Calibration Question

Steady state
1

Hi Prof,

  1. If I opt for normalizing a variable in the SS then is it possible to set a corresponding parameter using both the normalized variable and data/ratios rather than purely set the parameter within the model (as in @jpfeifer replication of King and Rebello 1999 ?

For example: P_N=\omega \frac{C^T}{C^N}

If I nomalized P_N and then using \frac{C^T}{C^N} along with P_N to set \omega to achieve the normalization is a valid approach ?

  1. Another calibration issue is when the model does not comprise a government sector and/or capital is fixed, then whenever their relevant ratios shows up in the calibration process, I should account for these ratios although they are not present in the model ? That is:

To calibrate \psi using the FOC: (1+r) = (C_t)^\psi

If I used the identity TB_t= Y_t-C_t-I_t-G_t)

then:

(1+r)^{1/\psi} = (Y-I-G -TB)

(1+r)^{1/\psi} /Y= 1-I/Y-G_t/Y -TB_t/Y

Then in order to calibrate \psi should I account for G/Y and I/Y despite they are not present in the model ?

Thank you so much.

2

@jpfeifer would you please advise

3
  1. Yes, that should be valid as long as P_N can actually be normalized, e.g. due to being a numeraire.
  2. The is no universal answer to this question. There are two approaches. Say C=60, I=20, G=10, NX=10, and Y=100. You could calibrate using C/Y=60/100=0.6 or using C/(Y-NX-G)=60/80=0.75. Both would be valid approaches. I would still prefer the first one.
4

Appreciate it Prof.

Regarding part 1: P_N is a relative price (tradable to nontradable) where tradable prices is the numeraire. As per a previous advice of yours (and your replication of King and Rebello 1999) I will use a parameter which is in my case A (tech) to achieve this normalization. Would this be still a valid calibration ?

5

Yes, in that case, you have fixed the numeraire and set two parameters to fix two more endogenous variables.

6

@jpfeifer

Prof., I thank you for this and all your previous guidance.

Best,