ABSTRACT
We are concerned here with a topic that crops up in several areas of applied economics: the relationship of one distribution to another. Sometimes the comparison of distributions is easy to do formally and easy to carry out in practice: if we are examining inequality in an empirical income distribution with reference to an artificial standard of perfect equality, or if we are comparing the distribution of returns on a risky financial asset with a riskless asset then there are well-known principles that can be applied to the distributional comparisons involved. What makes it simple is the simple reference point, such as the perfect-equality income distribution. But if we are looking at the relationship between two general distributions in situation A and two general distributions in situation B things can get more complicated. The complication arises, not because of some artificial tweaking of the basic problem, or the desire for mathematical sophistication, but because of the nature of the underlying economic issue. It arises quite naturally in fields such as income mobility, the measurement of horizontal inequity, the assessment of effective tax progression and even in related fields such as the statistical problem of ‘goodness-of-fit.’
