Simultaneous Equation Model

[Jheelum Sarkar]

I am trying to find effect of a shock on time spent on unpaid and paid work using simultaneous equations model. Variables of my interest are:
women_unpaid= time spent by women on unpaid work (endogenous variable)
women_paid=time spent by women on paid work (endogenous variable)
time_dummy=1 after the shock and 0 before the shock (exogenous variable)
treatment=1 if dwelling in treated districts and 0 if dwelling in control districts (exogenous variable)
DID=interaction of time_dummy and treatment (exogenous variable)

Code used: reg3 ( women_unpaid: women_paid time_dummy treatment DID ) ( women_paid: women_unpaid time_dummy treatment DID )

[Richard Williams]

I’m unclear. What exactly is the question?

[Jeff Wooldridge]

What’s shown is not what is usually called a simulataneous equations model. It appears you wanted to write each variable as a function of the other. But to me that’s meaningless. And you can’t, anyway, because you have no exclusion restrictions. Instead, you’ve estimated a seemingly unrelated regression (SUR) system. But this does nothing for you because you have the same RHS variables. You can do OLS on each equation and cluster the standard errors for serial correlation.

Just because two variables are simultaneously determined does not mean we should write one as a function of the other. We don’t write quantity of chicken demanded as a function of quantity of fish.

[Jeff Wooldridge]

I had to refresh my memory. Your syntax is incorrect if you intended to write each variable as a function of the other. If you do it correctly, you’ll get an error message about lack of identification. As I said, use OLS on each equation.

[Jheelum Sarkar]

Thank you for your feedback and insights, Prof. Wooldridge! I appreciate your clarification on the nature of the model. Your point about the lack of exclusion restrictions and the potential identification issues when writing each variable as a function of the other is duly noted. I understand now that a seemingly unrelated regression (SUR) system might not be the most appropriate approach in this context.

Your suggestion to use OLS on each equation and cluster the standard errors for serial correlation is well-taken. I will revisit the model and incorporate your recommendations to address the identified issues.