Hello Stata Listers,

I am using Stata 15.1. My dependent variable is nonreceipt of a measles, mumps, and rubella vaccination (MMR_Nonreceipt) by child i. I am interested in the relationship between being uninsured, which is a binary indicator (Uninsured), and MMR_Nonreceipt. I am concerned that Uninsured could be endogenous. I instrument for Uninsured using the upper income eligibility limits for Medicaid in the state where the child resides. I run the following code:

Code:
local xlist1 "FirstBorn Female Age_Group_24_29_Months Age_Group_30_35_Months
Non_Hispanic_White Non_Hispanic_Black Other_Multiple 
incporat Mother_Ed_12_Years Mother_Ed_GT12_Years Mother_Ed_CollegeGraduate Mother_Other
All_Private_Facilities Other_Facilities Uninsured"

local xlist1c "FirstBorn Female Age_Group_24_29_Months Age_Group_30_35_Months
Non_Hispanic_White Non_Hispanic_Black Other_Multiple 
incporat Mother_Ed_12_Years Mother_Ed_GT12_Years Mother_Ed_CollegeGraduate Mother_Other
All_Private_Facilities Other_Facilities"

ivreg2 MMR_Nonreceipt `xlist1c' i.year (Uninsured=childinc adultinc) [pw=adprdaweight], endog(Uninsured) ffirst robust

My results from this suggest no problem with my instruments (i.e. F-test is passed and the model is not overidentified). However, the endogeneity test indicates no rejection of the null that Uninsured can be treated as exogenous:

Endogeneity test of endogenous regressors: 0.134
Chi-sq(1) P-val = 0.7143


Because Uninsured is bivariate, I also run biprobit to check exogeneity:


Code:
biprobit (MMR_Nonreceipt = `xlist1' i.year) (Uninsured = childinc adultinc `xlist1c' i.year) [pw=adprdaweight], vce(robust)
Based on what I've read, the Wald test indicates that Uninsured should be treated as endogenous (I could be wrong about this):

Wald test of rho=0: chi2(1) = 8.96311
Prob > chi2 = 0.0028

My question is, can I use the ivreg2 results as justification to treat Uninsured as exogenous, even though the biprobit exogeneity test indicates an endogeneity problem? For additional context, the ivreg2 results indicate a positive relationship between MMR_Nonreceipt and Uninsured (like I expect) while the biprobit results indicate a negative relationship between MMR_Nonreceipt and Uninsured (this is not what I expect and I think something must be wrong for me to be getting this result). Also, I think Uninsured could plausibly be exogenous because a child's insurance status is due to factors outside the child's control. The literature and other Statalist posts I have reviewed do not appear to give a clear answer to my question. Finally, when I also run regress and probit while treating Uninsured as exogenous, the marginal effect for Uninsured from the probit regression and the Uninsured coefficient from the linear probability model are both significant, positive, and similar in magnitude.