You realize that the presence of the constant in this equation
implies that there is a trend in mental health status? Although many
of us may feel that way, I wonder if you really mean that. Same issue
arises for the second equation.
As to your question -- whether you can use parents' marital status
(presumably still married v. divorced or widowed) as an instrument
for the change in marital status observed in your sample... Surely
you will observe some changes in your sample. For parents' status to
be a valid instrument, it must be correlated with the endogenous
measure ( d(mar.status)) and independently distributed of the error
e1. The latter is reasonable, given that parental status is
predetermined; but I wonder how well correlated it will be to the
included measure. Look at the first stage regression results closely.
As you have written them, both of these equations appear exactly
identified, so that you cannot carry out any overid tests.
