1 The Causal Question

What is the causal return to an additional year of schooling on earnings? This question sits at the heart of human capital economics and has attracted decades of ingenious identification strategies. The challenge is selection bias: individuals who acquire more education differ from those who acquire less, not only in their schooling but in their family backgrounds, cognitive abilities, and motivation all of which independently affect earnings.

Ordinary least squares (OLS) estimation of the Mincer earnings equation:‍


where Wi is earnings, Si is years of schooling, and Xi includes experience and other controls, is biased by omitted ability (Ai). If Si = γ0 + γ1Ai + ηi and ln Wi = α + ρSi + δAi + ui then OLS recovers ρ̂ = ρ + δγ1Var(Ai)/Var(Si). With δ > 0 (ability raises earnings) and γ1 > 0 (ability raises schooling), the OLS coefficient on schooling is upward biased the "ability bias" [Griliches, 1977].

Ashenfelter and Krueger [1994] devised an elegant solution: study identical twins, who share genetic endowment and family background, and use differences in schooling within twin pairs to identify the return to education net of these shared factors.

2 The Identification Strategy

2.1 The Within-Twin Estimator

'where Af is the shared family endowment (ability, background) common to both twins. Taking the within-pair difference:

where Δ denotes twin 1 minus twin 2. Because Af cancels in the difference, the within-twin OLS estimator of ρ is free of omitted ability bias provided that ΔSf is uncorrelated with Δuf.

This approach was pioneered by Griliches [1979] and extended by Ashenfelter and Krueger. The key innovation of Ashenfelter and Krueger [1994] was to collect their own survey data the Princeton Twins Survey at the 1991 Twins Festival in Twinsburg, Ohio, enabling them to observe both self-reported and co-twin-reported schooling.

2.2 The Measurement Error Problem

The within-twin estimator creates a new problem: measurement error. If twins self-report their schooling with classical error, S̃if = Sif + vif, then within-pair differencing amplifies the noise-to-signal ratio. With two identically measured variables, the variance of the error difference v1f - v2f stays roughly constant while the variance of the signal difference S1f - S2f shrinks (because within-pair differences in schooling are much smaller than cross-sectional differences). The result is attenuation bias that pushes the within-twin estimate downward.

Ashenfelter and Krueger [1994] exploit a key feature of their data: they asked each twin to report not only their own schooling, but also their co-twin's schooling. This provides two independent measures of each twin's schooling. Using twin j's schooling as reported by the co-twin as an instrument for twin j's self-reported schooling an IV strategy corrects for the attenuation bias.

2.3 The IV Estimator

Let Sifself be twin i's self-reported schooling and Sifco be the schooling reported by the co-twin. The first-stage regression is:

and the IV estimator uses ΔSfco as an instrument for ΔSfself The instrument is relevant if co-twins report each other's schooling accurately (strong first stage), and it is valid if measurement errors in self-reports and co-twin reports are uncorrelated a reasonable assumption if errors arise from recall failures specific to each reporter.

3 Data and Setting

The Princeton Twins Survey was collected at the Twinsburg Twins Festival in Ohio in 1991, yielding a sample of 298 identical (monozygotic) twin pairs and 125 fraternal (dizygotic) twin pairs, with age ranging from 18 to 65. Earnings, education, and demographic characteristics were collected for both twins.

The survey's non-random sampling method (self-selected festival attendees) raises concerns about representativeness, but the within-pair differencing estimator is robust to selection on fixed twin-pair characteristics, since any fixed characteristic cancels in the difference.

4 Key Findings

Table 1 summarises the main estimates across the three estimators discussed.

Table 1: Estimated Returns to Schooling: Ashenfelter and Krueger (1994)

Source: Ashenfelter and Krueger [1994], Table III. Dependent variable: log weekly earnings. Sample: male MZ twins.

Three findings stand out:

The within-twin OLS estimate is similar to cross-sectional OLS. This was surprising: the conventional wisdom predicted that within-twin estimates would be lower than OLS (once ability bias was eliminated). Finding rough equality suggested that OLS ability bias may have been smaller than assumed or that within-twin estimates were attenuated downward by measurement error, roughly cancelling ability bias upward.

The IV estimate is higher than both OLS estimators. The within-twin IV estimate of approximately 12-13% per year of schooling is substantially higher than within-twin OLS (about 9%). This is consistent with measurement error attenuation in the within-twin OLS estimate, which the IV corrects.

The returns to schooling are large. Even after controlling for genetic and family background through within-twin differencing, and correcting for measurement error through IV, schooling has a large causal effect on earnings of 12-16% per year, depending on specification.

5 Limitations and the Ongoing Debate

5.1 Representativeness of the Sample

The Twinsburg festival sample is self-selected. Bound et al. [1995] raised concerns that the sample was unusual and that findings may not generalise to the broader population.

5.2 Non-Random Schooling Differences Within Pairs

The within-twin estimator is unbiased only if the within-pair difference in schooling ΔSf is uncorrelated with within-pair differences in earnings ability Δuf. However, twins' schooling differences may be driven by idiosyncratic shocks (illness, local school quality, random peer effects) that are themselves correlated with earnings. If a twin's schooling was curtailed by a health shock that also reduces earnings, the within-twin estimate will be downward biased.

5.3 Measurement Error in the Instrument

The co-twin-report instrument corrects for independent measurement error, but if errors in self-reports and co-twin reports are positively correlated (because both twins attended the same schools or share knowledge of each other's diplomas), the IV estimator remains attenuated. Ashenfelter and Rouse [1998] revisited these issues with a larger follow-up survey.

5.4 Ability May Not Be Purely Shared

Identical twins are genetically identical but not perfectly so epigenetic differences mean that cognitive abilities can diverge. If within-pair differences in schooling reflect within-pair differences in ability (ΔAf ≠ 0), the within-twin estimator will still be biased, though the bias is smaller than in cross-sectional OLS.

6 Legacy and Impact

The twins design became a foundational approach in the returns-to-education literature. Subsequent studies using administrative data on twins from Scandinavian registries where schooling is measured precisely from school records rather than self-reports have largely confirmed the Ashenfelter and Krueger [1994] findings: within-twin returns to education are in the range of 8-12% per year, comparable to or slightly below cross-sectional OLS estimates [Card, 1999].

The paper also made a methodological contribution that extends beyond the specific application: it demonstrated how the availability of multiple measures of the same variable (self-report and co-twin report) creates a within-study IV strategy for correcting measurement error bias a technique applicable far beyond twin studies.

7 Conclusion

Ashenfelter and Krueger [1994] tackled the ability-bias problem in returns to education through an ingenious design: within-identical-twin differences eliminate shared genetic and family background, and co-twin-reported schooling instruments correct for measurement error in self-reports. The resulting IV estimates of 12-16% per year are among the most credibly identified in the human capital literature. The study illustrates both the power and the limits of the within-family estimator, and the continuing importance of thinking carefully about the sources of identification in this case, from within-pair schooling variation and measurement error correction rather than relying on selection-on-observables assumptions.

References

1. Ashenfelter, O. and Krueger, A. B. (1994). Estimates of the economic return to schooling from a new sample of twins. American Economic Review, 84(5):1157-1173.
2. Ashenfelter, O. and Rouse, C. (1998). Income, schooling, and ability: Evidence from a new sample of identical twins. Quarterly Journal of Economics, 113(1):253-284.
3. Bound, J., Jaeger, D. A., and Baker, R. M. (1995). Problems with instrumental variables
4. estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association, 90(430):443-450.
5. Card, D. (1999). The causal effect of education on earnings. In Ashenfelter, O. and Card, D., editors, Handbook of Labor Economics, volume 3A. Elsevier.
6. Griliches, Z. (1977). Estimating the returns to schooling: Some econometric problems. Econometrica, 45(1):1-22.
7. Griliches, Z. (1979). Sibling models and data in economics: Beginnings of a survey. Journal of Political Economy, 87(5):S37-S64.
8. Mincer, J. (1974). Schooling, Experience, and Earnings. Columbia University Press.