Dear all,

I am getting different results from the Mundlak test and the Hansen-Sargan test (xtoverid). Can it be possible? When this happen, which one I should follow for my model specification?

Code:
. *** Choosing between FE and RE, Mundlak approach
. // Contrary to the Hausman test, Mundlak approach may be used when the errors 
> are heteroskedastic or have intragroup correlation.
. quietly asdoc xtreg excessmortalitypscores dt2-dt15 month2-month15 new_tests_p
> er_thousand people_vaccinated_ph population population_density median_age card
> iovasc_death_rate diabetes_prevalence hospital_beds_per_thousand life_expectan
> cy gdp_per_capita health_exp_percap urbanization_share internet_users air_pass
> engers smokers_share mean_new_tests mean_people_vaccinated , re vce(cluster co
> untry) replace

. 
. quietly estimates store mundlak

. 
. test mean_new_tests mean_people_vaccinated // We do not reject the null hypoth
> esis. This suggests that time-invariant unobservables are not related to our r
> egressors and that we can proceed with  RE model

 ( 1)  mean_new_tests = 0
 ( 2)  mean_people_vaccinated = 0

           chi2(  2) =    3.04
         Prob > chi2 =    0.2184

. 
. *** Choosing between FE and RE, Hansen-Sargan approach 
. qui asdoc xtreg excessmortalitypscores dt2-dt15 month2-month15 new_tests_per_t
> housand people_vaccinated_ph population population_density median_age cardiova
> sc_death_rate diabetes_prevalence hospital_beds_per_thousand life_expectancy g
> dp_per_capita health_exp_percap urbanization_share internet_users air_passenge
> rs smokers_share, fe vce(cluster country) 

. 
. estimates store fe 

. 
. qui asdoc xtreg excessmortalitypscores dt2-dt15 month2-month15 new_tests_per_t
> housand people_vaccinated_ph population population_density median_age cardiova
> sc_death_rate diabetes_prevalence hospital_beds_per_thousand life_expectancy g
> dp_per_capita health_exp_percap urbanization_share internet_users air_passenge
> rs smokers_share, re vce(cluster country)

. 
. estimates store re 

. 
. xtoverid // This confirm the previous results, the estimates from FE are  stat
> istically different from those of RE. Therefore, I opt for a FE model.

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(country)
Sargan-Hansen statistic 116.263  Chi-sq(14)   P-value = 0.0000
Best regards

Alessio Lombini