1. [Part 8] 1/27 Stochastic FrontierModels Applications Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction 1Efficiency Measurement 2Frontier Functions 3Stochastic Frontiers 4Production and Cost 5Heterogeneity 6Model Extensions 7Panel Data 8Applications

2. [Part 8] 2/27 Stochastic FrontierModels Applications 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…

3. [Part 8] 3/27 Stochastic FrontierModels Applications 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…”)

4. [Part 8] 4/27 Stochastic FrontierModels Applications 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.

5. [Part 8] 5/27 Stochastic FrontierModels Applications Alvarez, Arias, Greene Fixed Management  Y it = f(x it,m i *) where m i * = “management”  Actual m i = m i * - u i. Actual falls short of “ideal”  Translates to a random coefficients stochastic frontier model  Estimated by simulation  Application to Spanish dairy farms

6. [Part 8] 6/27 Stochastic FrontierModels Applications Fixed Management as an Input Implies Time Variation in Inefficiency

7. [Part 8] 7/27 Stochastic FrontierModels Applications Random Coefficients Frontier Model [Chamberlain/Mundlak: Correlation m i * (not m i -m i *) with x it ]

8. [Part 8] 8/27 Stochastic FrontierModels Applications Estimated Model First order production coefficients (standard errors). Quadratic terms not shown.

9. [Part 8] 9/27 Stochastic FrontierModels Applications Inefficiency Distributions Without Fixed Management With Fixed Management

10. [Part 8] 10/27 Stochastic FrontierModels Applications 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

11. [Part 8] 11/27 Stochastic FrontierModels Applications 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)

12. [Part 8] 12/27 Stochastic FrontierModels Applications Macro Performance Koop et al.  Productivity Growth in a stochastic frontier model  Country, year, Y it = f t (K it,L it )E it w it  Bayesian estimation  OECD Countries, 1979-1988

13. [Part 8] 13/27 Stochastic FrontierModels Applications 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

14. [Part 8] 14/27 Stochastic FrontierModels Applications Energy Consumption  Derived input to household and community production  Cost analogy  Panel data, statewide electricity consumption: Filippini, Farsi, et al.

15. [Part 8] 15/27 Stochastic FrontierModels Applications Hospitals  Usually cost studies Multiple outputs – case mix “Quality” is a recurrent theme  Complexity – unobserved variable  Endogeneity  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. [Part 8] 16/27 Stochastic FrontierModels Applications 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. [Part 8] 17/27 Stochastic FrontierModels Applications 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. [Part 8] 18/27 Stochastic FrontierModels Applications 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. [Part 8] 19/27 Stochastic FrontierModels Applications 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. [Part 8] 20/27 Stochastic FrontierModels Applications 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

21. [Part 8] 21/27 Stochastic FrontierModels Applications Summary

22. [Part 8] 22/27 Stochastic FrontierModels Applications Inefficiency

23. [Part 8] 23/27 Stochastic FrontierModels Applications Methodologies  Data Envelopment Analysis HUGE User base Largely atheoretical Applications in management, consulting, etc.  Stochastic Frontier Modeling More theoretically based – “model” based More active technique development literature Equally large applications pool

24. [Part 8] 24/27 Stochastic FrontierModels Applications SFA Models  Normal – Half Normal Truncation Heteroscedasticity Heterogeneity in the distribution of u i  Normal-Gamma, Exponential, Rayleigh Classical vs. Bayesian applications Flexible functional forms for inefficiency There are yet others in the literature

25. [Part 8] 25/27 Stochastic FrontierModels Applications Modeling Settings  Production and Cost Models  Multiple output models Cost functions Distance functions, profits and revenue functions

26. [Part 8] 26/27 Stochastic FrontierModels Applications Modeling Issues  Appropriate model framework Cost, production, etc. Functional form  How to handle observable heterogeneity – “where do we put the zs?”  Panel data Is inefficiency time invariant? Separating heterogeneity from inefficiency  Dealing with endogeneity  Allocative inefficiency and the Greene problem

27. [Part 8] 27/27 Stochastic FrontierModels Applications Range of Applications  Regulated industries – railroads, electricity, public services  Health care delivery – nursing homes, hospitals, health care systems (WHO, AHRQ)  Banking and Finance  Many other industries. See Lovell and Schmidt “Efficiency and Productivity” 27 page bibliography. Table of over 200 applications since 2000