estimated_params

estimated_params — specifies the estimated parameters and their prior

Synopsis

Syntax I (Maximum likelihood estimation)

estimated_params ;
{ stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME } , INITIAL_VALUE [ , LOWER_BOUND , UPPER_BOUND ] ; ...

end ;

Syntax II (Bayesian estimation)

estimated_params ;
{ stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME } [ , INITIAL_VALUE [ , LOWER_BOUND , UPPER_BOUND ] ] , (1) PRIOR_SHAPE , PRIOR_MEAN , PRIOR_STANDARD_ERROR [ , PRIOR_3RD_PARAMETER [ , PRIOR_4TH_PARAMETER [ , SCALE_PARAMETER ] ] ] ; ...

end ; (1) beta_pdf | gamma_pdf | normal_pdf | uniform_pdf | inv_gamma_pdf | inv_gamma1_pdf | inv_gamma2_pdf

Description

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

Estimated parameter specification

Each line corresponds to an estimated parameter and follows this syntax:

stderr VARIABLE_NAME

Indicates that the standard error of the exogenous variable VARIABLE_NAME, or of the observation error associated with endogenous observed variable VARIABLE_NAME, is to be estimated

corr VARIABLE_NAME_1, VARIABLE_NAME_2

Indicates that the correlation between the exogenous variables VARIABLE_NAME_1 and VARIABLE_NAME_2, or the correlation of the observation errors associated with endogenous observed variables VARIABLE_NAME_1 and VARIABLE_NAME_2, is to be estimated

PARAMETER_NAME

The name of a model parameter to be estimated

INITIAL_VALUE

Specifies a starting value for maximum likelihood estimation

LOWER_BOUND

Specifies a lower bound for the parameter value in maximum likelihood estimation

UPPER_BOUND

Specifies an upper bound for the parameter value in maximum likelihood estimation

PRIOR_SHAPE

A keyword specifying the shape of the prior density. See the list of possible values. 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

A third parameter of the prior used for generalized beta distribution, generalized gamma and for the uniform distribution. Default: 0

PRIOR_4TH_PARAMETER

A fourth parameter of the prior used for generalized beta distribution and for the uniform distribution. Default: 1

SCALE_PARAMETER

The scale parameter to be used for the jump distribution of the Metropolis-Hasting algorithm

Note

INITIAL_VALUE, LOWER_BOUND, UPPER_BOUND, PRIOR_MEAN, PRIOR_STANDARD_ERROR, PRIOR_3RD_PARAMETER, PRIOR_4TH_PARAMETER 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.

Note

At minimum, one must specify the name of the parameter and an initial guess. That will trigger unconstrained maximum likelihood estimation.

Note

As one uses options more towards the end of the list, all previous options must be filled: for example, if you want to specify SCALE_PARAMETER, you must specify PRIOR_3RD_PARAMETER and PRIOR_4TH_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 (see model).

Example

parameters bet;

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

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