Estimates of the Returns to Scale for US Manufacturing

This paper estimates the degree of the returns to scale for 2-digit U.S. manufacturing industries from the output-based primal and price-based dual equations implied by firms' cost-minimization problems. It seeks to reconcile the cyclical behavior of the primal and dual productivity residuals by allowing for nonconstant returns to scale and imperfect competition. We find significant differences between the estimates of the returns to scale parameter derived from the primal versus the dual equations. The existence of time-varying markups reduces the incidence of significant differences in the primal versus dual returns to scale estimates for the durable goods industries but not for the non-durable goods industries. Likewise, the presence of the quasi-fixity of capital helps to reconcile the behavior of the primal and dual productivity residuals for the durable but not for the non-durable goods industries.