The following model jointly determines monthly child support payments and monthly visitation rights for divorced couples with children:
$$support = d_1 + g_1 visits + d_1 finc + d_1 fremarr + d_1 dist + u_1$$ $$visits = d_2 + g_2 support + d_2 mremarr + d_2 dist + u_2$$
For expository purposes, assume that children live with their mothers, so that fathers pay child support. Thus, the first equation is the father’s ‘‘reaction function’’: it describes the amount of child support paid for any given level of visitation rights and the other exogenous variables finc (father’s income), fremarr (binary indicator if father remarried), and dist (miles currently between the mother and father). Similarly, the second equation is the mother’s reaction function: it describes visitation rights for a given amount of child support; mremarr is a binary indicator for whether the mother is remarried.
a. Discuss identification of each equation.
b. How would you estimate each equation using a single-equation method?
c. How would you test for endogeneity of visits in the father’s reaction function?
I'd like to get some help with the whole question and to have my reasoning on it checked, thank you:
a)identification not possible due to simultaneity (which causes endogeneity)
b)via instrumental variable (possible choice (fremarr and mremarr) or ( dist)
c) my only idea was to estimate visits via OLS then use Hausman test between OLS and IV
Is the approach correct? How can I answer C in an alternative way?