Microeconomic shocks need not wash out in the aggregate when the economy's input–output network is asymmetric. The standard diversification argument (Lucas 1977) says that with n sectors hit by independent shocks, aggregate volatility vanishes at rate 1/√n. This paper shows that the true decay rate is governed by the structure of the intersectoral network: if a few sectors are central suppliers, idiosyncratic shocks to those hubs propagate downstream and generate sizable aggregate fluctuations that decay far more slowly than 1/√n. Empirically, the US input–output structure implies aggregate volatility decays no faster than ~n^0.15 — much slower than the n^0.5 a balanced economy would deliver.
The question
Can purely idiosyncratic, sector-level shocks be the origin of business-cycle-scale aggregate fluctuations, despite the diversification ("law of large numbers") argument that says they should average out as the economy disaggregates?
The model
A static multi-sector general-equilibrium economy with Cobb–Douglas production; sectors use each other's output as intermediate inputs, encoded in an input–output matrix W.
Each sector receives an independent idiosyncratic productivity shock. Aggregate output (log GDP) is a weighted sum of sectoral shocks, with weights given by the influence/Domar vector v = (1/n)[I − (1−α)W']⁻¹ 1 — i.e., a sector's importance equals its direct plus higher-order role as a supplier.
Aggregate volatility scales with the Euclidean norm of v, not simply with 1/√n.
Key predictions
Theorem 2 (first-order): asymmetry in sectors' outdegrees (importance as direct suppliers) lowers the decay rate of aggregate volatility. If the empirical degree distribution follows a power law with shape β ∈ (1,2), aggregate volatility decays no faster than n^((β−1)/β) — slower than n^0.5.
Theorem 3 (second-order): even networks with identical first-order degree distributions can differ sharply in volatility because of "cascade effects" — sectors that are large indirect suppliers (suppliers of suppliers). A power law in second-order degrees with shape ζ ∈ (1,2) gives decay no faster than n^((ζ−1)/ζ).
Empirics (Section 4): US 6-digit input–output data exhibit heavy-tailed (power-law) first- and second-order degree distributions; the implied bound is decay slower than ~n^0.15 — the economy behaves more like a "star" network than a "complete" one. Sparseness of the matrix per se is not what matters.
Empirical status
A foundational and widely-cited result connecting network topology to macro volatility and to the "granular" origins of fluctuations (complements Gabaix 2011, whose firm-size channel is the n^a special case). It reframes systemic-risk thinking: diversification can fail at the system level when linkages are concentrated, so idiosyncratic shocks to central nodes become non-diversifiable aggregate risk.
Limitations
Static, real-side model with Cobb–Douglas technology and a specific frictionless equilibrium; abstracts from prices/demand dynamics.
Requires good input–output data; mapping sectoral networks to firm-level networks is nontrivial.
Financial-network amplification (interbank, funding spirals) is a distinct channel not modeled here.
Key references
Acemoglu, D., Carvalho, V., Ozdaglar, A. & Tahbaz-Salehi, A. (2012) — The Network Origins of Aggregate Fluctuations — Econometrica
Gabaix, X. (2011) — The Granular Origins of Aggregate Fluctuations — Econometrica
Lucas, R. (1977) — Understanding Business Cycles — Carnegie-Rochester Conference Series
Provenance: verified/generated from the paper's full text.
