A test of the relationship between the Pareto exponent and sample size

This paper uses un-truncated city population data from three countries—the United States, Spain and Italy—to empirically test Proposition 1 put forth by Eeckhout (2004 American Economic Review, 94: 1429–1451). Eeckhout’s hypothesis was that the estimate of the Pareto exponent in a standard Zipf regression decreases with sample size, if the underlying city size distribution is lognormal. Using rolling sample regressions, we find that this proposition is only valid once we enter the lognormal body of the distribution; for the Pareto-distributed upper-tail, the estimated exponent does not vary with sample size.