Finite and infinite sums

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Finite and infinite sums

Postby fisico69500 » Thu May 15, 2014 11:22 am

Dear All,

I am currently working on a New Keynesian model with Dynare. One equation has a particular form. The variable w is forward looking and notably depends on the expected future values for pi in the following way (here I omit arguments that have no impact on my topic):

w_t = E_t [Beta(pi_t+1) + Beta^2(pi_t+1 + pi_t+2) + Beta^3 (pi_t+1 + pi_t+2 + pi_t+3) + Beta^4 (pi_t+1 + pi_t+2 + pi_t+3 + pi_t+4) ..... up to infinity]

I would be grateful if you could tell me how to write it with Dynare. Especially the way to write the sequence for pi.

Best
fisico69500
 
Posts: 12
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Re: Finite and infinite sums

Postby jpfeifer » Thu May 15, 2014 12:11 pm

------------
Johannes Pfeifer
University of Cologne
https://sites.google.com/site/pfeiferecon/
jpfeifer
 
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Location: Cologne, Germany

Re: Finite and infinite sums

Postby fisico69500 » Thu May 15, 2014 1:54 pm

Thank you very much for this answer.

In fact, I have already tried to write this equation in a recursive way, as it is suggested in the user guide. However, I was not able to find such a representation, since what happens with pi is not exactly an infinite sum. This is rather an infinity of finite sums (pi_t+1 + pi_t+1 + pi_t+2 + pi_t+1 + pi_t+2 + pi_3 + ...).

Note also that the model is already written in a linear form, since pi is the inflation rate.

I think writing the pi in a recursive way would be the solution. But I do not see how to this with this kind of sum.

Thanks by advance for your help.

Best
fisico69500
 
Posts: 12
Joined: Mon Jul 02, 2012 10:34 am


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