RISE Toolbox (Modern) – Documentation

Welcome to the documentation for the modern version of the RISE toolbox. This branch is a ground-up redesign that consolidates DSGE, VAR, SVAR, proxy SVAR, BVAR-DSGE, and panel models behind a single model class with a single state-space, validated entry points via arguments blocks, and a small surface of plain-MATLAB operators.

For the legacy version, see rise-stable-docs.

Getting started

• 1. Installation
  • 1.1. Prerequisites
  • 1.2. Bootstrap
  • 1.3. Smoke test
  • 1.4. Optional tooling
• 2. First model
  • 2.1. The model file
  • 2.2. Build and solve
  • 2.3. Inspect
  • 2.4. What just happened
  • 2.5. Next steps
• 3. Hit the ground running: an introductory example
  • 3.1. The model economy
  • 3.2. The model file
  • 3.3. Building the model object
  • 3.4. Parameterizing the model
  • 3.5. Solving the non-stationary model
  • 3.6. A one-shot stoch_simul run
  • 3.7. Impulse responses
  • 3.8. 5th-order perturbation
  • 3.9. Data from FRED
  • 3.10. Priors
  • 3.11. Visualizing the priors
  • 3.12. Posterior maximisation
  • 3.13. Posterior simulation
  • 3.14. Marginal data density via the bridge estimator
  • 3.15. The full driver
• 4. Modern architecture
  • 4.1. Part A. Common across all shapes
    • 4.1.1. One model class
    • 4.1.2. Unified state-space
    • 4.1.3. Always regime-switching
    • 4.1.4. No construction metadata after build
    • 4.1.5. Estimate dispatches on properties, not class
    • 4.1.6. OOP only at the user boundary
    • 4.1.7. Arguments blocks systematically
    • 4.1.8. Stay close to plain MATLAB
    • 4.1.9. No internal switching syntax
    • 4.1.10. The common engine surface
  • 4.2. Part B. What each shape contributes
    • 4.2.1. DSGE – dsge_model
    • 4.2.2. Reduced-form VAR – rfvar_model
    • 4.2.3. Structural VAR – svar_model
    • 4.2.4. Proxy SVAR – proxy_svar_model
    • 4.2.5. Panel VAR – prfvar_model
    • 4.2.6. DSGE-VAR – dsge_var_model
  • 4.3. Summary

Working with a model

• 1. Understanding a rise_model object
  • 1.1. Ordering and information about atoms
    • 1.1.1. Endogenous variables
    • 1.1.2. Exogenous variables
    • 1.1.3. Parameters
    • 1.1.4. Observables
  • 1.2. Information on model equations
  • 1.3. Information on model results
    • 1.3.1. First-order structural form
    • 1.3.2. Solution results
    • 1.3.3. Posterior maximisation results
• 2. Setting up calibration and priors outside the model file
• 3. Filtering
  • 3.1. Linear filtration
    • 3.1.1. Historical decomposition
    • 3.1.2. Observables decomposition
  • 3.2. Conditional forecasting via filtering
    • 3.2.1. Hard conditions
    • 3.2.2. Soft conditions
    • 3.2.3. When to choose this route
    • 3.2.4. When the route is the wrong tool
  • 3.3. Nonlinear filtering
    • 3.3.1. When the nonlinear filter is used
    • 3.3.2. Choosing the filter
  • 3.4. Options
  • 3.5. User-defined filter
  • 3.6. The available sigma-point filters
    • 3.6.1. Switching divided-difference filter
    • 3.6.2. Switching unscented Kalman filter
    • 3.6.3. Switching cubature Kalman filter
• 4. Simulation plans
  • 4.1. Why a simulation plan
  • 4.2. Construction
    • 4.2.1. The shockInit rule
  • 4.3. Appending conditions
    • 4.3.1. Single variable, vector of values
    • 4.3.2. Multiple variables, struct form
    • 4.3.3. Algebraic constraint
  • 4.4. Boundary conditions: initval, endval, histval
  • 4.5. Anticipation: pages
  • 4.6. Hard endogenous conditions and the identification rule
    • 4.6.1. The recipe
    • 4.6.2. Soft conditions
  • 4.7. Inspecting a plan
  • 4.8. Consumption: the universal interface
  • 4.9. Scope: shapes other than DSGE
  • 4.10. See also
• 5. Forecasting and simulation
  • 5.1. simulate
    • 5.1.1. Common options
    • 5.1.2. Output shape
    • 5.1.3. Returning the regime path
  • 5.2. Theoretical and sample moments
  • 5.3. Pruned simulations (higher order)
  • 5.4. forecast
    • 5.4.1. Hard and soft conditions
    • 5.4.2. The option surface
  • 5.5. perfect_foresight
  • 5.6. Fan charts
  • 5.7. Relative-entropy tilting
  • 5.8. Smoother-based conditional forecasts
  • 5.9. See also
• 6. Solution accuracy
  • 6.1. The accuracy method
  • 6.2. Visualizing where a solution is accurate
  • 6.3. Where to evaluate: ergodic cloud versus grid
  • 6.4. Pruning and the accuracy verdict
  • 6.5. How it works (paradigm-free)
  • 6.6. Perturbation versus Taylor projection
• 7. Failure diagnosis: diagnose(m) and friends
  • 7.1. One entry point
  • 7.2. Fix-actions
  • 7.3. The volume knob
  • 7.4. Related tools
• 8. Storytelling
  • 8.1. filter
  • 8.2. Historical decomposition
  • 8.3. +resim_bridge – the resimulation surface
    • 8.3.1. Adapter
    • 8.3.2. Reconstruction
    • 8.3.3. Counterfactuals
    • 8.3.4. Shock decompositions
    • 8.3.5. Ergodic variance decomposition
  • 8.4. A worked story
  • 8.5. Where to look next
• 9. Time-varying transition probabilities
  • 9.1. When to use TVTP
  • 9.2. The @transition_functions block
  • 9.3. Driving the transition with an observed exogenous variable
    • 9.3.1. How it is evaluated
  • 9.4. Mixing constant and endogenous chains
  • 9.5. Estimation under TVTP
  • 9.6. @epilogue for diagnostics
  • 9.7. Where to look next
• 10. Extending RISE
  • 10.1. Extracting the structural form
  • 10.2. Extracting the solution
  • 10.3. Your own solver
  • 10.4. Your own filtering algorithm
  • 10.5. Your own optimizer
  • 10.6. Your own likelihood function
    • 10.6.1. Relation to Indirect Inference
  • 10.7. Your own posterior sampler
  • 10.8. Where this is not enough
• 11. Extending RISE through paradigms
  • 11.1. Goals
  • 11.2. What a paradigm is
  • 11.3. Responsibilities of a paradigm
  • 11.4. The standard solution envelope
  • 11.5. The minimum interface contract
  • 11.6. Mutable solution objects
  • 11.7. Responsibilities of RISE
  • 11.8. Isolation, safety and persistence
  • 11.9. Examples
    • 11.9.1. The OccBin paradigm
    • 11.9.2. Recursive local linearization (RLL)
    • 11.9.3. \(k\)-th order Taylor projection (TP)
    • 11.9.4. Risk-adjusted linear (RAL)
  • 11.10. Design principles

Model shapes

• 1. DSGE Modeling
  • 1.1. Model file language
    • 1.1.1. Block keywords at a glance
    • 1.1.2. Declarations
      • Endogenous variables
      • Exogenous variables (shocks)
      • Parameters
      • Switching parameters
      • Observables
    • 1.1.3. The @model block
      • Time indexing
      • Equation labels
      • Auxiliary definitions
      • Steady-state-form companion equations
      • Comments
    • 1.1.4. Steady state
      • Steady-state file (recommended)
      • @steady_state_model block (in-file alternative)
      • No steady-state specification
    • 1.1.5. Markov chains
      • Constant transition probabilities
      • Endogenous transition probabilities
      • Occasionally-binding constraints
    • 1.1.6. Optimal policy
      • Single-player problem
      • Multi-player problem (Nash, Stackelberg)
    • 1.1.7. Epilogue
    • 1.1.8. What does not go in the model file
      • Numerical parameter values
      • Steady-state values
      • Solve-time choices
      • Estimation priors
  • 1.2. Zero-th order approximation: steady state and balanced-growth path
    • 1.2.1. Anatomy of a steady-state file
    • 1.2.2. Incomplete analytical solution
    • 1.2.3. Steady-state loops
    • 1.2.4. Facilitators
      • Equation simplification
      • Declaring log and level variables
      • Setting bounds on variables
    • 1.2.5. Multiple regimes
  • 1.3. First-order perturbation
    • 1.3.1. The state vector
    • 1.3.2. Solvers for the quadratic matrix polynomial
      • Constant-parameter case (and the Maih-Waggoner perturbation)
      • Regime-switching case
    • 1.3.3. User-defined solver
  • 1.4. Higher-order perturbation
    • 1.4.1. Choosing the derivatives
    • 1.4.2. Solving the system of generalized Sylvester equations
  • 1.5. Solving
    • 1.5.1. The signature
    • 1.5.2. The retcode pattern
    • 1.5.3. Picking a solver
    • 1.5.4. Solver options
    • 1.5.5. Order of approximation
    • 1.5.6. Optimal policy
    • 1.5.7. Occasionally-binding constraints
    • 1.5.8. Perturbation strategy
    • 1.5.9. Other options worth knowing
    • 1.5.10. The diagnostic protocol when solve fails
    • 1.5.11. Return-code reference
      • Evaluation (pre-solve)
      • Solving
      • Filtering and likelihood (downstream of solve, listed for completeness)
    • 1.5.12. The retcode-aware pattern
  • 1.6. Optimal policy
    • 1.6.1. The modern distinctive
    • 1.6.2. Declaring the planner’s problem
    • 1.6.3. Solve-time choices
      • Restrictions on solve_policy_equilibrium
    • 1.6.4. Solver selection
    • 1.6.5. Loose commitment and stochastic replanning
    • 1.6.6. A worked example: Tatiana’s monetary-fiscal game
    • 1.6.7. Nonstationary optimal policy: geometric multipliers
      • The power-scaling multiplier charts (multiplier_charts)
    • 1.6.8. Where to look next
  • 1.7. Optimal (optimized) simple rules
    • 1.7.1. The loss function
    • 1.7.2. (Approximate) analytical loss
    • 1.7.3. Simulated loss
    • 1.7.4. OSR and indirect inference
    • 1.7.5. OSR with a user-defined objective
    • 1.7.6. Policy frontiers
  • 1.8. Occasionally-binding constraints
    • 1.8.1. Form 1. Kinky functions
      • Declaration
      • Deterministic context: exact enforcement
      • Stochastic context: approximate treatments
    • 1.8.2. Form 2. Regime-switching approximation
      • Solving with the OccBin paradigm
    • 1.8.3. Side constraints inside an optimization problem
    • 1.8.4. Simulation and IRFs under OBC
    • 1.8.5. Where to look next
  • 1.9. Deterministic and quasi-deterministic solutions
    • 1.9.1. The perfect-foresight problem
      • A first example
    • 1.9.2. Setting the conditions
      • Initial and terminal steady states
      • Initial policy multipliers: timeless vs reoptimize
    • 1.9.3. Free terminal: commitment and optimal-policy models
    • 1.9.4. Choosing the horizon
    • 1.9.5. Solvers and performance
      • Reusing the Jacobian factorization
      • Reusing the steady state
      • Other options
      • Convergence and tolerances
    • 1.9.6. Quasi-deterministic solutions: the extended path
    • 1.9.7. Regime switching
    • 1.9.8. See also
  • 1.10. Heterogeneous agents (HANK)
    • 1.10.1. Heterogeneity axes
    • 1.10.2. Deterministic axes
    • 1.10.3. Individual variables
    • 1.10.4. The individual block
    • 1.10.5. Aggregation: @Agg
    • 1.10.6. The aggregate block
    • 1.10.7. Setting grid and transition values
    • 1.10.8. Composing with regime switching
    • 1.10.9. Worked example
  • 1.11. Very large models
    • 1.11.1. Why RISE requires MATLAB R2023b
    • 1.11.2. Writing a large model
    • 1.11.3. Parsing, differentiation and memory
    • 1.11.4. Solving a large model
  • 1.12. Automatic translation of files
    • 1.12.1. Dynare files
    • 1.12.2. Dynare steady state files
    • 1.12.3. AIM/YADA files
• 2. Reduced-form VAR Modeling
  • 2.1. Description
  • 2.2. Quick-start example
    • 2.2.1. Collecting and transforming data
    • 2.2.2. Setting up the reduced-form VAR
    • 2.2.3. Estimating the VAR (classical / OLS)
    • 2.2.4. Restrictions on the VAR
  • 2.3. Identification
  • 2.4. Structural shocks, IRFs and decompositions
  • 2.5. Bootstrap and distributions
  • 2.6. Bayesian estimation
  • 2.7. Posterior sampling
  • 2.8. Bayesian forecasting
  • 2.9. Conditional forecasting
• 3. Structural VAR Modeling
  • 3.1. The model
  • 3.2. Creating an SVAR
  • 3.3. Identification
  • 3.4. Estimation
  • 3.5. Impulse responses, decompositions, forecasting
  • 3.6. Adding regime switching
• 4. Proxy (instrumental) SVAR Modeling
  • 4.1. The model
  • 4.2. Creating a proxy SVAR
  • 4.3. Estimation, IRFs, decompositions, forecasting
  • 4.4. Adding regime switching
• 5. Panel VAR Modeling
  • 5.1. The model
  • 5.2. Creating a panel VAR
  • 5.3. Estimation, identification, IRFs, decompositions, forecasting
  • 5.4. Adding regime switching
• 6. DSGE-VAR Modeling
  • 6.1. Description
  • 6.2. A quick-start example
    • 6.2.1. A simple New Keynesian DSGE model
    • 6.2.2. Setting up the BVAR-DSGE model
    • 6.2.3. Fixed parameters
    • 6.2.4. Priors
    • 6.2.5. Collecting and transforming the data
    • 6.2.6. Maximizing the posterior
    • 6.2.7. IRFs of the BVAR-DSGE at the maximized posterior
    • 6.2.8. IRFs of the DSGE model at the maximized posterior
    • 6.2.9. IRF comparison
  • 6.3. Choosing the VAR representation

Estimation

• 1. Estimation
  • 1.1. Restrictions on parameters during estimation
  • 1.2. Prior distributions and implementation
    • 1.2.1. Bayesian priors
    • 1.2.2. Endogenous Priors
    • 1.2.3. User-defined Priors
    • 1.2.4. Visualizing priors and posteriors
    • 1.2.5. List of prior distributions
  • 1.3. Posterior maximization
    • 1.3.1. Choosing an optimizer
    • 1.3.2. Bundled optimizers
    • 1.3.3. Running several optimizers in turn
    • 1.3.4. User-defined optimizers
  • 1.4. Posterior sampling
    • 1.4.1. The sampling function
    • 1.4.2. Algorithm : Random-walk Metropolis Hastings
    • 1.4.3. Algorithm : Independent Metropolis Hastings
    • 1.4.4. Algorithm : Adaptive parallel tempering
    • 1.4.5. Algorithm : Slice Sampler
    • 1.4.6. Algorithm : usrsmplr Sampler
    • 1.4.7. Delayed acceptance: surrogate-accelerated chains
    • 1.4.8. Checkpointing and resuming chains
    • 1.4.9. User-defined Algorithms: Another approach
  • 1.5. Processing Posterior draws : The mcmc class
    • 1.5.1. The properties
    • 1.5.2. The methods
    • 1.5.3. Visualizing posteriors (and priors)
  • 1.6. Marginal Data Density computation : the mdd class
    • 1.6.1. The properties
    • 1.6.2. The methods
  • 1.7. Indirect Inference
    • 1.7.1. The principle of indirect inference
    • 1.7.2. Indirect inference in RISE
    • 1.7.3. Generalized method of moments
    • 1.7.4. Simulated method of moments
    • 1.7.5. Impulse-response matching
  • 1.8. The estimation pipeline at a glance
  • 1.9. Dispatch on properties, not class
  • 1.10. Priors
    • 1.10.1. Uniform priors
    • 1.10.2. Means and standard deviations
    • 1.10.3. Quantiles
    • 1.10.4. Direct hyperparameters
    • 1.10.5. User-defined priors via PDF
    • 1.10.6. The t-student special case
    • 1.10.7. Dirichlet priors for transition matrices
  • 1.11. Endogenous (system / property / behavioral) priors
    • 1.11.1. Covariance and correlation
    • 1.11.2. Impulse responses
    • 1.11.3. Variance decomposition
    • 1.11.4. Historical decomposition
    • 1.11.5. First-order solution coefficients
    • 1.11.6. Filtered / updated / smoothed probabilities
    • 1.11.7. Aggregations and discontinuous ranges
    • 1.11.8. User-defined endogenous priors
  • 1.12. List of supported prior distributions
  • 1.13. Visualizing priors (and posteriors)
  • 1.14. Where priors live in the toolbox
  • 1.15. Maximum likelihood (no priors)
  • 1.16. Mode finding
    • 1.16.1. Bundled optimizers
    • 1.16.2. Common options accepted across optimizers
    • 1.16.3. Running several optimizers in turn
    • 1.16.4. User-defined optimizers
    • 1.16.5. What estimate puts on the model
  • 1.17. Posterior simulation
    • 1.17.1. Available samplers
    • 1.17.2. Constructing and running
    • 1.17.3. User-defined sampler via rsamplers.usrsmplr
  • 1.18. Marginal data density
  • 1.19. Chain diagnostics: @mcmc
  • 1.20. Estimation restrictions
  • 1.21. The pipeline, skeletally

Data and tools

• 1. Time Series and Data Management
  • 1.1. Dates
    • 1.1.1. Base Class Methods
    • 1.1.2. Help Text for Derived Classes
  • 1.2. Time Series
    • 1.2.1. Indexing and assignment
    • 1.2.2. Data Cleaning
    • 1.2.3. Time Series Transformations
    • 1.2.4. Time shifts
    • 1.2.5. Statistical Analysis
    • 1.2.6. Plotting tools for time series
• 2. RISE’s reporting system
  • 2.1. Description
  • 2.2. Quick start
  • 2.3. Structuring the document
  • 2.4. Adding content
  • 2.5. Page control
  • 2.6. Publishing
  • 2.7. Legacy @rprt compatibility
  • 2.8. Details
    • 2.8.1. The properties
    • 2.8.2. The methods
• 3. Plotting tools
  • 3.1. The myplot wrapper
  • 3.2. Time-series plotters
    • 3.2.1. Fan charts
    • 3.2.2. Decomposition bar plots
  • 3.3. Model plotters
    • 3.3.1. quick_irfs
    • 3.3.2. quick_plots
    • 3.3.3. Smoothed probabilities
  • 3.4. Decorations and layout
    • 3.4.1. shade
    • 3.4.2. recession_dates
    • 3.4.3. sup_label
    • 3.4.4. xrotate
    • 3.4.5. number_of_rows_and_columns_in_figure
    • 3.4.6. plot_specs
  • 3.5. Saving figures
    • 3.5.1. save_figure
  • 3.6. Default figure and print settings

Interactive demos

• 1. The interactive cockpit
  • 1.1. Description
  • 1.2. Features
  • 1.3. Quick start: one call from model to browser
  • 1.4. The ingredients: each one you add unlocks one exercise
  • 1.5. The bake functions
  • 1.6. Interpolation validation
  • 1.7. Bundle format
  • 1.8. Testing

Advanced

• 1. Global Sensitivity Analysis and Uncertainty Quantification
  • 1.1. Uncertainty Quantification
    • 1.1.1. Where the parameter draws come from
    • 1.1.2. Propagating uncertainty through the model
    • 1.1.3. From propagation to sensitivity
  • 1.2. Monte Carlo Filtering
    • 1.2.1. Description
    • 1.2.2. Quick start examples
    • 1.2.3. Details on the mcf class
    • 1.2.4. Support facility for filtration : the mcfprop class
  • 1.3. High Dimensional Model Representation
    • 1.3.1. Description
    • 1.3.2. Quick-start examples
    • 1.3.3. Details
  • 1.4. Surrogates: polynomial chaos, analytic Sobol’ indices
    • 1.4.1. Quick start
    • 1.4.2. The prior chooses the polynomials
    • 1.4.3. The Gaussian-process emulator: calibrated pointwise uncertainty
    • 1.4.4. Fitting on your own function
    • 1.4.5. Options
    • 1.4.6. Trust, but verify
    • 1.4.7. Delayed-acceptance MCMC: exact posterior, fraction of the cost
    • 1.4.8. Adaptive tools on top of the emulators
    • 1.4.9. One call, three views: the sensitivity front-end
• 2. Stochastic Global Optimization
  • 2.1. Why stochastic global optimization
  • 2.2. The unified shell
  • 2.3. Common calling convention
    • 2.3.1. Common options (every algorithm)
  • 2.4. The algorithm catalogue
    • 2.4.1. Differential Evolution family
    • 2.4.2. Population / swarm metaheuristics
    • 2.4.3. Knowledge-based
    • 2.4.4. Evolution strategy
    • 2.4.5. Direct-search baseline
  • 2.5. Calling from estimate
  • 2.6. Calling directly
  • 2.7. Manual stopping
  • 2.8. The legacy @bee class
  • 2.9. Algorithms not currently included

Indices and tables

• Index

• Search Page

[ABJ+11]

Stéphane Adjemian, Houtan Bastani, Michel Juillard, Fréderic Karamé, Junior Maih, Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto, and Sébastien Villemot. Dynare: Reference Manual Version 4. Dynare Working Papers 1, CEPREMAP, April 2011. URL: https://ideas.repec.org/p/cpm/dynare/001.html.

[And08]

Gary Anderson. Solving Linear Rational Expectations Models: A Horse Race. Computational Economics, 31(2):95–113, March 2008. URL: https://ideas.repec.org/a/kap/compec/v31y2008i2p95-113.html, doi:10.1007/s10614-007-9108-0.

[AFVRR13]

Martin M. Andreasen, Jesus Fernandez-Villaverde, and Juan Rubio-Ramirez. The pruned state-space system for non-linear dsge models: theory and empirical applications. NBER Working Papers 18983, National Bureau of Economic Research, Inc, Apr 2013. URL: http://ideas.repec.org/p/nbr/nberwo/18983.html.

[AB13]

Michal Andrle and Jaromir Benes. System Priors: Formulating Priors about DSGE Models' Properties. IMF Working Papers 2013/257, International Monetary Fund, Dec 2013. URL: https://ideas.repec.org/p/imf/imfwpa/2013-257.html, doi:.

[AP17]

Michal Andrle and Miroslav Plasil. System Priors for Econometric Time Series. Working Papers 2017/01, Czech National Bank, May 2017. URL: https://ideas.repec.org/p/cnb/wpaper/2017-01.html, doi:.

[AP18]

Michal Andrle and Miroslav Plašil. Econometrics with system priors. Economics Letters, 172:134–137, 2018. URL: https://www.sciencedirect.com/science/article/pii/S0165176518303598, doi:https://doi.org/10.1016/j.econlet.2018.08.038.

[BSLK01]

Y. Bar-Shalom, X.R. Li, and T. Kirubarajan. Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software. Electronic and electrical engineering. Wiley, 2001. ISBN 9780471416555. URL: https://books.google.no/books?id=j2dGkwEACAAJ.

[bsLK04]

Yaakov bar-shalom, X.‐Rong Li, and Thia Kirubarajan. Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software. The Author, 01 2004. ISBN 047141655X. doi:10.1002/0471221279.ch11.

[BM15]

Andrew Binning and Junior Maih. Sigma point filters for dynamic nonlinear regime switching models. Working Paper 2015/10, Norges Bank, 2015. URL: https://EconPapers.repec.org/RePEc:bno:worpap:2015_10.

[BG98]

Stephen P. Brooks and Andrew Gelman. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7(4):434–455, 1998. doi:10.1080/10618600.1998.10474787.

[CK13]

Adam Cagliarini and Mariano Kulish. Solving Linear Rational Expectations Models with Predictable Structural Changes. The Review of Economics and Statistics, 95(1):328–336, March 2013. URL: https://ideas.repec.org/a/tpr/restat/v95y2013i1p328-336.html.

[CMT21]

Yoosoon Chang, Junior Maih, and Fei Tan. Origins of monetary policy shifts: A New approach to regime switching in DSGE models. Journal of Economic Dynamics and Control, 2021. URL: https://ideas.repec.org/a/eee/dyncon/v133y2021ics0165188921001706.html, doi:10.1016/j.jedc.2021.10423.

[CJ01]

Siddhartha Chib and Ivan Jeliazkov. Marginal likelihood from the metropolis–hastings output. Journal of the American Statistical Association, 96(453):270–281, 2001.

[Cho14]

Seonghoon Cho. Characterizing Markov-Switching Rational Expectation Models. Working Paper, Yonsei University, February 2014.

[CTW11]

Lawrence J. Christiano, Mathias Trabandt, and Karl Walentin. Introducing financial frictions and unemployment into a small open economy model. Journal of Economic Dynamics and Control, 35(12):1999–2041, 2011. URL: https://ideas.repec.org/a/eee/dyncon/v35y2011i12p1999-2041.html, doi:10.1016/j.jedc.2011.09.00.

[CFM05]

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