Of empty boxes: Returns to scale revisited

This paper highlights the bias in returns to scale or price-cost markup coefficients when estimated from the inverse of a production relationship. Coefficients estimated from the inverse are larger than when estimated directly, and the size of the bias increases as the price-cost markup or the scale elasticity of the underlying production function gets smaller. An instrumental variables estimator, although consistent, still exhibits a small sample bias if more than one instrument is used. For comparison, direct estimates of scale elasticities are provided for two-digit SIC private business sectors and for four-digit manufacturing sectors. Little evidence is found for increasing returns to scale in the manufacturing sector.