Equivalence scales are routinely applied to adjust the income of households of different sizes and compositions. Because of their practical importance for the measurement of inequality and poverty, a large number of methods for the estimation of equivalence scales have been proposed. Until now, however, no comprehensive comparison of current methods has been conducted. In this paper, we employ German household expenditure data to estimate equivalence scales using several parametric, semiparametric, and nonparametric approaches. Using a single dataset, we find that some approaches yield more plausible results than others while implausible scales are mostly based on linear Engel curves. The results we consider plausible are close to the modified OECD scale, and to the square root scale for larger households.

Empirically analyzing household behavior usually relies on informal data preprocessing. That is, before an econometric model is estimated, observations are selected in such a way that the resulting subset of data is sufficiently homogeneous to be of interest for the specific research question pursued. In the context of estimating equivalence scales for household income, we use matching techniques and balance checking at this initial stage. This can be interpreted as a non-parametric approach to preprocessing data and as a way to formalize informal procedures. To illustrate this, we use German micro-data on household expenditure to estimate equivalence scales as a specific example. Our results show that matching leads to results which are more stable with respect to model specification and that this type of formal preprocessing is especially useful if one is mainly interested in results for specific subgroups, such as low-income households.

Income inequality and poverty risks receive a lot of attention in public debates and current research. To make income comparable across different types of households, applying the “(modified) OECD scale” – an equivalence scale with fixed weights for each household type – has become a quasi-standard in research. Instead, we derive a base-dependent equivalence scale allowing for scale weights that vary with income, building on micro-data from Germany. Our results suggest that appropriate equivalence scales are much steeper at the lower end of the income distribution than they are for higher income levels. We illustrate our findings by applying them to data on family income differentiated by household types. It turns out that using income-dependent equivalence scales matters for applied research on income inequality, especially if one is concerned with the composition, not just the size of the population at poverty risk.

Most equivalence scales that are applied in research on inequality do not depend on income, even though there is strong empirical evidence that equivalence scales are actually income-dependent. This paper explores the consistency of results derived from income-independent and income-dependent scales. We show that applying income-independent scales when income-dependent scales would be appropriate leads to violations of the transfer principle. Surprisingly, there are some exceptions, but these require unrealistic and strong assumptions. Thus, the use of income-dependent equivalence scales almost always leads to different assessments of inequality than the use of income-independent equivalence scales. Two examples illustrate our findings.

SOEPpapers on Multidisciplinary Panel Data Research at DIW Berlin This series presents research findings based either directly on data from the German SocioEconomic Panel study (SOEP) or using SOEP data as part of an internationally comparable data set (e.g. CNEF, ECHP, LIS, LWS, CHER/PACO). SOEP is a truly multidisciplinary household panel study covering a wide range of social and behavioral sciences: