Country fixed effects and dummy in IV regression

[Sergey Medvedev]

Hello everyone,

I want to use instrumental Variable regression and include country fixed effects into regression. However, when I am comparing IV regression with country fixed effects with IV regression using country dummy, I obtain identical coefficients, but different standard errors and probabilities. I am confused, which one is more appropriate to use.

 ivregress 2sls logypos logpop loginc logcap logimp logexp (logx = logpov) i.country_id
note: 3.country_id identifies no observations in the sample
note: 6.country_id identifies no observations in the sample
note: 9.country_id identifies no observations in the sample

Instrumental variables (2SLS) regression          Number of obs   =         37
                                                  Wald chi2(11)   =    8243.99
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.9955
                                                  Root MSE        =     .07142

------------------------------------------------------------------------------
     logypos |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        logx |   .1626126   .1006242     1.62   0.106    -.0346073    .3598325
      logpop |   .0657873   .0352119     1.87   0.062    -.0032268    .1348014
      loginc |   .6962592   .1737486     4.01   0.000     .3557181      1.0368
      logcap |   .6430313   .3184253     2.02   0.043     .0189292    1.267133
      logimp |  -.9756075   .5702401    -1.71   0.087    -2.093258    .1420426
      logexp |   .6030915   .2712483     2.22   0.026     .0714545    1.134728
             |
  country_id |
          2  |  -.3393737   .3598373    -0.94   0.346    -1.044642    .3658944
          3  |          0  (empty)
          4  |   .3950125   .1627105     2.43   0.015     .0761059    .7139191
          5  |  -.3727659   .2355299    -1.58   0.113     -.834396    .0888642
          6  |          0  (empty)
          7  |   .3678503   .2235957     1.65   0.100    -.0703892    .8060897
          8  |  -.4365519   .2588882    -1.69   0.092    -.9439635    .0708597
          9  |          0  (empty)
             |
       _cons |   1.920873   1.501911     1.28   0.201    -1.022818    4.864563
------------------------------------------------------------------------------
Instrumented:  logx
Instruments:   logpop loginc logcap logimp logexp 2.country_id 4.country_id
               5.country_id 7.country_id 8.country_id logpov

And

xtivreg logypos logpop loginc logcap logimp logexp (logx = logpov), fe

Fixed-effects (within) IV regression            Number of obs     =         37
Group variable: country_id                      Number of groups  =          6

R-sq:                                           Obs per group:
     within  = 0.9780                                         min =          1
     between = 0.9830                                         avg =        6.2
     overall = 0.9440                                         max =         17

                                                Wald chi2(6)      =  260270.35
corr(u_i, Xb)  = 0.7098                         Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     logypos |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        logx |   .1626126   .1224147     1.33   0.184    -.0773157     .402541
      logpop |   .0657873   .0428372     1.54   0.125     -.018172    .1497466
      loginc |   .6962592   .2113743     3.29   0.001     .2819731    1.110545
      logcap |   .6430313   .3873811     1.66   0.097    -.1162217    1.402284
      logimp |  -.9756075   .6937271    -1.41   0.160    -2.335288    .3840725
      logexp |   .6030915   .3299879     1.83   0.068    -.0436728    1.249856
       _cons |   1.799261     1.7111     1.05   0.293    -1.554434    5.152956
-------------+----------------------------------------------------------------
     sigma_u |    .377159
     sigma_e |  .08688437
         rho |  .94960611   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F  test that all u_i=0:     F(5,25) =     1.75            Prob > F    = 0.1598
------------------------------------------------------------------------------
Instrumented:   logx
Instruments:    logpop loginc logcap logimp logexp logpov
------------------------------------------------------------------------------

Or is that so because country fixed effects and country dummy are very similar to each other?

In addition, if I use IV regression with country fixed effects, I cannot later use Durbin-Wu-Hausman endogeneity test, but I can do it when I use country dummy. So, if I want to later on use endogeneity test and coefficients are identical in both regressions, should I then use country dummy instead of country fixed effects?

Thank you in advance,
Sergey Medvedev

[Andrew Musau]

Include the option small in the ivregress regression

ivregress 2sls logypos logpop loginc logcap logimp logexp (logx = logpov) i.country_id, small

[Sergey Medvedev]

Thank you very much, Andrew!

[Sergey Medvedev]

What does option "small" mean? So that I can explain its use in regression

[Andrew Musau]

small - make degrees-of-freedom adjustments and report small-sample statistics

The degrees of freedom differ between the two regressions as xtivregress includes panel dummies, so you need to adjust for these to match the output of xtivreg.

[Sergey Medvedev]

Thank you again, Andrew, for your help!