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Efficiency Measurement

Explore applications of efficiency measurement in regulated industries, healthcare, banking, sports, and more. Learn about frontier models, random coefficients, panel data, and Bayesian estimation techniques. Discover insights from studies in sectors like hospitals, farming, banking, and sewers.

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Efficiency Measurement

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  1. William Greene Stern School of Business New York University Efficiency Measurement

  2. Session 9 Applications

  3. Range of Applications • Regulated industries – railroads, electricity, public services • Health care delivery – nursing homes, hospitals, health care systems (WHO) • Banking and Finance • Many, many (many) other industries. See Lovell and Schmidt survey…

  4. Discrete Variables • Count data frontier • Outcomes inside the frontier: Preserve discrete outcome • Patents (Hofler, R. “A Count Data Stochastic Frontier Model,” • Infant Mortality (Fe, E., “On the Production of Economic Bads…”)

  5. Count Frontier P(y*|x)=Poisson Model for optimal outcome • Effects the distribution: P(y|y*,x)=P(y*-u|x)= a different count model for the mixture of two count variables • Effects the mean:E[y*|x]=λ(x) while E[y|x]=u λ(x) with 0 < u < 1. (A mixture model) • Other formulations.

  6. Alvarez, Arias, Greene Fixed Management • Yit = f(xit,mi*) where mi* = “management” • Actual mi = mi* - ui. Actual falls short of “ideal” • Translates to a random coefficients stochastic frontier model • Estimated by simulation • Application to Spanish dairy farms

  7. Fixed Management as an Input Implies Time Variation in Inefficiency

  8. Random Coefficients Frontier Model [Chamberlain/Mundlak: Correlation mi* (not mi-mi*) with xit]

  9. Estimated Model First order production coefficients (standard errors). Quadratic terms not shown.

  10. Inefficiency Distributions Without Fixed Management With Fixed Management

  11. Holloway, Tomberlin, Irz: Coastal Trawl Fisheries • Application of frontier to coastal fisheries • Hierarchical Bayes estimation • Truncated normal model and exponential • Panel data application • Time varying inefficiency • The “good captain” effect vs. inefficiency

  12. Sports • Kahane: Hiring practices in hockey • Output=payroll, Inputs=coaching, franchise measures • Efficiency in payroll related to team performance • Battese/Coelli panel data translog model • Koop: Performance of baseball players • Aggregate output: singles, doubles, etc. • Inputs = year, league, team • Policy relevance? (Just for fun)

  13. Macro Performance Koop et al. • Productivity Growth in a stochastic frontier model • Country, year, Yit = ft(Kit,Lit)Eitwit • Bayesian estimation • OECD Countries, 1979-1988

  14. Mutual Fund Performance • Standard CAPM • Stochastic frontier added • Excess return=a+b*Beta +v – u • Sub-model for determinants of inefficiency • Bayesian framework • Pooled various different distribution estimates

  15. Hospitals • Usually cost studies • Multiple outputs – caqse mix • “Quality” is a recurrent theme - complexity • Rosko: US Hospitals, multiple outputs, panel data, determinants of inefficiency = HMO penetration, payment policies, also includes indicators of heterogeneity • Australian hospitals: Fit both production and cost frontiers. Finds large cost savings from removing inefficiency.

  16. Law Firms • Stochastic frontier applied to service industry • Output=Revenue • Inputs=Lawyers, associates/partners ratio, paralegals, average legal experience, national firm • Analogy drawn to hospitals literature – quality aspect of output is a difficult problem

  17. Farming • Hundreds of applications • Major proving ground for new techniques • Many high quality, very low level micro data sets • O’Donnell/Griffiths – Philippine rice farms • Latent class – favorable or unfavorable climate • Panel data production model • Bayesian – has a difficult time with latent class models. Classical is a better approach

  18. Railroads and other Regulated Industries • Filippini – Maggi: Swiss railroads, scale effects etc. Also studied effect of different panel data estimators • Coelli – Perelman, European railroads. Distance function. Developed methodology for distance functions • Many authors: Electricity (C&G). Used as the standard test data for Bayesian estimators

  19. Banking • Dozens of studies • Wheelock and Wilson, U.S. commercial banks • Turkish Banking system • Banks in transition countries • U.S. Banks – Fed studies (hundreds of studies) • Typically multiple output cost functions • Development area for new techniques • Many countries have very high quality data available

  20. Sewers • New York State sewage treatment plants • 200+ statewide, several thousand employees • Used fixed coefficients technology • lnE = a + b*lnCapacity + v – u; b < 1 implies economies of scale (almost certain) • Fit as frontier functions, but the effect of market concentration was the main interest

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