Growth under Ignorance: Balanced Growth as a Perron Eigenray and the Identified Content of a Recovered Production Network

Standard growth theory treats the economy as a single stock of capital, drawn towards a steady state. This paper treats it as a production network, reading balanced growth as the leading eigenvalue and eigenvector of the production operator: the growth rate and the proportions that sustain it, with efficient paths bending onto that direction, the turnpike. Yet from the joint movement of growth rates alone, one firmly recovers the dominant direction and which sectors matter most, but not the input coefficients, growth-accounting weights, or total factor productivity, which observationally identical economies leave spread across an interval. The paper proves this and illustrates it on an exact two-sector example; it runs no empirical test. On this reading the Solow residual measures what such data cannot recover about the sources of growth.