OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION*

ABSTRACT The rank‐size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the t test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the t statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the t statistic explodes asymptotically even under the null, indicating that a mechanical application of the t test yields a serious type I error. To overcome this problem, critical regions of the t test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005) . By using the same database as that used in Soo (2005) , we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual t test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries.     

Illegal immigration,unemployment, and multiple destinations

We develop a multicountry model of illegal immigration with equilibrium unemployment. Two geographic cases are considered. One has two destinations adjacent to the source country while the other has just one destination country adjacent to it. In both cases, the equilibrium border control proves insufficient compared with the joint optimum, calling for enforcement by federal authorities. Absent such authorities, delegating border control to the country with a larger native labor force can improve each destination country’s welfare. In contrast, the equilibrium internal enforcement policy is efficient, obviating enforcement by supranational authorities.     

The Ghatikā of the Twice-Born in South Indian Inscriptions

Indo-Iranian Journal -