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SHADOW PRICE APPROACH TO PRODUCTIVITY MEASUREMENT: A Modified Malmquist Index

SHADOW PRICE APPROACH TO PRODUCTIVITY MEASUREMENT: A Modified Malmquist Index. Timo Kuosmanen Helsinki School of Economics and Business Administration FINLAND E-mail: kuosmane@hkkk.fi. Thierry Post Erasmus University Rotterdam, Faculty of Economics THE NETHERLANDS

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SHADOW PRICE APPROACH TO PRODUCTIVITY MEASUREMENT: A Modified Malmquist Index

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  1. SHADOW PRICE APPROACH TO PRODUCTIVITY MEASUREMENT:A Modified Malmquist Index Timo Kuosmanen Helsinki School of Economics and Business Administration FINLAND E-mail: kuosmane@hkkk.fi Thierry Post Erasmus University Rotterdam, Faculty of Economics THE NETHERLANDS E-mail: gtpost@few.eur.nl 8/25/2014

  2. Productivity change= Output change / Input change 8/25/2014

  3. Productivity can improve through - Technological development - Improved operational efficiency - Utilization of economies of scale and of specialization 8/25/2014

  4. Paasche output index 8/25/2014

  5. Laspayers output index 8/25/2014

  6. Fisher ideal output index 8/25/2014

  7. Törnqvist index 8/25/2014

  8. Fisher ideal TFP index 8/25/2014

  9. Törnqvist TFP index 8/25/2014

  10. Why Fisher index? • -Intuitive: Accounts for the “value” of inputs and outputs • -Diewert (1992: JPA) proved that the Fisher ideal index passes over 20 ‘axiomatic’ tests - more than any other candidate considered • -A problem: Perfect price information required. E.g. • i) depreciating durable capital inputs, • ii) new inputs/outputs introduced in the target period, • iii) pricing non-market inputs/outputs. 8/25/2014

  11. Malmquist index 8/25/2014

  12. The relationship of the Fisher andthe Malmquist indexes: • Diewert, W.E. (1992): Fisher Ideal Output, Input and Productivity Indexes Revisited, Journal of Productivity Analysis 3(3), 211-248 • The distance function D has a ‘flexible’ function form • => • the Fisher and the Malmquist indexes are equivalent 8/25/2014

  13. The relationship of the Fisher andthe Malmquist indexes: • Färe, R., and S. Grosskopf (1992): Malmquist Productivity Indexes and Fisher Ideas Indexes, The Economic Journal 102, 158-160 • 1) Production technology: Free disposability, Convexity, Constant Returns to Scale • 2) Allocative efficiency in terms of profit maximization (allows for the Farrell type of technical inefficiency) • => • the Fisher and the Malmquist indexes equivalent 8/25/2014

  14. The relationship of the Fisher andthe Malmquist indexes: • Balk, B. (1993): Malmquist Productivity Indexes and Fisher Ideas Indexes: Comment, The Economic Journal 103, 680-682 • -Does not suffice that (x0,y0) is allocatively efficient w.r.t. the prices and technology of the base period, and (x1,y1) is efficient w.r.t. the prices and technology of the target period. • -We need that (x0,y0) is allocatively efficient w.r.t. the prices and technology of the target period and (x1,y1) efficient w.r.t. the prices and technology of the base period!!?!!! • -Although the Fisher and the Malmquist indexes coincide only by accident, they are reasonable first-order approximations of each other. 8/25/2014

  15. Our research problem: • - Can we compute the exact value of the Fisher ideal index without the price data? • - What is the minimal set of assumptions needed? 8/25/2014

  16. The output distance function: • Define the distance function instead of T w.r.t. cmc(T), where cmc(T) = the smallest monotone convex cone that contains T. • Thus, the distance function has an equivalent dual formulation 8/25/2014

  17. Output distance function: 8/25/2014

  18. Example: y cmc(T) T x 8/25/2014

  19. Allocative efficiency: • Define the allocative efficiency in terms of the return-to-the-dollar (the profit margin). • The shadow price cone: 8/25/2014

  20. Intermediate result: 8/25/2014

  21. The modified Malmquist index: • -We propose to correct for the Balk’s approximation errors by ignoring the ‘irrelevant’ shadow prices. Assume for a moment that unique shadow prices exist: 8/25/2014

  22. Example 1: 8/25/2014

  23. A generalization: • -We propose an interval ‘estimator’: 8/25/2014

  24. Example 2: 8/25/2014

  25. A test application with real data: • -Aggregate production data of 14 OECD countries for years 1970, 1975, 1980, 1985, 1990, 1994 • -Variables: • Output: GDP (Mill. US$, 1990 prices). • Inputs: I) No. of employees. • II) The value of the capital stock (Mill. US$, 1990 prices). 8/25/2014

  26. 8/25/2014

  27. The empirical production frontier: • We fitted the Cobb-Douglas production function by the Corrected Ordinary Least Squares (COLS). 8/25/2014

  28. 8/25/2014

  29. 8/25/2014

  30. 6/1990: 1 US$ = 3.6 FIM 8/25/2014

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