solve_dsge: Solve a Linear or Linearized DSGE Model
In dsge: Dynamic Stochastic General Equilibrium Models

solve_dsge

R Documentation

Solve a Linear or Linearized DSGE Model

Description

Computes the state-space solution of a DSGE model using the Klein (2000) method. Accepts both linear models (dsge_model) and nonlinear models (dsgenl_model). For nonlinear models, the steady state is computed and the model is linearized automatically.

Usage

solve_dsge(model, params = NULL, shock_sd = NULL, tol = 1e-06, order = 1L)

Arguments

`model`	A `dsge_model` or `dsgenl_model` object, or a Dynare model imported with `read_dynare()`.
`params`	Named numeric vector of parameter values. If `NULL`, uses the model's fixed and start values (for an imported Dynare model, its calibration).
`shock_sd`	Named numeric vector of shock standard deviations. If `NULL`, defaults to 1 for all shocks (for an imported Dynare model, the standard deviations from its `shocks` block).
`tol`	Tolerance for classifying eigenvalues as stable (\|lambda\| < 1 + tol). Default is 1e-6.
`order`	Integer. Approximation order: 1 (default), 2 for second-order, or 3 for third-order perturbation. Orders 2 and 3 require a `dsgenl_model`.

Details

The stable solution is computed by cyclic reduction (as Dynare's cycle_reduction option); if that fails, for example with unit roots or a singular lead matrix, the stable deflating subspace of the model's matrix pencil is found with the inverse-free spectral divide of Bai, Demmel and Gu (1997), which needs no QZ decomposition; an undetermined-coefficients iteration is the last resort. As in Dynare, eigenvalues with modulus up to 1 + 1e-6 count as stable, so unit roots are allowed. Saddle-path stability requires that all eigenvalues of H have modulus below 1 + tol.

For nonlinear models, the solver first computes the deterministic steady state, then linearizes the model via first-order Taylor expansion, and finally solves the resulting linear system.