non-stationary dependent variable

[Katerina Petrou]

Dear all,

Hope you are well.
I am using panel data and I have found out that my dependent variable is non-stationary.
Is it possible to use the instrumental variable estimation using first difference variables?



Kind Regards,
Katerina
Stata/ SE 16.0

[Jeff Wooldridge]

There is no issue with this. Once you have specified your model -- where you decide whether to include a variable in level or differenced form -- then you can do the usual. I seem to remember you have a larger T and smaller N. That could affect standard error calculation.

But suppose you start with

y(i,t) = a*w(i,t) + x(i,t)*b + c(i) + u(i,t)

where w(i.t) is thought exogenous and z(i,t) are IVs. If you're worried y and/or w and x are I(1) you can difference the entire equation:

ivregress 2sls D.y (D.w = D.z) D.(x1 ... xK), vce(cluster id)

If you only difference y then your model is different, and you would drop D. from w, z, and x.

A problem is that when T is larger than N, the clustering might not work well. And doing a Newey-West with panel data is tricky.

[Katerina Petrou]

Jeff Wooldridge Thank you so much for your answer.
I also included control variables as you suggested;
When we run a simple first difference regression do we have to take the first difference of the control variables as well? (i.e controls= lagged of y or x variables)

[Jeff Wooldridge]

Katerina: You need to start by writing down the model of interest. If you dependent variable is differenced, you might not need to use fixed effects. In any case, you have to be careful using FE with lagged y, although a large T helps.

If you want to leave some of the xj in their level form then just drop the D. in front of those xj. The same is true of the endogenous variable, w.