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RE Probit vs. Chamberlein Probit RE

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Dear All,

I have a panel data of 2016 country-pairs for the period between 1990-2010 (5-year intervals). Dependent variable (RTA) is a binary and indicates whether dyads have a regional trade agreements or not and I have following explanatories as independent variables (GDP sum, GDP difference, Human Development Index diference, distance, remoteness and common colonizer dummy).

First, I run random effect probit model.

Code:
 iis id

. tis t

. xtset id t
       panel variable:  id (strongly balanced)
        time variable:  t, 1990 to 2010, but with gaps
                delta:  1 unit

. xtprobit rta sgdp dgdp dhdi lndist remote i.commoncolonizer, re

Random-effects probit regression                Number of obs      =      9050
Group variable: id                              Number of groups   =      2016

Random effects u_i ~ Gaussian                   Obs per group: min =         2
                                                               avg =       4.5
                                                               max =         5

                                                Wald chi2(6)       =    363.47
Log likelihood  =  -1115.682                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
         rta |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        sgdp |   .8437854   .0556821    15.15   0.000     .7346505    .9529204
        dgdp |  -.9613412   .1090365    -8.82   0.000    -1.175049   -.7476336
        dhdi |  -1.972117   1.092439    -1.81   0.071    -4.113259    .1690245
      lndist |  -3.615695   .2682057   -13.48   0.000    -4.141368   -3.090021
      remote |    .408067   .0518054     7.88   0.000     .3065303    .5096037
1.commonco~r |   1.584577   .7582801     2.09   0.037     .0983755    3.070779
       _cons |  -15.47044   3.007589    -5.14   0.000     -21.3652   -9.575671
-------------+----------------------------------------------------------------
    /lnsig2u |   2.686554   .1181208                      2.455041    2.918067
-------------+----------------------------------------------------------------
     sigma_u |   3.831579   .2262947                      3.412758    4.301799
         rho |   .9362285   .0070524                      .9209293    .9487323
------------------------------------------------------------------------------
Then, in order to adress the issue of unobservable heterogeneity, I estimate Chamberlein probit random effects in which the averages of time variant variables are adding as controls.

Code:
 egen  sgdpbar=mean( sgdp), by(id)

. egen  dgdpbar=mean( dgdp), by(id)

. egen  dhdibar=mean( dhdi), by(id)

. xtprobit rta sgdp dgdp dhdi sgdpbar dgdpbar dhdibar lndist remote i.commoncolonizer, re
Random-effects probit regression                Number of obs      =      9050
Group variable: id                              Number of groups   =      2016

Random effects u_i ~ Gaussian                   Obs per group: min =         2
                                                               avg =       4.5
                                                               max =         5

                                                Wald chi2(9)       =    326.03
Log likelihood  = -1070.8547                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
         rta |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        sgdp |   1.083604   .0770198    14.07   0.000     .9326484     1.23456
        dgdp |  -1.308282   .2440045    -5.36   0.000    -1.786522   -.8300415
        dhdi |   14.29419   2.598298     5.50   0.000      9.20162    19.38676
     sgdpbar |  -.4882945   .0742988    -6.57   0.000    -.6339175   -.3426715
     dgdpbar |   .7428298   .2560823     2.90   0.004     .2409177    1.244742
     dhdibar |   -21.8249   2.956264    -7.38   0.000    -27.61907   -16.03073
      lndist |  -3.335184   .2451413   -13.61   0.000    -3.815652   -2.854716
      remote |   .2710329   .0455683     5.95   0.000     .1817207    .3603452
1.commonco~r |   .7676127   .7005804     1.10   0.273    -.6054998    2.140725
       _cons |  -4.201492     2.8389    -1.48   0.139    -9.765633    1.362649
-------------+----------------------------------------------------------------
    /lnsig2u |    2.36992   .1290648                      2.116957    2.622882
-------------+----------------------------------------------------------------
     sigma_u |   3.270555   .2110567                      2.881983    3.711518
         rho |   .9145046   .0100911                      .8925404    .9323198
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  1194.90 Prob >= chibar2 = 0.000
Comparing the results show that except dhdi (Human development index difference) sign of the variables are the same.However, this variable is one of the main explanatory that I want to include and I expect negative sign like in the first regression. On the other hand why Chamberlein probit gave positive sign? Which one is reliable? Is there anything else that I can do?

Thank you in advance.

Elif

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