Economics & Market Microstructure
Suits Index of Tax Progressivity (S) Formula: Tax-vs-Income Trapezoidal Integral
Calculate Daniel B. Suits’s (1977) Tax Progressivity Index S = 1 - SUM((T_i + T_{i-1}) * (Y_i - Y_{i-1})) across income brackets (-1 regressive to +1 ultra-progressive, 0 flat tax) directly from cumulative income and tax shares.
Why US Congressional & State Revenue Offices love Suits’s Index: it plots Cumulative Tax directly against Cumulative Income!
Published in the same year as Kakwani (1977), Daniel B. Suits (1977, American Economic Review) formulated a Gini-style tax progressivity index that skips population percentiles entirely and plots Cumulative Share of Total Tax Burden T(Y) (vertical axis, 0 to 1) directly against Cumulative Share of Pre-Tax Income Y (horizontal axis, 0 to 1)! Under a strictly flat proportional tax, 30% of income pays 30% of tax, tracing the 45-degree diagonal (Area L = 0.50 -> S = 0)!
Across k ordered income brackets with cumulative income shares 0 = Y_0 < Y_1 < ... < Y_k = 1 and cumulative tax shares 0 = T_0 <= T_1 <= ... <= T_k = 1, trapezoidal integration gives 2 * L = SUM_{i=1..k} (T_i + T_{i-1}) * (Y_i - Y_{i-1}) = SUM_{i=1..k} (2 * T_{i-1} + t_i) * y_i (where y_i and t_i are each bracket’s incremental shares of total income and total tax!), and Suits’s Index is S = 1 - 2 * L! S ranges cleanly from -1.00 (entire tax paid by the poorest dollar of income) through 0.00 (proportional flat tax) to +1.00 (entire tax paid by the very top income)!
| Tax Schedule Across 4 Income Groups (y = [10%, 20%, 30%, 40%]) | Tax Shares t = [t_1, t_2, t_3, t_4] | Suits Progressivity Index S = 1 - 2*L |
|---|---|---|
| Progressive Graduated Income Tax | [2%, 10%, 28%, 60%] | +0.2540 (Progressive: S > 0) |
| Proportional Flat-Rate Payroll Tax | [10%, 20%, 30%, 40%] (t_i = y_i) | 0.0000 (Exact Flat Tax Benchmark) |
| Regressive Per-Pack Excise Tax | [22%, 28%, 28%, 22%] | -0.2620 (Regressive: S < 0) |
Exact Trapezoidal Suits Tax Progressivity Index S = 1 - SUM((T_i + T_{i-1}) * y_i)
Computes S in [-1, +1] across ordered income-bracket amounts B2:B5 and tax-paid amounts C2:C5 using cumulative tax shares D2:D5.
=IF(OR(SUM(B2:B5) <= 0, SUM(C2:C5) <= 0, MIN(B2:B5) < 0, MIN(C2:C5) < 0), "Invalid Income or Tax Bracket Totals", ROUND(1 - ((D2) * (B2 / SUM(B2:B5)) + (D2 + D3) * (B3 / SUM(B2:B5)) + (D3 + D4) * (B4 / SUM(B2:B5)) + (D4 + D5) * (B5 / SUM(B2:B5))), 4))Suits Fiscal Incidence Classification (Progressive S > 0 / Proportional S = 0 / Regressive S < 0)
Classifies the tax instrument from its Suits Index value.
=IF(OR(SUM(B2:B5) <= 0, SUM(C2:C5) <= 0), "Invalid Totals", IF(ROUND(1 - ((D2) * (B2 / SUM(B2:B5)) + (D2 + D3) * (B3 / SUM(B2:B5)) + (D3 + D4) * (B4 / SUM(B2:B5)) + (D4 + D5) * (B5 / SUM(B2:B5))), 4) > 0.01, "Progressive Tax (Suits S > 0)", IF(ROUND(1 - ((D2) * (B2 / SUM(B2:B5)) + (D2 + D3) * (B3 / SUM(B2:B5)) + (D3 + D4) * (B4 / SUM(B2:B5)) + (D4 + D5) * (B5 / SUM(B2:B5))), 4) < -0.01, "Regressive Tax (Suits S < 0)", "Proportional / Flat Tax (Suits S ≈ 0)")))Try the example
Use the original values or change them to test your understanding.