Langrange multipliers/shadow prices

[jpfeifer]

That comes from doing a polynomial approximation. See e.g.

Negative numbers

That is because a first-order approximation approximates exp(x) with a linear function exp(x_ss)*(x-x_ss), where x_ss is the steady state. Of course, a linear function will always hit negative values with some probability (as long as its slope is not 0). Using a second-order approximation means fitting a parabola to exp(x), thus preserving some of the curvature. This may avoid having negative values if the vertex is above 0 (but for extreme shocks does not preserve monotonicity of exp(x)). Th…