2-stage ordered probit Estimation

[Kebede]

Dear All,

I am trying to run a simultaneous equation model which is modeled as;

P*=D*+1X1+e
D*= zP*+ 2X2+e2

Where each of the above two equations are ordered probit equations and P* and D* are ordered latent endogenous variables which will have ordinal values between 1-4.

The reason the model is formulated in this manner is because the objective of the study is to determine if the existence of each of these endogenous variables have cause and effect relationship, like the existence of P causes D and vice versa. Literature supports applying 2-stage least square technique for ordered probit models and thus I am trying to fit the model in this way;
Given the original simultaneous equation,

P*=D*+1X1+e
D*= P*+ 2X2+e2


I will first regress each equation via ordered probit by Eviews software and have predicted values for P* and D* i.e P^ and D^

Next stage I will undertake ordered probit regression by replacing D* and P* in the right side by predicted values P^ and D^ that is,

P*=bD^+a1X1+z1
D*= cP^+ a2X2+z2


Now I want to request the Eviews community to help me decide on the following point;

Which predicted value should I use i.e predicted probabilities (catagories) or the linear prediction generated by Eviews where in my case (i_P or Phat variable as generated by eview automatically).


I really thank you for any assistance which you might be able to provide.

With kind regards,

Kebede

PhD Student