This post is taken from a longer study on the state of inequality in Germany commissioned by Forum New Economy. The full study by Charlotte Bartels (DIW) and Carsten Schröder (DIW) is titled „Income, consumption and wealth inequality in Germany: Three concepts, three stories?„.
When the media picks up results of a research study on inequalities, they usually condense the evidence into headlines claiming that, for example, “Inequality in Germany has increased.” In the public debate, the various working assumptions underlying the measurement of inequalities are often ignored. Each assumption, discussed below, may crucially affect the findings provided. In addition to the aforementioned obvious working assumptions regarding the choice of the time and region of analysis, the measurement of inequalities requires choices by the researcher (see Cowell, 2009):
- Choice of the inequality index. Many studies use the Gini coefficient to measure inequality. The index measures twice the area between the Lorenz curve and the equal-distribution line. It has particular properties. The index bounds from zero to one. It is transfer sensitive, meaning that the Gini index decreases if, through a mean-preserving transfer, income is shifted from the top to the bottom of the distribution. It is a relative measure, meaning that a multiplication of all incomes by the same positive factor leaves the Gini unchanged. Many indices share the same properties. The Theil index and the Atkinson index are examples. In empirical applications, the problem arises that although the indices share the same properties, they do not necessarily lead to the same conclusions regarding e.g., intertemporal changes in inequality or inequality comparisons across different societal groups. Different patterns may emerge because inequality measures are more or less sensitive toward changes in specific parts of the distribution, like the top or the middle. Other indices have different properties. For example, the generalized Gini index is an absolute measure, meaning it varies with average income. Of course, the choice of an absolute or relative measure changes the meaning of the findings.
- Choice of the focal variable. Many indicators of material well-being exist beyond the three most frequently used indicators of income, expenditure, and wealth. The relative advantages and disadvantages that people have, compared with each other, can be judged in terms of many different other variables, e.g. utilities, human capital, liberties, rights, quality of life, and so on. One may also argue that inequalities of opportunities (early in life) are more important than inequalities of outcomes. In sum, the plurality of variables on which we can focus (the focal variables) when evaluating inequality requires a decision regarding the perspective adopted (Sen, 1992).
- Choice of the reference unit. The reference unit is the economic entity for which the resources are measured. This can be an individual, if we are concerned with the distribution of individual earnings from employment. This can also be the household unit, if we are concerned with the distribution of disposable income, which is generated and consumed jointly at the household level. It can also be a taxpayer as determined by a legal definition. Certainly, inequality will vary with the choice of the reference unit: It makes an enormous difference when computing the Gini index.
- Adjustment for differences in needs. If references differ in composition, an identical level of material resources, say in terms of income, will imply different living standards: For example, if both a couple with two children and a single adult household dispose of the same monthly income of 2,000 euros, the material well-being of the single will be higher than that of the family. To obtain a meaningful measure of material well-being, resources must be adjusted for differences in needs. Equivalence scales serve for this adjustment. The most prominent equivalence scale is the so-called OECD modified equivalence scale. It assigns a weight of 1.0 to the first adult in the household, a weight of 0.5 for each additional adult, and a weight of 0.3 for each child. Hence, the equivalence scale for a single is 1.0, the equivalence scale for a couple with two children is 2.1, and both are equally well-off if the former has an income of 1,000 euros and the latter an income of 2,100 euros. In each case, the equivalent income is 1,000 euros/1 = 2,100 euros/2.1 = 1,000 euros.
- Weighting of reference unit. If all reference units are of equal size, the weighting of each unit should be the same as there is no reason to argue that one unit is more important than another (the so-called axiom of anonymity). For example, if we are concerned with individual workers, each worker should receive the same unit weight, a weight of 1. However, if we are concerned about households and agree with the principle of normative individualism, households should not have the same weight but each should be weighted by the number of individuals within the household unit. Thus a single adult household should receive a weight of 1.0 and a couple with two children a weight of four. As an example, suppose disposable equivalent income is 1,000 euros for a single and 2,000 euros for a couple. This results in a size-weighted equivalent-income distribution of .
- Comprehensiveness of the measure. Even after the choice of a particular focal variable, further issues remain. Assume the focal variable is disposable income. Should we consider the value of home production? Should we consider the value of non-cash transfers (e.g., free education opportunities)? If the focal variable is consumption, how should we deal with expenditures for durable goods (depreciation), or comparisons of housing-related costs between owner and tenants?
- Data source. Since the new millennium, research is benefitting enormously from advancements in data availability. For example, in Germany, researchers can not only choose between both various survey datasets (like the Income and Expenditure Survey or the German Socio Economic Panel (see Goebel et al., 2019)), but also administrative social security and tax datasets. Each data source has its comparative advantages and limitations. For example, survey data are usually easier to access and provide a much wider spectrum of variables – not only about the household context but also about various life domains. However, survey data suffer from item and ((partial) unit) non-response as well as other measurement issues (e.g., recall bias). The key argument made in favor of administrative data is its high validity and large sample sizes. As a downside, administrative data provide only selective and limited sets of variables (at least in Germany) and encompass only information on the relevant population (e.g., income-taxpayers).
- Data preparation. The analysis of the data itself requires further choices by the researchers. How should we deal with top/bottom coded data or if data are censored? What is the appropriate strategy if information in variables seems implausible (negative disposable income) or is missing?
 The above explanation ignores the issue of frequency weights here. Scientific surveys, however, usually provide frequency weights to produce generalizable statistics for the overall population. Then the unit weight should be multiplied with the unit-specific frequency weight.