Random Utilities and How to Find Them

Abstract

Ph.D.In this dissertation, I study the random utility model. The random utility model is an extension of the classic paradigm of economics which assumes that decision makers choose according to some underlying preference. The random utility model extends this paradigm by allowing for heterogeneity across either a population of decision makers or across time for the same decision maker. This heterogeneity is modeled as there being a distribution over preferences inducing a distribution over choices. In Chapter 1, I study when an analyst is able to recover the underlying distribution over preferences from choice data. I provide fully characteristic conditions under which we are able to recover the underlying distribution over preferences. In Chapter 2, I readdress the problem of testing the random utility model. While axiomatic tests of the random utility model have been known, only recently has a hypothesis test for the random utility model been developed which can be applied to real data. However, this hypothesis test is not computationally feasible in many reasonable applications. I provide an alternative hypothesis test, applicable to real data, that offers large computational improvements over the current standard methodology. In Chapter 3, I study the random utility model in a dynamic setting where a decision maker's past choices can impact their preference today. First, I broach the problem of aggregation. In general, if a decision maker's preference depends on their history of choices, the time average of their choices does not coincide with the random utility model. I provide characteristic conditions for when the random utility model is an accurate model of time aggregated choice. Second, I develop a test for this type of dynamic random utility when we have time disaggregated but population level data. I provide a fully characteristic axiomatic test as well as a hypothesis test for history dependent random utility for this type of data