# 2sls with lagged dependent

I have seen many papers using dynamic panel regressions when the lagged dependent is a regressor and the data has the standard panel format. so, y(t)=constant + beta1*y(t-1)+ beta2*X(t) is often assessed using dynamic panel data regression. My question is that I have a study where I want to use the predicted X in the regression instead of the realized X. So X(t) depends on X(t-1) and X2(t-1). Can I run in this context a 2sls regression where in the first stage: X(t)= constant+ gamma1*X(t-1)+ gamma2*X2(t-1). Then in the 2nd stage: y(t)=constant + beta1*y(t-1)+ beta2*Predicted X(t) from the 1st stage.... is it sound ?

• Presumably because your $X(t)$ is unobserved, or only parially-observed? Otherwise how do you get $X$ as a function of previous time periods? Also, sound in what way? Assuming that you've got enough data for a lagged panel approach to work, you'll need to do something to account for the fact that your regressor is estimated -- probably some sort of bootstrapping. – generic_user Aug 7 '17 at 21:07
• Thanls.Let me explain in more details. I am using 2sls because X is endogenous and depends on an lagged variable Z (which is X2 in my previous example). So , I ran a regression of X on Z in the first stage and the predicted X is used in the second regression to estimate Y. I am simply trying to prove that the X decisions based on Z are important in explaining Y. Does the 2sls work in this case if Y depends on Y-1 in the 2nd regression? – wesso Aug 8 '17 at 6:48