Intergenerational Elasticity Calculator

Observed matched-family log-income OLSelasticity with independently established known-pair evidence; preserve excluded family IDs. Actual compatible income/age/time definitions required; not causal mobility or predict a childs income.

Description

Intergenerational income elasticity relates log child income to log parent income in matched families.

Intergenerational income elasticity relates log child income to log parent income in matched families.^[1]

The observed association depends on cohort, income-period and sample-selection conventions.

When to use Intergenerational Elasticity Calculator

Use this tool to obtain observedKnownLogIncomeElasticity, includedFamilyIds, unknownFamilyIds 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 Intergenerational Elasticity Calculator and understand its results

Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
Enter callerFamilyIds, parentCompatibleIncomes, childCompatibleIncomes, pairedEvidenceKnownFlags, using the field meanings and rules below, then run the tool.
Read result.observedKnownLogIncomeElasticity, result.includedFamilyIds, result.unknownFamilyIds. 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
callerFamilyIds	Caller family ids	list of string	Required
parentCompatibleIncomes	Parent compatible incomes	list of number	Required
childCompatibleIncomes	Child compatible incomes	list of number	Required
pairedEvidenceKnownFlags	Paired evidence known flags; binary 1 means the matched observation is known, 0 means unknown	list of number	Required

Supply nonempty unique nonblank family IDs and aligned strictly positive parent/child incomes with binary known flags. All incomes, including unknown placeholders, must be positive. Fit a free-intercept ordinary least-squares slope on natural-log incomes for known pairs only; known parent-log variance must be positive. Return included and unknown IDs separately. No weights, causal inference or uncertainty estimate is supplied.

elasticity=Σ((ln(parent_i)−meanLogParent)×(ln(child_i)−meanLogChild))/Σ((ln(parent_i)−meanLogParent)²), over known pairs

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.observedKnownLogIncomeElasticity	Free-intercept least-squares slope of log child income against log parent income for known pairs.	number
result.includedFamilyIds	Known family pairs retained in the elasticity calculation.	list
result.unknownFamilyIds	Family pairs excluded because their evidence is marked unknown.	list

json

{
  "input": {
    "callerFamilyIds": [
      "a",
      "b",
      "c"
    ],
    "parentCompatibleIncomes": [
      1,
      2,
      4
    ],
    "childCompatibleIncomes": [
      2,
      4,
      8
    ],
    "pairedEvidenceKnownFlags": [
      1,
      1,
      1
    ]
  },
  "output": {
    "result": {
      "observedKnownLogIncomeElasticity": 1,
      "includedFamilyIds": [
        "a",
        "b",
        "c"
      ],
      "unknownFamilyIds": []
    }
  }
}

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. String lists allow at most 128 entries of at most 128 UTF-16 units each; blank and duplicate rules are stated above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Assortative Mating Correlation Calculator: Assortative-mating correlation describes a linear association between matched partner scores. For a complementary comparison, use Local Income Rank Status Anxiety Calculator: A local income midrank locates one observation within a declared reference sample.

References

Intergenerational Elasticity Calculator — tool.io

Similar or alternative tools

Assortative Mating Correlation Calculator
Assortative-mating correlation describes a linear association between matched partner scores.
Local Income Rank Status Anxiety Calculator
A local income midrank locates one observation within a declared reference sample.