Rising mean incomes for whom?

Not everybody is benefiting equally from rising mean incomes. We discuss the mean-income population share (MPS), the population percentage of earners below mean income, whose evolution can capture how representative rising mean values are for middle income households. Tracking MPS and its associated income share MIS over time indicates to what extent economic growth is inclusive of both the middle and the bottom of the income distribution. We characterize MPS and MIS analytically under different growth scenarios and compare their parametric estimation using micro-level and grouped income data. Our empirical application with panel data of 16 high- and middle-income countries shows that in the last decades rising mean incomes have mostly not favored middle income households in relative perspective, while the overall welfare effects of the changes in MPS and the correlation structure with the Gini coefficient are mixed.

-1 shows the countries and years used in our analysis. The number of observation years ranges between 8 (Denmark, Finland) and 26 (Germany). But thanks to the wave availability restriction imposed, they all span the period from the 1980s to the 2010s, allowing us to analyze the development over these decades. Table S-2 to Table S-17 show M P S, M IS = L(M P S) and the Gini coefficient computed for all available years per country. We do this both for total household income and disposable household income. In both cases, equivalized income is used, hence, we divide household income by the square root of the number of household members.
Following the literature, we also weight observations by the number of household members times household weights. There are a couple of countries which show marked increases in both M P S and the Gini coefficient, such as Germany, the US, and Australia. But in some other countries, such as Norway, Denmark, and Canada, M P S increased even though the Gini coefficient stayed relatively constant. In the Netherlands, M P S even decreased, a development that is not visible based on the Gini coefficient. M IS does not show pronounced changes over time in many countries. If M P S rises and M IS stays constant, such as in the US, Germany, and Finland, there are more households below the mean but their share of total income has not increased, indicating that they are relatively worse off. The tables show that the Gini coefficient based on disposable income is typically considerably lower than based on total household income, as the state redistributes from the top to the bottom. As discussed in the article, the differences between total and disposable income are only marginal for M P S, because middle-class households around the mean are often not affected as strongly by redistribution. Table S-18 provides the growth rate of mean income g µ , the growth rate of mean income for all individuals below the mean, g subµ , as well as distributional metrics between the first and last available year. We can see that the group-specific mean income of individuals below national mean increased more than national mean income for both gross and disposable incomes in three countries (Denmark, Mexico, and Poland), while both M IS and M P S increased in Denmark and Poland, and decreased in Mexico. So individuals below mean income were relatively better off in the three countries because their M IS increased more than M P S did. But in the other 13 countries M P S always increased more than M IS did, making individuals at the middle and the bottom of the distribution worse off. Table S-19 is based on the summary statistics of the 5-percentile income shares of each country. We find that the largest variation always happened to the top 5% income share, and the second largest happened to either the bottom or the second-highest (top 19th) 5% income share. We also look at the summary statistics of the interval percentiles between M IS and the bottom 6 decile income shares including M IS itself, and find that the largest variation happened to either M IS or the interval percentile between M IS and the bottom 60% income share. The second largest variation happened to the interval percentiles between M IS and either the bottom 5% income share or the bottom 50% income share.
The following three tables provide robustness checks to the panel data analysis in the paper. Table S-20 reruns the panel regressions of changes in M P S and M IS on mean income growth, both contemporaneously and with a lag. The lag is statistically insignificant in most specification, yielding no evidence for a delayed impact of growth on M P S and M IS. The main coefficients tend to change very little with the inclusion of the lags. Table S-21 and Table S-22 rerun the panel regressions including a country group dummy. It is remarkable that the country group dummies capture a lot of variation otherwise contained in the country fixed effects, hinting to the importance of regulatory, welfare and labor market regimes that distinguish the country groups.
While the paper used M P S and M IS as the dependent variables, Table S-23 considers the impact of mean income changes on the Gini coefficient, the skewness and the Pietra index instead. Most of the results are insignificant when the Gini coefficient and the skewness are used. The Pietra index shows similar reactions as M P S and M IS, which makes sense as they are components of the Pietra index. Table S-24 to Table S-27 show how well the development of M P S based on disposable income can be approximated by eight different parametric forms. For each country and year, 5-percentile income shares are used (5%, 10%, 15%...), mimicking the grouped-data available in many cross-country data sets. The eight parametric LCs from Table 2 in the paper (Lognormal, Chotikapanich, Pareto, Rohde, Weibull, Wang/Smyth, Villaseñor/Arnold and Kakwani) are fitted to these 20 data points. Based on their mean squared error minimizing parameter(s), these forms imply a particular M P S value, which one can compute with the formulas from Table 3 in the paper. Here we present the M P S implied by all the parametric forms, together with the empirical M P S, highlighting in bold which form comes closest to the empirical value. We can see that there is a lot of heterogeneity between the parametric functions in terms of their ability to capture the empirical M P S. The Pareto LC typically implies M P S values which are too high, while the Lognormal-implied ones often lie below the empirical values. Many of the other forms come quite close and in particular the Rohde and Wang/Smyth LCs perform best in capturing the evolution of M P S in many countries. As described in the article, the Kakwani LC clearly dominates the other forms in terms of fit at the 20 percentile points, but we see a different picture when it comes to representing M P S. Researchers choosing parametric LCs should take care.

Table S-18: Growth Rates of Mean Incomes and Distribution Metrics
Country Gross income data Disposable income data g µ g subµ g M P S g M IS g Gini g µ g subµ g M P S g M IS g Gini   IL 2010, MX 1994, and PL 1995 g µ is the growth rate of national mean income, g subµ is the growth rate of mean income for individuals below mean income. The left 5 columns are calculated from gross income data, and the right 5 columns are from disposable income data.   Notes: Standard errors are in parentheses. Compared to the main regressions in the text, these regressions include the lagged value of mean income growth. Significant at: * p < 0.10, * * p < 0.05, * * * p < 0.01. Notes: Standard errors are in parentheses. The country groups captured by the dummy are anglo-saxon (AU, CA, UK, US), nordic (DK, FI, NO), mediterranean (ES, IL, IT), and as the reference category the diverse group of remaining countries (DE, LU, MX, NL, PL, TW). Significant at: * p < 0.10, * * p < 0.05, * * * p < 0.01.  Notes: Standard errors clustered at the country level are in parentheses. Significant at: * p < 0.10, * * p < 0.05, * * * p < 0.01.      Notes: The table is the continuation of Table S-24.