Linearize or loglinearize: rate and level in one equation

[shuixing]

dear professor Pfeifer;

I have read your guide to specify observable equations, and you said variables like inflation and interest rate should be linearized rather than log-linearized, but what if we have both variables like interest rate and other level variable like capital in one equation, the level variable requires log-linearized while it’s best to linearize interest rate, how to deal with this issue?

best
shuixing

[jpfeifer]

Unless a variable has a negative or 0 steady state, you can always use loglinearization. Thus, you can easily loglinearize inflation and interest rates. The reason for often not doing this is simply a matter of convenient interpretation, nothing else. That being said, you can easily mix linearization and loglinearization in first order approximated models as both are variants of the same basic Taylor approximation.

[shuixing]

@jpfeifer

Unless a variable has a negative or 0 steady state, you can always use loglinearization. Thus, you can easily loglinearize inflation and interest rates. The reason for often not doing this is simply a matter of convenient interpretation, nothing else. That being said, you can easily mix linearization and loglinearization in first order approximated models as both are variants of the same basic Taylor approximation.

thanks professor Pfeifer, now I get it, and When I run my mod.file, one strange thing happens: the observable variable results in smoothedvariables are not equal to the data I have specified, that seems very weird.

[jpfeifer]

I guess that only happens for some of them? If yes, this is a sign of stochastic singularity in the model.