Card 1999 — The Causal Effect of Education on Earnings

Summary

Card's handbook chapter synthesizes the theoretical and empirical literature on the causal return to schooling. It formalizes the ordinary least squares (OLS) bias decomposition — $\text{plim}(b_{\text{OLS}}) = \bar{\beta} + \lambda_0 + \phi_0 \bar{S}$ , where $\lambda_0$ is intercept-ability bias and $\phi_0 \bar{S}$ is slope-ability bias from heterogeneous returns — and shows that the net ability bias in OLS estimates is empirically small ( $\approx 10\%$ ), partly because downward measurement-error attenuation ( $R_0 \approx 0.9$ ) offsets the upward ability bias. Card reviews the puzzling finding that instrumental variables (IV) estimates based on institutional features of the school system are $20$ – $40\%$ above OLS estimates and proposes that this reflects genuine local average treatment effect (LATE) heterogeneity: instruments like compulsory schooling or college proximity affect disadvantaged subgroups who face higher marginal returns due to financial constraints, not higher ability.

Key Claims

OLS ability bias is small ( $\approx 10\%$ ): The net upward ability bias in OLS estimates is approximately $10\%$ of the OLS coefficient once measurement error attenuation ( $\approx 10\%$ downward) partially offsets the positive ability correlation. OLS returns in 1994–96 Current Population Survey (CPS) data: $\approx 0.100$ (men), $\approx 0.109$ (women).
IV identifies a weighted average of subgroup marginal returns: Under Wooldridge's (1997) conditions (9a)–(9c), IV is consistent for $E[\beta_g \cdot \Delta S_g]/E[\Delta S_g]$ — a LATE weighted by the first-stage shift $\Delta S_g$ in each subgroup. This is not the population average treatment effect (ATE) and differs across instruments.
IV > OLS best explained by higher marginal returns for compliers: Card's preferred explanation for the $20$ – $40\%$ gap is that instruments affecting low-education subgroups identify compliers who face higher marginal returns — not because of higher ability but because of higher discount rates from credit constraints. Marginal returns decline with schooling, so less-educated individuals have higher returns at the margin.
Family background as IV is upward-biased relative to OLS: Using parental or sibling education as an instrument yields IV estimates systematically above the corresponding OLS estimates, not below. Family background correlates with own earnings independently of schooling through ability channels, violating the exclusion restriction unless $A_1 + \psi_1 S = 0$ .
Twins evidence: ability bias $\approx 10\%$ at most: Measurement-error-corrected within-family IV for identical twins (Ashenfelter and Rouse 1998) approximately equals the OLS estimate — ability bias is $10\%$ or less. Uncorrected within-family OLS is downward-biased by $20$ – $30\%$ due to measurement error amplification within families (reliability $R_A \approx 0.7$ for identical twins, versus $R_0 \approx 0.9$ cross-sectionally).
School quality raises both returns and attainment: Card and Krueger (1992a,b) show that reducing the pupil-teacher ratio by 10 students raises the causal return to education by $\approx 0.9$ percentage points (pp) and average attainment by $0.6$ years.
Publication bias in the IV literature: Ashenfelter and Harmon (1998) document a positive cross-study correlation between the IV-OLS gap and the standard error of the IV estimate, consistent with selective reporting of large, imprecise results.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"Consistent with the summary of the literature from the 1960s and 1970s by Griliches (1977, 1979), the average (or average marginal) return to education in a given population is not much below the estimate that emerges from a simple cross-sectional regression of earnings on education." (Section 5, Conclusion 1)

"IV estimates of the return to education based on interventions in the school system tend to be 20% or more above the corresponding OLS estimates. While there are several competing explanations for this finding, one plausible hypothesis is that the marginal returns to schooling for certain subgroups of the population — particularly those subgroups whose schooling decisions are most affected by structural innovations in the schooling system — are somewhat higher than the average marginal returns to education in the population as a whole." (Section 5, Conclusion 5)

My Take

Card's chapter is the canonical identification survey for the returns-to-schooling literature. Its lasting methodological contribution is reframing IV > OLS not as a bias problem but as evidence of genuine heterogeneity in marginal returns: compliers pushed into schooling by institutional factors tend to have higher returns because they face financial constraints. This interpretation anticipates the Heckman-Vytlacil marginal treatment effect (MTE) framework, but Card stays within the Wooldridge (1997) weighted-average IV characterization rather than recovering the full MTE curve. The twins and siblings evidence is carefully synthesized: Card's verdict — ability bias is $\approx 10\%$ , measurement error matters more than most researchers assumed — is more conservative than the MTE literature's emphasis on essential heterogeneity. The family-background-as-IV finding (IV > OLS) is underappreciated: it directly undermines a common identification strategy and shifts the burden of proof to structural models of family sorting.