Provided that you have observations on some endogenous variables, it is possible to use Dynare to estimate some or all parameters. Bayesian techniques (as in Fernández-Villaverde and Rubio-Ramírez (2004), Rabanal and Rubio-Ramirez (2003), Schorfheide (2000) or Smets and Wouters (2003)) are available. Using Bayesian methods, it is possible to estimate DSGE models.

Note that in order to avoid stochastic singularity, you must have at least as many shocks or measurement errors in your model as you have observed variables.

Before using the estimation commands described below, you need to define some elements of the state space representation of the model. At the minimum, you need to declare the observed variables with var_obs and, possibly, deterministic trends with observation_trends (see the previous section: State space, filtering and smoothing)

### Dynare commands

#### estimated_params

Block: estimated_params ;

Block: estimated_params (overwrite) ;

This block lists all parameters to be estimated and specifies bounds and priors as necessary.

Each line corresponds to an estimated parameter.

In a maximum likelihood or a method of moments estimation, each line follows this syntax:

    stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND ];

In a Bayesian MCMC or a penalized method of moments estimation, each line follows this syntax:

    stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME | DSGE_PRIOR_WEIGHT
[, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND]], PRIOR_SHAPE,
PRIOR_MEAN, PRIOR_STANDARD_ERROR [, PRIOR_3RD_PARAMETER [,
PRIOR_4TH_PARAMETER [, SCALE_PARAMETER ] ] ];

The first part of the line consists of one of the four following alternatives:

• stderr VARIABLE_NAME

Indicates that the standard error of the exogenous variable VARIABLENAME, or of the observation error/measurement errors associated with endogenous observed variable VARIABLENAME, is to be estimated.

• corr VARIABLE_NAME1, VARIABLE_NAME2

Indicates that the correlation between the exogenous variables VARIABLENAME1 and VARIABLENAME2, or the correlation of the observation errors/measurement errors associated with endogenous observed variables VARIABLENAME1 and VARIABLENAME2, is to be estimated. Note that correlations set by previous shocks-blocks or estimation-commands are kept at their value set prior to estimation if they are not estimated again subsequently. Thus, the treatment is the same as in the case of deep parameters set during model calibration and not estimated.

• PARAMETER_NAME

The name of a model parameter to be estimated

• DSGE_PRIOR_WEIGHT

Special name for the weigh of the DSGE model in DSGE-VAR model.

The rest of the line consists of the following fields, some of them being optional:

• INITIAL_VALUE

Specifies a starting value for the posterior mode optimizer or the maximum likelihood estimation. If unset, defaults to the prior mean.

• LOWER_BOUND

Currently not supported

• UPPER_BOUND

Currently not supported

• PRIOR_SHAPE

A keyword specifying the shape of the prior density. The possible values are: beta_pdf, gamma_pdf, normal_pdf, uniform_pdf, inv_gamma_pdf, inv_gamma1_pdf, inv_gamma2_pdf and weibull_pdf. Note that inv_gamma_pdf is equivalent to inv_gamma1_pdf.

• PRIOR_MEAN

The mean of the prior distribution.

• PRIOR_STANDARD_ERROR

The standard error of the prior distribution.

• PRIOR_3RD_PARAMETER

Currently not supported except for the Uniform

• PRIOR_4TH_PARAMETER

Currently not supported

• SCALE_PARAMETER

A parameter specific scale parameter for the jumping distribution's covariance matrix of the Metropolis-Hasting algorithm.

Note that INITIALVALUE, LOWERBOUND, UPPERBOUND, PRIORMEAN, PRIORSTANDARDERROR, PRIOR3RDPARAMETER, PRIOR4THPARAMETER and SCALE_PARAMETER can be any valid EXPRESSION. Some of them can be empty, in which Dynare will select a default value depending on the context and the prior shape.

In case of the uniform distribution, it can be specified either by providing an upper and a lower bound using PRIOR_3RD_PARAMETER and PRIOR_4TH_PARAMETER or via mean and standard deviation using PRIOR_MEAN, PRIOR_STANDARD_ERROR. The other two will automatically be filled out. Note that providing both sets of hyperparameters will yield an error message.

As one uses options more towards the end of the list, all previous options must be filled: for example, if you want to specify SCALEPARAMETER, you must specify PRIOR3RDPARAMETERandPRIOR4TH_PARAMETER. Use empty values, if these parameters don't apply.

#### Parameter transformation

Sometimes, it is desirable to estimate a transformation of a parameter appearing in the model, rather than the parameter itself. It is of course possible to replace the original parameter by a function of the estimated parameter everywhere is the model, but it is often unpractical.

In such a case, it is possible to declare the parameter to be estimated in the parameters statement and to define the transformation, using a pound sign (#) expression.

##### Example
     parameters bet;

model;
# sig = 1/bet;
c = sig*c(+1)*mpk;
end;

estimated_params;
bet, normal_pdf, 1, 0.05;
end;

It is possible to have several estimated_params blocks. By default, subsequent blocks are concatenated with the previous ones; this can be useful when building models in a modular fashion (see also estimated_params_remove for that use case). However, if an estimated_params block has the overwrite option, its contents becomes the new list of estimated parameters, cancelling previous blocks; this can be useful when doing several estimations in a single .mod file.

#### estimated_params_init

Block: estimated_params_init ;

Block: estimated_params_init (OPTIONS...);

This block declares numerical initial values for the optimizer when these ones are different from the prior mean. It should be specified after the estimated_params block as otherwise the specified starting values are overwritten by the latter.

Each line has the following syntax:

    stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME, INITIAL_VALUE;

#### estimation

Command: estimation [VARIABLE_NAME...];

Command: estimation (OPTIONS...)[VARIABLE_NAME...];

This command runs Bayesian estimation.

##### Options
• datafile = FILENAME

The datafile must be in CSV format

    estimation(datafile='../fsdat_simul.csv',...);
• nobs = INTEGER

The number of observations following first_obs to be used. Default: all observations in the file after first_obs.

• first_obs = INTEGER

The number of the first observation to be used. In case of estimating a DSGE-VAR, first_obs needs to be larger than the number of lags. Default: 1.

• plot_priors = INTEGER: Control the plotting of priors, 0, no prior plot, 1, pPrior density for each estimated parameter is plotted. It is important to check that the actual shape of prior densities matches what you have in mind. Ill-chosen values for the prior standard density can result in absurd prior densities (default valueL 1).

• mh_replic = INTEGER

Number of replications for each chain of the Metropolis-Hastings algorithm. The number of draws should be sufficient to achieve convergence of the MCMC and to meaningfully compute posterior objects. Default: 20000.

• mh_nblocks = INTEGER

Number of parallel chains for Metropolis-Hastings algorithm. Default: 2.

• mh_jscale = DOUBLE

The scale parameter of the jumping distribution's covariance matrix. The default value is rarely satisfactory. This option must be tuned to obtain, ideally, an acceptance ratio of 25%-33%. Basically, the idea is to increase the variance of the jumping distribution if the acceptance ratio is too high, and decrease the same variance if the acceptance ratio is too low. In some situations it may help to consider parameter-specific values for this scale parameter. This can be done in the estimated_params block. Default: 0.2.

### Julia functions

Dynare.mode_compute!Function
 mode_compute!(;
context=context,
data = AxisArrayTable(AxisArrayTables.AxisArray(Matrix(undef, 0, 0))),
datafile = "",
diffuse_filter::Bool = false,
display::Bool = false,
fast_kalman_filter::Bool = true,
first_obs::PeriodsSinceEpoch = Undated(typemin(Int)),
initial_values = get_initial_value_or_mean(),
last_obs::PeriodsSinceEpoch = Undated(typemin(Int)),
mode_check::Bool = false,
nobs::Int = 0,
order::Int = 1,
presample::Int = 0,
transformed_parameters = true)

computes the posterior mode.

Keyword arguments

• context::Context=context: context of the computation
• data::AxisArrayTable: AxisArrayTable containing observed variables
• datafile::String: data filename (can't be used as the same time asdataset)
• first_obs::PeriodsSinceEpoch: first observation (default: first observation in the dataset)
• initial_values: initival parameter values for optimization algorithm (default: estimated_params_init block if present or prior mean)
• last_obs::PeriodsSinceEpoch: last period (default: last period of the dataset)
• nobs::Int = 0: number of observations (default: entire dataset)
• transformed_parameters = true: whether to transform estimated parameter so as they take their value on R

Either data or datafile must be specified.

Dynare.plot_priorsFunction
plot_priors(; context::Context = context, n_points::Int = 100)

plots prior density

Keyword arguments

• context::Context = context: context in which to take the date to be ploted
• n_points::Int = 100: number of points used for a curve
Dynare.plot_prior_posteriorFunction
plot_prior_posterior(chains; context::Context=context)

plots priors posterios and mode if computed on the same plots

Keyword arguments

• context::Context=context: context used to get the estimation results

Output

• the plots are saved in ./<modfilename>/Graphs/PriorPosterior_<x>.png
Dynare.prior!Function
 prior!(s::Symbol; shape::{<:Distributions}, initialvalue::Union{Real,Missing}=missing, mean::Union{Real,Missing}=missing, stdev::Union{Real,Missing}=missing, domain=[], variance ::Union{Real,Missing}=missing, context::Context=context)
prior!(s::stdev; shape::{<:Distributions}, initialvalue::Union{Real,Missing}=missing, mean::Union{Real,Missing}=missing, stdev::Union{Real,Missing}=missing, domain=[], variance ::Union{Real,Missing}=missing, context::Context=context)
prior!(s::variance; shape::{<:Distributions}, initialvalue::Union{Real,Missing}=missing, mean::Union{Real,Missing}=missing, stdev::Union{Real,Missing}=missing, domain=[], variance ::Union{Real,Missing}=missing, context::Context=context)
prior!(s::corr; shape::{<:Distributions}, initialvalue::Union{Real,Missing}=missing, mean::Union{Real,Missing}=missing, stdev::Union{Real,Missing}=missing, domain=[], variance ::Union{Real,Missing}=missing, context::Context=context)

generates a prior for a symbol of a parameter, the standard deviation (stdev) or the variance (variance) of an exogenous variable or an endogenous variable (measurement error) or the correlation (corr) between 2 endogenous or exogenous variables

Keyword arguments

• shape <: Distributions: the shape of the prior distribution (Beta, InvertedGamma, InvertedGamma1, Gamma, Normal, Uniform, Weibull) [required]
• context::Context=context: context in which the prior is declared
• domain::Vector{<:Real}=Float64[]: domain for a uniform distribution
• initialvalue::Union{Real,Missing}=missing: initialvalue for mode finding or MCMC iterations
• mean::Union{Real,Missing}=missing: mean of the prior distribution
• stdev::Union{Real,Missing}=missing: stdev of the prior distribution
• variance::Union{Real,Missing}=missing: variance of the prior distribution
Dynare.rwmh_compute!Function
rwmh_compute!(;context::Context=context,
back_transformation::Bool = true,
datafile::String = "",
data::AxisArrayTable = AxisArrayTable(AxisArrayTables.AxisArray(Matrix(undef, 0, 0))),
diffuse_filter::Bool = false,
display::Bool = true,
fast_kalman_filter::Bool = true,
first_obs::PeriodsSinceEpoch = Undated(typemin(Int)),
initial_values = prior_mean(context.work.estimated_parameters),
covariance::AbstractMatrix{Float64} = Matrix(prior_variance(context.work.estimated_parameters)),
transformed_covariance::Matrix{Float64} = Matrix{Float64}(undef, 0,0),
last_obs::PeriodsSinceEpoch = Undated(typemin(Int)),
mcmc_chains::Int = 1,
mcmc_init_scale::Float64 = 0.0,
mcmc_jscale::Float64 = 0.0,
mcmc_replic::Int =  0,
mode_compute::Bool = true,
nobs::Int = 0,
order::Int = 1,
plot_chain::Bool = true,
plot_posterior_density::Bool = false,
presample::Int = 0,
transformed_parameters::Bool = true

)

runs random walk Monte Carlo simulations of the posterior

Keyword arguments

• context::Context=context: context of the computation
• covariance::AbstractMatrix{Float64}:
• data::AxisArrayTable: AxisArrayTable containing observed variables
• datafile::String: data filename
• first_obs::PeriodsSinceEpoch: first observation (default: first observation in the dataset)
• initial_values: initival parameter values for optimization algorithm (default: estimated_params_init block if present or prior mean)
• last_obs::PeriodsSinceEpoch: last period (default: last observation in the dataset)
• mcmc_chains::Int number of MCMC chains (default: 1)
• mcmc_jscale::Float64: scale factor of proposal
• mcmc_replic::Int: = 0,
• nobs::Int = 0: number of observations (default: entire dataset)
• plot_chain::Bool: whether to display standard MCMC chain output (default:true)
• plot_posterior_density::Bool: wether to display plots with prior and posterior densities (default: false)
• transformed_covariance::Matrix{Float64}: covariance of transformed parameters (default: empty)
• transformed_parameters = true: whether to transform estimated parameter so as they take their value on R

Either data or datafile` must be specified.