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 } , PRIOR_SHAPE , PRIOR_MEAN , PRIOR_STANDARD_ERROR [ , PRIOR_3RD_PARAMETER ] [ , PRIOR_4TH_PARAMETER ] [ , SCALE_PARAMETER ] ;
...
end;

Description

The estimated_params;....end; 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 is a keyword indicating 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 is a keyword indicating 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 is 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 is prior density among beta_pdf, gamma_pdf, normal_pdf, inv_gamma_pdf, inv_gamma1_pdf, inv_gamma2_pdf, uniform_pdf

  • PRIOR_MEAN is the mean of the prior distribution

  • PRIOR_STANDARD_ERROR is the standard error of the prior distribution

  • PRIOR_3RD_PARAMETER is a third parameter of the prior used for generalized beta distribution, generalized gamma and for the uniform distribution (default 0)

  • PRIOR_4TH_PARAMETER is a fourth parameter of the prior used for generalized beta distribution, generalized gamma and for the uniform distribution (default 1)

  • SCALE_PARAMETER is the scale parameter to be used for the jump distribution of the Metropolis-Hasting algorithm

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: if you want to specify jscale, you must specify prior_p3 and prior_p4. Use default 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 at the top of the model section, as a Matlab® expression. The first character of the line must be a pound sign (#).

Example

      parameters bet;

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

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