Measurement equations issuee

Estimation ML/Bayesian estimation
1

Hi, I have a question about measurement equation. My model variables are in level and irfs in deviation from steady state. I want to specify measurement equations for parameter estimaation and proceed in the following way:

1- I filtered the observed data using qwf filter (Quast-Wolters filter)

2- define measurement variables as:

  • y_obs= log(y_model)-log(y_model_ss) or y_obs= log(y_model)
  • cpi_obs = pi_cpi_model^4 - pi_cpi_model_ss^4 or cpi_obs = pi_cpi_model^4
  • Same structure for all other model variables.

A- I wonder which of the above specification are correct

B- Can I also specify the measurement equations in growth rate ie dly_obs = difflog(Y_model). I’m asking because some of my variables are in different currency (usd vs local currency).

C- I want to estimate some sectoral parameters like sectoral price rigidity parameters and elasticities. Do I necessary need sectoral data?

D- My model is in quarterly frequency; can I use a mix of quarterly and annual data to estimate the parameters.

Thanks

2
  1. If you correctly define the mapping, you can either use first differences or the filtered versions you currently use.
  2. Whether your equations are correct, depends particularly on the scaling (percentages, multiplied by 100 etc.)
  3. You don’t necessarily need sectoral data, but it cannot hurt. You should check identification.
  4. Yes, you can mix quarterly and annual data if you like. See Data with different frequency - #4 by jpfeifer