Fiscal multiplier - Stochastic setting - Permanent vs/ transitory shocks

Stochastic simulations
#1

Hello, we are working on the DSGE model developed in Smets and Wouters 2003 for the eurozone in a bayesian setting. We would like to compute the reaction of GDP and inflation to transitory and permanent shocks to public spending.

We managed to estimate the fiscal multiplier with bayesian IRF from estimation command, but now we have struggle to compute the effect of a permanent and transitory shock.

  1. We don’t understand exactly how to study both the effect of a transitory and permanent shock with stock_simul. In order to do so we tried to set in the shock block the government spending shock as follow:

rho_g=0;

shocks;
var E_G;
periods 1:2;
values 0.1;
end;

and then call stoch_simul after the command estimation.

Does this compute the reaction to a shock of the variable E_G during period 1 and 2 ?

  1. From our research, it seems that a permanent shock can only be computed in a deterministic setting. Therefore we tried to call perfect_foresight_setup(); perfect_foresight_solver(); after estimation but we get this error:

The ‘simul’ statement is deprecated. Please use ‘perfect_foresight_setup’ and ‘perfect_foresight_solver’ instead.
ERROR: A .mod file cannot contain both one of {perfect_foresight_solver,simul} and one of {stoch_simul, estimation, osr, ramsey_policy, discretionary_policy}. This is not possible: one cannot mix perfect foresight context with stochastic context in the same file.

Therefore it seems that our model under rational expectation is incompatible with a deterministic framework.

We understand the economic intuition behind stochastic (rational expectation) and deterministic framework. However, we don’t know how to link the two : using the bayesian model estimated by Smets and Wouters in order to compute permanent vs/ transitory shocks.

Thank you in advance,

#2

There are essentially two ways to proceed.

  1. You stay in the stochastic context and model the permanent shock as a shock to a unit root process.
  2. You can switch to perfect foresight context and treat the shock as purely exogenous as you tried above.

Due to certainty equivalence holding in a linear model, it should not matter which of the two approaches you select. But in any case, you need to implement the the simulation in a different mod-file than the estimation (although code parts and even parameters can be easily share, e.g. using the macro processor include directive and loading parameters from M_.params)