Testing Hypotheses in Nonparametric Models of Production

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods exist for making consistent inference about differences in mean efficiency across groups of producers or for testing hypotheses about model structure such as returns to scale or convexity of the production set. We use central limit theorem results from our previous work to develop additional theoretical results permitting consistent tests of model structure and provide Monte Carlo evidence on the performance of the tests in terms of size and power. In addition, the variable returns to scale version of the DEA estimator is proved to attain the faster convergence rate of the CRS-DEA estimator under CRS. Using a sample of U.S. commercial banks, we test and reject convexity of the production set, calling into question results from numerous banking studies that have imposed convexity assumptions. Supplementary materials for this article are available online.     

The impact of taxation on the distribution of wealth in an economy with changing population

The paper investigates into the determinants of the personal distribution of income and wealth. In an overlapping generations model all individuals are assumed to be identical except for their inherited wealth. Since life time is random the bequest of an individual and thus the inherited stock of capital of its children are stochastic variables. Taxation and social security contributions affect life cycle savings, bequests, and, eventually, the distribution of income and wealth in the society. It is shown that, in general, higher tax rates reduce distributive inequality as long as the rate of interest is exogenously given. In steady state, however, where the rate of interest is determined endogenously, increasing taxation and higher social security payments both diminish the capital labor ratio so that the rate of interest rises. If this interest effect is strong enough then it may outbalance the tendency toward more equality because higher interest rates enhance initial differences in the distribution of both income and wealth and, eventually, the inequality in the distribution of income and wealth in the society.