# GPU (2010) replication: interest rate definition

Dear Prof Johannes,

I am trying to extend the model as in GPU (2010) and I found in you replication mod file equation 1, interest rate defined as:

r(t) = rstar + psi*(exp(d(t) - dbar) - 1) + exp(mu-1) - 1

I think in this formula it shoud be psi*(exp(d(t+1) - dbar) -1) since in the paper nowhere shows that r(t) related to D(t). r(t) is interest rate of debt issued at time t, and you defined “predetermined_variables k, d” so that it should appear d(t+1).

I think GPU made mistake here as all formula in the main text they wrote:

r(t) = rstar + psi*(exp(d(t+1) - dbar) - 1)

but in the appendix they nevertheless wrote:

r(t) = rstar + psi*(exp(d(t) - dbar) - 1)

It makes me confused or maybe I was wrong.

Could you please confirm which one is right?

Another question is how can you specify the observation equation as:

g_y = y/y(-1)*g(-1).

I do not understand this calculation though I read your guide. Basically, if Y = y*X(-1) then growth rate of Y is as

g_y = log(Y / Y(-1)) or g_y = log(y / y(-1)) + log(X(-1) / X(-2)) = log (y / y(-1)) + log(g(-1)).

In the model variable y is level so that g_y is gross growth rate. But the datafile you provide g_y, g_c and g_i are net growth rate. Could you please show me where I was wrong?

Thank you and best regards,

Hi,
thanks for pointing this out. I have added a clarifying note to the file. I think that the equation in the paper is the one that makes sense (using `d(+1)`, i.e. the debt level decided upon today). However, the results presented in the paper are generated using the specification in the Appendix with `d`, i.e. the debt level decided upon yesterday. This can be seen from the replication codes that also use this timing. I will notify the authors of this.

Regarding the observation equation: the equation is in levels, because the `loglinear` option will implicitly takes logs of all variables, making the equation log-linear. Normally, that option would trigger taking the log of the data as well. That is why the `logdata` option is specified to tell Dynare to not take the log again.

Thanh you very much Prof Johannes, I’ve got it.