This paper examines the nonparametric identifiability of production functions, considering firm heterogeneity beyond Hicks-neutral technology terms. We propose a finite
mixture model to account for unobserved heterogeneity in production technology and
productivity growth processes. Our analysis demonstrates that the production function for each latent type can be nonparametrically identified using four periods of
panel data, relying on assumptions similar to those employed in existing literature on
production function and panel data identification. By analyzing Japanese plant-level
panel data, we uncover significant disparities in estimated input elasticities and productivity growth processes among latent types within narrowly defined industries. We
further show that neglecting unobserved heterogeneity in input elasticities may lead to
substantial and systematic bias in the estimation of productivity growth.