  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.
