Example with rigid prices

Here I have an example with rigid prices
rigidprices_model.mod (1.34 KB)

It seems to me, that the capital evolution eq in your model
does not comply to the dynare timing convention

k = (1-delta)k(-1)+deltai(-1);

here the LHS and the investment should be timed the same, because they are decided (determined) at the same time.

But I might be wrong… someone else?

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

Best

Daney

I think

k(+1)=(1-DELTA)k+DELTAI

would be still incorrect with respect to timing: in the above equation k and i are not determined in the same period. I mean in time period t predetermined capital is determined in period t-1 and investment is determined in t. So predetermined capital and investment cannot have the same time index. I think your eq should be:

k=(1-DELTA)k(-1)+DELTAI

Regards,
Henrik

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

Hi!

I didn’t say your eq is incorrect per se, or it is not in the form which
is mostly used in the literature…
Dynare has a less frequently used (albeit rather logical) convention:
every variable gets the time index of the period its value is determined in.

In connection with capital the timing difference can be referred to as beginning of period vs. end of period capital.

regards,
Henrik

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

k=(1-DELTA)k(-1)+DELTAI

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

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