Need some help interpreting fe in StataMP

[Darnell Grant]

I've been teaching myself STATA code for my research paper.
I've copied the code and the output of it. I am trying to determine the impact of international tourism receipts
on economic growth. These are the results.

xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC logSSE, fe

all I ask is for your interpretation on the model with regards to logEFI and logHEX, and the model's overall explanatory powers.

Fixed-effects (within) regression Number of obs = 59
Group variable: country1 Number of groups = 5

R-sq: Obs per group:
within = 0.8873 min = 8
between = 0.1898 avg = 11.8
overall = 0.0616 max = 15

F(7,47) = 52.87
corr(u_i, Xb) = -0.4745 Prob > F = 0.0000

------------------------------------------------------------------------------
logRGDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logHEX | .1963005 .0648447 3.03 0.004 .0658499 .3267511
logEFI | .4264748 .2278597 1.87 0.067 -.0319198 .8848693
logFDI | -.0063768 .0096017 -0.66 0.510 -.025693 .0129394
logITR | .0487573 .0797226 0.61 0.544 -.1116239 .2091385
logTOT | .5705303 .0839943 6.79 0.000 .4015555 .7395052
logGFC | .0064086 .0601755 0.11 0.916 -.1146488 .127466
logSSE | .467424 .1074243 4.35 0.000 .2513142 .6835339
_cons | -.8900144 .6539754 -1.36 0.180 -2.205643 .4256144
-------------+----------------------------------------------------------------
sigma_u | .3697412
sigma_e | .02192702
rho | .9964954 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4, 47) = 113.27 Prob > F = 0.0000

. . xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC logSSE, fe robust

Fixed-effects (within) regression Number of obs = 59
Group variable: country1 Number of groups = 5

R-sq: Obs per group:
within = 0.8873 min = 8
between = 0.1898 avg = 11.8
overall = 0.0616 max = 15

F(4,4) = .
corr(u_i, Xb) = -0.4745 Prob > F = .

(Std. Err. adjusted for 5 clusters in country1)
------------------------------------------------------------------------------
| Robust
logRGDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logHEX | .1963005 .0797979 2.46 0.070 -.0252539 .4178549
logEFI | .4264748 .2400364 1.78 0.150 -.2399733 1.092923
logFDI | -.0063768 .0103506 -0.62 0.571 -.0351147 .0223612
logITR | .0487573 .1150103 0.42 0.693 -.2705624 .368077
logTOT | .5705303 .0717878 7.95 0.001 .3712154 .7698453
logGFC | .0064086 .03539 0.18 0.865 -.0918497 .1046669
logSSE | .467424 .1060196 4.41 0.012 .1730663 .7617817
_cons | -.8900144 .7271928 -1.22 0.288 -2.909025 1.128996
-------------+----------------------------------------------------------------
sigma_u | .3697412
sigma_e | .02192702
rho | .9964954 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Darnell Grant]

Also, any comments as to how I can bolster the format of my questions or posting is also welcomed.

[Clyde Schechter]

So, the second model you show, which uses robust standard errors, is invalid and you should not use it for anything. With only 5 groups, you cannot validly do cluster robust standard errors (and when you specify vce(robust) with -xtreg- it automatically gives you the cluster robust standard error). So just discard that.

The first model is more interpretable, although I have to say that most people would agree that with only 59 observations, you really shouldn't be trying to fit a model with 7 predictor variables. That's only a little more than 8 observations per predictor--way too low. But let's ignore that problem.

Both your outcome and predictor variables, I infer from their names, have been log transformed. Let's look at logHEX. The coefficient you get is 0.1963005. That implies that a unit difference in logHEX is associated with a difference of 0.1963005 in logGDP. Now, people often like to translate that back to the un-log-transformed metric. Here's how that works.

Let's imagine a 1% increase in HEX. That means multiplying HEX by 1.01. When you do that, logHEX increases by log(1.01) = 0.00995033. As noted, this is then associated with an incraese in logGDP of 0.1963005*0.00995033 = 0.00195325. To say that logGDP has increased by that amount is to say that GDP itself has multiplicatively increased by a factor of exp(0.00195325) = 1.0019552, or, in percentage terms, GDP has increased by 0.19552%. You will note that 0.19552 is nearly the same as 0.1963005. So people sometimes short-circuit these calculations by saying that a 1% increase in HEX is associated with a 0.1963005% increase in GDP. As you can see, that is, strictly speaking, incorrect, but it's a very good approximation as long as the coefficient is small. And all of the coefficients in your output are small enough for this approximation to be adequate.

As for explanatory powers, it is important to understand that none of the so-called R-square statistics that you get with -xtreg- is fully analogous to the ordinary R-square from OLS regression. Of the three, probably the most useful is the within-R square (for most purposes). So at 0.8873 this model looks pretty good as a predictor of the within-country1 variation in logGDP.

[Darnell Grant]

Thank you so much.

[Darnell Grant]

I hope Clyde sees this, so I've been reading around the page, so my SSE variable in the previous analysis had a lot of missing variables (30), in removing it I believe I've made the model stronger. I also have to run this using Arellano - Bond GMM and of course, random effects; The Wald Chi on the random looks ridiculous to me. Any tips ?

xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC , fe

Fixed-effects (within) regression Number of obs = 78
Group variable: country1 Number of groups = 5

R-sq: Obs per group:
within = 0.8197 min = 12
between = 0.6786 avg = 15.6
overall = 0.5129 max = 18

F(6,67) = 50.75
corr(u_i, Xb) = -0.8605 Prob > F = 0.0000

------------------------------------------------------------------------------
logRGDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logHEX | .3402696 .0528806 6.43 0.000 .2347195 .4458197
logEFI | .9587078 .2092515 4.58 0.000 .54104 1.376375
logFDI | -.0063311 .0093109 -0.68 0.499 -.0249157 .0122535
logITR | -.0193821 .0821578 -0.24 0.814 -.1833697 .1446055
logTOT | .6136095 .0789772 7.77 0.000 .4559703 .7712487
logGFC | .0736409 .0565694 1.30 0.197 -.039272 .1865539
_cons | -2.385598 .6017878 -3.96 0.000 -3.586772 -1.184425
-------------+----------------------------------------------------------------
sigma_u | .47489634
sigma_e | .0248297
rho | .99727379 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4, 67) = 143.52 Prob > F = 0.0000

the random effects test looks like this


xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC , re

Random-effects GLS regression Number of obs = 78
Group variable: country1 Number of groups = 5

R-sq: Obs per group:
within = 0.5098 min = 12
between = 0.9846 avg = 15.6
overall = 0.9512 max = 18

Wald chi2(6) = 1384.28
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
logRGDP | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logHEX | .1566833 .042009 3.73 0.000 .0743473 .2390194
logEFI | -.4012841 .5681224 -0.71 0.480 -1.514784 .7122154
logFDI | -.0036256 .0240802 -0.15 0.880 -.0508219 .0435708
logITR | .8364499 .0368702 22.69 0.000 .7641857 .9087141
logTOT | -.1515418 .1776796 -0.85 0.394 -.4997874 .1967038
logGFC | -.3250574 .0207115 -15.69 0.000 -.3656512 -.2844637
_cons | 1.244023 1.479061 0.84 0.400 -1.654882 4.142929
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .0248297
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Darnell:
1) removing variables because of missing values does not make your sample "stronger" (whatever that may mean) but simply creates an artifact of the original sample which is usually far from a random subsample of it. I would recommend to take a look at -mi- related entries in Stata .pdf manual and read references reported therein.
2) Arellano-Bond (-xtabond- in Stataish) estimator is for dynamic panel data regression. You're dealing with a static panel data (as per -xtreg-). What's the reason why you should switch to such a different and exponentially more complex model?
3) the results of your -re- model look very different from the previous -fe- estimator. Basically, you do not have panel-wise effect. Are you sure you ran the -re- model using the very same predictors and data?
Unsolicited advice: you should probably improve your knowledge of panel data regression (that can have really trickier facets than one-wave data regression, such as OLS) studying any decent panel data econometrics textbook (Stata users dealing with your same stuff like https://www.stata.com/bookstore/micr...metrics-stata/).
Eventually, please use CODE delimiters to post what you typed and what Stata gave you back (see the FAQ on this and other posting-related topics). Thanks.

[Darnell Grant]

Carlo Lazzaro Thanks for the feedback. My paper is a Caribbean application of a previous study "Impact of Tourism on Economic Growth and Development in Africa" by Bichaka Fayissa, Christian Nsiah, and Badassa Tadass. to answer your question, Yes I used the same data for both tests. Due to the deadline of my paper, I was trying to avoid things that I never did before,, MI being one. So I've been doing a lot of reading beofre I attempt things, you're unsolicited was spot on. The results have changed a bit. You would notice the paper I'm attempting to model actually uses both fixed and random effect then uses Hausman to reject one. Subsequently showing the results of both one step one year lag and one step two year lag Arellano.

mi estimate : xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC logSSE, fe

Multiple-imputation estimates                   Imputations       =         35
Fixed-effects (within) regression               Number of obs     =         78

Group variable: country1                        Number of groups  =          5
                                                Obs per group:
                                                              min =         12
                                                              avg =       15.6
                                                              max =         18
                                                Average RVI       =     0.1001
                                                Largest FMI       =     0.3281
                                                Complete DF       =         66
DF adjustment:   Small sample                   DF:     min       =      38.92
                                                        avg       =      56.78
                                                        max       =      62.60
Model F test:       Equal FMI                   F(   7,   63.5)   =      46.28
Within VCE type: Conventional                   Prob > F          =     0.0000

------------------------------------------------------------------------------
     logRGDP |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      logHEX |   .2815834   .0549308     5.13   0.000     .1716704    .3914965
      logEFI |    .729028   .2204457     3.31   0.002     .2874652    1.170591
      logFDI |  -.0033547    .009057    -0.37   0.712    -.0214724    .0147631
      logITR |   .0024732   .0781818     0.03   0.975      -.15378    .1587263
      logTOT |   .5877549   .0767703     7.66   0.000     .4341938    .7413161
      logGFC |   .0325302   .0569277     0.57   0.570    -.0814062    .1464666
      logSSE |   .2457275   .0929267     2.64   0.012     .0577529     .433702
       _cons |  -1.801766   .6143847    -2.93   0.005     -3.03112   -.5724112
-------------+----------------------------------------------------------------
     sigma_u |  .42978272
     sigma_e |  .02322257
         rho |   .9970889   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Note: sigma_u and sigma_e are combined in the original metric.

.  mi estimate : xtreg logRGDP logHEX logEFI logFDI logITR logTOT logGFC logSSE, re

Multiple-imputation estimates                   Imputations       =         35
Random-effects GLS regression                   Number of obs     =         78

Group variable: country1                        Number of groups  =          5
                                                Obs per group:
                                                              min =         12
                                                              avg =       15.6
                                                              max =         18
                                                Average RVI       =     0.0626
                                                Largest FMI       =     0.2430
DF adjustment:   Large sample                   DF:     min       =     588.06
                                                        avg       =  69,249.15
                                                        max       = 452,554.40
Model F test:       Equal FMI                   F(   7,58215.7)   =     204.38
Within VCE type: Conventional                   Prob > F          =     0.0000

------------------------------------------------------------------------------
     logRGDP |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      logHEX |    .153518   .0401362     3.82   0.000     .0748523    .2321837
      logEFI |    .359572   .6311166     0.57   0.569     -.877745    1.596889
      logFDI |  -.0164746   .0237467    -0.69   0.488    -.0630191    .0300699
      logITR |   .8583568    .036692    23.39   0.000     .7864387    .9302749
      logTOT |  -.0114504   .1812405    -0.06   0.950    -.3667159    .3438151
      logGFC |  -.2552992   .0348349    -7.33   0.000    -.3236669   -.1869315
      logSSE |  -.5168598   .2069382    -2.50   0.013    -.9232878   -.1104318
       _cons |   .4233031   1.463708     0.29   0.772    -2.445649    3.292255
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  .02322257
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Note: sigma_u and sigma_e are combined in the original metric.

[Darnell Grant]

after using post option in order to get to run the hausman, the results are such.

.  hausman FE RE

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       FE           RE         Difference          S.E.
-------------+----------------------------------------------------------------
      logHEX |    .2815834      .153518        .1280654        .0375031
      logEFI |     .729028      .359572         .369456               .
      logFDI |   -.0033547    -.0164746          .01312               .
      logITR |    .0024732     .8583568       -.8558836        .0690369
      logTOT |    .5877549    -.0114504        .5992054               .
      logGFC |    .0325302    -.2552992        .2878294        .0450255
      logSSE |    .2457275    -.5168598        .7625873               .
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =  -222.62    chi2<0 ==> model fitted on these
                                        data fails to meet the asymptotic
                                        assumptions of the Hausman test;
                                        see suest for a generalized test

.

[Darnell Grant]

Since my data is not suitable for hausman, consider mundlak, constraints dropping though, will research and seek to amend accordingly.

. test  mean_HEX mean_EFI mean_FDI mean_ITR mean_TOT mean_GFC mean_SSE

 ( 1)  mean_HEX = 0
 ( 2)  mean_EFI = 0
 ( 3)  mean_FDI = 0
 ( 4)  mean_ITR = 0
 ( 5)  o.mean_TOT = 0
 ( 6)  o.mean_GFC = 0
 ( 7)  o.mean_SSE = 0
       Constraint 5 dropped
       Constraint 6 dropped
       Constraint 7 dropped

           chi2(  4) = 1471.18
         Prob > chi2 =    0.0000