Some Problems with calibration, shocks and mode_check？

Dear Professor Pfeifer,

When I was reading some classic papers, I feel a little confused about the questions bellow. Would you please give me a hint ? Thank you for your time !

(1) Sometimes when doing the calibration, we may use the ratios of economic data as targets to adjust the steady states of variables in the model, e.g. C/Y, I/Y and so on. While I find it’s not quite easy to do this especially when the model is a little complicated. Is it always necessary to keep the ratios of variables’ steady states close to the ratios of practical data ？( I find that they are not so closed in some papers ) Does the calibration results impact the estimation of other parameters?

(2) In some papers, the model contains the entrepreneurs’ consumption (C_E) besides patient and impatient households’ (C_P and C_I). What does this entrepreneurs’ consumption really mean in practice (what practical data) ? Is it finally belong to the household consumption? (because the steady state of C_E is even much larger then C_P after my calibration of model, which seems so wierd. )
And also why the consumption preference shock only relates to the households’ consumption but not the entrepreneurs’ consumption ?

(3) I have encountered bad mode plot as attached. (all parameters are identified. ) For some parameters the vertical line is not through the peak of blue line, and even the shape like rhoRUU, rhocUU appears. What should I do to improve this ? Change the prior mean or some other way ?

Any reply will be appreciated. Thanks again !

1. It’s not necessary, but it is often a convenient way of fixing parameter values. We observe those ratios and typically have no clue about parameter values. Take the depreciation rate. It will determine the investment to capital ratio. Is delta 0.05 or 0.07 or 0.1? The steady state capital to investment ratio can inform this.
2. That very much depends on your interpretation/setup of your model. There is no general answer. Entrepreneurial consumption can mean something like the net income of proprietors. Where you put a preference also depends on your modeling choices. There is no rule here.
3. `rhoRUU, rhocUU` are not really problematic. Look at the scaling of the y-axis. The bigger issue are the ones where the detected “mode” is not at the peak. You should try a different mode-finder, e.g. `mode_compute=5`.

Thank you Professor Pfeifer ! Your reply is really helpful !

A little further question about the third probelm:
When I try mode_compute=5, the result says
‘’(minus) the hessian matrix at the “mode” is not positive definite!
=> posterior variance of the estimated parameters are not positive.
You should try to change the initial values of the parameters using
the estimated_params_init block, or use another optimization routine.’’

Then I try mode_compute=9, the results are still not ideal ( mode is not at the peak).

How should I improve this ? Will it work if I change the observation varibales ? or change the initial values of prior (e.g. change ‘‘iotapUU,0.5, , ,BETA_PDF,0.5,0.2;’’ to ‘‘iotapUU,0.8, , ,BETA_PDF,0.5,0.2;’’ )? Is there any tricks on choosing the initial value ?

Any reply will be appreciated. Thank you for your time !

Have you tried a sequence of mode-finders? Of course you can try different priors.