Log and level in dynare

[RogersH99]

Hi there, I have a puzzling question that annoys me much and I wonder if you could help.

In my dynare code, if I write the mod file in LEVEL, with a relatively large shock, some of my variables simulated are negative. This negative value is not wished. So I want to avoid this.

One way is to decrease the shock volatility.

However, if the shock volatility remains as before, but I write my mod file in terms of EXP (i.e do log-transformation), then is it by construction my variables are positive?? This is my Q1. Am I allowed to do this and I can really get what i want (non-negative variable values in simulation)?

Q2:
If not, what is the difference between this LEVEL form and log form in dynare simulation?

Q3:
If so, is this a way to impose non-negative constraint in my dynare mod file?

Thanks.

Best,
R

[jpfeifer]

In a nutshell

Parameter drift with parameters' bounds

What is the reference for what you are trying to do? In general, if you work with a log-linear approximation, there is not way to bound variables (like your capital share) due to linearity. One has to live with this and hope that the data do not assign much probability to it violating the theoretical bounds.

[RogersH99]

Hi Prof.,

Thanks for your prompt reply. Yes I understand the conclusion you were trying to convey that we cannot simply replace level (say X) with exp(log(X)) in dynare mod file to impose the non-negative constraints.

However, I am curious why so. As it seems that all my variables defined this way do has the property of not being negative.

Many thanks.

[jpfeifer]

As my reply said: it is about the linear model solution. Whether you use the level or the log-level in the nonlinear model, you will be approximating it with a linear function at first order. Linear functions, by construction, are unbounded. That is an approximation error you will have to live with.