Why second moments get extremely large under sticky prices?

Stochastic simulations
1

Hi all, I set a model with New Keynesian sticky prices.
I found second moments got unrealistically large even under low price stickiness (i.e. share of firms cannot rest prices is over 0.3). Would it still be reasonable when only low price stickiness in model setting? Thanks.

2

Which order of approximation are you using? And are you using theoretical or simulated moments?

3

Hi Prof. Pfeifer, I use third-order. My code is,
stoch_simul(order = 3, periods=65000,pruning,nograph) ;

By the way, what kind of variables or equations should not be included into ‘auxiliary equations’? Thanks a lot!

4

Have a look at the simulated series then. That should give you an indication what is happening. What do you mean with

?

5

Dear Prof. Pfeifer,

I want to know whether nonlinear model such as those with volatility shocks cannot be simulated without initial values or calibrated values? I know dynare can simulate linear models without giving steady state values. Thanks a lot.

By the way, the eigenvalues from my model are as belows,

EIGENVALUES:
Modulus Real Imaginary

   2.138e-08       -2.138e-08                0
     0.02215         0.005181          0.02153
     0.02215         0.005181         -0.02153
      0.2514           0.2514                0
      0.6019           0.6019                0
       0.745            0.745                0
       0.748            0.748                0
       0.765            0.765                0
        0.88             0.88                0
        0.93             0.93                0
        0.93             0.93                0
        0.95             0.95                0
      0.9569           0.9569                0
       1.011            1.011                0
       1.058            1.058                0
       1.684           -1.684                0
        3.97             3.97                0
       46.57            46.57                0
   3.998e+08        3.998e+08                0
   1.079e+15        1.079e+15                0
   1.763e+18        1.763e+18                0
   3.101e+18       -3.101e+18                0
         Inf             -Inf                0
         Inf             -Inf                0

Are them reasonable. One of them is approaching zero.

Best

6

for what? Steady state computation? Simulations, i.e. starting values for the states in the simulation process? Or a fully specified set of parameters.

0 or infinite generalized eigenvalues are not a problem.

7

Hi Prof. Peifer, thanks for your reply.

I mean, whether nonlinear model such as those with volatility shocks can be simulated without initial values or calibrated values, for starting values for the states in simulations? That is, whether I can use ''model(linear)" without setting starting values at third order approximation?

By the way, if one of my static eqs’ residuals is not equal to zero, are the results of its simulations still creditable or reasonable? Thanks a lot.

Residuals of the static equations:
Equation number 1 : 0
Equation number 2 : 0
Equation number 3 : 0
Equation number 4 : 0
Equation number 5 : 0
Equation number 6 : 0
Equation number 7 : 0
Equation number 8 : 0.00021039
Equation number 9 : 0
Equation number 10 : 0
Equation number 11 : 0
Equation number 12 : 0
Equation number 13 : 0
Equation number 14 : 0
Equation number 15 : 0
Equation number 16 : 0
Equation number 17 : 0
Equation number 18 : 0
Equation number 19 : 0
Equation number 20 : 0
Equation number 21 : 0
Equation number 22 : 0
Equation number 23 : 0
Equation number 24 : 0
Equation number 25 : 0
Equation number 26 : 0
Equation number 27 : 0
Equation number 28 : 0
Equation number 29 : 0
Equation number 30 : 0
Equation number 31 : 0
Equation number 32 : 0

8
  1. I still don’t understand. You cannot use model(linear) at higher order, because the model is not linear.
  2. Having a small residual like this is typically not problematic. Or did you analytically compute the steady state? Then it may be a warning sign (unless you have an extreme form of nonlinearity that leads to under/overflow)
9

Hi Prof. Pfeifer, thanks for your reply.

  1. So the model at high order should be given initial s-s values through calibration? But in some dynare codes, models are not needed to set initial values, like your code about Basu(2017). Or can it be log linearized to calibrate to attain the s-s values? Or can I simulate a model without given starting s-s values?

  2. Yes, I did. But I use some solver like ‘fzero’, since some of s-s values are hard to sole by p&p for me.

Thanks a lot.

Best

10

Calibrating a model is about setting parameters, not computing steady states, so there is no relation between the two. Starting values are also conceptually different from steady state values. Of course, Dynare usually uses the steady state as the initial point, but in your case, the steady state was computed numerically, so you should be fine.

11

Dear Prof. Pfeifer,

Thanks for your reply!