Of empty boxes: Returns to scale revisited

Eric J. Bartelsman*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)59-67
Number of pages9
JournalEconomics Letters
Issue number1
Publication statusPublished - 1995


  • Instrumental variables
  • Price markup
  • Returns to scale
  • Small sample bias

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