Test of variable output and scale elasticities for 20 US manufacturing industries

Abstract

The production function is examined and tests are made to determine whether or not output and scale elasticities vary across individual industries based on a new CES or the Box-Cox production function and a pooled data set of 20 US manufacturing industries during 1987–91. This approach differs from the conventional method of using long time-series data to estimate output or scale elasticities for each of the 20 manufacturing industries. This new CES function has the advantages of including the Cobb-Douglas and linear functions as special cases, less multicollinearity problems, and more flexibility of output and scale elasticities. Empirical work shows that the new CES function yields better results. Both the Cobb-Douglas (double-log) and linear functions can be rejected at the 1% level. Output-labour elasticities varied from a low of 0.18 for tobacco to a high of 0.70 for apparel. Output-capital elasticities also ranged from 0.31 for apparel to 0.88 for petroleum. Total output or scale elasticities ranged from 0.51 for tobacco to 1.24 for primary metal. Thus, individual industries exhibit different output and scale elasticities. Although many industries show constant returns to scale, there are a number of industries that display decreasing or increasing returns to scale.