Spatial relationships in high-dimensional, international, and historical data

My dissertation, "Spatial Relationships in High-Dimensional, International, and Historical Data" examines the effects of distance not only in a geographical sense, but also in a higher dimensional sense where statistical distance metrics are widely used. The first two chapters of my Ph.D. thesis are closely related, and together they represent an attempt to develop a new method for computing index numbers, which are applications of statistical distance metrics. I consider distance metrics on categorical shares data, for example the proportions of a consumer's income spent on food, clothing, entertainment, and housing. Distance metrics are frequently used on such data, although all suffer from an essential flaw, which is that they treat each category as a separate, orthogonal dimension. That is, each metric assumes that every category is equally different from every other one. That assumption would be like saying Fuji apples are equally as different from Gala apples as either are to oranges, and then the distance metric is like adding apples to apples as well as apples to oranges. Because of this, the policy conclusions reached through distance measures could be greatly distorted. The third chapter of my dissertation looks at the effect of railroads on retail prices in the United States from 1851–1892. Consistent with the theory of comparative advantage, railroads in more remote areas caused the price of agricultural goods to increase and the price of manufactured and imported goods to decline