1. Estimating Average Causal Effects Under General Interference

Citation: Aronow and Samii [2017]. "Estimating Average Causal Effects Under General Interference, with Application to a Social Network Experiment." Annals of Applied Statistics, 11(4): 1912-1947.

       Research question. How can researchers define and estimate causal effects when treatment of unit i can affect the outcome of unit j that is, when SUTVA is violated? 

       Identification strategy. The paper introduces the exposure mapping framework: a function f_i(D) that summarises the treatment assignment of the full population in the way relevant for unit i's outcome. Under a known randomisation mechanism, Horvitz-Thompson-style inverse probability weighting identifies the mean potential outcome at any exposure level.

       Key result. Applied to a social network experiment in which information was seeded among connected units, the exposure mapping approach recovers distinct direct effects (being treated yourself) and spillover effects (having treated neighbours), with tighter standard errors than the naive comparison of treated to control. In the application, the spillover effect was statistically significant and economically meaningful.

      Takeaway. A carefully specified exposure mapping can recover both direct and indirect causal effects from experiments that appear to violate SUTVA, at the cost of requiring a known or well-estimated propensity function.

2. Causal Inference Under Approximate Neighbourhood Interference

Citation: Leung [2022]. "Causal Inference Under Approximate Neighborhood Interference." Econometrica, 90(1): 267-293.

      Research question. How can we perform valid inference on average causal effects in large networks when the interference structure is not precisely known, only approximately?

      Identification strategy. Assumes that unit i's outcome depends primarily on the treatment of units within K network steps of i, with the influence of distant units decaying to zero as network distance increases. This is "approximate neighbourhood interference" (ANI). Under ANI, central limit theorems hold for DIM and Horvitz-Thompson estimators under Bernoulli assignment, enabling standard asymptotic inference.
      Key result. The estimator is consistent and asymptotically normal as the network grows, even though units are correlated within a neighbourhood. The key condition is that the network satisfies certain sparsity and mixing properties that limit the extent of long-range correlation. The paper provides conditions under which heteroskedasticity-robust standard errors are valid.‍

      Takeaway. Researchers working with observational social network data do not need to specify an exact interference structure; ANI provides a tractable and verifiable condition that enables inference under realistic network interaction patterns.

3. The Diffusion of Microfinance

Citation: Banerjee et al. [2013]. "The Diffusion of Microfinance." Science, 341(6144): 1236498.‍

       Research question. Which network characteristics of initial seed households predict the eventual village-wide adoption of microfinance? Can network centrality measures be used to improve the targeting of information seeding in development programmes?

      Identification strategy. Village-randomised natural experiment: microfinance was introduced in 43 villages in Karnataka, India. Information was seeded with households of varying network positions (as measured by pre-programme census-based network surveys). The outcome is the fraction of households in the village that ultimately adopted microfinance.

      Key result. Villages where initial seeds had higher "diffusion centrality"-a measure of how well-connected a node is for spreading information across the network showed significantly higher microfinance adoption rates. The effect is economically large: a one-standard-deviation increase in diffusion centrality of seeds raises village-wide adoption by approximately 7 percentage points (from a mean of 18%).‍

      Takeaway. Network structure is a first-order determinant of information diffusion in development settings; seeding with high-centrality households can substantially amplify programme take-up, with direct implications for targeting in public health, agricultural extension, and financial inclusion programmes.

4. Spillovers in Education: Peer Effects in the Tennessee STAR Experiment

Citation: Krueger [1999]. "Experimental Estimates of Education Production Functions." Quarterly Journal of Economics, 114(2): 497-532. Reanalysis by Graham [2008].‍

      Research question. In the Tennessee STAR randomised experiment (which randomised class sizes), do the outcomes of students in one classroom spill over to students in another? And if so, what does this imply for the estimated effect of class size on student achievement?

      Identification strategy. Graham [2008] uses the experimental variation in peer group composition induced by the STAR randomisation to identify peer effects. When students are randomly assigned across classes of different sizes, within-school variation in peer group characteristics (e.g., fraction of high-ability classmates) is quasi-randomly assigned.
      Key result. Peer effects in STAR are positive and statistically significant: having more high-ability classmates raises test scores by approximately 0.1-0.2 standard deviations. Accounting for peer effects substantially reduces but does not eliminate the estimated class-size effect, since smaller classes also have lower-variance peer compositions.

      Takeaway. Ignoring spillovers in education randomised experiments leads to biased estimates of both class-size effects and peer effects. The STAR data, with its multi-level randomisation, provides one of the few clean designs for separating direct treatment effects from peer spillovers.

References

1. Aronow, P. M. and Samii, C. (2017). Estimating average causal effects under general interference, with application to a social network experiment. Annals of Applied Statistics, 11(4):1912-1947.
2. Banerjee, A., Chandrasekhar, A. G., Duflo, E., and Jackson, M. O. (2013). The diffusion of microfinance. Science, 341(6144):1236498.
3. Graham, B. S. (2008). Identifying social interactions through conditional variance restrictions. Econometrica, 76(3):643-660.
4. Krueger, A. B. (1999). Experimental estimates of education production functions. Quarterly Journal of Economics, 114(2):497-532.
5. Leung, M. P. (2022). Causal inference under approximate neighborhood interference. Econometrica, 90(1):267-293.[cite: 12]

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