Experiments in Replicating Science

Replication Analysis

Income and emotional well-being: Evidence for well-being plateauing around $200,000 per year
Mikkel Bennedsen — 33391 observations

Summary

Original finding (KKM2023, threshold at $100,000): Emotional well-being increases monotonically with income without a plateau. Slope above threshold: 0.1088 (SE: 0.0205) — positive and similar to below-threshold slope.
Replication (Bennedsen, data-driven threshold at $175,000): Emotional well-being plateaus above ~$175,000/year. Slope above threshold: -0.0015 (SE: 0.0541) — essentially zero.

Step 1: Finding the Optimal Threshold

The sum of squared residuals (SSR) is computed for each candidate income threshold. The threshold that minimizes SSR gives the best-fitting structural break point.

Step 2: OLS Regression Comparison

Piecewise linear model: E(zi|xi) = (a + b·x) below threshold, (c + d·x) above threshold. The z-scored well-being is the dependent variable; log-income is the independent variable.

$100,000 Threshold$175,000 Threshold
RegimeSlopeSESlopeSE
Below threshold 0.1121 0.0133 0.1108 0.0088
Above threshold 0.1088 0.0205 -0.0015 0.0541
SSR 33137.90 33132.75

$100,000 Threshold

$175,000 Threshold (Data-driven)

Step 3: Quantile Regression Comparison

Quantile regression examines different parts of the well-being distribution. t-statistics above ~2 indicate statistical significance.

$100,000 Threshold

QuantileSlope belowtSlope abovet
15% 1.900 8.13 0.335 0.92
30% 1.329 6.86 1.228 4.10
50% 1.237 6.46 1.459 4.94
70% 1.178 5.32 1.907 5.60
85% 0.791 2.96 1.983 4.87

$175,000 Threshold

QuantileSlope belowtSlope abovet
15% 1.826 11.67 -0.036 -0.04
30% 1.344 10.45 0.381 0.48
50% 1.233 9.73 0.147 0.19
70% 1.153 7.89 0.547 0.61
85% 1.003 5.62 -0.354 -0.32

Quantile Regression: $100k Threshold

Quantile Regression: $175,000 Threshold

Conclusion

The replication confirms the paper's central finding: the conclusion that emotional well-being increases monotonically with income (KKM2023) is sensitive to the placement of the income threshold. When the threshold is chosen in a data-driven way (minimizing SSR), it shifts from $100,000 to $175,000, and the relationship above that threshold becomes flat — both in the OLS analysis and across all quantiles of the well-being distribution.