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

This paper uses output- and input-quantity information and external instruments for materials and labor choices to improve production-function estimates. In rich Colombian data on producers of rubber and plastic products, we construct the external instruments from exchange-rate movements and variation in the “bite” of the minimum wage. Under assumptions of constant elasticities of substitution among outputs and inputs within firms, we aggregate from the firm-product to the firm level and show how quality and variety choices may bias quantity-based estimators. We supplement the external instruments with internal instruments — lagged levels and differences of input choices — in a two-step approach, estimating a difference equation to recover the materials and labor coefficients and a levels equation to recover the capital coefficient. Our estimates imply markups that are 67-70% of those implied by standard proxy-variable methods. A simple Monte Carlo simulation illustrates the advantages of our approach in a controlled setting with firm-level input-quality differences.