I examined a new metric for measuring urban decentralization and found that it failed to yield useful results when applied to U.S. cities from 1910-1940. I conducted this research independently as a senior at Rice in the spring of 1994, supervised by Prof. Peter Mieszkowski at Rice.
The structure and evolution of city organization has long interested economists. Patterns of population and employment density are difficult to measure despite the availability of detailed data. The chief problem lies in finding an accurate metric. Most analyses have used a simple, city-center-oriented exponential density model, but a landmark paper by D. Harrison and J. F. Kain  argues the model is unrealistic and these analyses are suspect. E. S. Mills recently suggested a new metric  embodying only the assumption that urban population densities are related to the urban area's physical size.
As part of my urban economics course in the spring of 1993, I studied urban decentralization in postwar German cities using Mills's metric . Although I found the expected decentralization in West Germany, I was surprised by results indicating centralization in East German cities.
Prof. Peter Mieszkowski invited me to continue this work, and suggested a focus on pre-WWII U.S. cities. I found the necessary data for 55 cities and conducted a series of linear regressions to Mills' formula, seeking trends over the period 1910-40 . Regrettably, the Mills metric failed for this sample. Although some data suggested centralization, other data suggested decentralization, and most results lacked stability, with slight changes in sample composition giving significantly different results.
Despite the lack of results for the pre-WWII sample, the study of German cities suggests the Mills metric warrants further study, and I would be interested to hear about any ongoing work or results related to this topic.
2. E. S. Mills. ``The Measurement and Determinants of Suburbanization''. Journal of Urban Economics, 32:377-387, 1992.
3. Urban Centralization in U.S. Cities prior to World War II: Experience with a New Metric. Kevin Skadron, with Peter Mieszkowski. Rice University Department of Economics. April 28, 1994.
4. A New Method for Measurement of Urban Decentralization. Kevin Skadron, with Peter Mieszkowski. Rice University Department of Economics. May 5, 1993.