• EstimationModule

Proposed specification for estimation functions

This includes factorization of common code and extensions for (unexpected) structural change

Estimated parameters description

xparam1 is a column n by 1 vector holding the current values of the estimated parameters (n is the number of parameters).

xparam1 becomes parameters_description is a (global?) strucure array (with n lines) describing the estimated parameters with the following fields:

• type (1,2,3,4,5)
  • - 1: standard deviation of a structural shock. - 2: standard deviation of a measurement error. - 3: correlation betwwen two structural shocks. - 4: correlation between two measurement errors. - 5: "deep" parameter.
• ID1 (first exogenous or endogenous variable index for the estimated standard deviation)
• ID2 (second exogenous or endogenous variable index for the estimated correlations)
• Period1 (beginning of sub-period)
• Period2 (end of sub-period)

Remark 1. Field ID2 is empty if the corresponding estimated parameter is not a correlation.

Remark 2. Field ID1 is empty if the corresponding estimated parameter is not a correlation or standard deviation.

Remark 3. Period1 and Period2 specify the closed sub sample used to estimate the parameter.

Functions

• Likelihood/posterior evaluation (separate two functions ?)
  • - INPUTS: xparam1, data, prior_specifications, ys, coeff_trends, M_.params, M_.Sigma_e, M_.H, list_of_observed_variables - OUTPUTS: likelihood/posterior value, info
  • parameter updates (for period 1):
    • - INPUTS: xparam1, ys, coeff_trends,M_.params, M_.Sigma_e, M_.H - OUTUTS: coeff_trends, params, Sigma_e, H
  • reduced form (for period 1):
    • - INPUTS: params - OUTPUTS: T R ys - computes steady state - computes linear solution for state variables + observed variables
  • data_filtering (for period 1):
    • - INPUTS: data, ys, coeff_trends, Period1, Period2 - OUTPUTS: centered_data for subperiod
  • Kalman filter initialization
    • - INPUTS: Sigma_e T R list_of_observed_variables - OUTPUTS: a0 P0 Z - Remark: Z is computed only for nonstationary models. mfs is computed once before these functions
      • Diffuse Kalman filter recursions takes place here ?
    LOOP on periods 1 to NP:
    • Kalman filter - INPUTS: a0 Po Z T R centered_data Sigma_e H - OUTPUTS: log-likelihood, a(t|t-1), P(t|t-1)

      if period < NP:

      • parameter updates
      • reduced form
      • data_filtering
    END LOOP
  • priors evaluation