Hi, I'm a student and I'm trying to determine a model to use for my dataset. The goal is to estimate the enrolment ratio for MBA programs, however there's a potential endogeneity issue between enorlment and tuition fees.

I tried to use an Anderson Hsiao (1981) method of instrumenting the tuition fees in a 3sls regression model.

of which, I use:
reg3 ( d.tuition1 d.gmat l2.lenrolment ) ( d.lenrolment d.avgmat l2.tuition)
but found no significant relationship between tuition and enrolment. I'm unsure how to interpret this?

a normal
xtreg lenrolment tuition gmat, fe
would have the coefficient on tuition to be significant at 5%. But in the reg3 model I found no relationship with p-values at above 0.5.

I'm unsure of how to do an endogeneity test as I'm unsure whether a twice lagged variable would be appropriate as an IV, since the reg3 model gave no significant results.

I did a 2sls endogeneity test :
ivregress 2sls d.lenrolment d.avgmat (l.d.tuition = l2.tuition) estat endog
which returns a durbin and hausman wu of above 0.4 each respectively.

which suggests that the tuition is exogenous? Which is contradictory to prior literature