Sims

Sims Solver

RationalExpectations.sims โ€” Method.
sims(G0,G1,Pi,Psi)

This function solves a rational expectations model using Sims(2000) (aka gensys). The model should be written in the following way:

\[\Gamma_0 \mathbf{x_{t+1}} = \Gamma_1 \mathbf{x_{t}} + \Psi \mathbf{\varepsilon_t} + \Pi \mathbf{\eta_t}\]

The arguments of the function are:

  • G0 is $\Gamma_0$
  • G1 is $\Gamma_1$
  • Pi is $\Pi$
  • Psi is $\Psi$

Where $\Gamma_0$ can be singular. $\eta_t$ is the expectation error and $E_{t}(\nu_{t+1})=0$ by construction.

Sims's solver does not require that we say what variables are jump variables.

Value

If the model has a unique solution, the function returns theta1 and theta2, such that:

\[y_t = \Theta_1 y_{t-1} + \Theta_2 \varepsilon_t\]

Otherwise, it may be the case in which there is no stable solution (and the function throws an error) or multiple solutions (sunspots). In this last case, the function also returns a matrix theta3, such that:

\[y_t = \Theta_1 y_{t-1} + \Theta_2 \varepsilon_t + \Theta_3 u_t\]

Where $u_t$ is a sunspot shock

Notes

  • Sims's orignal implementation also provide as an output a vector eu, signalling if there is an equilibrium and if it is unique. This information is given as an info or an error by our function.
  • We don't force Julia to use the complex Schur decomposition. If you want it, just use sims(complex(G0),complex(G1),Pi,Psi). However, you will not be able to plot (yet) simply passing the model to irf.
  • We don't check the usual Blanchard Khan conditions with this function (since there are no jump variables defined). klein(A,B,C,t,k0,shock_exp,jumps) does that. However, it takes a different set of matrices.
source
RationalExpectations.irf โ€” Method.
irf(model::SimsSol,t::Int,shock)
irf(Theta1,Theta2,t,shock)

Generates the IRF from the matrices calculate using the gensys.

This function allows you to pass the matrices directly or to provide the whole model.

  • model receives the full output of the function sims
  • Theta1 is the theta1 matrix from sims
  • Theta2 is the theta1 matrix from sims
  • t is the number of periodos to be simulated
  • shock is the size of the shock

See also sims(G0,G1,Pi,Psi)

source

Important

When you add an autocorrelated shock to the system, the value on the lhs must be on t+1. Otherwise, the IRF will be wrongly computed.