Calculator Inputs
Example Data Table
| Parent Earnings | Child Earnings | Weight | Use Case |
|---|---|---|---|
| 42,000 | 47,000 | 1.15 | Moderate income pair |
| 84,000 | 93,000 | 0.85 | Weighted survey pair |
| 158,000 | 184,000 | 0.65 | Upper tail record |
Formula Used
The calculator estimates intergenerational earnings elasticity with a log-log regression:
ln(child earnings) = α + β × ln(parent earnings) + ε
The elasticity is β. A value of 0.40 means a 10% higher parent income is linked with about 4% higher child income.
Weighted slope formula:
β = Σw(x - x̄)(y - ȳ) / Σw(x - x̄)²
The page also calculates confidence limits, R squared, a rank-rank slope, a fitted line, residuals, and a mobility score.
How to Use This Calculator
- Paste parent earnings, child earnings, and optional weights.
- Use positive earnings only because log values are required.
- Set adjustment factors when values need price-level correction.
- Choose trimming or winsorizing to manage extreme values.
- Press calculate to view the result above the form.
- Use the chart to inspect the fitted relationship.
- Download CSV or PDF results for reporting.
Understanding Intergenerational Earnings Elasticity
Understanding Intergenerational Earnings Elasticity
Intergenerational earnings elasticity, or IGE, measures how strongly a child’s earnings follow a parent’s earnings. It is often used in mobility research. A higher value means family income position is more persistent. A lower value means earnings are less tied to family background.
Why This Calculator Matters
This calculator turns parent and child income pairs into a log-log regression. The slope is the elasticity estimate. For example, an elasticity of 0.40 suggests a ten percent higher parent income is associated with about four percent higher child income. The tool also shows confidence limits, rank links, fitted values, and residuals.
Using Good Data
Good estimates need careful data. Use long-run or averaged earnings where possible. Single-year income can be noisy. Remove rows with missing, zero, or negative earnings before using logs. Keep weights when your data represents a survey sample. Use trimming when extreme records distort the regression.
Reading the Result
The main result is the IGE slope. The intercept is less important for mobility interpretation. The R squared value shows how much log child earnings variation is explained by log parent earnings. The rank slope gives another view. It compares positions in the parent and child distributions instead of currency amounts.
Advanced Options
The adjustment fields help align earnings to a common price level. Trimming removes extreme income observations. Winsorizing keeps records but caps extremes. Weighted mode lets large survey weights influence the estimate more. These options help you test sensitivity. A stable estimate across settings is more credible.
Practical Use
Students can use the page to learn regression and mobility concepts. Researchers can test small samples before deeper work. Analysts can compare cohorts, regions, or groups. The chart gives a fast visual check. A steep fitted line means stronger persistence. A flatter line means greater mobility.
Limitations
This calculator is educational. It does not prove causation. Earnings mobility depends on age, measurement period, taxes, transfers, education, migration, and family structure. Use the results as a diagnostic summary. For formal research, document every cleaning rule and compare several model specifications. Report sample size, uncertainty, and data source notes beside every published estimate for readers clearly.
FAQs
1. What does intergenerational earnings elasticity mean?
It measures how strongly child earnings are associated with parent earnings. Higher values suggest stronger persistence across generations. Lower values suggest greater relative mobility.
2. What is a good IGE value?
There is no universal good value. A lower value usually means more mobility. A higher value means income rank is more strongly transmitted across generations.
3. Why does the calculator use logs?
Logs turn the regression into an elasticity model. They make the slope easier to interpret as a percentage relationship between parent and child earnings.
4. Can I use survey weights?
Yes. Add a third column for weight. Keep the weight option checked when rows represent different population shares or sampling probabilities.
5. What happens to zero earnings?
Rows with zero or negative adjusted earnings are skipped. Log regression requires positive values for both parent and child earnings.
6. Should I trim extreme values?
Trimming can reduce the effect of outliers. Winsorizing caps extremes instead of removing them. Compare both results before reporting final estimates.
7. What is the rank-rank slope?
It measures the relationship between parent and child positions in their earnings distributions. It is less sensitive to currency scale than log earnings.
8. Does IGE prove causation?
No. IGE is an association measure. Causal claims need stronger research designs, better controls, and careful treatment of measurement issues.