The steady state contains NaN or Inf

[jpfeifer]

1. I don't understand this point. If there is a singularity caused by a missing equation, it usually does not go away for other parameter sets.
2. To start the MCMC, you usually need a positive definite Hessian. A positive definite Hessian indicates that you are at a maximum of the objective function. If that is not the case, estimation will crash at this stage. That's why I said you should look at the

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mode_check

plots.
3. Yes, in steady state

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y_obs=g_bar

Thus, you should indicate this in the initval block (or even better, a steady_state_model-block)

[qianq_1625]

Hi Professor,

With current parameter initial values, I'm able to run stoch_simul code successfully. So based on your suggestion, I guess my model setup should be correct. I also closely look at the matlab error message. It mentions that the parameters have wrong initial values. So I'm wondering if the inappropriate parameter initial values could cause non-positive hessian matrix. Thank you very much!

Eric

[jpfeifer]

I keep repeating myself: what do the mode_check plots say?

[qianq_1625]

Hi Professor,

Do you mind taking a look at my code? I checked the mode_check. It mentioned some parameters have negative variance. I'm not sure this is due to my initial values or my model setup. Thanks a lot!

Eric

[jpfeifer]

Please use Dynare 4.5. It will tell you

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ERROR: If the model is declared linear the second derivatives must be equal to zero.
       The following equations had non-zero second derivatives:
       * Eq # 18


Please fix this

[qianq_1625]

Hi Professor,

Thanks a lot! The equation #18 is one of my observation equations. The observation data is one of the great ratios in my data: c(t)/y(t). I'm currently having difficulty to write this equation in linear way.

My plan is:
Since I know both c(t) and y(t) have positive values and positive steady states, I simply take log on the variable.
So ln[c(t)/y(t)]=ln[c(t)]-ln[y(t)]=ln[c(t)/c_bar]-ln[y(t)/y_bar]+ln[c_bar/y_bar].
Eventually, I can have c/y_obs=ln[c(t)/y(t)]=c(t)_hat-y(t)_hat+ln[c_bar/y_bar], where c(t)_hat=ln[c(t)/c_bar] and y(t)_hat=ln[y(t)/y_bar].
In dynare, I have c_y_obs=c-y+ln(c_bar/y_bar) as the new equation #18.

Is this the correct way to write observation equation? Also I concern that if I write this way, the standard deviation would be based on ln[c(t)/y(t)], instead of c(t)/y(t).

I read the your document, but couldn't find appropriate example for this case. Do you mind giving me some suggestions on this case? If I keep this nonlinear equation in my model block, and take the option "linear" off, will dynare log linearize the equation automatically? Thank you very much for your great help!

Eric

[jpfeifer]

You need to consistently (log)linearize your model. If the rest of your model is loglinearized, then a purely multiplicative equation like c_y=c/y simply becomes c_y_hat=c_hat-y_hat. The question is now what you observe in the data. Because in the model, there will be no trend.

[qianq_1625]

Hi Professor,

This variable is consumption to output ratio in my data. It have already been stationary. Are you saying I need to log linearize this variable by ln[c/y(t)/mean(c/y)] as my observation variable?
Thank you very much!

Eric

[jpfeifer]

In that case, you need to use the demeaned consumption share as your observable and then use

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c_y_hat=c_hat-y_hat

as your observation equation where

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c_y_hat

is the observed data.

[qianq_1625]

Sorry Professor,

I'm still confused. When you say demean the ratio, do you mean: c_y(t)-mean(c_y) or ln(c_y(t))-mean(ln(c_y))? The latter one would generate much bigger standard deviation which might not be reasonable.
Can you make it more specifically? Thank you very much!!

Eric

[jpfeifer]

If you loglinearized everything, the data should be

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ln(c_y(t))-mean(ln(c_y))

That will obviously have a bigger standard deviation, because it measures the percentage deviations of the c/y ratio from its mean which is smaller than 1.