PARETO EXTRAPOLATION USING GROUPED INCOME DATA*

ABSTRACT. The distribution of above-median income groups can be described accurately by OLS regression of the Pareto distribution. The excellent fit of log-linear regression has led some researchers to conclude that extrapolated income measures in the open end of the distribution are reliable. The analysis of income distribution data for metropolitan areas reveals: (1) that OLS tends to consistently overestimate the number of families in the tail, and (2) that the overestimation can have serious implications for hypothesis testing.     

LOCATION AND MARKET POWER HOTELLING REVISITED*

ABSTRACT This paper analyzes the determination of industry structure in a product market, given a monopolistic factor market. The characteristics of industry structure examined include the number of firms, their pricing and locational pattern. It is shown how a monopolistic factor owner–a landowner–structures the product market in order to extract maximum rent. Asymmetry characterizes the resulting locational pattern. All the product market firms charge different prices in equilibrium. No matter how large the number of firms competing in the product market, the landowner can always guarantee himself positive profits. The paper concludes with a discussion of possible applications and tests of the theory.     

TESTING SIZE-DENSITY RELATIONSHIPS WITHOUT RATIO-VARIABLES,MULTICOLLINEARITY, LOGARITHMIC TRANSFORMATIONS,OR REGRESSION ANALYSIS*

Using data describing the historical distribution of county seats in the United States, we (1) replicate the traditional ratio-variable test of the size-density law, (2) test a new multivariate, nonratio form of the law, and (3) introduce an alternative method of testing, one which avoids three possible problems in traditional analyses: ratio-variables, multicollinearity, and logarithmic transformation.