Glenn Firebaugh

Firebaugh summarizes the principles for good research in his book Seven Rules for Social Research.[2] The first rule is that "There should be the possibility of surprise in social research." Good research also will "look for differences that make a difference" (Rule 2) and "build in reality checks" (Rule 3). Rule 4 advises researchers to replicate, that is, "to see if identical analyses yield similar results for different samples of people" (p. 90). The next two rules urge researchers to "compare like with like" (Rule 5) and to "study change" (Rule 6); these two rules are especially important when researchers want to estimate the effect of one variable on another. The final rule, "Let method be the servant, not the master," reminds researchers that methods are the means, not the end, of social research; it is critical from the outset to fit the research design to the research issue, rather than the other way around.

Inequality indices are scalar measures designed to quantify the degree of inequality in distributions of some valued good, such as income. Researchers often use inequality indices to compare the degree of inequality across populations (for example, to determine if there is greater income inequality in California than in Texas, or in Brazil versus South Africa). The best-known inequality index is the Gini coefficient; others include the Atkinson measure, the Theil index, the Hoover index (a.k.a. Robin Hood index), and many others.

Firebaugh has shown that standard inequality indices reduce to a convenient common form.[3] He begins by noting that perfect equality exists when the inequality ratio, r_j = X_j / ${\displaystyle \scriptstyle {\overline {X}},}$ equals 1.0 for all j units in some population (for example, there is perfect income inequality when everyone’s income X_j equals the mean income ${\displaystyle \scriptstyle {\overline {X}}}$, so that r_j = 1.0 for everyone). Inequality, then, refers to deviations of the r_j from 1.0; the greater the average deviation, the greater the inequality. Inequality indices reflect that fact because they have this common form:

Inequality Index = ${\displaystyle \Sigma _{j}p_{j}f(r_{j}),}$

where p_j weights the units by their population share (necessary in a cross-country analysis, for example, since countries vary in population), and f(r_j) is a function of the deviation of each unit’s r_j from 1.0, the point of equality. The important insight of Firebaugh’s general inequality equation is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the r_j) from 1.0.

Firebaugh was among the first to note that income inequality for the world as a whole leveled off in the last decades of the 20th century, after rising for more than two centuries. Firebaugh describes this important turning point in a 1999 lead article in the American Journal of Sociology[4] and in a 2003 book.[5] While global income inequality is massive, it has remained relatively steady or declined somewhat in recent years due to rapid income growth in China and India. Firebaugh’s findings challenged earlier claims that global income inequality continues to rise rapidly. According to Firebaugh, that claim was based on a flaw: Each country was assigned equal weighting, despite vast differences in population size. When populous countries such as China and India are given their due weight, the data show that global income inequality has not been rising sharply, and most likely is not rising at all. Firebaugh’s findings have been verified by others.[6] As a result, earlier claims by the United Nations[7] and the World Bank[8] of rapidly rising global income inequality have been modified in their more recent publications.

Researchers are said to commit the ecological fallacy when they make untested inferences about individual-level relationships from aggregate data. It is called a fallacy because it is based on the problematic assumption that relationships at one level of aggregation also hold at another level of aggregation.[9] To illustrate, consider the fact that George Wallace, a four-term governor of Alabama and well-known segregationist who ran as a third-party candidate well in the 1968 US Presidential election, received a higher share of votes in regions with higher percentages of blacks.[10] From this one might erroneously conclude that blacks were disproportionately inclined to vote for Wallace (post-election surveys showed that, while one in eight whites voted for Wallace, virtually no blacks did).[11] Firebaugh has contributed to this literature by delineating theoretical conditions or rules under which it is possible to infer individual-level relationships from aggregate data.[12] These conditions are important because researchers are subject to the ecological fallacy in virtually all the social and behavioral sciences - from history to political science to epidemiology – since individual-level data often are unavailable.