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Empirical Estimation and Quantitative Analysis

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Part of the Transportation Research, Economics and Policy book series (TRES)

Abstract

The translog variable cost function (equation 6.2) in our study is specified with one output (Y) revenue passenger miles, one quasi-fixed factor, the capital stock (K) of flight equipment that has been quality adjusted with technological parameters — payload, SFC, range, thrust and passenger capacity — and five variable inputs, labor (L), energy (E), materials (M), business services (S) and other expenses (O). A full description of the model can be found in Chapter 6. Efficient estimates of The Restricted Variable Cost Function (RVCF) over the period 1970-1992 (161 observations) for the seven major carriers were obtained using the Generalized Method of Moments (GMM)1 estimation algorithm in the TSP (Time Series Processor) econometric software program.2 All of the parameters in the RVCF model are identified by estimating a pooled time series cross-sectional translog variable cost function jointly with a revenue equation, and five input demand equations, instead of the value shares of inputs. The input demand equations are subject to the same linear homogeneity and symmetry restrictions as the share equations. Our regression coefficients are therefore in quantity terms rather than input value shares. The techniques of estimating translog cost functions with input demand quantities are described by McElroy (1987)3 and Norsworthy and Jang (1992)4. The fitted variable cost function satisfies at every sample point the regularity conditions that it be non-decreasing and concave in input prices.

Keywords

Total Factor Productivity Capacity Utilization Airline Industry Cross Price Elasticity Shadow Cost 
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Endnotes

  1. 1.
    Hansen, L., (1982) “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, Vol. 50, pp. 1029–1054; Hansen, L. and Singleton, K. (1982) “Generalized Instrumental Variables Estimation of Non-Linear Rational Expectations Models,” Econometrica, Vol. 50, pp. 1269-1286.CrossRefGoogle Scholar
  2. 2.
    TSP International Software, P.O. Box 61015, Station A, Palo Alto, CA. 94306.Google Scholar
  3. 3.
    McElroy, M. (1987) “Additive General Error Models for Production Cost, and Derived Demand or Shared Systems,” Journal of Political Economy, Vol. 95(4), pp. 737–757.CrossRefGoogle Scholar
  4. 4.
    Norsworthy, J.R. and Jang, S.L. (1992) Empirical Analysis of Technology and Productivity in High Technology and Service Industries, North-Holland Press.Google Scholar
  5. 5.
    The Restricted Variable Cost Function specification is Equation (6.2).Google Scholar
  6. 6.
    Input Demand Equations are specified by Equation (6.6).Google Scholar
  7. 7.
    See Norsworthy and Jang (1992), Chapter 12, pp.277-298 for a detailed discussion on how to specify a revenue equation that is to be jointly estimated with a restricted variable cost function.Google Scholar
  8. 8.
    Judge, G. Griffiths, W., Hill, C, Lutkepohl, H., and Lee, T. (1985) The Theory and Practice of Econometrics, John Wiley and Sons, New York, Chapter 13, pp. 515–560.Google Scholar
  9. 9.
    Boeing Commercial Airplane Group Current Market Outlook (1993), Seattle, Section 2.8.Google Scholar
  10. 10.
    ibid., Section 2.5Google Scholar
  11. 11.
    Economies of scale is specified in equation (5.70).Google Scholar
  12. 12.
    The term “equilibrium” means little in this context.Google Scholar
  13. 13.
    See the discussion in Norsworthy and Jang (1992), Chapter 4, pp. 83-104.Google Scholar
  14. 14.
    Brown, R. and Christensen, L. (1981) “Estimating Elasticities of Substitution in a Model of Partial Static Equilibrium: An Application to U.S. Agriculture, 1947-1974,” in Modeling and Measuring Natural Resource Substitution, edited by E. Berndt and B. Field, The MIT Press, Mass.Google Scholar
  15. 15.
    Berndt E. (1991) The Practice of Econometrics, Addison-Wesley, Mass., page 484. See also Berndt, E. R. and M. Fuss (1986) for a detailed exposition of the relationship between shadow cost and capacity utilization.Google Scholar
  16. 16.
    Our model produced shadow cost of capital estimates in which 98% of the observations were negative The shadow cost of capital estimates were positive in the years 1987, 1991 and 1992 for Continental Airlines and in 1992 for TWA. These two carriers were among the weakest carriers in industry at the time. See Equation (5.72) for the specification of the shadow cost of capital.Google Scholar
  17. 17.
    The Boeing Company Boeing World Jet Airplane Inventory Year End 1990 Seattle Washington p. 30Google Scholar
  18. 18.
    Loftin, L. (1985) Quest for PerformanceThe Evolution of Modern Aircraft, NASA, Washington, D.C. pp. 227–228Google Scholar
  19. 19.
    ibid., pp. 439-440.Google Scholar
  20. 20.
    Brown I. (1981) “The Sources of Airline Productivity-Technical Report on Total Factor Productivity and Specific Factor Contributions,” Air Transport Association of American, Washington, D.C, Appendix B, pp. 79–99.Google Scholar
  21. 21.
    Norsworthy and Jang (1992).Google Scholar
  22. 22.
    Berndt(1991).Google Scholar
  23. 23.
    Loftin (1985), p. 407Google Scholar
  24. 24.
    See Equation (6.3) for our method of incorporating the quality variables into the model.Google Scholar
  25. 25.
    Own and Cross Price Elasticities of Demand are specified by Equation (5.54).Google Scholar
  26. 26.
    Gordon, R. (1991) “Productivity in the Transportation Sector,” Working Paper, National Bureau of Economic Research, Cambridge, MA.Google Scholar
  27. 27.
    Jorgenson(1987).Google Scholar
  28. 28.
    See the TFP discussion in Chapter 5, section (5.7).Google Scholar
  29. 29.
    One may reasonably ask, however, why such an industry would have been regulated in the first place.Google Scholar
  30. 30.
    It may be argued that US Air underwent a transition from a regional to a national airline during the observation period, and is therefore atypical.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  1. 1.Center for Science and Technology PolicyRensselaer Polytechnic InstituteTroyUSA
  2. 2.Lally School of Management and TechnologyRensselaer Polytechnic InstituteTroyUSA

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