Asymmetry and Gradient Asymmetry Functions: Density-Based Skewness and Kurtosis

Abstract.  Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed.     

FISCAL STRUCTURES AND ECONOMIC GROWTH: INTERNATIONAL EVIDENCE

Our paper systematically examines the effects of fiscal structure on economic growth. We find that for developing countries, debt-financed increases in government expenditure retard growth and tax-financed increases stimulate growth, while for developed countries, debt-financed increases in government expenditure do not affect growth and tax-financed increases lower growth. We impose the government budget constraint on the regression equations so that the precise changes in fiscal policy can be identified (e.g., the effect of a debt-financed increase in health expenditure), employing a pooled cross-section, time-series sample and fixed- and random-effect methods. (JEL 04, E6)     

The Influence of Socio-Economic Variables on Family Size in Wentworth County, Ontario, 1871: A Statistical Analysis of Historical Micro-Data

Les techniques de l'analyse régressive transversale sont appliquées aux microdonnées du recensement historique du Canada. On a soutiré systématiquement des documents microfilmés un échantillon de 1100 families "normales" résidant dans le comté de Wentworth, de la province d'Ontario, en 1871. On a tenté de determiner l'influence de l'âge, du lieu de naissance, de la religion, de l'origine ethnique, de l'occupation, de la résidence dans un milieu rural ou urbain, et de toutes les autres variables disponibles sur la grandeur de la famille. On utilisa dans l'analyse regressive sur une vaste échelle des variables d'emprunt ("dummy variables"). Les variables démographiques et celles associées au milieu de résidence s'avérèrent très significatives. On découvrit, cependant, que les influences socio-économiques, en autant qu'elles sont reflétées par la profession, la religion, le lieu de naissance, et l'origine ethnique, exercent une faible influence sur la composition de la famille.
Techniques of cross-section regression analysis are applied to historical census of Canada micro-data. A sample of 1100 "normal" families in Wentworth County, Ontario, was drawn systematically from microfilm records of the 1871 census. An attempt was made to determine the influence on family size of age, birthplace, religion, ethnic origin, occupation, urban and rural residence, and other variables for which the census provided information. Extensive use was made of dummy variables in the regression analysis. "Demographic" and urban-rural factors were found to be highly significant. However, socio-economic influences, as represented by occupation, religion, birthplace, and ethnic origin, were found generally to be weak.     

EXPERIMENTAL TESTS OF RICARDIAN EQUIVALENCE

This study employs laboratory experiments to test aspects of Ricardian equivalence. An overlapping generations model forms the basis of the experimental design. Whenever Ricardian equivalence predicts a positive bequest, outcomes close to those predicted occur, after allowance for learning. Observed deviations from Ricardian equilibrium are small, but biased in a Keynesian direction: changes in bequests do not fully offset changes in government debt. The imposition of a binding nonnegativity constraint on bequests produces the predicted neoclassical behavior. The cost to the players of deviations from the theoretical equilibrium is apparently an important determinant of the variability of observed deviations.     

INEQUALITY AND GROWTH IN THE UNITED STATES: EVIDENCE FROM A NEW STATE-LEVEL PANEL OF INCOME INEQUALITY MEASURES

This paper introduces a new comprehensive panel of annual state-level income inequality measures spanning the postwar period 1945–2004. For many states, the share of income held by the top decile experienced a prolonged period of stability after World War II, followed by a substantial increase in inequality during the 1980s and 1990s. This paper also presents an examination of the long-run relationship between income inequality and economic growth. Our findings indicate that the long-run relationship between inequality and growth is positive in nature and driven principally by the concentration of income in the upper end of the income distribution. ( JEL D31, O40)