Tom Kwok

Income tax


Income tax in most territories in the world is collected based on a progressive tax system with higher tax rates for higher income earners.

This post presents plots for effective (i.e. average) personal income tax rates in selected territories in the world as of assessment year 2020. A plot visualizes the effective tax rates for all income amounts in a specific range for each territory. This is more informative than listing only a few specific income amounts and their corresponding effective tax rates for each territory as seen in a journalistic comparative analysis article found online.

Effective tax rate from tax brackets #

A visual explanation of the shape of the graphs of effective income tax rate against income amount, along with an explicit mathematical formula for effective tax rate is drawn out on a whiteboard, captured, cleaned and vector traced as follows.

My whiteboard explanation of the graphs of effective tax rate presented in vector graphics format

Assumptions and limitations #

Tax laws in different territories are complicated in implementation details. Some assumptions need to be taken for consistency.

The plots are meant to be for reference only. A direct comparison of a specific metric in different territories with vastly different social security systems and with currencies that have varying purchasing power parity would be over-simplistic.

In practical terms, the values of income tax rates given do not reflect the varying tax situations and law enforcement in different territories. For example, in mainland China, the income of only a small portion of the working population exceeded the allowance level, and a small portion of that actually paid income tax.

The income tax rates for only a limited number of territories are included in this study due to time constraint. For each territory, manual research is conducted to understand its income tax scheme from which a rates table and/or a formula for contributions is derived. There is no aggregated dataset of income tax schemes for different countries in the world that is currently publicly available.

Calculation and expression #

For each territory, the yearly tax bracket graduated rates sourced from the government website are applied on a range of yearly income amounts scaled by the latest exchange rates to compute an effective rate in percentages. The effective rates are plotted against equivalent monthly income amounts (yearly income amounts divided by 12) graphed with a line in a distinct named color.

In addition, for each territory, the rates for pension fund and unemployment insurance contributions from the employee, if applicable, are applied on the income amounts to compute an effective contributions rate and then a combined effective rate, which is the sum of (i) effective tax rate and (ii) effective contributions rate, graphed with a dashed line.

The percentage value levels computed are cross-checked with online tools found by searching for "net income calculator" for each territory.

A secondary x-axis scaled for a second currency is added on top border for convenience of reading.

Some territories #

A plot is generated for territories with low but non-zero income tax rates, including:

with the following notes.

Line plot of effective income tax rate against income in different territories

More territories #

A plot is generated for territories with higher income tax rates, including:

in addition to the territories mentioned previously.

Line plot of effective income tax rate against income in different territories

Higher income earners #

A plot with a larger range of income amounts is generated to show the highest rate levels possible for higher income earners, such as executives and celebrities.

Line plot of effective income tax rate against income in different territories

Plot by others #

While this sort of visualization seems to be uncommon, a similar graphic of effective tax rates found by searching for "tax curve".

Line plot of effective income tax rate against income in Hong Kong in 1998-1999
(Source: Hong Kong Government 1998-99 Budget)

Further work #

The income tax rate is a flat zero for some territories in the world, which would give an uninteresting plot. A negative income tax, which would give a more interesting plot, is not implemented in practice.

An interactive presentation of the plots is suggested to reduce clutter due to sometimes intersecting or overlapping lines, and to accommodate lines for rates with a different personal allowance level applied.