Panel Data. Fixed and Random effect. Prediction for each panel

[Elizabeth Real]

Hello,

I´m working with panel data for my thesis and it is a small panel data only 17 countries and 15 years. What I´m exactly doing is analyzing the effect that corruption has on gdppercapita. I also use other variables but they are considered as "control variables" . I started with a simple model where I estimated FE and then RE but I cluster the SEs in order to deal with heteroskedasticity and autocorrelation problems (as it was recommmened previously in one of my quesion in the forum) and then to decide which one would be better I used the command "xtoverid". You can see my commands


. xtreg gdppercapita cpi, fe cluster(country)

Fixed-effects (within) regression Number of obs = 264

Group variable: country1 Number of groups = 17

R-sq: within = 0.1327 Obs per group: min = 14

between = 0.4349 avg = 15.5

overall = 0.3896 max = 16

F(1,16) = 9.22

corr(u_i, Xb) = 0.1529 Prob > F = 0.0079

(Std. Err. adjusted for 17 clusters in country)

Robust

gdppercapita Coef. Std. Err. t P>t [95% Conf. Interval]

cpi 179.3757 59.06557 3.04 0.008 54.16224 304.5891

_cons 3996.204 2172.897 1.84 0.085 -610.1317 8602.54

sigma_u 3507.3843

sigma_e 1664.3803

rho .81620361 (fraction of variance due to u_i)

. estimates store fixed

. xtreg gdppercapita cpi, re cluster(country)

Random-effects GLS regression Number of obs = 264

Group variable: country1 Number of groups = 17

R-sq: Obs per group:

within = 0.1327 min = 14

between = 0.4349 avg = 15.5

overall = 0.3896 max = 16
Wald chi2(1) = 16.28

corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0001

(Std. Err. adjusted for 17 clusters in country)

------------------------------------------------------------------------------

| Robust

gdppercapita | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

cpi | 186.4174 46.20276 4.03 0.000 95.86163 276.9731

_cons | 3706.284 1861.555 1.99 0.046 57.70428 7354.864

-------------+----------------------------------------------------------------

sigma_u | 3548.098

sigma_e | 1664.3803

rho | .81964107 (fraction of variance due to u_i)

------------------------------------------------------------------------------

. estimates store random

. xtoverid

Test of overidentifying restrictions: fixed vs random effects

Cross-section time-series model: xtreg re robust cluster(country)

Sargan-Hansen statistic 0.277 Chi-sq(1) P-value = 0.5984


So, "RE" would be better.

But now what I want to do is to see is the effect of corruption on GDPpc for each panel or country that are 17. Thus to get it I considered the command :
regress gdppercapita cpi i.country1, robust and my result was:

. regress gdppercapita cpi i.country1, robust

Linear regression Number of obs = 264
F(17, 246) = 304.54
Prob > F = 0.0000
R-squared = 0.8871
Root MSE = 1664.4

---------------------------------------------------------------------------------
| Robust
gdppercapita | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------+----------------------------------------------------------------
cpi | 179.3757 28.66853 6.26 0.000 122.9086 235.8428
|
country1 |
Bolivia | -11210.48 573.2138 -19.56 0.000 -12339.51 -10081.45
Brazil | -4950.039 715.173 -6.92 0.000 -6358.682 -3541.395
Chile | -5945.007 1482.088 -4.01 0.000 -8864.208 -3025.806
Colombia | -7667.335 730.9905 -10.49 0.000 -9107.133 -6227.536
Costa Rica | -8053.332 839.9772 -9.59 0.000 -9707.797 -6398.867
Dominican Rep. | -6624.862 731.7051 -9.05 0.000 -8066.068 -5183.656
Ecuador | -6946.394 603.4958 -11.51 0.000 -8135.072 -5757.716
El Salvador | -11079.91 634.8929 -17.45 0.000 -12330.43 -9829.387
Guatemala | -9865.383 580.6589 -16.99 0.000 -11009.08 -8721.686
Honduras | -12210.32 580.5106 -21.03 0.000 -13353.73 -11066.92
Mexico | -1950.287 622.7526 -3.13 0.002 -3176.895 -723.6802
Nicaragua | -12037.28 579.9553 -20.76 0.000 -13179.59 -10894.97
Panama | -2904.92 1025.237 -2.83 0.005 -4924.282 -885.5568
Paraguay | -8425.054 634.557 -13.28 0.000 -9674.912 -7175.196
Peru | -9102.088 778.4872 -11.69 0.000 -10635.44 -7568.738
Uruguay | -7608.453 1186.654 -6.41 0.000 -9945.751 -5271.155
|
_cons | 11409.83 1018.999 11.20 0.000 9402.753 13416.91
---------------------------------------------------------------------------------


Therefore, my specific question is whether the command used to analyze the effect for each panel is correct ? Also because in the first time when I perform the xtoverid test to decides FE or RE, the result was RE and the corruption´s coefficient has "positive"sign in RE model but then when I perform for each panel, each panel coefficient is "negative".

Thanks in advance.
Elizabeth.

[Carlo Lazzaro]

Elizabeth:
- you should cluster on -country- the standard errors in -regress-, as your variable are not independent, due to their panel structure.
Pease also note that, unlike -xtreg-, -robust- and -cluster- option do different jobs under -regress- (-robust- accounts for heteroskedasticity; -cluster- accounts for autocorrelation);
- see the results of -predict- after -regress- and check whether they are positive or not;
- for the future, please use CODE delimiters to share what you typed and what Stata gave you back. Thanks.

[Elizabeth Real]

Thank you so much for your help Carlo.

1) Regarding your first advice, cluster on -country-the standard error in -regress, that mean that instead of :
regress gdppercapita cpi i.country1, robust
I will have to write now
regress gdppercapita cpi i.country1, robust cluster (country) ?

2)I was using the option "predict" after my estimation and the command written is:
predict gdppercapita_predict,xb
scatter gdppercapita_predict cpi

3) You can see again my result:

. regress gdppercapita cpi i.country1, robust cluster (country)

Linear regression                               Number of obs     =        264
                                                F(0, 16)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8871
                                                Root MSE          =     1664.4

                                  (Std. Err. adjusted for 17 clusters in country)
---------------------------------------------------------------------------------
                |               Robust
   gdppercapita |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            cpi |   179.3757   60.95615     2.94   0.010      50.1544    308.5969
                |
       country1 |
       Bolivia  |  -11210.48   156.2001   -71.77   0.000    -11541.61   -10879.35
        Brazil  |  -4950.039   491.4589   -10.07   0.000    -5991.885   -3908.192
         Chile  |  -5945.007   2544.919    -2.34   0.033    -11339.99   -550.0195
      Colombia  |  -7667.335   388.5954   -19.73   0.000     -8491.12   -6843.549
   Costa Rica   |  -8053.332   1158.167    -6.95   0.000    -10508.54   -5598.128
Dominican Rep.  |  -6624.862    9.65139  -686.42   0.000    -6645.322   -6604.402
       Ecuador  |  -6946.394   278.1124   -24.98   0.000    -7535.966   -6356.822
  El Salvador   |  -11079.91   468.6004   -23.64   0.000     -12073.3   -10086.52
     Guatemala  |  -9865.383   124.4521   -79.27   0.000    -10129.21   -9601.556
      Honduras  |  -12210.32   262.6194   -46.49   0.000    -12767.05   -11653.59
        Mexico  |  -1950.287   228.5855    -8.53   0.000    -2434.867   -1465.708
     Nicaragua  |  -12037.28   258.5557   -46.56   0.000     -12585.4   -11489.17
        Panama  |   -2904.92   269.7309   -10.77   0.000    -3476.724   -2333.116
      Paraguay  |  -8425.054   493.0917   -17.09   0.000    -9470.362   -7379.746
          Peru  |  -9102.088   403.8345   -22.54   0.000    -9958.179   -8245.997
       Uruguay  |  -7608.453   2106.543    -3.61   0.002    -12074.12   -3142.782
                |
          _cons |   11409.83   1851.543     6.16   0.000     7484.734    15334.92
---------------------------------------------------------------------------------

And then after that, the postestimation option "predict"

. predict gdppercapita_predict2, xb
(8 missing values generated)

. scatter gdppercapita_predict2 cpi

So, with the "predict" option when I explore again my data I can see that I get the linear prediction from the fitted model but to conclude whether there is a positive or negative effect of corruption on gdppercapita for each country or panel I usually see or I interpret the sign of my coeeficient that I get in my regression that is he first estimation posted with the comman: regress gdppercapit cpi i.country, robust cluster(country). Is it right?

4) I´m trying to use the CODE delimiters to share my results, I do not if now is right how is show my result.

Thank you Carlo,
Elizabeth.

[Carlo Lazzaro]

Elizabeth:
1) your code should be (-robust- in redundant):

regress gdppercapita cpi i.country1,  cluster (country)

2) and 3) If I get your results right, the -_cons- of your regression represent the omitted country (as Stata omits one of the level of each categorical variable to avoid dummy trap) when -cpi- is 0.
Hence the predicted value for, say, Uruguay should be (what follows is a sort of -predict- by hand):

(11409.83-7608.453) + (cpi*<thevalueofcpireportedforUruguay>)

That's the way I would follow to study the sign of coefficients.

4) The way you used CODE delimiters is laudable.