Dear Statalist members,
Please my apologies in advance if I ask a silly question.
I am trying to estimate a bivariate probit model using one instrumental variable for three endogenous variables (the outcome variable and the endogenous variables are categorical variables with 0 or 1 value). That means that I estimate three separate bivariate probit models using a similar instrument for each model. However, I learned that this approach doesn’t account for the indirect effect of the instrument that operates through the omitted endogenous variables. If we denote endogenous variables as X1, X2, X3, and the instrumental variable as Z, when I estimate the first bivariate probit model, it omits the effect of the instrument on the outcome variable through its effect on the omitted endogenous variables X2 and X3. The same is true for the other models as well.
I use this code
where Q is a vector of other controls.
As a solution, I am trying to approach it as follows.
First, I estimate a probit model for each respective endogenous variable by including the instrument and other controls and generate the predicted values. i.e,
X1 =b0+b1Z +b2Q +e1
X2 =b0+b1Z +b2Q +e2
X3 =b0+b1Z +b2Q +e3,
From these three models, I generate three predicted values.
Then, I estimate a separate bivariate probit model using the predicted values from step 1 as a regressor. That means that when I estimate the bivariate probit model for the first endogenous variable, I only include the predicted values from the other two models. And I will do the same for the other models as well.
Now, my question is does my approach make sense, and is it a good way to address my problem? If not, what would be the best way to deal with it?
Thank you!
Fissha
Please my apologies in advance if I ask a silly question.
I am trying to estimate a bivariate probit model using one instrumental variable for three endogenous variables (the outcome variable and the endogenous variables are categorical variables with 0 or 1 value). That means that I estimate three separate bivariate probit models using a similar instrument for each model. However, I learned that this approach doesn’t account for the indirect effect of the instrument that operates through the omitted endogenous variables. If we denote endogenous variables as X1, X2, X3, and the instrumental variable as Z, when I estimate the first bivariate probit model, it omits the effect of the instrument on the outcome variable through its effect on the omitted endogenous variables X2 and X3. The same is true for the other models as well.
I use this code
biprobit (Y = X1 Q) (X1 =Z Q)
biprobit (Y= X2 Q) (X2 = Z Q)
biprobit (Y = X3 Q) (X3 = Z Q),
biprobit (Y= X2 Q) (X2 = Z Q)
biprobit (Y = X3 Q) (X3 = Z Q),
As a solution, I am trying to approach it as follows.
First, I estimate a probit model for each respective endogenous variable by including the instrument and other controls and generate the predicted values. i.e,
X1 =b0+b1Z +b2Q +e1
X2 =b0+b1Z +b2Q +e2
X3 =b0+b1Z +b2Q +e3,
From these three models, I generate three predicted values.
Then, I estimate a separate bivariate probit model using the predicted values from step 1 as a regressor. That means that when I estimate the bivariate probit model for the first endogenous variable, I only include the predicted values from the other two models. And I will do the same for the other models as well.
Now, my question is does my approach make sense, and is it a good way to address my problem? If not, what would be the best way to deal with it?
Thank you!
Fissha
