Can DYNARE simulate from BGP

[kofiemma]

Hi Prof. Pfeifer, I know your non-stationary solow mod file that studies transition dynamics from 90% below BGP to BGP. May I kindly ask if dynare can simulate, not to BGP, but from BGP like in this graph.

1. They initially have the model in extensive form (x_t)
2. And they covert it to intensive form (\hat{x_t} = \frac{x_t}{A_t H_t}), where A_t = A_0\gamma_a^t, H_t = H_0\gamma_h^t)
3. They find steady-state (\hat{x_{ss}}) and simulate the model. The policy here is a drop in some parameter \pi_1 (no reduction in barrier) to \pi_2 (baseline reduction in barrier) in 1945.

So this simulation is like from old steady-state to new steady-state after policy. But since they are comparing with data, it seems they transform the results back to extensive form (x_t) and compare with data (x^{data}_t).

How to get a non-stationary extensive form transition path (with BGP) after simulating in intensive form in dynare? Seems not possible in dynare.

Outside dynare, maybe just compute the BGP (the trend line) from data (before policy) and simply add it to the stationary transition path computed from the model? (of course assuming the model is nonlinear).

[jpfeifer]

See

Random walk with a drift process

Detrending is just a convenient normalization for the solution technique. You can later add the trend back. See e.g. https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Aguiar_Gopinath_2007/Aguiar_Gopinath_2007.mod

[kofiemma]

Many thanks!!! So like if the intensive form is, say, y_t = \frac{Y_t}{A_{t-1}}, then we have,

log_Gamma(ii,1)=g(ii,1)+log_Gamma(ii-1,1); \approx logA_t = log(g_t + 1) + log A_{t-1}

And

log_y_nonstationary(ii,1)=log_y(ii,1)+log_Gamma(ii-1,1); \approx log\; Y_t = log\; y_t + logA_{t-1}

And we can get the trend of extensive form Y_t
[ytrend,ycyclical]=sample_hp_filter([log_y_nonstationary],1600);

But in my case, g_t is not stochastic. growth is constant, g_t = g . Thus, exogenous but constant and computed from data.

Then I combine ytrend and IRF of non-stationary model as below…

to get

t=0 is the period of impact (like 1945 in the figure in my original question). I guess something like this, right? Like the economy is moving along BGP before period 0, and in period zero some policy happens.

[jpfeifer]

Yes, that looks OK, except for the HP filter trend not implying a constant growth rate.

[nakov]

Dear Dynare team,
Can Dynare simulate forward a purely backward-looking, but unbalanced growth model, starting from some initial values and letting it run forward until some final time T?
Kind regards,
Anton

[jpfeifer]

Yes, e.g.

var k invest;
parameters delta g;

g=0.02;
delta=0.05;

model;
k=(1-delta)*k(-1)+invest;
invest=(1+g)*invest(-1);
end;

initval;
invest=1;
k=1;
end;

perfect_foresight_setup(periods=100);
perfect_foresight_solver;
rplot k invest;

[nakov]

Thank you!