Welcome to RISE Toolbox’s documentation!

Getting started

• 1. Getting started
  • 1.1. RISE at a glance
  • 1.2. What’s new
    • 1.2.1. Current release
    • 1.2.2. Where the canonical changelog lives
  • 1.3. RISE Toolbox License
  • 1.4. Setting up your RISE environment
    • 1.4.1. Requirements
    • 1.4.2. Obtaining RISE
    • 1.4.3. Loading RISE
    • 1.4.4. Testing your installation
    • 1.4.5. Updating RISE
    • 1.4.6. The work environment
  • 1.5. Quickstart
    • 1.5.1. The fastest check
    • 1.5.2. Step 1 – write a model file
    • 1.5.3. Step 2 – load and solve
    • 1.5.4. Step 3 – impulse responses and a simulation
    • 1.5.5. Step 4 – estimating a model
    • 1.5.6. Where to go next
  • 1.6. Documentation of the +rise package
    • 1.6.1. Opening the PDF documentation
    • 1.6.2. Leaving/Quitting RISE
    • 1.6.3. Obtaining the release information
    • 1.6.4. Starting RISE
    • 1.6.5. Obtaining the toolbox information
    • 1.6.6. Obtaining the version of the Toolbox
    • 1.6.7. Why : Answers to random question rhyming with RISE
    • 1.6.8. Whatsup : Random sentences rhyming with RISE
  • 1.7. Finding help
  • 1.8. Citing RISE in your research
  • 1.9. Contributing to RISE
  • 1.10. Acknowledgements
    • 1.10.1. Credits

Modeling

• 1. Hit the ground running : An introductory example
  • 1.1. The model economy
  • 1.2. Baseline calibration
  • 1.3. Preparing the model for RISE
  • 1.4. Creating the model object (rising the model)
  • 1.5. Parameterizing the model
  • 1.6. Setting some options for the solution
  • 1.7. Stochastic simulation in a Dynare-like run
  • 1.8. Solving the model and printing the solution
  • 1.9. Solving a 5th-order perturbation
  • 1.10. Checking the accuracy of derivatives
  • 1.11. Impulse response functions
  • 1.12. Collecting Data from FRED
  • 1.13. Filtration
  • 1.14. Priors for Bayesian estimation
  • 1.15. Visualizing the priors
  • 1.16. Posterior maximization
  • 1.17. Posterior simulation
  • 1.18. Computation of the marginal data density using the Bridge approach
• 2. DSGE Modeling
  • 2.1. Description
  • 2.2. An example
  • 2.3. The model(rise/dsge) file language
    • 2.3.1. Conventions
      • Comments and block comments
      • Time and steady state
      • Auxiliary variables
      • Functions
      • Discountinous functions
      • Shock distributions
    • 2.3.2. Ways to declare a model
      • Declaring a model in a file
      • Declaring a Model as an Inline Snippet
      • Declaring a model as a Cell Array
    • 2.3.3. Handling Multiple Model Specifications
      • Method 1: Simple Model File
      • Method 2: Multiple Model Files
      • Method 3: Declaring a Model with a Cell Array
      • Method 4: Multiple Cell Arrays for Different Model Parts
      • Method 5: Combination of Model Files and Cell Arrays
    • 2.3.4. Atoms declarations
      • @endogenous
      • @exogenous
      • @parameters
      • @observables
      • Log-approximated variables
      • On-the-fly atoms declarations
    • 2.3.5. The @functions block
    • 2.3.6. The @model block
      • Regular equations
      • Equations broken across multiple lines
      • The @E operator for expectations
      • Equations with auxiliary expressions :"…$[]$…"
      • Regular equations with equation simplification :"…#…"
      • Definitions : # Equation
      • Time-varying transition probabilities : ! Equation
    • 2.3.7. The @optimization_problem block
      • Generic Syntax
      • Optimal Policy with No U-Turn
      • Ramsey Policy
      • Discretionary Policy
      • Loose Commitment
      • Stochastic Replanning
      • Multiple Policymakers : Non-cooperative games
      • Switching Games
    • 2.3.8. The @steady_state_model block (optional)
    • 2.3.9. The @transition_functions block (optional)
    • 2.3.10. The @epilogue block (optional)
    • 2.3.11. The @parameterization block (optional)
    • 2.3.12. The @parameter_restrictions block (optional)
    • 2.3.13. Tools for bounded rationality (Non-rational expectations)
      • Hybrid Expectations
      • Cognitive discounting
    • 2.3.14. Macro Language for preparsing
      • Inclusion of files
      • Pseudo functions
      • Control flow : for loops
      • control flows : zipped for loops
      • control flows : enumerated for loops
      • Evaluations
      • Control flow : @if … @elseif … @else … @end
      • Control flow : @switch …@case … @otherwise … @end
      • lower and upper cases
  • 2.4. Deriving models with rise.microfound
    • 2.4.1. Write the economics, not the algebra
    • 2.4.2. A first example: the RBC model
    • 2.4.3. What is generated
    • 2.4.4. Multiple agents
    • 2.4.5. Regime switching
    • 2.4.6. Output methods
    • 2.4.7. API reference
    • 2.4.8. Scope and roadmap
    • 2.4.9. Validation
  • 2.5. Very large models
    • 2.5.1. Why RISE requires MATLAB R2023b
    • 2.5.2. Writing a large model
    • 2.5.3. Parsing, differentiation and memory
    • 2.5.4. Solving a large model
  • 2.6. Setting up calibration and priors outside the model file
  • 2.7. Deterministic and quasi-deterministic solutions
    • 2.7.1. The perfect-foresight problem
      • A first example
    • 2.7.2. Setting the conditions
      • Initial and terminal steady states
    • 2.7.3. Choosing the horizon
    • 2.7.4. Solvers and performance
      • Reusing the Jacobian factorization
      • Reusing the steady state
      • Other options
      • Convergence and tolerances
    • 2.7.5. Quasi-deterministic solutions: the extended path
    • 2.7.6. Regime switching
    • 2.7.7. See also
  • 2.8. Stochastic solution via perturbation
    • 2.8.1. Zero-th order approximation : The steady state and the balanced-growth path
      • Incomplete analytical solution
      • Steady state loops
      • Facilitators
      • The case of multiple regimes
    • 2.8.2. First-order perturbation
      • The state vector
      • Solvers for the quadratic matrix polynomial
    • 2.8.3. Higher-order perturbation
      • Choosing the derivatives
      • Solving the system of generalized Sylvester equations
  • 2.9. Optimal (Ramsey) policy
    • 2.9.1. Declaring the planner’s problem
    • 2.9.2. Choosing the policy type at solve time
    • 2.9.3. Loose commitment and stochastic replanning
    • 2.9.4. Non-cooperative games: OLE vs MPE
      • Restrictions
      • Nash commitment fragility (Tatiana)
    • 2.9.5. Welfare and comparing policies
    • 2.9.6. Worked example: Ramsey optimal capital taxation
    • 2.9.7. Worked example: comparing policy types in a New Keynesian model
  • 2.10. Optimal (optimized) simple rules
    • 2.10.1. The loss function
    • 2.10.2. (Approximate) analytical loss
    • 2.10.3. Simulated loss
    • 2.10.4. OSR and indirect inference
    • 2.10.5. OSR with a user-defined objective
    • 2.10.6. Policy frontiers
  • 2.11. Stochastic simulations
    • 2.11.1. Artificial data
    • 2.11.2. Pruned simulations
    • 2.11.3. Theoretical and Simulated moments
    • 2.11.4. Variance decomposition
    • 2.11.5. Impulse responses
      • Simple Impulse Responses
      • Generalized Impulse Responses
  • 2.12. Generic simulations with plans
    • 2.12.1. The properties
      • endo_list
      • exo_list
      • par_list
      • def_list
      • start_date
      • end_date
      • InitialRegime
      • DynamicConstraints
      • ConditionMatrix
      • partitions
      • simul_periods
      • variable_list
    • 2.12.2. The methods
      • append
      • details
      • disp
      • endval
      • export
      • histval
      • initval
      • query
      • simplan
  • 2.13. Forecasting
    • 2.13.1. The three routes
    • 2.13.2. Kalman filter with conditions as observed data
    • 2.13.3. Conditional forecasting via perfect foresight
    • 2.13.4. Conditional forecasting in a stochastic context
    • 2.13.5. Choosing among the three
  • 2.14. Resimulation and counterfactuals
    • 2.14.1. Adapter
    • 2.14.2. Reconstruction methods
    • 2.14.3. Counterfactuals
    • 2.14.4. Shock decompositions
    • 2.14.5. Ergodic variance decomposition
    • 2.14.6. API reference
  • 2.15. DSGE Filtering
    • 2.15.1. Filtering and decompositions
      • Linear filtration
      • Historical Decomposition
      • Observables decomposition
      • Conditional forecasting via filtering
      • User-defined filter
    • 2.15.2. Linear filtration with real-time information
      • Data setup
      • routine
    • 2.15.3. Nonlinear filtering
      • When the nonlinear filter is used
      • Choosing the filter
      • Options
      • User-defined nonlinear filter
      • The available sigma-point filters
  • 2.16. Occasionally-binding constraints
    • 2.16.1. How constraints are declared
      • Occasionally-binding constraints by anticipated shocks
      • Occasionally-binding constraints by piecewise-linear approximations
      • Occasionally-binding constraints by regime switching
  • 2.17. Understanding a rise or dsge model object
    • 2.17.1. Ordering and information about atoms
      • Endogenous variables
      • Exogenous variables
      • Parameters
      • Observables
    • 2.17.2. Information on Model equations
    • 2.17.3. Information on Model results
      • First-order structural form
      • Solution results
      • Posterior maximization results
  • 2.18. Extending the DSGE functionalities
    • 2.18.1. Extracting the structural form
    • 2.18.2. Extracting the solution
    • 2.18.3. Your own solver
    • 2.18.4. Your own filtering algorithm
    • 2.18.5. Your own optimizer
    • 2.18.6. Your own Likelihood function
      • Relation to Indirect Inference
    • 2.18.7. Your own posterior sampler
    • 2.18.8. Where this is not enough
  • 2.19. Automatic Translation of files
    • 2.19.1. Dynare files
    • 2.19.2. Dynare steady state files
    • 2.19.3. AIM/YADA files
  • 2.20. Technical documentation for rise/dsge objects
    • 2.20.1. The properties
      • user_data
      • nsols
      • definitions
      • equations
      • filename
      • model_description
      • legend
      • endogenous
      • exogenous
      • observables
      • options
      • parameters
      • markov_chains
      • estimation
    • 2.20.2. The methods
      • abcd
      • accuracy
      • calculate_loss
      • calibrate
      • check_derivatives
      • condition_draws_on_model
      • counterfactual
      • dbminusdb
      • draw_parameter
      • drop
      • estimate
      • extract_first_order_structure
      • filter
      • fisher
      • fold_solution
      • forecast
      • forecast_real_time
      • frontier
      • get
      • growth_database
      • hessian
      • historical_decomposition
      • historical_decomposition_switch
      • indirect_inference
      • initial_conditions
      • initial_sstate
      • irf
      • is_forward_guidance_puzzle
      • is_stable_system
      • is_stationary_system
      • isnan
      • itranslate
      • link_parameters
      • loadObj
      • load_parameters
      • log_posterior_kernel
      • log_prior_density
      • map_solution
      • max_discrepancy
      • mode_curvature
      • model_information
      • observables_decomposition
      • optimal_simple_rule
      • parameters_to_file
      • perfect_foresight
      • plan2database
      • posterior_sample
      • predictive_analysis
      • print_estimation_results
      • print_solution
      • pull_objective
      • randsample
      • refresh
      • regime_partition_analysis
      • resid
      • resimulate
      • rise
      • saveObj
      • set
      • set_z_eplus_horizon
      • simulate
      • simulate_nonlinear
      • solve
      • solve_alternatives
      • srf
      • sstate
      • state_var_list
      • stoch_simul
      • summary
      • table
      • theoretical_autocorrelations
      • theoretical_autocovariances
      • translate
      • unlink_parameters
      • update_file
      • variance_decomposition
      • view_linked_parameters
• 3. DSGE-VAR Modeling
  • 3.1. Description
  • 3.2. A quick-start example
    • 3.2.1. A simple New Keynesian DSGE model
    • 3.2.2. Setting up the BVAR-DSGE model
    • 3.2.3. Fixed parameters
    • 3.2.4. Setting up and visualing the priors
    • 3.2.5. Collecting and transforming the data
    • 3.2.6. Maximizing the posterior
    • 3.2.7. IRFs of the BVAR-DSGE at the maximized posterior
    • 3.2.8. IRFs of the DSGE model at the maximized posterior
    • 3.2.9. IRF comparison
  • 3.3. Technical documentation for dsge_var objects
    • 3.3.1. The properties
      • nlags
      • constant
      • endogenous
      • options
      • shocks
      • parameters
      • markov_chains
      • estimation
    • 3.3.2. The methods
      • autocov
      • bvar_dsge
      • draw_parameter
      • estimate
      • fisher
      • forecast
      • get
      • hessian
      • historical_decomposition
      • irf
      • load_parameters
      • log_posterior_kernel
      • log_prior_density
      • mode_curvature
      • posterior_sample
      • print_estimation_results
      • pull_objective
      • residuals
      • set
      • solve
      • variance_decomposition
• 4. Reduced-form VAR Modeling
  • 4.1. Description
  • 4.2. Quick-start examples
    • 4.2.1. A constant-parameter VAR
      • Collecting and transforming data
      • Setting up the Reduced.form VAR
      • Estimating the VAR using classical techniques
      • Restrictions on the VAR : Domestic variables do not affect oil prices
      • Estimate the restricted VAR
      • Identification
      • Compare structural shocks
      • Compare CHOLESKI irfs
      • Compare irfs based on the identification scheme
      • Variance decomposition
      • Historical decomposition
      • Bootstrap
      • Variance decomposition distribution
      • Historical decomposition distribution
      • IRF distribution
      • Bayesian estimation
      • Posterior sampling of parameters
      • Bayesian forecasting
      • Conditional forecasting
    • 4.2.2. Adding regime switching with constant transition probabilities
    • 4.2.3. Adding regime switching with time~varying transition probabilities
  • 4.3. Technical documentation for rfvar objects
    • 4.3.1. The properties
      • endogenous
      • exogenous
      • parameters
      • nonvar_parameters
      • constant
      • debug
      • markov_chains
      • is_time_varying_trans_prob
      • is_switching
      • nlags
      • nx
      • nvars
      • nparams
      • nregs
    • 4.3.2. The methods
      • autocov
      • bootstrap
      • codify
      • estimate
      • filter
      • forecast
      • get
      • historical_decomposition
      • identification
      • irf
      • posterior_mode
      • print_solution
      • prior_template
      • pull_objective
      • residuals
      • rfvar
      • set
      • solve
      • structural_shocks
      • transform_var_into_dsge
      • variance_decomposition
• 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
  • 5.5. Technical documentation for prfvar objects
    • 5.5.1. The properties
      • members
      • homogeneity
      • endogenous
      • exogenous
      • parameters
      • nonvar_parameters
      • constant
      • debug
      • markov_chains
      • is_time_varying_trans_prob
      • is_switching
      • nlags
      • nx
      • nvars
      • nparams
      • nregs
    • 5.5.2. The methods
      • autocov
      • bootstrap
      • codify
      • estimate
      • filter
      • forecast
      • get
      • historical_decomposition
      • identification
      • irf
      • posterior_mode
      • prfvar
      • print_solution
      • prior_template
      • pull_objective
      • residuals
      • set
      • solve
      • structural_shocks
      • transform_var_into_dsge
      • variance_decomposition
• 6. Structural VAR Modeling
  • 6.1. Modelling structural VARs
    • 6.1.1. The model
    • 6.1.2. Creating an SVAR
    • 6.1.3. Identification
    • 6.1.4. Estimation
    • 6.1.5. Impulse responses, variance and historical decompositions, forecasting
    • 6.1.6. Adding regime switching
    • 6.1.7. Technical documentation for svar objects
      • The properties
      • The methods
• 7. Proxy (instrumental) SVAR Modeling
  • 7.1. The model
  • 7.2. Creating a proxy SVAR
  • 7.3. Estimation, IRFs, decompositions, forecasting
  • 7.4. Adding regime switching
  • 7.5. Technical documentation for proxy_svar objects
    • 7.5.1. The properties
      • proxies
      • endogenous
      • exogenous
      • parameters
      • nonvar_parameters
      • constant
      • debug
      • markov_chains
      • is_time_varying_trans_prob
      • is_switching
      • nlags
      • nx
      • nvars
      • nparams
      • nregs
    • 7.5.2. The methods
      • autocov
      • codify
      • estimate
      • filter
      • forecast
      • get
      • historical_decomposition
      • identification
      • irf
      • posterior_mode
      • print_solution
      • print_structural_form
      • prior_template
      • proxy_svar
      • pull_objective
      • residuals
      • set
      • solve
      • transform_var_into_dsge
      • variance_decomposition

Estimation, data and analysis

• 1. Bayesian Estimation
  • 1.1. Restrictions on parameters during estimation
  • 1.2. Prior distributions and implementation
    • 1.2.1. Bayesian priors
      • Setting Uniform Priors
      • Setting priors using Means and Standard deviations
      • Setting priors using quantiles
      • Setting priors using hyperparameters
      • About the t-student prior
      • The dirichlet prior
    • 1.2.2. Endogenous Priors
      • General Syntax for Endogenous Priors
      • Types of Endogenous Priors
      • Advanced Variants and Complex Functions
      • Summary of Endogenous Prior Cases
    • 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
      • Quick reference
      • Options accepted across optimizers
    • 1.3.3. Running several optimizers in turn
    • 1.3.4. User-defined optimizers
      • Interface specification
      • RISE-added options
      • Minimal worked example
  • 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. User-defined Algorithms: Another approach
      • Obtaining the DRAM inputs
      • Running DRAM
      • Transforming the DRAM output
  • 1.5. Processing Posterior draws : The mcmc class
    • 1.5.1. The properties
      • pnames
      • nchains
      • chain_names
      • npop
      • nparams
      • draws
      • psrf
      • best
      • log_post
    • 1.5.2. The methods
      • autocorrplot
      • brooks_gelman
      • densplot
      • draws2struct
      • geweke
      • inefficiency_factors
      • mcmc
      • meanplot
      • plot_brooks_gelman
      • posterior_parameter_statistics
      • process_draws
      • psrf_plot
      • raftery_lewis
      • reload_draws
      • scatterplot
      • statistics
      • summary
      • traceplot
    • 1.5.3. Visualizing posteriors (and priors)
  • 1.6. Marginal Data Density computation : the mdd class
    • 1.6.1. The properties
      • log_post_kern
      • theta_draws
      • lb
      • ub
      • maximization
      • H
      • subset
      • thecoef
    • 1.6.2. The methods
      • bridge
      • cj
      • global_options
      • is
      • laplace
      • laplace_mcmc
      • laplace_mdd
      • mdd
      • mhm
      • mueller
      • normal_weighting
      • ris
      • swz
  • 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
• 2. Time Series and Data Management
  • 2.1. Dates
    • 2.1.1. Base Class Methods
    • 2.1.2. Help Text for Derived Classes
      • Daily dates : rd
      • Weekly dates : rw
      • Monthly dates : rm
      • Quarterly dates : rq
      • Half-yearly dates : rh
      • Yearly dates : ry
      • Annual dates : ra
    • 2.1.3. Technical documentation for rise_dates.dates objects
      • The properties
      • The methods
  • 2.2. Time Series
    • 2.2.1. Indexing and assignment
    • 2.2.2. Data Cleaning
    • 2.2.3. Time Series Transformations
    • 2.2.4. Time shifts
    • 2.2.5. Statistical Analysis
    • 2.2.6. Plotting tools for time series
    • 2.2.7. Other Automations
    • 2.2.8. Technical documentation for ts objects
      • The properties
      • The methods
• 3. Global Sensitivity Analysis and Uncertainty Quantification
  • 3.1. Uncertainty Quantification
    • 3.1.1. Where the parameter draws come from
    • 3.1.2. Propagating uncertainty through the model
    • 3.1.3. From propagation to sensitivity
  • 3.2. Monte Carlo Filtering
    • 3.2.1. Description
    • 3.2.2. Quick start examples
      • A very simple example
      • A simple DSGE example
    • 3.2.3. Details on the mcf class
      • The properties
      • The methods
    • 3.2.4. Support facility for filtration : the mcfprop class
      • The properties
      • The methods
      • An example
  • 3.3. High Dimensional Model Representation
    • 3.3.1. Description
    • 3.3.2. Quick-start examples
      • A known Polynomial function
    • 3.3.3. Details
      • The properties
      • The methods
• 4. Conditional forecasting using relative entropy
  • 4.1. The idea
  • 4.2. When to use it
  • 4.3. The API
  • 4.4. A sketch
  • 4.5. Solver options
    • 4.5.1. Companion helper
  • 4.6. Worked example shipped with the toolbox
  • 4.7. References
• 5. RISE’s reporting system
  • 5.1. Description
  • 5.2. Quick start
  • 5.3. Structuring the document
  • 5.4. Adding content
  • 5.5. Page control
  • 5.6. Publishing
  • 5.7. Legacy @rprt compatibility
  • 5.8. Details
    • 5.8.1. The properties
      • Title
      • Author
      • Date
      • Body
      • Counters
      • Labels
      • WorkDir
      • figsDir
      • filesToDelete
    • 5.8.2. The methods
      • addParameterTable
      • chapter
      • checkLatexLiteralSafety
      • cleardoublepage
      • clearpage
      • create_figure
      • description
      • dsge
      • enumerate
      • equation
      • figure
      • footnote
      • getfieldWithDefault
      • input
      • itemize
      • latexSafe
      • maketitle
      • newpage
      • pagebreak
      • paragraph
      • publish
      • quotation
      • quote
      • rnotes
      • section
      • subparagraph
      • subsection
      • subsubsection
      • table
      • text
      • toc
      • url
      • verbatim
• 6. Stochastic Global Optimization
  • 6.1. Why stochastic global optimization
  • 6.2. The unified shell
  • 6.3. Common calling convention
    • 6.3.1. Common options (every algorithm)
  • 6.4. The algorithm catalogue
    • 6.4.1. Differential Evolution family
    • 6.4.2. Population / swarm metaheuristics
    • 6.4.3. Knowledge-based
    • 6.4.4. Evolution strategy
    • 6.4.5. Direct-search baseline
  • 6.5. Calling from estimate
  • 6.6. Calling directly
  • 6.7. Manual stopping
  • 6.8. The legacy @bee class
  • 6.9. Algorithms not currently included
• 7. Plotting tools
  • 7.1. The myplot wrapper
  • 7.2. Time-series plotters
    • 7.2.1. Fan charts
    • 7.2.2. Decomposition bar plots
  • 7.3. Model plotters
    • 7.3.1. quick_irfs
    • 7.3.2. quick_plots
    • 7.3.3. Smoothed probabilities
  • 7.4. Decorations and layout
    • 7.4.1. shade
    • 7.4.2. recession_dates
    • 7.4.3. sup_label
    • 7.4.4. xrotate
    • 7.4.5. number_of_rows_and_columns_in_figure
    • 7.4.6. plot_specs
  • 7.5. Saving figures
    • 7.5.1. save_figure
  • 7.6. Default figure and print settings

Extending RISE

• 1. Extending RISE through paradigms
  • 1.1. Goals
  • 1.2. What a paradigm is
  • 1.3. Responsibilities of a paradigm
  • 1.4. The standard solution envelope
  • 1.5. The minimum interface contract
  • 1.6. Mutable solution objects
  • 1.7. Responsibilities of RISE
  • 1.8. Isolation, safety and persistence
  • 1.9. Examples
    • 1.9.1. Recursive local linearization (RLL)
    • 1.9.2. \(k\)-th order Taylor projection (TP)
  • 1.10. Design principles

Reference and help

• Troubleshooting
  • Deciphering return codes
  • When the steady state does not solve
  • When the model does not solve (but the steady state does)
  • When filtering or likelihood fails
  • Debug toggles
  • Tightening tolerances and iteration caps
  • Profiling

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.

[CGomezT09]

Javier Castro, Daniel Gómez, and Juan Tejada. Polynomial calculation of the Shapley value based on sampling. Computers & Operations Research, 36(5):1726–1730, 2009. doi:10.1016/j.cor.2008.04.004.

[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]

Oswaldo Luiz do Valle Costa, M. D. (Marcelo Dutra) Fragoso, and Ricardo Paulino Marques. Discrete-time Markov jump linear systems. Probability and its applications. Springer, London, 2005. ISBN 1-85233-761-3. URL: http://opac.inria.fr/record=b1120049.

[DJChuChunLin03]

Piet De Jong and Singfat Chu‐Chun‐Lin. Smoothing With An Unknown Initial Condition. Journal of Time Series Analysis, 24(2):141–148, March 2003. URL: https://ideas.repec.org/a/bla/jtsera/v24y2003i2p141-148.html, doi:10.1111/1467-9892.00298.

[DNS04]

Marco Del Negro and Frank Schorfheide. Priors from General Equilibrium Models for VARS. International Economic Review, 45(2):643–673, May 2004. URL: https://ideas.repec.org/a/ier/iecrev/v45y2004i2p643-673.html, doi:.

[DNS08]

Marco Del Negro and Frank Schorfheide. Forming priors for dsge models (and how it affects the assessment of nominal rigidities). Journal of Monetary Economics, 55(7):1191–1208, 2008. URL: https://www.sciencedirect.com/science/article/pii/S0304393208001396, doi:https://doi.org/10.1016/j.jmoneco.2008.09.006.

[DNSSW07]

Marco Del Negro, Frank Schorfheide, Frank Smets, and Rafael Wouters. On the Fit of New Keynesian Models. Journal of Business & Economic Statistics, 25:123–143, April 2007. URL: https://ideas.repec.org/a/bes/jnlbes/v25y2007p123-143.html.

[DK12]

James Durbin and Siem Jan Koopman. Time Series Analysis by State Space Methods. Volume of OUP Catalogue. Oxford University Press, edition, November 2012. ISBN ARRAY(0x60272498). URL: https://ideas.repec.org/b/oxp/obooks/9780199641178.html, doi:.

[FWZ11]

Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha. Minimal state variable solutions to Markov-switching rational expectations models. Journal of Economic Dynamics and Control, 35(12):2150–2166, 2011. URL: https://ideas.repec.org/a/eee/dyncon/v35y2011i12p2150-2166.html, doi:10.1016/j.jedc.2011.08.00.

[FRRWZ16]

Andrew Foerster, Juan F. Rubio-Ramirez, Daniel F. Waggoner, and Tao Zha. Perturbation methods for Markov-switching dynamic stochastic general equilibrium models. Quantitative Economics, 7(2):637–669, 07 2016. URL: https://ideas.repec.org/a/wly/quante/v7y2016i2p637-669.html, doi:.

[FruhwirthS06]

Sylvia Frühwirth-Schnatter. Finite mixture and Markov switching models. Springer, Berlin, 1st edition, 2006.

[GLM13]

Paolo Gelain, Kevin J. Lansing, and Caterina Mendicino. House Prices, Credit Growth, and Excess Volatility: Implications for Monetary and Macroprudential Policy. International Journal of Central Banking, 9(2):219–276, June 2013. URL: https://ideas.repec.org/a/ijc/ijcjou/y2013q2a11.html.

[GCSR04]

Andrew Gelman, John B. Carlin, Hal S. Stern, and Donald B. Rubin. Bayesian Data Analysis. Chapman & Hall/CRC, 2 edition, 2004.

[GR92]

Andrew Gelman and Donald B. Rubin. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4):457 – 472, 1992. URL: https://doi.org/10.1214/ss/1177011136, doi:10.1214/ss/1177011136.

[Gew99]

John Geweke. Using simulation methods for bayesian econometric models: inference, development,and communication. Econometric Reviews, 18(1):1–73, 1999.

[GI15]

Luca Guerrieri and Matteo Iacoviello. OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily. Journal of Monetary Economics, 70(C):22–38, 2015. URL: https://ideas.repec.org/a/eee/moneco/v70y2015icp22-38.html, doi:10.1016/j.jmoneco.2014.08.

[GI17]

Luca Guerrieri and Matteo Iacoviello. Collateral constraints and macroeconomic asymmetries. Journal of Monetary Economics, 90(C):28–49, 2017. URL: https://ideas.repec.org/a/eee/moneco/v90y2017icp28-49.html, doi:10.1016/j.jmoneco.2017.06.

[GMH03]

V. Gupta, R.M. Murray, and B. Hassibi. On the control of jump linear markov systems with markov state estimation. In American Control Conference, 2003. Proceedings of the 2003, volume 4, 2893–2898 vol.4. June 2003. doi:10.1109/ACC.2003.1243762.

[Ire04]

Peter N. Ireland. A method for taking models to the data. Journal of Economic Dynamics and Control, 28(6):1205–1226, 2004. URL: https://www.sciencedirect.com/science/article/pii/S0165188903000800, doi:https://doi.org/10.1016/S0165-1889(03)00080-0.

[JM10]

Michel Juillard and Junior Maih. Estimating DSGE Models with Observed Real-Time Expectation Data. 2010. URL: https://www.kansascityfed.org/publicat/events/research/2010CenBankForecasting/Maih_paper.pdf.

[KN99]

C.J. Kim and C.R. Nelson. State-space Models with Regime Switching: Classical and Gibbs-sampling Approaches with Applications. MIT Press, 1999. ISBN 9780262112383. URL: http://books.google.no/books?id=eQFsQgAACAAJ.

[KN01]

Chang-Jin Kim and Charles Nelson. A bayesian approach to testing for markov-switching in univariate and dynamic factor models. International Economic Review, 42(4):989–1013, 2001. URL: http://EconPapers.repec.org/RePEc:ier:iecrev:v:42:y:2001:i:4:p:989-1013.

[Kle00]

Paul Klein. Using the generalized schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control, 24(10):1405–1423, September 2000. URL: http://ideas.repec.org/a/eee/dyncon/v24y2000i10p1405-1423.html.

[KD00]

S. J. Koopman and J. Durbin. Fast Filtering and Smoothing for Multivariate State Space Models. Journal of Time Series Analysis, 21(3):281–296, May 2000. URL: https://ideas.repec.org/a/bla/jtsera/v21y2000i3p281-296.html, doi:10.1111/1467-9892.00186.

[KD03]

S. J. Koopman and J. Durbin. Filtering and smoothing of state vector for diffuse state‐space models. Journal of Time Series Analysis, 24(1):85–98, January 2003. URL: https://ideas.repec.org/a/bla/jtsera/v24y2003i1p85-98.html, doi:10.1111/1467-9892.00294.

[Mai10]

Junior Maih. Conditional forecasts in DSGE models. Working Paper 2010/07, Norges Bank, April 2010. URL: https://ideas.repec.org/p/bno/worpap/2010_07.html.

[Mai15]

Junior Maih. Efficient perturbation methods for solving regime-switching DSGE models. Working Paper 2015/01, Norges Bank, January 2015. URL: https://ideas.repec.org/p/bno/worpap/2015_01.html, doi:.

[MW18]

Junior Maih and Daniel Waggoner. Perturbation Methods for DSGE Models with Time Varying Coefficients and Transition Matrices. Mimeograph, Norges Bank, 2018.

[MW96]

Xiao-Li Meng and Wing Hung Wong. Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica, 6(4):831–860, 1996. URL: http://www.jstor.org/stable/24306045.

[MMV13]

Btażej Miasojedow, Eric Moulines, and Matti Vihola. An adaptive parallel tempering algorithm. Journal of Computational and Graphical Statistics, 22(3):649–664, 2013.

[PRR15]

Christophe Planas, Marco Ratto, and Alessandro Rossi. Slice sampling in bayesian estimation of dsge models. Working Papers, Joint Research Centre, European Commission, 2015.

[PR18]

Christophe Planas and Alessandro Rossi. The slice sampler and centrally symmetric distributions. Working Papers 2018-11, Joint Research Centre, European Commission, November 2018. URL: https://ideas.repec.org/p/jrs/wpaper/201811.html, doi:.

[RL92]

Adrian E. Raftery and Steven Lewis. How many iterations in the gibbs sampler? In A. P. Dawid J. M. Bernardo, J. Berger and A. F. M. Smith, editors, Bayesian Statistics, volume 4, 763–73. Oxford University Press, 1992.

[Rat08]

Marco Ratto. Analysing dsge models with global sensitivity analysis. Computational Economics, 31:115–139, 02 2008. doi:10.1007/s10614-007-9110-6.

[RM12]

Francisco Ruge-Murcia. Estimating nonlinear dsge models by the simulated method of moments: with an application to business cycles. Journal of Economic Dynamics and Control, 36(6):914–938, 2012. URL: https://www.sciencedirect.com/science/article/pii/S0165188912000231, doi:https://doi.org/10.1016/j.jedc.2012.01.008.

[Sim02]

Christopher A Sims. Solving Linear Rational Expectations Models. Computational Economics, 20(1-2):1–20, October 2002. URL: https://ideas.repec.org/a/kap/compec/v20y2002i1-2p1-20.html.

[SWZ08]

Christopher A. Sims, Daniel F. Waggoner, and Tao Zha. Methods for inference in large multiple-equation Markov-switching models. Journal of Econometrics, 146(2):255–274, October 2008. URL: https://ideas.repec.org/a/eee/econom/v146y2008i2p255-274.html, doi:.

[VanLoan00]

Charles F. Van Loan. The ubiquitous Kronecker product. Journal of Computational and Applied Mathematics, 123(123):85–100, 2000.