Parameter calibration

Estimation ML/Bayesian estimation
1

Dear members,

I am encountering an issue in my calibration exercise. After rearranging the CPOs, I obtain for my parameter the following equation,

20

My issue is with “sigma es”. All ratios and parameters present in the equation are already known, except for “sigma es”, which is a parameter I would like to estimate via bayesian estimation. That “sigma” represents an elasticity of substitution.

Can I specify to the “parameter” block in dynare the equation for the parameter “alpha d”, so that when it computes “sigma es” via the estimation block, dynare computes from the equation the final value for “alpha d” from the value of “sigma es”?
Or do I have to impose a value to “sigma es” in order to compute the value of “alpha d”?

Thank you in advance.

Best,

2

What you describe sounds like a case of parameter dependence. You should define \alpha_d as a model-local variable with the #-operator and then estimate \sigma_{es}

3

Thank you very much.

Is normalization compulsory when having CES functions? I’ve seen several authors saying that it is when one wants to compare two economies.

Thanks,

4

Have a look at the Cantore/Levin (2012) paper on Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics

5

Would you recommend to use net national product rather than gross national product to compute steady state ratios and factor’s share ?

Thank you.

Best,

6

That is impossible to answer in general. Model and data should be consistent. Thus, you need to use the suitable data concept.

7

Good morning,

Is it ok if alpha_d depends not only on other parameters (sigma_es, beta, deal_d) as well as endogenous variables (e_h and d) and exogenous variables (p_e and t_e t_c)? From what I saw, most codes uses the #-operator with an equation linking parameters to other parameters (and not exo and endogenous variables).

THANKS

8

If it depends on a variable, it is not a parameter.

9

Right. But I have nested CES functions that gives me at SS parameters depending upon variables … I’m going to try to simplify more the equations then.

Thanks

10

A variable in steady state is constant and only depends on parameters. Therefore it is not a variable anymore. If your parameter depends on a steady state value, that is fine.

11

Yes, when I was saying “endogenous variables” or “exogenous” I meant at steady state. The above equation is at SS.

Should I specify SS variables as well?

#alpha_d= 1/(beta*(1+t_c)p_e(1+t_e)(e_h_ss/d_ss)^(1/sigma_es)+beta(1-delta_d)+1
// In my code I have declared in the var-block: e_h and d. Should I add as well e_h_ss and d_ss or can I just put the following equation:

#alpha_d= 1/(beta*(1+t_c)p_e(1+t_e)(e_h/d)^(1/sigma_es)+beta(1-delta_d)+1
But I’m afraid in that case Dynare will take e_h and d as non SS values

Thanks

12

Either define parameters that store the steady state values or use the STEADY_STATE()-operator.

13

Thank you.

Have a nice day