1. Carneiro, Heckman, and Vytlacil (2011): Marginal Returns to Schooling
Citation: Carneiro et al. [2011]. Estimating Marginal Returns to Education. AmericanEconomic Review, 101(6):2754-2781.
Research question: Do individuals at the margin of college attendance have higher orlower returns to college than the average college attendee?
Identification strategy: The authors use the National Longitudinal Survey of Youth(NLSY) with instruments for college attendance: local labour market conditions, local tu-ition, and the presence of a four-year college nearby. These instruments shift the probabilityof college attendance in different populations, identifying the MTE at different points of theselection distribution.
Key results: The MTE function is downward-sloping: individuals with low resistance tocollege attendance (those who would attend almost regardless of economic conditions) havethe highest returns to college, approximately 20 per cent per year of schooling. Individualsat the margin of attendance—those just barely induced to attend by the instruments—havereturns close to the opportunity cost of college (roughly 8-10 per cent). The estimated ATEis around 14 per cent, but the marginal return (the LATE for the most marginal compliers)is much lower.
Takeaway: IV estimates using college proximity instruments overstate the returns forthe marginal entrant, because the instrument-induced compliers have above-average returnsrelative to truly marginal students. Policies that expand college access to the most reluc-tant potential students will yield smaller wage returns than the LATE suggests. The MTEframework is essential for translating IV estimates into policy advice.
2. Walters (2018): School Choice and Marginal Treatment Effects
Citation: Walters [2018]. The Demand for Effective Charter Schools. Journal of PoliticalEconomy, 126(1):103-159.
Research question: What is the distribution of treatment effects in charter schools,and are lottery-based IV estimates representative of the full distribution?
Identification strategy: Charter school admissions lotteries in Boston provide randomvariation in charter attendance for oversubscribed schools. These lotteries are clean instru-ments: assignment is mechanical and the exclusion restriction is plausible (lottery offersaffect outcomes only through charter attendance). Walters estimates the MTE as a functionof unobserved resistance to charter school attendance.
Key results: Contrary to the college case, the charter school MTE is upward-sloping:students with the highest unobserved resistance to attending charter schools benefit themost from doing so. This means the lottery-based LATE (averaging over compliers whoare induced by oversubscription) underestimates the benefits of forcing the most resistantstudents into effective charter schools. The ATE exceeds the LATE in this setting.
Takeaway: Selection on gains is negative in the charter school context—families whomost resist charter attendance have the most to gain. This is the opposite pattern fromcollege attendance, and it has important policy implications: mandating or strongly encour-aging resistant students to attend effective charter schools would yield larger benefits thanthe lottery estimates suggest.
3. Mogstad, Santos, and Torgovitsky (2018): Using IV Moments for Partial Identification
Citation: Mogstad et al. [2018]. Using Instrumental Variables for Inference About PolicyRelevant Treatment Parameters. Econometrica, 86(5):1589-1619.
Research question: When an instrument's support covers only part of the distributionof unobserved selection, what can we learn about policy-relevant treatment effects?
Methods: The authors develop a partial identification approach based on the MTEframework. They show that any IV moment (IV slope, OLS slope, second moment) con-strains the MTE function, and that the identified set for any policy-relevant parameter canbe characterised by a linear programme. Shape restrictions (monotonicity of the MTE,non-negative treatment effects) further tighten the bounds.
Key results: The paper provides sharp bounds on the PRTE for several hypotheticaleducation policies using the Carneiro et al. (2011) data. The bounds are informative evenwhen the instrument's support covers only 30-40 per cent of the selection distribution. Whenthe PRTE's sign is identified, the policy recommendation is robust; when only the magnitudeis uncertain, the researcher can report the range of plausible effect sizes.
Takeaway: Partial identification via the MTE framework allows honest extrapolationfrom existing IV estimates to new policy scenarios, replacing a point estimate that requiresstrong untestable assumptions with an informative identified set. The ivmte R packageimplements this approach.
4. Cornelissen, Dustmann, Raute, and Schönberg (2016): MTE and Returns to Early Childhood Education
Citation: Cornelissen et al. [2018]. Who Benefits from Universal Child Care? Esti-mating Marginal Returns to Early Child Care Attendance. Journal of Political Economy,126(6):2356-2409.
Research question: Who benefits most from universal childcare programmes—the chil-dren whose families would choose care anyway, or those at the margin of enrolment?
Identification strategy: Using administrative data from Germany and variation inchildcare availability as instruments (expansion of childcare slots in different regions at dif-ferent times), the authors estimate the MTE for childcare attendance on children's schoolreadiness outcomes.
Key results: The MTE for universal childcare is upward-sloping: children of familieswith the highest unobserved resistance to childcare use benefit the most. The IV estimatesusing the childcare expansion instrument focus on late compliers who face binding capacityconstraints—these children have the highest LATE (above-average gains). The ATE is sub-stantially lower: average benefits for the full population are modest. Heterogeneity by familysocioeconomic status is also large: children from disadvantaged backgrounds gain more.
Takeaway: MTE analysis reveals that universal childcare expansions generate largeeffects for children facing the biggest access barriers, but average effects across the fullpopulation are more modest. Targeted programmes for disadvantaged children may dominateuniversal expansions in terms of cost-effectiveness.
References
- Carneiro, P., Heckman, J. J., and Vytlacil, E. J. Estimating marginal returns to education.American Economic Review, 101(6):2754-2781, 2011.
- Cornelissen, T., Dustmann, C., Raute, A., and Schönberg, U. Who benefits from universalchild care? Estimating marginal returns to early child care attendance. Journal of PoliticalEconomy, 126(6):2356-2409, 2018.
- Mogstad, M., Santos, A., and Torgovitsky, A. Using instrumental variables for inferenceabout policy relevant treatment parameters. Econometrica, 86(5):1589-1619, 2018.
- Walters, C. R. The demand for effective charter schools. Journal of Political Economy,126(1):103-159, 2018.