Scalable Structural Estimation of Networked Infrastructure: Exact Decomposition for Localized Coordination

Interaction effects are often economically central in environments where structural dynamic estimation becomes computationally infeasible. Under fixed group membership and sparse within-group interaction structure, the Bellman operator admits a block-diagonal decomposition that allows high-dimensional dynamic programs to be solved through independent group-level subproblems while preserving the original structural problem exactly. The result applies to a class of dynamic discrete choice models in which interactions are confined within stable local groups and state transitions depend only on within-group conditions. We apply the framework to replacement decisions across 14,344 GPU node locations in the Titan supercomputer, where operating environments differ systematically across cage positions. The structural estimates reveal significant spatial coordination: both neighboring failures and recent local replacement activity increase replacement incentives. Accounting for these interaction effects materially shifts predicted replacement timing and reveals significant misoptimization costs in benchmarks that assume conditional independence. More broadly, the results show how exploiting sparsity in interaction structures can make fully structural estimation feasible in large-scale networked systems without relying on simulation-based auxiliary moments or numerical approximation.