Detrending in dsge

Steady state
1

Hi everybody,

I am struggling with the use of trend_var and deflator commands in dynare to find out the steady state of a non stationary dsge model (here you find attacched a simplified version of the model with a trend in TFP affecting a CES aggregator over 2 intermediate inputs). In particular:

1)If I have one or more trending variables, I must express the non-stationary model in the model; block so that dynare automatically deflate the non-stationary variables by the indicated deflators, correct?

2)In the auxiliary file for steady state computation, I should instead provide the stationary model by modifying nonstationary equations with growth rates? In that case, I can’t understand why my model produces residuals relating to the taylor rule.

Thank you very much

reduced_trend.mod (6.3 KB)

findssreduced_trend.m (1.3 KB)

reduced_trend_steadystate.m (2.1 KB)

2

You need to provide the equations in a consistent way, i.e. if they contain non-stationary elements that are deflated by Dynare, the trends in the respective variables need to be consistent. Take your Taylor rule

r/r_ss = ((r(-1)/r_ss)^rho_r)*((((pi/pi_ss)^phi_pi)*((y/y(-1))^phi_y))^(1-rho_r))*exp(epsa_r);

It is problematic because y/y(-1) will not be 1 in steady state due to the trend growth rate. You would end up with

1 = ((gb)^phi_y))^(1-rho_r));

which explains the residual. Your Taylor rule needs to express output growth relative to steady state growth:

r/r_ss = ((r(-1)/r_ss)^rho_r)*((((pi/pi_ss)^phi_pi)*((y/y(-1)/gb)^phi_y))^(1-rho_r))*exp(epsa_r);

reduced_trend.mod (6.3 KB)