# **Appendix A: Methodological details**

## **A.1 Tabulations by National Statistical Offices**

For Australia, we use data on income growth by quintile from Table 2 of Australian Bureau of Statistics (2021) and apply these growth rates to the 2019 welfare vector for Australia. The data from the Australian Bureau of Statistics reflects gross equivalized income while the 2019 welfare vector we use reflects per capita disposable income, creating an inconsistency between our 2019 and 2020 welfare vectors. The Australian Bureau of Statistics (2021) only makes growth rates available comparing the second half of 2020 with the second half of 2019. We do not have data from the first half of 2020.

For Canada, we rely on growth rates of disposable income by quintile for 2020 (Statistics Canada 2022). Though the growth rates use equivalence scales, we apply them to our 2019 welfare vector that is per capita based. The growth rates are nominal, so we deflate them all with the CPI.

In China we rely on growth rates in per capita disposable income of rural/urban households by quintile (Table 6-3 and 6-12 in National Bureau of Statistics of China 2022). We face two challenges when using this information: (1) the quintiles are created at the household level in contrast to our 2019 welfare vector for China which is at the individual level, and (2) we use consumption data for China, for which no quintile tabulation is published. We ignore the first issue and match the growth rates implied by each quintile to the 2019 distribution for China. Since the National Bureau of Statistics of China (2021) publishes _mean_ growth rates of consumption by urban/rural areas, we subsequently scale the urban/rural vectors to match the growth rates in consumption in 2020. We thus assume that the differences in growth rates along the distribution are the same whether income or consumption is used.

For Japan, we use quintile-level data on the growth in disposable income per capita from Table 22-1 of the 2021 and 2022 Statistical Yearbook (Statistics Japan 2022). The quintiles rank households, not individuals, and are only available for “workers’ households” and hence lack data for a certain part of the population.

For the Republic of Korea, we rely on annual growth rates in disposable income by quintile from Statistics Korea (2021). These growth rates are reported four times for each quarter of 2020, each comparing the income to the same quarter of the previous year. We factor data in from all four quarters.

For the United Kingdom, we use information on mean disposable income by decile from Table 14 of Office of National Statistics (2022). The means are expressed in UK fiscal years rather than calendar years. We create quarterly decile means by scaling the fiscal year means in a manner such that the overall quarterly growth rate in real disposable income from Office of National Statistics (2022b) is respected, and then convert these quarterly means to calendar averages.

For the United States, we use data on the household-level changes in post-tax income shares by quintile and for the median household (Table C-1 and C-3 in Shrider et al. 2021). To apply this data, we assume that the changes also apply at the individual level, i.e. that the growth 36