Reynolds-Smolensky Redistribution Effect Calculator
Actual matched sample pre/post tax Gini difference, retaining negative redistribution. Does not establish causal policy effect, reranking decomposition or legal tax liability.
Description
The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality.
The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality.1
Compatible before/after income records are necessary to interpret that signed redistribution measure.
When to use Reynolds-Smolensky Redistribution Effect Calculator
Use this tool to obtain observedReynoldsSmolenskyDifference from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
How to use Reynolds-Smolensky Redistribution Effect Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter matchedBeforeTaxIncomes, matchedAfterTaxIncomes, using the field meanings and rules below, then run the tool.
- Read result.observedReynoldsSmolenskyDifference. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| matchedBeforeTaxIncomes | Matched before tax incomes | list of number | Required |
| matchedAfterTaxIncomes | Matched after tax incomes | list of number | Required |
Require aligned nonempty nonnegative pre/post income lists, each with positive total. For each list independently sort incomes and calculate the unweighted sorted-sum Gini. Return before-minus-after Gini. No causal tax attribution, person weights or matching verification is supplied.2
difference=Gini(before)−Gini(after); Gini(y_sorted)=2×Σ((i+1)×y_i)/(n×Σy)−(n+1)/n Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or qualified reference | object |
| result.observedReynoldsSmolenskyDifference | Before-tax Gini minus after-tax Gini for the supplied compatible samples. | number |
{
"input": {
"matchedBeforeTaxIncomes": [
1,
3
],
"matchedAfterTaxIncomes": [
2,
2
]
},
"output": {
"result": {
"observedReynoldsSmolenskyDifference": 0.25
}
}
}Limitations and assumptions
Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Theil Index Calculator: The Theil T index summarizes inequality relative to a sample's mean income. For a complementary comparison, use Atkinson Index Calculator: The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.
References
Similar or alternative tools
- Theil Index Calculator
The Theil T index summarizes inequality relative to a sample's mean income.
- Atkinson Index Calculator
The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.