## htnea2025007 — How to Summarize and Interpret Income Tax Schedules

## Source details

**Canonical URL:** [htnea2025007 — How to Summarize and Interpret Income Tax Schedules](https://www.imf.org/-/media/files/publications/howtonotes/2025/english/htnea2025007.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/howtonotes/2025/english/htnea2025007.pdf.md)
- [Structured JSON version](/-/media/files/publications/howtonotes/2025/english/htnea2025007.pdf.json)

---

### Overview and purpose
- IMF | How to Notes NOTE/2025/007, authored by Alexander Klemm, dated September 2025.
- Purpose: describe how most features of an income tax system can be summarized as a combination of lump sums and marginal tax rates and plotted in a summary chart to aid understanding of tax reforms and avoid unintended humps or notches.
- Scope focus: the second step in applying an income tax—the application of the tax rate schedule (allowances, credits, rates)—while noting the first step (defining the tax base) remains important.

### Key concepts: average and marginal tax rates
- Definitions:
  - Average tax rate = total amount of tax paid as a share of total income.
  - Marginal tax rate = amount of tax paid on one additional unit of income.
- Roles:
  - Average tax rate: welfare comparisons across income groups; participation decisions at the extensive margin.
  - Marginal tax rate: intensive-margin decisions (work an extra hour, supply more effort); compliance and declaration decisions.

### Economic theory and practical interpretation
- Theoretical effects:
  - Raising marginal tax rates reduces labor supply via the substitution effect.
  - Raising average tax rates can increase labor supply via the income effect.
  - Most feasible reforms that raise average tax rates will also raise at least some people’s marginal tax rates.
- Robust bounds and shapes:
  - Optimal marginal tax rate between 0 and 100 percent.
  - Optimal marginal tax-rate schedule is U-shaped (Diamond and Saez 2011): relatively high at low and high incomes, relatively low at middle incomes.
  - When analyzing tax systems in isolation, expect a rising marginal tax rate schedule rather than a U-shape.

### Practical pitfalls and common confusions
- Interactions:
  - Personal allowances deductible before rate application effectively increase the thresholds used for the rate structure.
  - Tax credits, surtaxes, and benefit withdrawals can create complex effective tax-rate patterns.
- Policy-design pitfalls:
  - Phasing out allowances or child credits above a threshold can create nonmonotonic marginal-rate patterns (humps, notches).
  - Increasing personal allowances often yields the greatest monetary benefit to taxpayers in the highest tax bracket.

### Method and structure recommended
- Method: summarize complex tax (and some social security/welfare) systems using charts of marginal and average tax rates as a function of income to reveal unexpected effects and provide a factual basis for debate.
- Structure of the note: “Principles,” “Some Applications,” “Limitations,” and “Conclusions.”

---

### Box 1 — Practical steps to construct marginal and average tax charts
- Axes and ranges:
  - Plot income on horizontal axis (typically local currency units) and tax rates on vertical axis (percent).
  - No income-distribution data required; choose income range starting at zero and ending above the highest income threshold.
  - If highest threshold is extreme, consider multiple charts; if top threshold is low, show income up to at least the median income.
- Granularity and calculation:
  - Split chosen income range into sufficiently granular steps (example used: 1000 income steps).
  - For complex systems, compute tax liability at each income; approximate marginal rate by difference in tax liability between adjacent incomes divided by incremental income.
  - Average tax rate = tax liability / income.

### Features to include and modeling principles
- Rate structures (as bands/brackets with lower and upper thresholds); flat rates require no thresholds.
- Mechanisms leaving some income untaxed:
  - Exemption (personal allowance), zero-rate bracket, tax credit, refundable tax credit, universal income.
- Modeling principle:
  - Lump-sum items (refunds, universal income, head taxes) affect average tax rates but not marginal rates.
  - Everything else can be modeled as marginal tax rates (including withdrawals of credits/benefits).

### Illustrative baseline progressive system (Table 1)
- Thresholds and rates (percent of GDP per capita; percent):
  - Lower Threshold 0, Upper Threshold 30, Tax Rate 0
  - Lower Threshold 30, Upper Threshold 100, Tax Rate 10
  - Lower Threshold 100, Upper Threshold 200, Tax Rate 20
  - Lower Threshold 200, Upper Threshold (blank), Tax Rate 30

### Illustrative simple systems and lessons
- Flat tax: statutory, marginal, and average rates identical.
- Flat rate with personal allowance example: tax rate 25 percent and tax-free allowance of 30 percent of GDP per capita.
  - Average tax rate rises for incomes exceeding the personal allowance.
- Notches:
  - Notches (sudden loss of benefits or sudden tax jumps) can produce effectively infinite marginal tax rates at the discontinuity.
  - Illustrative notch: personal allowance lost at 300 percent of GDP per capita.
    - Person just below 300 percent of GDP per capita has post-tax income of 243 percent of GDP per capita.
    - Increasing earnings to meet the threshold reduces net income to 234 percent of GDP per capita.
    - Gross income must rise to at least 313 percent of GDP per capita to recover the loss.
  - Policy implication: notches create major disincentives and are best avoided.

### Smoothing withdrawals and top-rate alternatives
- Gradual withdrawal example: allowance withdrawn over incomes from 300 to 400 percent of GDP per capita.
  - Causes a finite increase in marginal tax rate (example increase of 9 percentage points in the illustrative case).
  - Marginal rate jumps then falls back; average tax rate rises without jumps.
- Alternative: introduce a higher top tax rate (example top rate set at 35 percent at 300 percent of GDP per capita).
  - Revenue-neutral top-rate calculation requires income-distribution data; the illustrative 5 percentage point difference is not a general rule.
- Comparative judgment:
  - Sudden removal, gradual withdrawal, and new top rate produce different marginal-rate shapes.
  - An additional top rate generally avoids jumps or reversals and yields a more sensible schedule.
  - Economic theory suggests marginal tax rates should rise with income; temporary humps are hard to justify.

### Personal allowances, zero-rate bands, and tax credits — plotting rules and policy-equivalence caveat
- Plotting rules:
  - Zero-rate band: chart directly from thresholds and rates.
  - Personal allowance: increase all higher rate thresholds by the allowance amount when plotting.
  - Nonrefundable tax credit: divide the credit by the tax rate before plotting the tax-free amount.
- Policy-equivalence caveat:
  - In a static arithmetic sense, allowance, zero-rate band, and tax credit can be made equivalent with adjustments.
  - In practice, changes have different distributional and incentive implications.
  - Example: doubling a personal allowance shifts the entire marginal schedule right and significantly lowers average tax rates; doubling a zero-rate band changes the marginal schedule only over a narrow range and yields smaller reductions for higher incomes.
- Reform design guidance:
  - If intent is not to shift effective thresholds for upper rates when increasing allowances, combine allowance increases with corresponding reductions in upper-rate thresholds.
  - If intent is to shift the entire schedule in a system with a zero-rate band, raise all thresholds by the same amount.
  - Plot pre- and post-reform scenarios on the same chart to clarify implications.

---

### Section 1 — Marginal Tax Rates: applications, interactions, and limitations

#### Refundable tax credits, negative income tax, universal income, and means-tested benefits
- Equivalences:
  - Refundable tax credit = negative income tax effect on low incomes.
  - Unconditional universal income (administered through spending) = refundable tax credit in effect on marginal rates.
  - Means-tested benefit contingent only on income is indistinguishable from a refundable credit in marginal-rate schedules.
- Illustration assumptions:
  - Reference tax system of Table 1 plus a lump sum of 3 percent of per capita GDP.
  - With this provision, the 10 percent starting rate (or benefit withdrawal rate) is applied from the first unit of currency earned.
  - Average tax rate tends to negative infinity as income → 0 (vertical axis truncated in figures).
  - The lump sum is set to exactly make up for removal of the zero-rate band in the example.
- Consequences:
  - Average tax rate lower for any income below the top threshold of the zero-rate band of the reference tax system; identical for higher incomes.
  - Replacing zero-rate band by a refundable tax credit reduces revenue; revenue neutrality would require raising other tax rates.
  - A much higher unconditional universal income covering basic needs would likely require much higher marginal tax rates from the start.

#### Inflation and bracket creep
- Inflation erodes real value of nominal-fixed tax features (allowances, thresholds).
- Illustration assumption: inflation of 10 percent and no real growth using the reference system of Table 1 (income expressed in percent of per capita GDP).
- Effect: inflation shifts the tax schedule left (bracket creep); tax rate increases apply at lower real incomes.
- Policy response: index thresholds to inflation to avoid bracket creep.

#### Interactions with social security
- Combining tax and social security:
  - If fully separate, rates can be added; if social security is deductible from tax, adjust calculations.
  - Exact combined-rate formula when social security is deductible: with tax rate t and social security rate s, combined rate T = s + (1 − s)t.
  - Include employer contributions when relevant; the combined rate including employer contributions is the marginal tax wedge; employer contributions should be included in denominator of the average rate.
- Illustrative example:
  - Reference tax system of Table 1 plus a flat employee-paid social security contribution of 20 percent applicable on income ranging from 10 to 300 percent of GDP per capita; contribution fully paid by employee and not deductible from tax.
  - Resulting shape: hump-shaped marginal tax rate schedule and regressivity at the top are common when social security is collected only up to an upper limit.
  - Some countries avoid regressivity by aligning the starting threshold of their top tax rate with the upper threshold for social security.
- Caveats:
  - Some social security contributions resemble forced savings tied to future benefits and are not equivalent to taxes.
  - Adding social security and tax is an oversimplification but useful to reveal overall payments and progressivity.

#### Household taxation effects
- Household taxation with differing thresholds by household type requires accounting for partner/dependent incomes to infer individual schedules.
- Illustrative cases with Table 1:
  - Married partners taxed jointly under double the thresholds applicable to singles.
  - If both partners earn the same, each partner’s marginal schedule matches the individual schedule.
  - If partner earns no income, the earning partner benefits from twice the zero-rate band and delays reaching top rates.
  - If partner earns 150 percent of GDP per capita, the secondary earner faces higher marginal rates sooner and may face the starting tax rate immediately.
  - If partner’s income alone exceeds household top-rate threshold (example: 400 percent of GDP per capita), the secondary earner faces the top rate from the start.
- General rule: when someone earns less than their partner, marginal rates are raised or at best the same; when someone earns more, marginal rates are lower or at best the same.
- Practical implication: household taxation can negatively affect secondary earners, often women, and thus female labor supply.

#### Social welfare, dual/schedular systems, and foreign income
- Social welfare features depending on conditions other than taxable income (age, children, assets, activity requirements, minimum hours) may mislead combined schedules.
- Dual/schedular systems:
  - Separate charts for each income type reveal marginal rates; average rates for total income require assumptions about income composition.
  - Example dual system:
    - Labor income taxed under Table 1; capital income taxed at flat rate of 20 percent.
    - Two taxpayers:
      - “Worker”: 80 percent labor, 20 percent capital.
      - “Capitalist”: 80 percent capital, 20 percent labor.
    - Implications: low incomes can favor those whose main source is work; high incomes relying on capital face lower tax rates.
    - Caveat: fixed income-share assumptions are unrealistic as high-income earners typically have larger capital income shares.
- Taxpayers with foreign income:
  - Worldwide taxation with credits: if foreign taxes < domestic taxes, effective schedule unchanged; if foreign taxes exceed domestic, excess credits typically not refunded and schedule differs.
  - If foreign income exempt, domestic schedule applies only to domestic income and total-tax representation depends on income distribution across countries, preventing a simple universal schedule.

### Conclusion: uses and limits of marginal and average rate schedules
- Preparing marginal tax-rate schedules is critical to understand incentives and the effects of reforms.
- They reveal notches and cliffs that discourage earnings or participation and allow analysis of interactions with social security, welfare, and household taxation effects on primary and secondary earners.
- Combined with average tax rates, schedules illustrate progressivity (or its absence).
- They do not resolve normative debates about tax reform but provide factual clarity on how reforms affect tax schedules.

*Source: htnea2025007 — How to Summarize and Interpret Income Tax Schedules; IMF | How to Notes NOTE/2025/007; Alexander Klemm; September 2025*

### Introduction   .........................................................................................................

### Introduction

### Overview
- This note is IMF | How to Notes NOTE/2025/007, authored by Alexander Klemm, dated September 2025.
- Purpose: describe how most features of an income tax system can be summarized as a combination of lump sums and marginal tax rates and plotted in a summary chart to aid understanding of tax reforms and avoid unintended humps or notches.
- Scope: focuses on the second of two fundamental steps in applying an income tax—the application of the tax rate schedule (allowances, credits, rates)—while noting the first step (defining the tax base) is also important.

### Key Concepts: Average and Marginal Tax Rates
- Two summary measures emphasized:
  - The average tax rate is the total amount of tax paid as a share of total income.
  - The marginal tax rate is the amount of tax paid on one additional unit (for example, dollar) of income.
- Roles:
  - Average tax rate:
    - Important for welfare comparisons across income groups.
    - Relevant for participation decisions at the extensive margin (whether to accept a job offer or work in the formal vs. informal economy).
  - Marginal tax rate:
    - Important for intensive-margin decisions (whether to work an additional hour or supply more effort).
    - Relevant for self-employed, part-time workers with flexible hours, and compliance decisions about income declaration.

### Economic Implications and Theory
- Economic theory implication stated:
  - Raising the marginal tax rate will always reduce labor supply because it reduces the value of work relative to leisure (“substitution effect”).
  - Raising average tax rates can increase labor supply because people may need to make up for the income loss (“income effect”).
- Practical observation:
  - Most feasible reforms that raise average tax rates will also raise at least some people’s marginal tax rates.

### Practical Issues and Common Confusions
- Interactions and translation of statutory provisions:
  - Personal allowances that are deductible before applying rate structures effectively increase the thresholds used for the rate structure—this can be non-obvious.
  - Combinations of tax credits, surtaxes, and benefit withdrawals can create complex effective tax-rate patterns.
- Policy design pitfalls illustrated:
  - Phasing out personal allowances or child credits above a high-income threshold can raise marginal tax rates over an income range and then reduce them at higher incomes; such nonmonotonic patterns may be unintended.
  - Increasing personal allowances often yields the greatest monetary benefit to taxpayers in the highest tax bracket.

### Method, Structure, and Limitations Highlighted
- Method advocated: summarize complex tax (and to some extent social security and welfare) systems using charts of marginal and average tax rates as a function of income to reveal unexpected effects and provide a basis for debate focused on factual effects.
- Historical roots and related literature cited:
  - Pigou (1928, pp. 46–51)
  - Musgrave and Thin (1948)
  - McCrae (1997)
- Structure of the note:
  - “Principles” section: defines marginal and average tax rates, discusses their importance, and outlines economic-theory insights.
  - “Some Applications” section: applies measures to examples (including universal basic incomes, phasing out allowances, tax credits vs allowances).
  - “Limitations” section: discusses conditions that cannot be summarized in these schedules.
  - “Conclusions” section: summarizes findings.
- Footnote emphasis:
  - While the first step (defining the tax base) is relevant for many taxes, the second step (applying the rate schedule) is particularly important for personal income taxes, which are typically the only or main tax with a progressive schedule. The methods described can also be applied to progressive inheritance taxes.

*IMF | How to Notes NOTE/2025/007 — How to Summarize and Interpret Income Tax Schedules; Alexander Klemm; September 2025*

### Box 1. How to Practically Prepare Marginal and Average Tax Charts

### Box 1. How to Practically Prepare Marginal and Average Tax Charts

### Practical steps to construct charts
- Plot income on the horizontal axis (typically in local currency units) and tax rates on the vertical axis (in percent).
- No data on income distribution are required to describe the tax system; choose an income range starting at zero and ending at an income that exceeds the highest income threshold so the entire tax system is depicted.
- If the highest threshold is extreme, consider additional charts with smaller ranges; if the top threshold is very low, consider showing income up to the median income at least.
- Split the chosen income range into sufficiently granular steps. Example used in this note: 1000 income steps.
- For simple systems, marginal tax rates can be read from the statutory schedule. For complex systems:
  - Calculate tax liability for each income (may require many "if statements" in a spreadsheet).
  - Approximate the marginal rate by dividing the difference in tax liability between two adjacent incomes by the incremental income (precision increases with the number of intervals).
- Average tax rate = tax liability divided by income.

### Parameters and features to include
- Rate structures:
  - Rising tax rates applied to income bands (brackets/slabs) defined by lower and upper thresholds (upper threshold of a band = next band’s lower threshold; final band may have no upper threshold).
  - Flat rates require no thresholds.
- Common mechanisms to leave some income untaxed:
  - Exemption (personal allowance): fixed amount deducted from total income.
  - Zero-rate bracket: first bracket tax rate set to zero; may be presentationally similar to an exemption but can differ in how changes affect higher thresholds.
  - Tax credit: offsets the tax bill; appears similar but is worth the same to all taxpayers except those without sufficient tax liability.
  - Refundable tax credit: paid out if it exceeds tax liability; worth the same to all taxpayers even those earning little or nothing.
  - Universal income: administered through spending system; effect essentially the same as a refundable tax credit.
- Additional features that affect modeling:
  - Surtaxes.
  - Allowances or credits for children, education, health.
  - Deductibility or super-deductibility (more than 100 percent) for incentivized spending.
  - Reduced or increased rates for certain income types.
  - Interactions with other taxes (for example, crediting VAT against income tax).
- Modeling principle:
  - Lump-sum items (refunds, universal income, head taxes) affect average tax rates but not marginal rates.
  - Everything else can be modeled as marginal tax rates (including withdrawals of credits/benefits).

### Key economic-theory insights for interpretation
- Robust theoretical bounds: optimal marginal tax rate is between 0 and 100 percent (Mirrlees 1971).
- Optimal marginal tax rate schedule is U-shaped (Diamond and Saez 2011): relatively high on low and high incomes, relatively low on middle incomes.
  - High marginal rates on low incomes raise revenue from many people while affecting labor supply marginally for a small subset.
  - Low marginal rates on middle incomes reduce efficiency costs because most people occupy these incomes.
  - High marginal rates on large incomes can be justified by equity considerations and smaller efficiency costs given group size.
- Caveats:
  - High marginal tax rates on low incomes do not imply high average taxes for low-income people (average can be low or negative if combined with refundable credits).
  - Theoretical high marginal rates on low incomes refer to the entire tax-and-benefit system; when analyzing tax systems in isolation, expect a rising marginal tax rate schedule rather than a U-shape.

### Illustrative applications and specific examples
- Baseline simple systems:
  - Flat tax: statutory, marginal, and average rates identical (flat line).
  - Flat rate with personal allowance: two marginal rates (0 and flat rate). Example used: tax rate of 25 percent and tax-free allowance of 30 percent of GDP per capita.
    - Charts using income in percent of GDP per capita for illustration.
    - Average tax rate rises for incomes exceeding the personal allowance, visually confirming progressivity.
- Reference progressive tax system (Table 1):
  - Table 1 thresholds and rates (percent of GDP per capita; percent):
    - Lower Threshold 0, Upper Threshold 30, Tax Rate 0
    - Lower Threshold 30, Upper Threshold 100, Tax Rate 10
    - Lower Threshold 100, Upper Threshold 200, Tax Rate 20
    - Lower Threshold 200, Upper Threshold (blank), Tax Rate 30
  - Figure 2 (descriptive): plots marginal and average tax rates; multiple rates cause average tax to rise more steeply at the start of each band.
- Notches (discrete loss of benefits or sudden tax jumps):
  - Examples of provisions that create notches:
    - Loss of allowance above a threshold.
    - Applying higher rate on all income when crossing a threshold.
    - Additional tax on all income (or on tax) when crossing a threshold.
    - Loss of benefit or a fixed tax emerging at a given income level.
  - Implication: marginal tax rate at a notch can be theoretically infinite; at the unit-economy granularity it can be extremely large in practice.
  - Illustration: reference system with personal allowance lost at 300 percent of per capita GDP.
    - Someone earning just below 300 percent of per capita GDP has post-tax income of 243 percent of GDP per capita.
    - Increasing earnings to meet the threshold reduces net income to 234 percent of GDP per capita.
    - Gross income must rise to at least 313 percent of GDP per capita to recover the loss.
  - Policy implication: notches create major disincentives to earn marginal income and are best avoided.
- Withdrawal of allowances or reduced rates (smoothing notches):
  - Withdraw allowance gradually over an income range to avoid infinite marginal rates. Example: allowance withdrawn over incomes from 300 to 400 percent of GDP per capita.
    - Causes a finite increase in marginal tax rate (example increase of 9 percentage points in the illustrative case).
    - Marginal rate jumps then falls back; average tax rate rises without jumps.
  - Alternative: introduce a higher top tax rate (example top rate set at 35 percent at 300 percent of GDP per capita).
    - Revenue-neutral top-rate calculation requires income-distribution data; the illustrative 5 percentage point difference is not a general rule.
  - Comparative judgment:
    - Sudden removal, gradual withdrawal, and new top rate lead to different marginal-rate shapes; an additional top rate generally avoids jumps or reversals and yields a more sensible schedule.
    - Economic theory suggests marginal tax rates should rise with income; temporary humps are hard to justify.
    - Figure 6 (descriptive) shows incomes up to 1000 percent of GDP per capita: new top rate keeps raising average tax rates, whereas removal/withdrawal effects fade.
- Personal allowances, zero-rate bands, and tax credits:
  - Plotting rules:
    - Zero-rate band: chart directly from thresholds and rates.
    - Personal allowance: increase all higher rate thresholds by the allowance amount when plotting.
    - Nonrefundable tax credit: divide the credit by the tax rate before plotting the tax-free amount.
  - Policy-equivalence caveat:
    - In a static system, allowance, zero-rate band, and tax credit can be made equivalent with arithmetic adjustments.
    - Changes to these features have different distributional and incentive implications in practice.
    - Example: doubling a personal allowance shifts the entire marginal schedule right and significantly lowers average tax rates; doubling a zero-rate band changes the marginal schedule only over a narrow range and yields smaller tax reductions for higher incomes.
    - Tax credit changes resemble zero-rate band changes insofar as they are worth the same to all taxpayers (except those tax-exhausted).
  - Reform design guidance:
    - If the intent is not to shift effective thresholds for upper rates when increasing allowances, combine allowance increases with corresponding reductions in upper-rate thresholds.
    - If the system has a zero-rate band but the intent is to shift the entire schedule, raise all thresholds by the same amount.
    - Plotting pre- and post-reform scenarios on the same chart clarifies the reform’s implications.

*htnea2025007 - Box 1. How to Practically Prepare Marginal and Average Tax Charts*

### 1. Marginal Tax Rates

### 1. Marginal Tax Rates

### Refundable Tax Credits, Negative Income Taxes, Unconditional Universal Income, and Means-Tested Benefits
- Refundable tax credits (where credits exceed tax liability and produce a net payment) are equivalent in effect to a negative income tax on low incomes.
- An unconditional universal income operates through spending but is equivalent to a refundable tax credit in its effect on marginal rates.
- A means-tested benefit contingent only on income is indistinguishable in its effect on marginal tax schedules from a refundable credit or negative income tax.
- Illustration assumptions and implications:
  - The example assumes the reference tax system of Table 1 plus a lump sum (refundable tax credit/negative income tax/universal income/means-tested benefit) of 3 percent of per capita GDP.
  - With this provision, the 10 percent starting rate (or benefit withdrawal rate) is applied from the first unit of currency earned.
  - The average tax rate tends to negative infinity as income goes toward zero (vertical axis truncated for legibility).
  - In the example, the lump sum is set to exactly make up for the removal of the zero-rate band.
  - Consequences:
    - The average tax rate is lower for any income below the top threshold of the zero-rate band of the reference tax system of Table 1, and exactly the same for any higher income.
    - Replacing the zero-rate band by a refundable tax credit (or making an existing tax credit refundable) reduces revenue.
    - A revenue-neutral reform would require raising one or more other tax rates.
    - A much higher unconditional universal income that would cover basic needs would likely require much higher marginal tax rates from the start.

### Inflation
- Inflation erodes the real value of tax features fixed in nominal terms, including allowances and thresholds.
- Illustration assumptions and implications:
  - The figure illustrating inflation assumes inflation of 10 percent and no real growth, using the reference tax system of Table 1, with income expressed in percent of per capita GDP to focus on the effect of inflation.
  - Effect: inflation shifts the tax schedule to the left (bracket creep), so tax rate increases apply at lower real incomes.
  - Policy response: index thresholds to inflation to avoid bracket creep.

### Limitations and Interactions with Social Security
- When social security contributions are significant, analyzing tax in isolation can be misleading; combine tax and social security to assess overall incentives.
- Key points for combining systems:
  - If social security and tax are fully separate, rates can simply be added. If one (more likely social security) is deductible from the other, this must be accounted for.
  - Exact combined-rate formula when social security is deductible: with a tax rate of t and a social security rate of s, the combined rate T is then T = s + (1 − s)t.
  - Include employer contributions when relevant; the combined rate including employer contributions is the marginal tax wedge and employer contributions should be included in the denominator of the average rate.
- Example and typical patterns:
  - Example combines the reference tax system of Table 1 with a flat employee-paid social security contribution of 20 percent applicable on income ranging from 10 to 300 percent of GDP per capita; this contribution is fully paid by employee and not deductible from tax.
  - Resulting shape: a hump-shaped marginal tax rate schedule and regressivity at the top are common outcomes when social security is only collected up to an upper limit.
  - Some countries avoid regressivity by aligning the starting threshold of their top tax rate with the upper threshold for social security.
- Caveats:
  - Not all social security contributions are equivalent to taxes (some, e.g., pensions, resemble forced savings tied to future benefits).
  - Adding social security and tax is an oversimplification but useful for revealing overall payments and progressivity.

### Household Taxation
- Some countries tax at the household level with thresholds differing by household type (single, married, with or without children).
- To understand an individual’s tax schedule, one must consider their partner’s or dependents’ income.
- Illustration and implications:
  - Example: reference tax system of Table 1, but married partners are taxed jointly under double the thresholds applicable to singles.
  - If both partners earn the same, each partner’s marginal tax rate schedule matches the individual schedule (as in Figure 2).
  - If married to a partner earning no income, the earning partner benefits from twice the zero-rate band and reduced tax rates, reaching the top rate much later.
  - If married to a well-earning partner (example partner earning 150 percent of GDP per capita), the secondary earner faces higher marginal rates sooner and may face the starting tax rate immediately.
  - Extreme case: if the partner’s income alone exceeds the household top-rate threshold (in this example, 400 percent of GDP per capita), the secondary earner faces the top rate from the start.
  - General rule: when someone earns less than their partner, marginal rates are raised or at best the same; when someone earns more than their partner, marginal rates are lower or at worst the same.
  - Practical implication: household taxation can negatively affect secondary earners, often women, and thus female labor supply.

### Social Welfare, Dual and Schedular Tax Systems
- Social welfare features (income support, employment tax credits) can be added to combined schedules but may be misleading if benefits depend on conditions other than taxable income (age, children, assets, activity requirements, minimum hours worked).
- Dual/schedular systems:
  - Some countries tax capital and labor differently; others have multiple defined income types with separate schedules.
  - Separate charts for each income type can reveal marginal rates; average rates for total income require assumptions about income composition.
- Example dual system:
  - Labor income taxed under the reference tax system of Table 1; capital income taxed at a flat rate of 20 percent.
  - Two illustrative taxpayers:
    - “Worker”: 80 percent of income from labor and 20 percent from capital.
    - “Capitalist”: 80 percent of income from capital and 20 percent from labor.
  - Implications:
    - For low incomes, dual systems can favor people whose main source is work.
    - For high incomes, people relying mostly on capital income face lower tax rates.
  - Caveat: assuming fixed income shares as income rises is unrealistic; high-income earners typically have a greater proportional share of capital income, so charts relying on fixed shares represent specific scenarios rather than universal taxpayer realities.

### Taxpayers with Foreign Income
- Countries taxing worldwide income typically provide credits for foreign taxes paid:
  - If foreign taxes are less than domestic taxes, the effective tax schedule is unchanged whether income is domestic or foreign.
  - If foreign taxes exceed domestic ones, excess credits are typically not refunded and the taxpayer faces a different effective schedule.
  - If foreign income is exempt, the domestic schedule applies only to domestic income and total-tax representations depend on the distribution of income across countries and their tax systems, preventing a simple universal schedule.

### Conclusion: Uses and Limits of Marginal and Average Rate Schedules
- Preparing marginal tax rate schedules is a critical tool for understanding tax-system incentives and the effects of reforms.
- They reveal notches and cliffs that may discourage earnings or workforce participation and allow analysis of interactions with social security and welfare, as well as household taxation effects on primary and secondary earners.
- Combined with average tax rates, these schedules can illustrate progressivity (or its absence).
- They do not resolve normative debates about tax reform (which involve value judgments and tradeoffs) but provide factual clarity on how reforms affect tax schedules.

*Source: htnea2025007 - 1. Marginal Tax Rates (IMF How to Notes).*

---


_Source: https://www.imf.org/-/media/files/publications/howtonotes/2025/english/htnea2025007.pdf_