Uniformity Models:
Pareto’s Law, Lassalle’s Conjecture, and Bowley’s Law
One set of theories are uniformity models. They describe inequality as more or less constant in history and explain it as the inexorable result of something fixed and fundamental in human nature or the social condition.
The leading uniformity theory is Pareto’s Law. It takes its name from Vilfredo Pareto (1848–1923), an Italian scholar who studied income statistics in many nations, and concluded that the pattern of inequality was a curve of constant shape for all incomes, all countries, and all periods of history. Pareto’s Law is an equation that may be written in the form of:
logN = logA — alogX
where X is income of a given size, N is the number of people with that income or more, and A is an empirical constant. When plotted on a double-log graph, the result is a line with a slope of a.
Pareto believed that the slope of a was always approximately 1.5 for upper income-holders. He concluded that this statistical regularity was a law of inequality, which derived mainly from biological differences in the distribution of human ability. It is interesting that Pareto himself was born to the nobility of Genoa. In later life he embraced many social causes, but his attitudes remained aristocratic, and his law has found many supporters on the political right. It has been used to prove that inequality is natural and inexorable.
Another and very different uniformity theory might be called Lassalle’s Conjecture, or the Monte Carlo model. It comes not from the right but from the left, and takes its name from Ferdinand Lassalle, a German socialist with a sense of humor, who observed a statistical similarity between the distribution of wealth in European society and the distribution of winners at the roulette table in Monte Carlo. He framed a proposition that both results were ruled by the laws of chance, and would continue to be so until socialism shut down the game. Lassalle’s idea of inequality was a constant curve of probability.
A third uniformity model is known to economists of advanced years as Bowley’s Law. It bears the name of Arthur Bowley, a British statistician who constructed some of the earliest estimates of national income for the United Kingdom. Bowley discovered evidence that income shares of capital and labor remained approximately constant in Britain through the late nineteenth and early twentieth centuries. This finding was called Bowley’s Law, which John Maynard Keynes celebrated as “one of the most surprising, yet best established facts in the whole range of economic statistics.” Bowley also reported evidence that the distribution of incomes among individual workers in Britain remained stable over a period of nearly a century. His model was extended to individual income-shares, as well as to factor shares between labor and capital. See Y. S. Brenner, Hartmut Kaelbe and Mark Thomas, eds., Income Distribution in Historical Perspective (Cambridge, 1991), 35; A. L. Bowley, Wages in the United Kingdom in the Nineteenth Century (Cambridge, 1900); idem, Wages and Income in the United Kingdom since 1860 (Cambridge, 1937).
Continuity Models: Persistent Cultural Values
Most historians reject the idea of uniformity in all periods and places, but some have developed models of continuity of a sort that can coexist with patterns of change through time, and with variation from one culture to another. A theory of continuity in regard to inequality appears in one of my own works, Albion’s Seed (Oxford, 1989). This work reports empirical evidence that very different patterns of wealth-inequality developed in the various cultural regions of British America during the seventeenth and eighteenth centuries. These relative differences in wealth-distribution within American regions have persisted for many generations, and cannot be explained by material or environmental factors. They could only have arisen from enduring cultural values and institutional processes.
Ecological Models: Environmental Conditions
Other historical models give more attention to ecological and material conditions. An example is the work of Jackson Turner Main, who studied the distribution of wealth in early America and concluded that patterns of wealth inequality were “not so much cultural as social and economic” in their origin. He believed that frontier conditions supported equality during the seventeenth, eighteenth and nineteenth centuries, while urbanization and commercialization caused inequality. See Jackson Turner Main, The Social Structure of Revolutionary America (Princeton, 1965), 286; idem, Society and Economy in Colonial Connecticut (Princeton, 1985), 376.
Population Models: Malthus and Population Growth
Another theory of inequality derives from the work of Thomas Malthus and academic Malthusians. This is a change-model. It holds that the growth of population promotes the growth of inequality in a variety of ways. It expands the supply of labor relative to demand, lowers wages as more people compete for jobs, and drives the poor to the margin of subsistence. This theory has been widely accepted by economic historians of the medieval and early modern world. It has also been applied to global trends in the modern era. See Michael Postan, The Medieval Economy and Society (1972, Harmondsworth, 1975), 40, 275).
Dialectical Models: Systems of Production and Exchange
Yet another set of theories holds that inequality has increased or diminished through time as a consequence of structural changes in economic systems. Among them are Marxist theories, which assert that inequality of wealth and income is determined principally by ownership of means of production. Two of Karl Marx’s most creative ideas were his “law of capitalist accumulation” and his theory of surplus value, which holds that as productivity increases above subsistence, capitalist owners appropriate to themselves “surplus value” above the value equal to labor’s subsistence, thereby increasing inequality.
Many Marxist writers have theorized that inequality increases with the growth of capitalism—that is, with private ownership of the means of production. A related theory is the argument that inequality has increased with the separation of capital and labor in the industrial revolution. Many Marxist historians believe that inequality increased rapidly during the industrial revolution from the eighteenth to the twentieth century.
In the United States, non-Marxist historians on the left have developed a related theory of inequality which attributes its growth not primarily to changes in systems of production but to processes of exchange and in particular to “market revolutions.” They believe that the effect of an expanding free market within a capitalist system was thought to cause a growth of inequality. The precise linkages were apt to be a little fuzzy, but in general it has been argued that the effect of “commercialization” has been to create larger and more integrated markets in which the rich became richer, and inequality increased.
Economic Models: Growth-Processes and the Kuznets Curve
A very different theory of inequality has been invented by neo-classical economists. It is called the Kuznets model, after the work of American economist Simon Kuznets. Like many econometric historians, Kuznets was interested primarily in the problem of economic growth and development, and studied changes in inequality primarily in relation to those processes. The Kuznets model hypothesized that as “traditional” agricultural economies developed into “modern” industrial systems, inequality at first increased and then declined in a curve that resembled an inverted U. Kuznets and his colleagues found many mechanisms to explain this pattern. One of them, which Kuznets himself suggested, was the role of intersectoral shifts. In early stages of development, some workers moved into more highly paid jobs in sectors of the economy which had higher productivity. Other workers remained behind, and inequality increased. In later stages of economic growth, workers who had been left behind also made that same sectoral transition, and inequality diminished. Another mechanism was demographic: increasing rates of population growth in early stages; declining rates thereafter. A third factor was an acceleration in later stages of education and economic skills. See Jeffrey C. Williamson and Peter H. Lindert, American Inequality, A Macroeconomic History [New York, 1980]; Jeffrey C. Williamson, Did British Capitalism
Breed Inequality? [Boston, 1985])
Cyclical Models: Life Cycle Theories
An interesting theory of inequality centers on individuals rather than economies. One such approach developed from the work of B. S. Rowntree on poverty in the city of York, England (Poverty, A Study of Town Life [London, 1899]). He found that distribution of income and wealth varied through the life cycle. Laborers in York lived through periods of poverty and comparative affluence, with poverty occurring in childhood, early adulthood and old age, and affluence in late youth and middle age. Other scholars have found different life-cycle rhythms of income and wealth for blue-collar and white-collar workers, and have linked this approach to differences of class, education, job-type, ethnicity, and race. These findings have been aggregated into macroeconomic theories that changes in age-composition, skill-distribution, and educational attainment have changed the distribution of wealth and income in entire social and economic systems.
Institutional Models:
The Welfare State and the Robin Hood Paradox
Historians commonly believe that laws, institutions, reform movements, and conservative counter-movements have made a major difference in the distribution of wealth and income. Most liberal textbooks in American history (which is to say, most textbooks) have been written around the belief that Franklin Roosevelt’s New Deal and Lyndon Johnson’s war on poverty caused an increase in equality, and that the Robber Barons and Republican presidents before 1932 and after 1968 caused inequality to grow. These ideas rest on the idea that laws and institutions make a difference.
A very different institutional model comes from economic historian Peter Lindert, who has framed the counterhypothesis called the “Robin Hood Paradox,” which holds that “across time and jurisdictions, redistribution toward the poor is least given when most needed . . . Robin Hood shows up least when needed most.” (“Toward a Comparative History of Income and Wealth Inequality,” in Brenner, Kaelbe and Thomas, eds., Income Distribution in Historical Perspective,” 226–29
Empirical Evidence
Which of these many theories of inequality is correct? Altogether, evidence now in hand is strong enough to support several generalizations
First, the uniformity models are mistaken. Pareto’s Law, Lassalle’s Conjecture and Bowley’s Law all derived from early data, mainly for the mid-nineteenth and early twentieth centuries. That era was a period of comparatively little change in wealth and income distribution and appeared to confirm these models. But subsequent research yielded very different results. More evidence accumulated from the 1930s to 1968; most of it found growing of equality in that period. Yet more data is now available from 1968 to 1996, and shows the opposite trend in that period: a rapid increase in inequality. Projects of historical research have been completed for earlier periods. By and large they find evidence of growing inequality in the late eighteenth and early nineteenth centuries, stability in the late nineteenth and early twentieth centuries, growing equality in the mid-twentieth century, and growing inequality thereafter. All of this evidence supports a firm conclusion. The history of inequality is the history of change.
Further, there is strong evidence that wealth and income distribution have varied broadly one culture to another, and that some of these relative differences have remained highly persistent through time, even as change has occurred everywhere in levels and trends. Even within the narrow limits of American history, for example, the range of regional and local differences in inequality is nearly as broad as the limits of possibility. In terms of Gini ratios (where .00 equals perfect equality and .99 represents perfect inequality), the first distribution of lands in Roger Williams’s Rhode Island Plantation briefly approached zero, but the distribution of land in Adams County, Mississippi, on the eve of the Civil War was above .95. Relative differences of that sort have persisted between northern and southern regions of the United States for two centuries. From these findings one may draw a second conclusion. Elements of cultural persistence have coexisted with patterns of change.
How do these combinations of change and persistence compare with leading theories of inequality? In general, one may say that most of the leading theorists of inequality have accurately described inequality-trends in the half-century or century before they wrote. But all were mistaken in building a universal theory on that narrow historical base. This conclusion holds for Malthus, Ricardo and Marx; for Lassalle, Pareto and Bowley; for Kuznets, Williamson and Lindert. All testified truly to their own immediate historical experience, but erred in over-generalizing to other periods.
It is well known, for example, that the relationship between population and wealth changed fundamentally just after Malthus published his work; that the relationship between capitalism and distribution was transformed after Marx. In the same way, the Kuznets-Williamson-Lindert inverted-U model appears to fit the facts from the mid-nineteenth to the mid-twentieth century, but not from the 1960s to our own time.
Other theories of inequality have been falsified by historical research. The institutional models fail the test of chronology. Inequality did not increase in the age of the Robber Barons. It did not diminish after 1968. Recent theoretical models of a market revolution as the driver of inequality during the nineteenth century fail every test, both for the timing of market-growth and inequality. The Robin Hood paradox works in the 1980s, but not in the 1930s. The idea that capitalism caused inequality is also incorrect in the same way: it works for some periods, but not for others. In terms of chronology the history of capitalism and the history of inequality do not coincide. In short, all of the theoretical models listed above are unsupported by historical evidence.
This evidence suggests the possibility of another theory. Let us look again at the descriptive patterns. In the past five centuries the predominant change pattern is not precisely linear or cyclical. Levels of inequality have tended to rise and fall in long wavelike movements. In what is now the northern United States, patterns appear to have been more or less as follows: 1630–1670, growing inequality; 1680–1730, growing equality; 1740–1840, growing inequality; 1850–1932, fluctuations on a fixed plateau; 1932–68, growing equality; 1968–96+, growing inequality.
Figure 5.07 summarizes many studies of wealth-distribution in the northern United States. It finds three periods of growing inequality which coincide with later stages of price revolutions and early years of price equilibria: 1630–1670, 1760–1850, and 1968–1996+. It also finds two periods of stability or increasing equality which coincide with the later phases of price equilibria and the early stages of price revolutions: 1680–1760, and 1860–1968.
All time series are analyses of estates in probate except Hingham (taxable wealth), and the U.S.A. (census data and household surveys). All are computed as Gini ratios except Hingham, which is the size-share of the top ten percent. A Gini ratio is a measure of distribution, which ranges from .00 (perfect equality) to .99 (perfect inequality, where the top percentile owns everything).
Sources include Jeffrey G. Williamson and Peter H. Lindert, American Inequality; A Macroeconomic History (Madison, 1964); Lee Soltow, “Distribution of Income and Wealth,” in Glenn Porter ed., Encyclopedia of American Economic History, III, 1087–1102; idem, Men and Wealth in the United States, 1850–1870 (New Haven, 1975); idem, Patterns of Wealthholding in Wisconsin since 1850 (Madison, 1971); W. I. King, Wealth and Income of the People of the United States (New York, 1915); Daniel Scott Smith, “Population, Family, and Society in Hingham. . . ” (diss., Univ. of California at Berkeley, 1973); Donald Koch, “Income Distribution and Political Structure in Seventeenth-Century Salem,” Essex Institute Historical Collections 105 (1969) 50–71; Jackson Turner Main, Society and Economy in Colonial Connecticut (Princeton, 1985).
The main lines of change in European data are more obscure. But in England, inequality increased during the sixteenth and early seventeenth centuries, diminished in the late seventeenth and early eighteenth centuries, increased again from the mid-eighteenth century to th
e mid-nineteenth century, fluctuated on the same plane circa 1850–1930, declined in the mid-twentieth century, and have been rising in the late twentieth century. In summary, British trends are broadly similar to those in the United States.
We find a wave pattern in the wealth-histories of both nations. These waves do not synchronize exactly with price-revolutions and price-equilibria. But if one lags price-movements against inequality-trends, then a correlation begins to emerge. In descriptive terms it might be summarized as follows. The later stages of every price revolution and the early stages of each equilibrium were periods when inequality increased. On the other hand, the latter stages of each equilibrium, and the early stages of each price revolution were marked by stability or decline in levels of inequality. These trends appear to have recurred in every price revolution since the late middle ages.
This descriptive pattern strongly suggests a theory of inequality. First, changes in relative returns to capital and labor were caused by the dynamics of price revolutions and price equilibria as discussed in the main body of this work. Second, changes in the distribution of income were caused by those prior changes in relative returns to labor and capital, lagged in time. Third, changes in wealth-distribution were caused by changes in income-distribution, also lagged in time. All of this would explain a correlation between price revolutions and inequality, but one that is offset in time, with strong inertial effects. This theory also suggests many obvious possibilities for the regulation of inequality. Here again, a wave-pattern is an opportunity for a policy-maker in a free society.
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