Hi everyone,

I am studying the impact of Board independence on firm performance. Board independence is measured by the percentage of independent directors. Firm performance is measured by ROA, ROE.
As suggested by literature review, Board independence is an endogenous variable. To deal with that problem, I use IV-2SLS estimation as following:

Code:
xtivreg ROA BoardSize (BoardDe = Sector_Depend Province_Depend) FirmAge logAsset FirmLev GrowthOppor i.Year, fe vce(cluster CompanyID)
outreg2 using Firm-BoardDe.doc, append ctitle(FE-2SLS ROA) label keep(BoardSize BoardDe FirmAge logAsset FirmLev GrowthOppor)
xtivreg ROE BoardSize (BoardDe = Sector_Depend Province_Depend) FirmAge logAsset FirmLev GrowthOppor i.Year, fe vce(cluster CompanyID)
Then, I want to test for endogeneity of the independent variable and exogeneity of instruments. However, there is no post Postestimation tools for xtivreg. I follow the post to test by band:
Code:
* Test for endogenuity of the variable
* https://www.statalist.org/forums/forum/general-stata-discussion/general/1347371-endogeneity-test-panel-data
reg BoardDe BoardSize FirmAge logAsset FirmLev GrowthOppor Sector_Depend Province_Depend i.sectorcode i.Year
predict v2hat, resid
xtreg ROA BoardSize BoardDe v2hat FirmAge logAsset FirmLev GrowthOppor i.sectorcode i.Year, fe cluster(CompanyID)
* => P-value < 0,05 => BoarDe is not exogenous => IV is needed
xtreg ROE BoardSize BoardDe v2hat FirmAge logAsset FirmLev GrowthOppor i.sectorcode i.Year, fe cluster(CompanyID)
* => P-value < 0,1 => BoarDe is not exogenous => IV is needed
Code:
* J-test of overidentifying instrumental variables
* we are testing at 5% level
drop uhat
ivregress 2sls ROA BoardSize FirmAge logAsset FirmLev GrowthOppor i.sectorcode i.Year (BoardDe = Sector_Depend Province_Depend), robust
predict uhat, resid
regress uhat Sector_Depend Province_Depend BoardSize FirmAge logAsset FirmLev GrowthOppor i.sectorcode i.Year
* F=stat
test Sector_Depend Province_Depen
* J-stat = 2*F-stat
display 2*r(F)
* it show value of 2.733856
* m = number of instrumental variable, k = number of endogenous variable
* we have m-k=1 degree of freedom and a 5% significance level so the creitical value is 3,84. Since 2,733856 < 3,84 we fail to reject the null hypothesis of exogeneity
The results show that independent variable is an endogenous variable and my instruments are exogenous.

On the other hand, I use the post Postestimation tools for ivregress:
Code:
* Tests of endogeneity
ivregress 2sls ROA BoardSize (BoardDe = Sector_Depend Province_Depend) FirmAge logAsset FirmLev GrowthOppor i.sectorcode i.Year, vce(robust)
estat endogenous BoardDe
* => P-value > 0,1. Cannot reject the null hypothesis BoardDe is exogenous.
estat firststage
estat overid
* => P-value < 0,05. instruments are invalid

Which result do I should follow? And, in the case of fe model, is there any other methods to Test for endogeneity of the independent variable and exogeneity of instruments?

Thank you in advance!