -.0020935 .0095502 -0.22 0.828 -.0217241 .0175371
shareofirr_final | -.0011273 .0027372 -0.41 0.684 -.0067536 .0044991
sharemarginal | .0060785 .0141346 0.43 0.671 -.0229755 .0351325
averagelandsize_ha | .0982632 .2479518 0.40 0.695 -.4114091 .6079354
numberofbanksper1000sqkm | -.0013158 .0028744 -0.46 0.651 -.0072242 .0045926
gddppercapitaRS | -2.66e-07 7.35e-07 -0.36 0.721 -1.78e-06 1.24e-06
populationdensitypersqkm | -.0004451 .0010278 -0.43 0.669 -.0025577 .0016676
rainfall | .0001241 .0002985 0.42 0.681 -.0004894 .0007377
meantemperature | -.0174455 .0447509 -0.39 0.700 -.1094322 .0745413
|
year |
2006 | -.0122392 .053166 -0.23 0.820 -.1215235 .0970451
2011 | .069215 .1674032 0.41 0.683 -.2748873 .4133172
2016 | .122974 .2958828 0.42 0.681 -.4852218 .7311698
|
districtid |
2 | -.0678719 .3835728 -0.18 0.861 -.8563171 .7205733
3 | .5690612 1.376117 0.41 0.683 -2.259588 3.39771
4 | -.0180442 .065865 -0.27 0.786 -.1534317 .1173432
5 | .2570924 .6486736 0.40 0.695 -1.076275 1.59046
6 | -.1107871 .296793 -0.37 0.712 -.7208538 .4992796
7 | -.0686227 .1893786 -0.36 0.720 -.4578959 .3206506
8 | -.1248093 .4000975 -0.31 0.758 -.9472214 .6976028
9 | -.3191816 .8003814 -0.40 0.693 -1.964389 1.326026
10 | .1396474 .3769918 0.37 0.714 -.6352704 .9145651
11 | -.4873015 1.157049 -0.42 0.677 -2.865649 1.891046
12 | .1352137 .3367608 0.40 0.691 -.5570081 .8274355
13 | -.2421283 .5848953 -0.41 0.682 -1.444398 .9601411
14 | -.148724 .3642982 -0.41 0.686 -.8975497 .6001017
15 | .1933754 .4681125 0.41 0.683 -.7688437 1.155594
16 | -.2351227 .5848216 -0.40 0.691 -1.437241 .9669952
17 | -.1189267 .3215855 -0.37 0.715 -.7799552 .5421019
18 | -.8229281 1.996134 -0.41 0.684 -4.926041 3.280184
19 | .0105197 .1989641 0.05 0.958 -.3984569 .4194962
20 | -.1043723 .3018641 -0.35 0.732 -.7248628 .5161182
21 | -.4180865 1.019608 -0.41 0.685 -2.513921 1.677748
22 | .0589139 .2294369 0.26 0.799 -.4127005 .5305282
23 | .3687463 .8705373 0.42 0.675 -1.420669 2.158161
24 | -.3918049 .9175749 -0.43 0.673 -2.277907 1.494297
25 | -.1290813 .3443146 -0.37 0.711 -.8368301 .5786675
26 | -.6936927 1.667608 -0.42 0.681 -4.121511 2.734126
27 | -.784753 1.866871 -0.42 0.678 -4.622161 3.052655
|
fitted | 0 (omitted)
sq_fitted | -.6839938 3.481756 -0.20 0.846 -7.840846 6.472858
_cons | 1.616369 3.218361 0.50 0.620 -4.999067 8.231805
------------------------------------------------------------------------------------------

.
Thank you very much
Regards
Radhika

[Carlo Lazzaro]

Radhika:
1) your interpretation is correct;
2) a very trivial explanation: if you enter new predictors (fitted and, especially, sq_fitted, that may show the evidence of non linear relationship with the regessand) and they prove to have explanatory powers (=reach statistical significance), your previous model specification lacked for something . More elaborated and theoretically robust explanations are reported in -linktest- entry, Stata .pdf manual, and relate references.

[Radhika Channanamchery]

Radhika:
1) your interpretation is correct;
2) a very trivial explanation: if you enter new predictors (fitted and, especially, sq_fitted, that may show the evidence of non linear relationship with the regessand) and they prove to have explanatory powers (=reach statistical significance), your previous model specification lacked for something . More elaborated and theoretically robust explanations are reported in -linktest- entry, Stata .pdf manual, and relate references.

Dear Carlo,

Thank you so much for your kind suggestions which has brought lots of clarity in my research using panel data.

I would like to express my gratitude and appreciate your help here.

It has helped me to learn new things about Panel data analysis using Stata along with the theoretical insights you have shared.

I would like to appreciate your kindness and willingness to help which is invaluable and a blessing.

Best Regards

Radhika

[Carlo Lazzaro]

Radhika:
many thanks indeed for your kind words.
I'm simply trying to give back, as far as my capabilities allow me to do, a small fraction of what I continuously get from this forum.
I do hope that the time you spent on this forum can be rewarding for you and your research.