I am trying to solve the optimal policy problem in a New Keynesian DSGE with capital accumulation. Given that capital at time t is predetermined (standard law of motion of capital), after using the linear quadratic approach, I get an objective function with inflation, output and investments at the current period and capital at the current period but also with a lag.

Please notice, that the last one is not an independent of policy term for two reasons: 1) current investments are affected from k(-1), 2)In the objective function I get also two product terms where lagged capital is multiplied with current output, so it is dependent of policy for sure.

Any suggestions on what to do? I have thought the obvious, that is, solve for k(-1) from the law of motion and then substitute with k and investm. Is there any other way to solve this issue, or do you agree to go with the substitution?

I am sorry but I do not understand. It is true that for the law of motion of capital I have taken a first order approximation. However, how a second order approximation will solve the “lag” problem? Would the lagged value still exist?

Maybe I don’t understand your problem. But if you go for full second order, you don’t need to do a linear-quadratic approach, which, if I understood you correctly, gives rise to the lag.

Thank you very much for your reply. I think I resolved this problem. Can you please also have a comment on my other very recent post about a problem I have with discretionary policy only? (I think it should be a problem of quadratic terms, but I was hoping for a help on that).