Example with rigid prices

[daney]

Here I have an example with rigid prices

[daney]

The correct law of motion should (log - linearized) be k(+1)=(1-DELTA)*k+DELTA*I, but it will not work, and since capital is predetermined you must delayed the eq. and variables related to capital

Best

Daney

[daney]

this is new formationof new capital, new capital k(+1) is formed by reposition of old kapital (1-delta)k and new investment I.

F.e. (amog lost of examples and books) you should cheked:

Obsfeld and Rogoff - Foundation of international Macroeconomics - 1.2.1 eq 11.

King and Rebelo "Resuscitating Real Business cycles" NBER-WP 7534 eq 3.6

Best

Daney

[daney]

I mean, the correct one is the one you told me. Since, capital is predetermined, you can't do

k=(1-DELTA)*k(-1)+DELTA*I

Why?, the correct one, when you have your model log-lin is:

K(+1)=(1-delta)K+DELTA*I

because it shows capital formation by two ways: new investment and reposition that we have to hold the structure of the model. And when we do it in Dynare we must delay the hole eq:

k = (1-delta)k(-1)+delta*i(-1)

and eqs where capital is. On the contrary, I think, the model doesn't run.


Best

Daney

[p.gelain]

Hi,

at the Dynare summer school I remembered that Professor Juillard clearly told us to lag all stocks (and only the stocks!!!) if expressed at time t+1. In this respect, the right way to write the capital formation equation in Dynare is

k(t) = (1-delta)k(-1)+delta*i

This is also confirmed by the Dynare_UserGuide.pdf at page 19, paragraph 3.5.4.
Nevertheless, the equation k(t) = (1-delta)k(-1)+delta*i(-1) is not incorrect. Many authors use them (e.g. Smets and Wouters 2003), but I don't think that it can safely be used in Dynare.

Paolo