Likelihood-based inference for regular functions with fractional polynomial approximations

This paper shows that regular fractional polynomials can approximate regular cost, production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of Euclidean space arbitrarily well. These functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology. Using canonical cost function data, it shows that full Bayesian inference for these approximations can be implemented using standard Markov chain Monte Carlo methods.