Conventional productivity estimation treats unobserved heterogeneity as a single efficiency term, conflating product quality with physical output efficiency. This paper shows that unobserved quality and quantity-based productivity (TFPQ) can be separately identified from panel data on prices, quantities, and inputs when the two latent variables exhibit differential persistence. A constructive nonparametric identification argument based on transformation models is developed, alongside a parametric estimator for implementation. Applied to Japanese cotton spinning (1914-1920), instrumenting for electric motor adoption with geographic variation in electricity grid access, quality increased by 1.5 percent per percentage point increase in electric motor share while TFPQ remained unchanged. Full electrification raised quality by nearly 60 percent relative to no adoption.
Keywords: Production function; quality; productivity; electrification
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.