A nonparametric estimation of the local Zipf exponent for all US Cities

In this paper we apply the methodology proposed by Ioannides and Overman (2003) to estimate a local Zipf exponent using data for the entire twentieth century of the complete distribution of cities (incorporated places) without any size restrictions in the US. First, we run kernel regressions using the Nadaraya–Watson estimator, excluding some atypical observations (5.66% of the sample). The results reject Zipf’s Law from a long-term perspective, but the evidence supports Gibrat’s Law. In the short term, decade by decade, the evidence in favour of Zipf’s Law is stronger. Second, to consider the whole sample we apply the LOcally WEighted Scatter plot Smoothing (LOWESS) algorithm. From a long-term perspective the evidence supporting Zipf’s Law increases, but the evidence supporting Gibrat Law’s is weaker, as small cities exhibit higher variance than the rest of the cities. Finally, the estimated values by decade are again closer to Zipf’s Law.