Beyond Hulten under Ignorance: The Cumulant Hierarchy of Identification in a Recovered Production Network

When one industry stumbles, how much does the whole economy feel it? Economists increasingly recover the web of who-buys-from-whom not from accounting tables but from how industries move together over time. This paper maps what that comovement can and cannot reveal. It proves that the nonlinear part of propagation, the curvature that amplifies large shocks and skews output into fat tails, cannot be read from the comovement at all, because it depends on a substitution elasticity the data never carry. But the sign of that effect, whether large shocks are amplified or damped, does surface one step further out, in the third-order comovement, under symmetric shocks. A small reproducible numerical example illustrates the results; it demonstrates the theory rather than testing it empirically.