Re: [Gretl-users] Help on simultaneous equation model
On Sun, 6 Mar 2011, Lemma Tenessa wrote:
I am trying to run a simultaneous equation model which is modeled
as;
P*=D*+1X1+1
D*= zP*+ 2X2+2
Where each of the above two equations are ordered probit
equations and P* and D* defined as, poverty and natural
resources degradation are ordered latent endogenous variables
which will have ordinal values between 1-4. [...]
Of course I am trying to fit the model in this way;
Given the original simultaneous equation,
P*=D*+1X1+1
D*= P*+ 2X2+2
I will first regress each equation via ordered probit by GERTL
software and have predicted probabilities for P* and D* i.e P^
and D^
Is your plan to use X2 as an instrument in the first-stage
equation for P*, and X1 as an instrument for D*? If not, then
you'll have to find at least one additional instrument for each of
P* and D*, just as in two-stage least squares.
Next stage I will undertake ordered probit regression by
replacing D* and P* in the right side by P^ and D^ that is
P*=bD^+a1X1+e1
D*= cP^+ a2X2+e2
Finally interpret the output brought by the last regression(2nd
stage)
Now I want to be confident on two things
1) if the above way I propose is the right one
Given two or more suitable instruments, this sounds OK. But I'm
not sure offhand how to get a consistent estimate of the
covariance matrix for the second-stage ordered probit. Hopefully,
someone who knows more about this than I may step in.
2) If the the GERTL simultaneous equation technique can solve
this
No, the "system" command for simultaneous equations expects a set
of linear equations.
Allin Cottrell