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The Inconsistency of Common Scales Estimators when Output Prices are Unobserved and Endogenous

This paper explores the inconsistency of common scale estimators when output is proxied by deflated sales, based on a common output deflator across firms. The problems arise when firms operate in an imperfectly competitive environment and prices differ between firms. In particular, we show that this problem reveals itself as a downward bias in the scale estimates obtained from production function regressions, under a variety of assumptions about the pattern of technology, demand and factor price shocks. The result also holds for scale estimates obtained from cost functions. The analysis is carried one step further by adding a model of product demand. Within this augmented model we examine the probability limit of the scale estimate obtained from an ordinary production function regression. This analysis reveals that the OLS estimate will be biased towards unity - or possibly a value below unity. We have included an empirical section which illustrates the issues. The empirical analysis presents a tentative approach to avoid the problems discussed in the theoretical part of this paper.

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Paper provided by Statistics Norway, Research Department in its series Discussion Papers with number 127.

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Date of creation: Oct 1994
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Handle: RePEc:ssb:dispap:127
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  1. Jacques Mairesse & Zvi Griliches, 1988. "Heterogeneity in Panel Data: Are There Stable Production Functions?," NBER Working Papers 2619, National Bureau of Economic Research, Inc.
  2. Eric J. Bartelsman & Ricardo J. Caballero & Richard K. Lyons, 1991. "Short and Long Run Externalities," NBER Working Papers 3810, National Bureau of Economic Research, Inc.
  3. Benjamin Eden & Zvi Griliches, 1991. "Productivity, Market Power and Capacity Utilization When Spot Markets are Complete," NBER Working Papers 3697, National Bureau of Economic Research, Inc.
  4. Caballero, R.J. & Lyons, R.K., 1991. "Some Evidence of Productivity Linkages in Manufacturing," Papers fb-27, Columbia - Graduate School of Business.
  5. Zvi Griliches & Jacques Mairesse, 1981. "Productivity and R and D at the Firm Level," NBER Working Papers 0826, National Bureau of Economic Research, Inc.
  6. Kenneth Arrow, 1962. "Economic Welfare and the Allocation of Resources for Invention," NBER Chapters, in: The Rate and Direction of Inventive Activity: Economic and Social Factors, pages 609-626 National Bureau of Economic Research, Inc.
  7. Mankiw, N Gregory, 1990. "A Quick Refresher Course in Macroeconomics," Journal of Economic Literature, American Economic Association, vol. 28(4), pages 1645-60, December.
  8. Matthew D. Shapiro, 1987. "Are Cyclical Fluctuations in Productivity Due More to Supply Shocks or Demand Shocks?," Cowles Foundation Discussion Papers 822, Cowles Foundation for Research in Economics, Yale University.
  9. Paul Krugman, 1986. "Industrial Organization and International Trade," NBER Working Papers 1957, National Bureau of Economic Research, Inc.
  10. Zvi Griliches & Jerry A. Hausman, 1984. "Errors in Variables in Panel Data," NBER Technical Working Papers 0037, National Bureau of Economic Research, Inc.
  11. Robert E. Hall, 1986. "The Relation Between Price and Marginal Cost in U.S. Industry," NBER Working Papers 1785, National Bureau of Economic Research, Inc.
  12. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
  13. Caleb A. Smith, 1955. "Survey of the Empirical Evidence on Economies of Scale," NBER Chapters, in: Business Concentration and Price Policy, pages 213-238 National Bureau of Economic Research, Inc.
  14. Ringstad, Vidar, 1974. "Some Empirical Evidence on the Decreasing Scale Elasticity," Econometrica, Econometric Society, vol. 42(1), pages 87-101, January.
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