Hi All,
I am searching for the unpublished manuscript De Wind, J., 2008. Punishment functions. mimeo, University of Amsterdam.
I have faced the problem that at the higher order of approximation with reasonable shock levels, my penalty function exhibits unexpected behavior. For starters, it stops looking like an exponent or takes negative values.
Brzoza-Brzezina, Kolasa, and Makarski(2015) started discussing this feature and referred to the unpublished manuscript.
From what I can see, that was Joris’s master thesis at Tinbergen. You may be able to obtain it from the university.
Be that as it may be, keep in mind that you are approximating an exponential penalty function by a polynomial. As discussed in e.g. De Wind/den Haan there is no way to have such a polynomial generally obey monotonicity and asymptotic behavior. A polynomial will always go to either plus or minus infinity. What you describe is therefore not surprising.