B.4 5 Methodological Blueprint for Applied Researchers

B.4.1 5.1 Diagnosing Interference

• Step 1: Theorize likely spillover channels (e.g., ranking algorithms, price comparisons).
• Step 2: Conduct a meta-experiment with dual randomization and compare TATEs.
• Step 3: Quantify exposure probabilities using network or item similarity matrices.

B.4.2 5.2 Cluster Construction Algorithm

Input: substitution matrix S (from clicks/bookings)

Steps:
1. Symmetrize: W = (S + Sᵀ)/2
2. Compute normalized graph Laplacian L
3. Embed nodes via top-k eigenvectors of L
4. Apply k-means clustering (k via gap statistic)
5. Merge tiny clusters (<m listings) if needed

Evaluate using neighbor purity: proportion of nearest neighbors within the same cluster. Airbnb threshold: ≥0.9 → <5% cross-cluster exposure.

B.4.3 5.3 Analysis Plan

• Use cluster-robust standard errors or Horvitz–Thompson weights.
• Adjust for intra-cluster correlation using methods from Eckles et al.
• Apply OLS with pre-stratification to improve power.

B.4.4 5.4 Practical Considerations

Challenge	Recommended Approach
Power loss	Increase experiment duration; pre-stratify clusters
Uneven traffic	Weight treatment assignment by expected demand
Two-sided interactions	Analyze both market sides separately and track cross-effects

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