Icarus and Daedalus: Non-Gaussian Micro Shocks and Aggregate Productivity Risk

How does productivity evolve at the microeconomic level, and how does that evolution shape aggregate risk? Using restricted-use plant--product data from India's Annual Survey of Industries (2010-11 to 2022-23), we construct annual physical-output Solow-residual growth accounting for markups, inventories, and heterogeneous input costs. Productivity growth is sharply peaked and fat-tailed, with nonlinear mean reversion that varies with producer size. Larger producers recover more strongly after adverse shocks and retain more of their favorable gains-the Daedalian level effect-yet their shocks extend farther into both tails conditional on entry. Smaller producers exhibit sharper reversals after large favorable shocks-Icarian fallout. We capture these patterns with a three-regime Markov normal mixture conditioned on productivity history and size. Our law of motion yields the distribution of aggregate technology growth. Relative to a size-dependent Gaussian distribution, our regime model has lower aggregate dispersion but substantially thicker standardized tails and raises the probability of an aggregate technology contraction from 0.05% to 0.31%. Removing size dependence while retaining three regimes instead lowers expected growth and raises contraction probability to 2.47%. These separately estimated alternatives show that nonnormality and size dependence have distinct implications for aggregate risk. Granularity is distributional: aggregation weights determine whose shocks matter; productivity dynamics determine the risks they carry.