Leads and lags in planner's objective_policy with capital

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Leads and lags in planner's objective_policy with capital

Postby nk178 » Sun May 17, 2015 2:38 pm

Dear all,

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?

Thank you a lot in advance.
nk178
 
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Re: Leads and lags in planner's objective_policy with capita

Postby jpfeifer » Sun May 17, 2015 4:53 pm

Why don't you go for a full second order approximation?
------------
Johannes Pfeifer
University of Cologne
https://sites.google.com/site/pfeiferecon/
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Re: Leads and lags in planner's objective_policy with capita

Postby nk178 » Mon May 18, 2015 11:49 am

Dear Johannes,

Thank you a lot again for your answer.

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?
nk178
 
Posts: 32
Joined: Sat May 24, 2014 1:05 pm

Re: Leads and lags in planner's objective_policy with capita

Postby jpfeifer » Mon May 18, 2015 1:46 pm

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.
------------
Johannes Pfeifer
University of Cologne
https://sites.google.com/site/pfeiferecon/
jpfeifer
 
Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

Re: Leads and lags in planner's objective_policy with capita

Postby nk178 » Wed May 20, 2015 7:18 pm

Dear Johannes,

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).

Again,

thank you a lot.
nk178
 
Posts: 32
Joined: Sat May 24, 2014 1:05 pm


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