Home

DynareJulia Wiki

This Wiki is for discussing design issues about DynareJulia

Introduction

• Original thoughts about the project

DynareJulia packages

• Dynare.jl
• AxisArrayTables.jl
• ExtendedDates.jl
• FastLapackInterface.jl
• GeneralizedSylvesterSolver.jl
• KalmanFilterTools.jl
• KroneckerTools.jl
• LinearRationalExpectations.jl
• PolynomialMatrixEquations.jl
• QuasiUpperTriangular.jl

Dynare.jl

• Deals with Dynare instructions
• The preprocessor is the same executable as for Dynare Matlab/Octave
• The state of computations is kept in context as structure of Context type

struct Context
    symboltable::SymbolTable
    models::Vector{Model}
    modelfileinfo::ModFileInfo
    results::Results
    work::Work
end

• Instructions are extracted from

 ./<MODFILENAME>/model/json/modfile.json 

that is written by the C++ preprocessor

• Global approximation methods

LinearRationalExpectations.jl

• Solves model of the form latex E_t \{ A y_{t+1} + B y_t + C y_{t-1} + D u_t + e\} = 0
• The deterministic steady state of the model is defined as latex \bar y = -(I - A - B - C)^{-1}e
• The solution takes the form latex y_t - \bar y= G_y (y_{t-1} - \bar y) + G_u u_t
• G_y is the solution of the polynomial matrix equation latex A G_y G_y + B G_y + C = 0 and latex G_u = -(A G_y + B)^{-1}Du_t

PolynomialMatrixEquations.jl

Two different algorithms are provided:

• generalized Schur decomposition (\cite{klein_using_2000, sims_solving_2002, soderlind_solution_1999}(
• cyclic reduction (\cite{bini_numerical_2012})
• the package provides functions to reduce the problem size by eliminating static variables.

QuasiTriangular.jl

• Multiplication and linear system solution for upper quasi triangular matrices
• Useful for handling real generalized Schur decomposition

KalmanFilterTools.jl

• Kalman filter
• Monitored Kalman filter
• Fast Kalman filter (\cite{herbst_using_2012})
• Kalman smoother
• Diffuse filter/smoother (\cite{durbin_time_2012})
• Univariate filter/smoother

TimeDataFrames and ExtendedDates

• A data frame where the first column represents dates
• Extension of dates in Julia to Year, Semester, Quarter, Month, Week, Day and Undated
• Each frequency is represented by an integer starting at some epoch (January 1st of year 1970)
• See also TimeDataFrames

FastLapackInterface.jl

• Pre-allocate workspace for some Lapack function
• LU decomposition and solution of linear systems
• QR decomposition
• Schur decomposition

KroneckerTools.jl

• Chains of Kronecker products

  \begin{align*}
  c &= (Ip \otimes A \otimes Iq)*b\\
  c &= (Ip \otimes AT \otimes Iq)*b\\
  c &= (A \otimes A \otimes ... \otimes A)*b\\
  d &= (AT \otimes AT \otimes ... \otimes AT \otimes B)*c\\
  C &= A * (B \otimes B \otimes .... \otimes B)\\
  D &= A * B * (C \otimes C \otimes .... \otimes C)\\
  D &= AT * B * (C \otimes C \otimes .... \otimes C)\\
  E &= AB(C \otimes D \otimes ... \otimes D) 
  \end{align*}
- Implements algorithms in \cite{kamenik_solving_2005}

### GeneralizedSylvesterSolver.jl
 solves
```latex
a x + b x (c \otimes c \otimes ... \otimes c) = d

by using

(I + c^T \otimes c^T \otimes ... \otimes c^T \otimes b)x = d

Currently implemented functionalities

• calib_smoother
• check
• deterministic_trends
• histval
• initval
• perfect_foresight_setup (only some options)
• perfect_foresight_solver (only some options)
• planner_objective
• ramsey_model
• shocks
• steady
• stoch_simul (only order=1, no moments)

DynareJulia roadmap

• Estimation of linear(-ized) models
• Address \emph{time to first result} problem
• Mixed complementarity problems
• Forecasting
• Making existing packages production grade (tests, documentation, benchmarking)
• Dynare-Julia documentation
• $k$-order approximation
• Multiple models
• Linear models with occasionally binding constraints
• Nonlinear estimation - particle filters
• Nonlinear estimation - simulated methods of moments
• Markov-Switching DSGE models
• Global sensitivity analysis
• Global methods of approximation
• Limited rationality