A simple and efficient test for the Pareto law

This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows the good small sample properties of the test under the null of the Pareto law and also its power against some sensible and interesting alternatives. In addition, the proposed test is compared to a goodness of fit test which is powerful against more or less all alternatives. Eventually, a simple application to urban economics is performed. Copyright Springer-Verlag Berlin Heidelberg 2013