Using Proxy Variables to Control for Unobservables When Estimating Productivity: A Sensitivity Analysis

The use of proxy variables to control for unobservables when estimating a production function has become increasingly popular in empirical works in recent years. The present paper aims to contribute to this literature in three important ways. First, we provide a structured review of the different estimators and their underlying assumptions. Second, we compare the results obtained using different estimators for a sample of Spanish manufacturing firms, using definitions and data comparable to those used in most empirical works. In comparing the performance of the different estimators, we rely on various proxy variables, apply different definitions of capital, use alternative moment conditions and allow for different timing assumptions of the inputs. Third, in the empirical analysis we propose a simple (non-graphical) test of the monotonicity assumption between productivity and the proxy variable. Our results suggest that productivity measures are more sensitive to the estimator choice rather than to the choice of proxy variables. Moreover, we find that the monotonicity assumption does not hold for a non-negligible proportion of the observations in our data. Importantly, results of a simple evaluation exercise where we compare productivity distributions of exporters versus non-exporters shows that different estimators yield different results, pointing to the importance of making suitable timing assumptions and choosing the appropriate estimator for the data at hand.