endogeneity test (option endog of xtivreg2 rountine)

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endogeneity test (option endog of xtivreg2 rountine)

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Dear all

 I estimated model with the routine xtivreg2, fe robust bw/cluster(id). My questions concerns the endogeneity test using this routine and adding "endog" option where we list one or more variables that I consider as endogenous.
Firstly I hope to ensure that I understand correctly this test: If we reject the null (p-value<0.05), this mean that my endogenous variables tested are endogenous as expected and my model is correctly specified ?

Secondly, I would like if it is sufficient to do just this test to ensure that the model with instrumental variable is more appropriate than the OLS in my case where the heteroskedasticity hypothesis is violated (because as I understood in p.17 from paper of Christopher Baum Shaffer and Stillman entitled "enhanced routine for instrumental variables/GMM estimation and testing " the help file of stata and p.16 of the same paper say that this test is superior of Durbain-Wu-Hausman endogeneity test in the case where the hypothesis of homoskedasticity is violated

Thirdly, I have more than one endogenous variable. When I perform this test, we include all my endogenous variables (we have p-value<0.05). If I list only one or some of my endogenous variables, I obtain p-value >0.05 in some cases . Is it correct to ignore this last result because according to theory the variables are in fact endogenous but this test works well if I can find the most relevant instrumental variable ( that is not easy always)
Many thanks