On the nonparametric identification of productivity growth in the presence of selection

How much of aggregate productivity growth is driven by common productivity improvements across firms and how much is driven by the better selection of firms? In this short paper, I study the non- parametric identification of these two sources of productivity growth. I propose a framework that nests various endogenous and exogenous growth models and requires only (mild) restrictions on exit behavior and the shocks that drive heterogeneity in productivity. In this framework, separate identification of selection and a common, time-varying productivity growth term involves solving two selection biases. The first is a static or compositional selection bias whereby average productivity can increase due to entry and exit in the absence of any within-firm changes in productivity. The second, dynamic selection bias, arises from the persistence of productivity shocks and is driven by mean reversion. I show how a weighted average of within-plant productivity changes allows separate identification. Weights are chosen such that the dynamic selection bias exactly cancels and can be found by constructing a stationary distribution of the underlying productivity shocks from a synthetic panel of firms over time. I show how the identification approach can be extended to studying cohort effects and more general forms of heterogeneous productivity growth.