The Distribution of Ability and Earnings

ONE of the standard problems in distribution theory has been to explain the skewness of the personal income distribution. In particular much has been written to explain the apparent contradiction between the allegedly normal distribution of abilities and the skewed distribution of income.' While this attempt to relate the distribution of earnings to the underlying distribution of ability is still with us,2 another approach has become popular in recent years.3 This new approach is not concerned with the distribution of abilities; instead it shows how chance elements can generate a lognormal, a Pareto, or a similar income distribution.4 This chance approach has provided a new way of looking at the income distribution, but its proponents have paid too little attention to the economic meaning of the proportional shock mechanism.5 The present paper tries to combine parts of both of these approaches. It starts with the assumption of a normal distribution of ability and then shows how this leads to a lognormal distribution of earnings. This assumption of a normal ability distribution is only an expository device; as is shown in the Appendix there is little reason to assume that ability is in fact normally distributed. The theory to be developed here deals only with earnings, i.e., wages and salaries. For property income the economic rationale of the multiplicative assumption used by the chance theories presents no problem. If a man's income increases so will his savings, at least in dollar terms, and hence, next year he will have a greater stock of income-bearing property.