Sandpile Economics: Theory, Identification, and Evidence
Forman-Ricci curvature of input-output networks predicts recessions better than standard macro metrics — and capitalism is structurally wired for collapse.
The Thesis
Sandpile Economics formalizes a testable mechanism: as economies specialize and supply chains tighten, the Forman-Ricci curvature of inter-sectoral networks turns negative, pushing cascade-size distributions into power-law territory with tail index α∈(1,2) — meaning variance is literally infinite. The paper shows empirically that a one-standard-deviation rise in curvature correlates with meaningfully higher cumulative GDP growth over three-year horizons, outperforming degree centrality and other standard graph metrics. If curvature is a reliable leading indicator, it belongs in every macro hedge fund's signal library alongside yield curves and PMIs.
Catalyst
Global input-output datasets (WIOD, OECD TiVA) have matured to the point where granular cross-country network topology can actually be computed and compared over time. Forman-Ricci curvature tools from discrete geometry became computationally tractable on large graphs only in the last few years, making this kind of empirical application feasible now rather than theoretically possible in principle.
What's New
Prior network-macro work (Acemoglu et al. 2012, Baqaee-Farhi) focused on degree distributions and Hulten-style productivity shocks — linear amplification through network centrality. This paper argues those frameworks miss the nonlinear geometry: curvature captures local substitution possibilities at each node, which determines whether a disruption gets absorbed or avalanches, something centrality measures cannot see.
The Counter
The history of macro early-warning indicators is a graveyard of in-sample champions that fail out-of-sample. Yield curve inversions, credit-to-GDP gaps, and Minsky ratios all looked robust in backtests and then missed or false-alarmed on the episodes that mattered. Curvature-based prediction using input-output data faces a compounding problem: the data is lagged, coarsely sectored, and constructed partly from surveys rather than transactions, meaning the 'network' being analyzed is a statistical artifact smoothed by national statistical offices, not the actual web of supplier relationships that transmits shocks in real time. More fundamentally, the paper's own framework is non-ergodic and path-dependent — which is intellectually honest but also means any regression coefficient estimated on historical data carries an unknown instability. The three-year horizon result is suggestive but three years is long enough that hundreds of other macro variables (terms of trade, monetary policy stance, fiscal space) will dominate curvature in any serious horse race. The theoretical elegance of mapping Forman-Ricci curvature onto substitutability is real, but elegance and tradeable alpha are different things.
Longs
- MSCI
- SPGI
- ICE
- RELX
Shorts
- DSGE-model vendors and consultancies whose representative-agent frameworks are explicitly declared unable to capture these dynamics
- Rating agencies (Moody's, S&P) whose sovereign risk models rely on linear macro indicators rather than structural network topology
- Central banks whose existing stress-testing infrastructure ignores network curvature as a systemic risk variable
Enablers (Picks & Shovels)
- OECD and World Bank as data providers for input-output tables
- NetworkX / graph-tool open-source maintainers enabling curvature computation
- AWS and GCP for large-scale graph processing workloads
- NVIDIA (graph neural network acceleration)
Private Watchlist
- Kensho Technologies
- Predata
- Visible Alpha
The Paper
Why do capitalist economies recurrently generate crises whose severity is disproportionate to the size of the triggering shock? This paper proposes a structural answer grounded in the evolutionary geometry of production networks. As economies evolve through specialization, integration, and competitive selection, their inter-sectoral linkages drift toward configurations of increasing geometric fragility, eventually crossing a threshold beyond which small disturbances generate disproportionately large cascades. We introduce Sandpile Economics, a formal framework that interprets macroeconomic instability as an emergent property of disequilibrium production networks. The key state variable is the Forman--Ricci curvature of the input--output graph, capturing local substitution possibilities when supply chains are disrupted. We show that when curvature falls below an endogenous threshold, the distribution of cascade sizes follows a power law with tail index $α\in (1,2)$, implying a regime of unbounded amplification. The underlying mechanism is evolutionary: specialization reduces input substitutability, pushing the economy toward criticality, while crisis episodes induce endogenous network reconfiguration and path dependence. These dynamics are inherently non-ergodic and cannot be captured by representative-agent frameworks. Empirically, using global input--output data, we document that production networks operate in persistently negative curvature regimes and that curvature robustly predicts medium-run output dynamics. A one-standard-deviation increase in curvature is associated with higher cumulative growth over three-year horizons, and curvature systematically outperforms standard network metrics in explaining cross-country differences in resilience.