| This dissertation develops mathematical tests for properties of utility functions, and statistical estimations of utility functions, without imposing any parametric structure for them.;In the mathematical part, I first characterize finite sets of demand observations generated by strictly concave and monotonic utility functions. These new methods allow us to test the consistency of perfectly and imperfectly competitive demand data with a strictly concave utility function.;Second, I prove that when the demand function is income-Lipschitzian and invertible, the Strong Axiom and a Concavity Axiom imply the existence of a strictly concave and monotonic utility function, when the number of observations is infinite as well as finite.;In the statistical part, I develop non-parametric estimation methods for the utility-of-attributes in discrete choice models. The only assumptions imposed on the deterministic part of the utility function are its monotonicity and either bounded rate of change or concavity. The stochastic part is assumed to be distributed with a known distribution.;The consistency of the estimates is proved by applying results of maximum likelihood estimation on infinite dimensional spaces.;I wrote a FORTRAN program to perform the estimations, and I performed simulations to compare these methods with the parametric ones. |
