The personal income tax is the workhorse of redistribution in rich countries and a narrow, troubled instrument in most poor ones. This module covers how it is designed — what to tax, at what rates, from what threshold — and why the same tax that collects a third of revenue in Europe collects a sliver in much of Africa.
The base: what is income?
The Haig-Simons definition
The comprehensive (Haig-Simons) definition: income = consumption + the change in net worth over the period. In principle this captures wages, business profits, interest, dividends, rent, capital gains, and even imputed income (the rent you save by owning your home). It is the benchmark of a 'complete' income tax. Every real income tax departs from it — excluding capital gains until realised, exempting imputed rent, taxing some income schedularly — and each departure is a policy choice with efficiency and equity consequences. Knowing the benchmark lets you see what a system has chosen to leave out.
Schedular versus global
A global income tax pools all of a person's income and applies one progressive schedule to the total. A schedular system taxes different income types (employment, business, rental, investment) separately, often at different rates and via different mechanisms. Most systems are hybrids. Developing countries lean schedular because it allows withholding at source on each stream (the only way to collect from a population that won't file), at the cost of horizontal equity (two people with the same total income pay differently depending on its composition) and opportunities to recharacterise income into the lowest-taxed schedule.
The rate schedule
Three design levers: the threshold (the tax-free allowance below which no tax is due — sets who is in the net and protects subsistence income), the marginal rate schedule (the bracket rates, which determine progressivity), and the top rate and where it bites. Marginal rates (the rate on the next shilling) drive behaviour; average rates (total tax ÷ total income) drive how much is paid and the system's progressivity. Confusing the two is the most common public error about income tax ('moving into a higher bracket' never lowers take-home pay, because only the income within the bracket is taxed at the higher rate).
Optimal rates and the elasticity of taxable income
The Saez top-rate formula
Emmanuel Saez (2001) gave the revenue-maximising top marginal rate: τ* = 1 / (1 + a · e) • a = the Pareto parameter of the top of the income distribution (how thick the tail is; typically ~1.5–2) • e = the elasticity of taxable income (ETI) — how much reported taxable income falls when the net-of-tax rate rises by 1% The ETI is the key sufficient statistic: it captures all behavioural responses (real labour supply, but also avoidance, evasion, and recharacterisation) in one number. A high ETI (lots of avoidance) means a low revenue-maximising rate; a low ETI means you can tax the top heavily without losing revenue. Crucially, the ETI is not a constant of nature — it depends on the tax base and enforcement. Broaden the base and close avoidance routes, and the ETI falls, so the economy can sustain higher rates. Design and enforcement determine the trade-off, not just taste.
Why the developing-country base is narrow
- Informality — most workers are self-employed or in informal firms with no payroll, no records, and no withholding agent, so they are effectively outside the income tax. The tax falls almost entirely on formal-sector employees (PAYE) and a few large firms.
- The 'missing middle' — small formal firms and self-employed professionals under-report; the income tax catches wage-earners (whose tax is withheld and third-party-reported) far more effectively than the self-employed (who self-report), creating horizontal inequity.
- Agriculture — a large share of the population and often lightly taxed or exempt for political and administrative reasons.
- The result — personal income tax in many African countries is a tax on the formal salariat, not a broad-based instrument, which limits both its revenue and its redistributive reach and concentrates the burden on a visible, organised group (the politics of which the final module takes up).
Exercise
A country is debating raising its top marginal income-tax rate from 30% to 40%. Treasury wants the extra revenue; business groups warn of capital flight and reduced effort. (1) Use the Saez formula to frame the debate — what would you need to know to estimate the revenue-maximising rate? (2) Suppose studies suggest a Pareto parameter of 2 and an ETI of 0.5; compute the revenue-maximising top rate and interpret it. (3) The ETI is high partly because the rich can shift income into a lightly-taxed corporate or capital schedule. What policy change would lower the ETI, and how does that change the answer? (4) Connect the narrow-base problem: why might raising the top PAYE rate be both the easiest and the least broadening way to raise revenue?