Estimating Production Functions in Differentiated-Product Industries with Quantity Information and External Instruments

This paper highlights shortcomings of standard methods of production-function estimation when quality or variety vary at the firm level and develops a new approach that can be applied in such contexts. We take advantage of input and output quantity data from Colombian producers of rubber and plastic products. Using constant-elasticity-of-substitution aggregators of outputs and material inputs at the firm level, we derive a simple expression showing how quality and variety choices may bias standard estimators. Using real exchange rates and variation in the “bite” of the national minimum wage, we construct external instruments for materials and labor choices to supplement standard internal instruments. We implement a two-step instrumental-variables method, estimating a difference equation to recover the materials and labor coefficients and then a levels equation to recover the capital coefficient. A simple Monte-Carlo simulation illustrates the advantages of our method in a setting with firm-level input-quality differences.