In this paper we take up the analysis of production functions / frontiers removing the assumptions of known functional form for the productivity equation, given the heterogeneity of productivity and the endogeneity of inputs at firm level. The assumption of exogenous regressors is removed through taking account of the first order conditions of profit maximization. We introduce latent dynamic stochastic productivity in our framework and perform Bayesian analysis using a Sequential Monte Carlo Particle-Filtering approach. We investigate the performance of the new approach relative to alternative methods in the literature, in a substantive application to Indian non-financial firms, and find that total factor productivity (TFP) growth has remained stagnant at firm level in India despite rapid growth at the aggregate level, with technical efficiency or catching-up effect driving TFP growth in the recent years rather than technological progress or frontier shift. © 2018 Elsevier B.V.