xtivreg FE or RE?

[graziano ceddia]

Dear all,
I am estimating the following models with xtivreg. I run both FE and RE. I have different nested version. I just present below the most comprehensive specification.
The Sargan-Hansen test tells me that the instruments are valid and they are in general significant in the first-stage regressions.
My issue is that the coefficient associated with the variable lichag differs significantly between the FE and RE model.
Could somebody clarify what is the issue? I assume that probably the idiosyncratic error term is correlated with the individual effect, and therefore the FE model should be preferred.
Is that the case? How can I chose between the FE and RE specification in this case?
Any help and references would be very appreciated.

Below the Stata code and the results.
Thanks to all for your attention
Graziano

FE
xtivreg lfbi lpe_g clpeg2 lcnue (licha_g licha_g2 lichaglpeg = l4.licha_g l4.licha_g2 cl4lichaglpe l5.licha_g l5.licha_g2 cl5lichaglpe), fe vce(robust) first
xtoverid, robust

Results of the second-stage

Fixed-effects (within) IV regression Number of obs = 393
Group variable: id Number of groups = 25

R-sq: Obs per group:
within = . min = 5
between = 0.2818 avg = 15.7
overall = 0.2107 max = 18


Wald chi2(6) = 258.71
corr(u_i, Xb) = -0.9635 Prob > chi2 = 0.0000

(Std. Err. adjusted for 25 clusters in id)
------------------------------------------------------------------------------
| Robust
lfbi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
licha_g | -.9405396 .237025 -3.97 0.000 -1.4051 -.4759792
licha_g2 | .0158741 .078312 0.20 0.839 -.1376146 .1693628
lichaglpeg | -.4737727 .1959167 -2.42 0.016 -.8577624 -.089783
lpe_g | -.1696352 .128303 -1.32 0.186 -.4211046 .0818341
clpeg2 | -.0756746 .0971869 -0.78 0.436 -.2661573 .1148082
lcnue | .2535706 .0953389 2.66 0.008 .0667097 .4404315
_cons | 3.656424 .3356151 10.89 0.000 2.99863 4.314217
-------------+----------------------------------------------------------------
sigma_u | .69424319
sigma_e | .15216016
rho | .9541645 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: licha_g licha_g2 lichaglpeg
Instruments: lpe_g clpeg2 lcnue L4.licha_g L4.licha_g2 cl4lichaglpe
L5.licha_g L5.licha_g2 cl5lichaglpe
------------------------------------------------------------------------------


Test of overidentifying restrictions:
Cross-section time-series model: xtivreg fe robust cluster(id)
Sargan-Hansen statistic 2.700 Chi-sq(3) P-value = 0.4403



RE
xtivreg lfbi lpe_g clpeg2 lcnue (licha_g licha_g2 lichaglpeg = l4.licha_g l4.licha_g2 cl4lichaglpe l5.licha_g l5.licha_g2 cl5lichaglpe), re vce(robust) first
xtoverid, robust


G2SLS random-effects IV regression Number of obs = 393
Group variable: id Number of groups = 25

R-sq: Obs per group:
within = 0.1248 min = 5
between = 0.2950 avg = 15.7
overall = 0.2304 max = 18


Wald chi2(6) = 50.65
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. Err. adjusted for 25 clusters in id)
------------------------------------------------------------------------------
| Robust
lfbi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
licha_g | -.3638185 .0636239 -5.72 0.000 -.4885192 -.2391179
licha_g2 | .0298688 .0256152 1.17 0.244 -.0203361 .0800737
lichaglpeg | -.1218395 .09623 -1.27 0.205 -.3104468 .0667679
lpe_g | -.1910224 .0603397 -3.17 0.002 -.3092861 -.0727587
clpeg2 | -.1101412 .0540899 -2.04 0.042 -.2161553 -.004127
lcnue | -.0137156 .0488238 -0.28 0.779 -.1094084 .0819773
_cons | 4.544073 .1758325 25.84 0.000 4.199447 4.888698
-------------+----------------------------------------------------------------
sigma_u | .15031847
sigma_e | .15174156
rho | .49528882 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: licha_g licha_g2 lichaglpeg
Instruments: lpe_g clpeg2 lcnue L4.licha_g L4.licha_g2 cl4lichaglpe
L5.licha_g L5.licha_g2 cl5lichaglpe
------------------------------------------------------------------------------

Test of overidentifying restrictions:
Cross-section time-series model: xtivreg g2sls robust cluster(id)
Sargan-Hansen statistic 5.108 Chi-sq(3) P-value = 0.1640

[Manh Hoang Ba]

The Mundlak regression approach can be used to determine whether FE2SLS or RE2SLS is more appropriate. For a detailed discussion, see Joshi and Wooldridge (2019): https://www.jstor.org/stable/10.1560...134.0243?seq=1

global time_varying_indepvars lpe_g clpeg2 lcnue licha_g licha_g2 lichaglpeg // Only include independent variables that change with both i and t
global time_varying_indepvars_i

foreach v of global time_varying_indepvars {
    egen double `v'_i = mean(`v'), by(id)
    global time_varying_indepvars_i $time_varying_indepvars_i `v'_i
}

xtivreg lfbi lpe_g clpeg2 lcnue $time_varying_indepvars_i ///
    (licha_g licha_g2 lichaglpeg = ///
    l4.licha_g l4.licha_g2 cl4lichaglpe ///
    l5.licha_g l5.licha_g2 cl5lichaglpe), ///
    re vce(robust)

test $time_varying_indepvars_i //  Robust Hausman test: p-value < 0.05 => FE2SLS