1. Calonico et al.

[2014] Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs

Citation: Calonico, S., Cattaneo, M. D., and Titiunik, R. (2014). Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica, 82(6), 2295-2326.

Research Question: Standard confidence intervals in RD designs have incorrect cover- age because the bias of the local polynomial estimator is of the same asymptotic order as its standard deviation at the MSE-optimal bandwidth. Can we construct confidence intervals with correct coverage?

Identification Strategy: The paper is methodological. It develops the asymptotic the- ory for local polynomial RD estimation and derives a bias-corrected robust (BCR) confidence interval that accounts for both bias and the uncertainty introduced by bias estimation. The key insight is that using a higher-order polynomial to estimate the bias, then constructing a studentised confidence interval using the inflated variance, achieves correct $1-\alpha$ coverage.

Key Result: The CCT BCR confidence interval has correct asymptotic coverage, unlike the conventional CI which under-covers.  The approach is implemented in the rdrobust package. Simulations show substantial improvements in coverage conventional CIs may have 80% actual coverage when nominal coverage is 95%. The paper also derives the MSE- optimal bandwidth formula $h^{*}\propto n^{-1/5}$.

Takeaway: Every applied RD paper should use the CCT bias-corrected robust confi- dence intervals from rdrobust, not naive OLS-based intervals. The conventional CI is too narrow and leads to over-rejection of true nulls.

2. Dell [2010] The Persistent Effects of Peru's Mining Mita

Citation: Dell, M. (2010). The persistent effects of Peru's mining mita. Econometrica, 78(6), 1863-1903.

Research Question: Does colonial forced labour leave a persistent legacy of poverty? Specifically, does being subject to the mita a Spanish colonial forced labour draft that operated in Peru and Bolivia from 1573 to 1812 cause lower living standards today, 200 years after its abolition?

Identification Strategy: A geographic regression discontinuity. The mita boundary was drawn in 1573 to determine which districts supplied forced labourers to silver and mer- cury mines. Dell compares communities just inside and just outside the mita boundary, controlling flexibly for geography. The identification assumption is that communities on either side of the boundary were similar in all relevant respects except mita exposure. The boundary was determined by administrative convenience in the 16th century, not by pre- existing differences in productivity or wealth.

Key Result: Mita-subject districts have household consumption 25% lower today and stunting rates 6 percentage points higher than comparable non-mita districts. Mechanisms include: lower road density within mita districts (the Spanish crown's land tenure system created by the mita discouraged infrastructure investment that might benefit indigenous communities), lower rates of market integration, and lower public goods provision. Effects persist 200 years after abolition.

Takeaway: Colonial extractive institutions can have long-run persistent effects on eco- nomic development, even after the institutions themselves are abolished. The geographic RD provides unusually compelling identification by using a historical administrative boundary as the source of quasi-random variation.

3. Angrist and Lavy [1999] Using Maimonides' Rule to Estimate the Effect of Class Size

Citation: Angrist, J. D. and Lavy, V. (1999). Using Maimonides' rule to estimate the effect of class size on scholastic achievement. Quarterly Journal of Economics, 114(2), 533-575.

Research Question: Do smaller classes improve student academic achievement? This is one of the most contested questions in education economics, because families with greater resources sort into lower-class-size schools, making OLS estimates spurious.

Identification Strategy: A fuzzy regression discontinuity exploiting Maimonides Rule an administrative rule in Israeli schools that requires classes to be split whenever enroll- ment exceeds a multiple of 40. A school with 41 students must have two classes averaging 20.5 students; a school with 40 has one class of 40. This creates sharp jumps in class size at enrollment thresholds of 40, 80, 120, etc. The instrument is the class size predicted by Maimonides' Rule (a deterministic function of enrollment), which generates quasi-random variation in actual class size.

Key Result: Smaller classes significantly improve test scores in reading and mathemat- ics. A 10-student reduction in class size raises average math scores by about 5 percentile points and reading scores by about 3 percentile points. Effects are strongest in lower grades and for pupils in disadvantaged schools.

Takeaway: Class size matters for learning, at least in the Israeli context. The Mai- monides' Rule instrument provides clean identification and the fuzzy RD approach has be- come a model for subsequent work on class size effects.

4. Londoño-Vélez et al.

[2020] Upstream and Downstream Impacts of College Merit Aid

Citation: Londoño-Vélez, J., Rodríguez, C., and Sánchez, F. (2020). Upstream and down- stream impacts of college merit aid: Long-run evidence from Colombia's Ser Pilo Paga. American Economic Journal: Economic Policy, 12(2), 193-227.

Research Question: Does merit-based college financial aid for disadvantaged high- achieving students improve long-run earnings and social mobility? Colombia's Ser Pilo Paga programme provided full scholarships to low-income students scoring above a threshold on the national exam.

Identification Strategy: A regression discontinuity at the programme eligibility thresh- old in the national college admission test score. Students just above the threshold received scholarships worth full tuition at elite universities; students just below did not. The authors supplement the RD with administrative data linking exam records to tax and social security earnings data.

Key Result: Receiving the scholarship substantially increases enrollment at elite uni- versities (first-stage effect of roughly 50 percentage points) and, five years after eligibility, increases formal employment by 14 percentage points and monthly earnings by 35%.  Effects are concentrated among first-generation college students. The paper also documents up- stream effects: programme announcement raised test preparation effort among low-income students, increasing their scores.

Takeaway: Well-targeted merit aid for disadvantaged high-achievers can generate large, persistent earnings gains. The combination of RD with matched administrative earnings data is a powerful template for evaluating education policy.

References

1. Angrist, J. D. and Lavy, V. (1999). Using Maimonides' rule to estimate the effect of class size on scholastic achievement. Quarterly Journal of Economics, 114(2):533-575.
2. Calonico, S., Cattaneo, M. D., and Titiunik, R. (2014). Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica, 82(6):2295-2326.
3. Dell, M. (2010). The persistent effects of Peru's mining mita. Econometrica, 78(6):1863-1903.
4. Londoño-Vélez, J., Rodríguez, C., and Sánchez, F. (2020). Upstream and downstream im- pacts of college merit aid: Long-run evidence from Colombia's Ser Pilo Paga. American Economic Journal: Economic Policy, 12(2):193-227.