A cross-market model of income rank and lived purchasing power
This paper documents the calculator’s scope, source anchors, interpolation, top-tail treatment and uncertainty. The aim is not a spurious decimal-perfect global rank, but a reviewable estimate of income bands and lived purchasing power under explicit assumptions.
The model first harmonizes heterogeneous regional statistics into annual individual after-tax economic income. Official surveys anchor the middle; tax files and WID top shares constrain the upper range; adjacent anchors are joined in log-income/log-tail-probability space. Purchasing power is not reduced to one PPP divisor. Lower and middle incomes depend more on local housing and services, while travel, imported goods, luxury consumption and globally priced assets gain weight at high incomes. The conversion therefore moves smoothly from the PPP side toward market FX. Each regional income is then mapped into a common US lifestyle-equivalent dollar scale and pooled using the age-20+ population.
Population and common income definition
The unit is an adult individual, not a household. Annual after-tax economic income includes wages and bonuses, proprietor or owner distributions, dividends, interest, rent, and equity gains actually sold or settled during the year. Unrealized stock gains, private-company valuation changes and owner-occupied home appreciation are excluded. This places employees and business owners on one realized-resource measure without treating paper wealth as annual income.
Wages, business income, dividends, rent, interest, realized equity gains
Unrealized gains, home appreciation, other household members, wealth stock
Source years are normalized as closely as practical to roughly 2025 prices
Adult population and pooling weights
The pool does not give each market equal weight. It uses about 1.10bn adults in China, 260m in the US, 362m in the EU‑27 and 104m in Japan, for 1.826bn total. Japan is derived from the Statistics Bureau’s 2024 population and single-year age structure; the EU uses Eurostat population and age structure. Small changes in cutoff or population have modest middle-percentile effects but can matter in the extreme tail.
Adults age 20+ (estimated)
1.826 bnFpool(y) = Σr Nr · Fr(gr−1(y)) / Σr Nry is US lifestyle-equivalent income; gᵣ maps local after-tax income in region r to y; Nᵣ is the adult population.
The four adult populations are disjoint, so a pooled headcount must mathematically be their sum. The critical step comes first: every market gets a different local after-tax threshold that buys the same lifestyle y. Adults above those four purchasing-power-adjusted thresholds are pooled; local ranks from one nominal amount are never added.
How the four regional income ladders are built
China
P10–P90 is anchored mainly to NBS disposable-income groups and earnings data, transformed from household-survey concepts toward individual economic income. P95–P99 is adjusted with WID top shares, business income and the known direction of high-income survey undercoverage. Above P99, top shares and affluent-population counts constrain a Pareto tail that includes realized equity monetization.
United States
The middle is constrained by Census CPS/ASEC personal-income distributions and earnings data. Upper anchors rely primarily on IRS SOI adjusted-gross-income percentile tables, translated toward after-tax resources. AGI is not identical to economic income: business losses, capital gains and tax-exempt items create differences, so the P99+ range is treated as a band rather than a point truth.
European Union (27)
P10–P95 cross-checks EU‑SILC equivalized disposable income, the median, S80/S20 and full-time adjusted earnings. Household-equivalized measures are translated toward individual after-tax resources and aggregated with country population weights. The top uses WID European top-10% and top-1% shares with a Pareto tail. This is an EU‑27 curve, not Germany, France or another single country.
Japan
P10–P95 cross-calibrates the NTA 2024 private-sector salary survey (JPY 4.78m average gross pay for full-year workers; JPY 5.87m men and JPY 3.33m women) with household, population and employment structure, then translates toward after-tax personal resources using representative social insurance, national and resident taxes. P99+ uses high-income filing evidence, WID top shares and a Pareto tail. Japan’s older population makes pensions, part-time work and non-employment especially important at the lower end.
Published percentile anchors
Annual individual after-tax economic income. “—” means interpolation rather than a separately calibrated anchor.
| Percentile | China | United States | EU‑27 | Japan |
|---|---|---|---|---|
| P10 | ¥5,000 | $10,000 | €3,000 | ¥0.60m |
| P20 | — | — | €8,000 | — |
| P30 | ¥22,000 | $25,000 | €13,000 | ¥1.60m |
| P50 | ¥40,000 | $47,500 | €22,500 | ¥2.70m |
| P70 | ¥75,000 | $70,000 | €35,000 | ¥3.70m |
| P80 | ¥110,000 | $92,500 | €44,000 | ¥4.50m |
| P90 | ¥170,000 | $125,000 | €60,000 | ¥6.20m |
| P95 | ¥265,000 | $167,500 | €78,000 | ¥8.00m |
| P99 | ¥560,000 | $340,000 | €155,000 | ¥14.0m |
| P99.5 | ¥710,000 | $557,000 | €220,000 | ¥20.0m |
| P99.8 | ¥1.07m | $950,000 | €330,000 | ¥32.0m |
| P99.9 | ¥1.63m | $1.65m | €550,000 | ¥45.0m |
| P99.95 | ¥2.65m | $2.40m | €800,000 | ¥65.0m |
| P99.97 | ¥4.00m | $3.60m | €1.15m | ¥90.0m |
| P99.99 | ¥9.25m | $9.50m | €2.50m | ¥180m |
Interpolation, extrapolation and the top tail
Income is highly skewed at the top, so linear interpolation in money would materially understate the jump from P99.9 to P99.99. Between anchors, the model interpolates linearly between log(1+x) and log(1−p), where x is income and 1−p is the share above it. Each short segment therefore behaves like a local Pareto curve while remaining continuous at every anchor. Beyond the last anchor, the final two-point elasticity is extrapolated with conservative interface caps.
log(1 − p(x)) = log(1 − p₀) + t · [log(1 − p₁) − log(1 − p₀)]t = [log(1 + x) − log(1 + x₀)] / [log(1 + x₁) − log(1 + x₀)]Mostly official surveys
Surveys + tax files + WID
Tax files + top-share fit
Sparse samples + Pareto tail
Purchasing power: why one fixed PPP rate is insufficient
Official PPP compares the overall price of a representative basket and is useful for broad living-standard comparisons. Market FX governs imported goods, international travel, overseas education, luxury consumption and global assets. Within one country, the latter usually takes a larger share as income rises. The model therefore separates a local-price component from a globally priced component: lower incomes stay nearer the PPP side, while high incomes move progressively toward market FX.
Shares illustrate the basket logic, not a survey of each user’s spending. The final conversion uses the piecewise anchors described below.
log g(x) = [1 − w(x)] · log(x · κPPP) + w(x) · log(x · κFX) + c(x)w(x) rises with income; c(x) calibrates housing, after-tax scope and the lived basket. The live calculator does not apply this closed form mechanically: it uses piecewise anchors calibrated with this logic and joins them smoothly in log–log space.
2025 market annual average; Federal Reserve G.5A
2025 market annual average; ECB
Approx. 2025 market average; OECD PPP-side reference 94.68
Basket weights vary with income level
Sensitivity, uncertainty and interpretation
The broad P20–P95 ordering is most stable; exact P99.9+ thresholds are least stable. Four forces dominate: survey undercoverage of the rich, volatile realized gains, owner discretion across salary/dividends/retained profit, and large differences among EU member states. The pooled purchasing-power result is additionally sensitive to city, homeownership, household size and spending preferences.
Sources and reproducibility
The references prioritize official statistics, international methodology and public tax tables. Their statistical units are not naturally identical, so the anchors are cross-calibrated model inputs—not an “official answer” copied row by row from one table. Updating a source year requires jointly reviewing population, price base, after-tax translation and top shares.
- 01China NBS, 2025 household income↗
- 02World Inequality Database — China↗
- 03IRS Statistics of Income — percentile tables↗
- 04U.S. Census Bureau — CPS income data↗
- 05Eurostat EU-SILC methodology↗
- 06Eurostat, full-time adjusted salary 2024↗
- 07World Inequality Report 2026 — regional income inequality↗
- 08Eurostat purchasing-power parities↗
- 09OECD purchasing-power parity FAQ↗
- 10Federal Reserve G.5A exchange rates↗
- 11ECB USD/EUR reference-rate series↗
- 12Eurostat Demography of Europe 2026↗
- 13Japan NTA, 2024 private-sector salary survey↗
- 14Statistics Bureau of Japan, population estimates 2024↗
- 15Statistics Bureau of Japan, 2024 National Survey of Family Income, Consumption and Wealth↗
- 16OECD, Japan PPP and market exchange rates↗
- 17NBS expert explanation of the 600m-income statement↗