A Unified Approach to Estimating Production Functions: Proxy Variables and Dynamic Panel Data

We propose a new approach to production function estimation that integrates the strengths of the proxy‐variable (PV) and dynamic panel data (DPD) methods. Our framework augments the set of instruments for the level equation in Blundell and Bond [8] with a Berkson‐type instrument motivated by economic theory, following Olley and Pakes [28], Levinsohn and Petrin [24], and Ackerberg et al. [4]. This modification allows unobserved productivity to include both a time‐invariant (“fixed‐effect”) component and a time‐varying component that follows a potentially nonlinear Markov process. Whereas the PV approach accommodates nonlinear Markov dynamics but not fixed effects, and the DPD approach accounts for fixed effects but only with linear Markov dynamics, our method relaxes both restrictions. Our estimator is straightforward to implement using GMM. Monte Carlo simulations demonstrate that it outperforms the canonical PV and DPD estimators when productivity persistence is low and fixed‐effect heterogeneity is substantial.