Interesting…
The reason why I’m using this function is because I am trying to model downward wage rigidity (DELTA_W_HAT) and partially irreversible investment (DELTA_I), which are asymmetric adjustment cost functions. I could technically take out the term that is raised to the power PHI_I or PHI_W_HAT, but then the asymmetric component in the adjustment costs do not have a sufficient bite (its quantitatively small and makes little difference). Introducing this term was an idea of how to get an increase in the magnitude.
The reason I’m using this is because it gives rise to very neat first order conditions (as opposed to using some smooth transition function) and yet it can still be estimated using Bayesian methods (as opposed to using a piecewise-quadratic functional form).
In other words, there is a good reason why it is used, but I may have to come up with a slightly different functional form, unless you have any further suggestions?
Thanks