Efficiency Measurement William Greene Stern School of Business New York University

Session 8 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…

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…”)

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.

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

Fixed Management as an Input Implies Time Variation in Inefficiency

Random Coefficients Frontier Model [Chamberlain/Mundlak: Correlation m i * (not m i -m i *) with x it ]

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

Inefficiency Distributions Without Fixed Management With Fixed Management

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

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)

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,

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

Energy Consumption  Derived input to household and community production  Cost analogy  Panel data, statewide electricity consumption: Filippini, Farsi, et al.

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.

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

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

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

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

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

Summary

Inefficiency

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

SFA Models  Normal – Half Normal Truncation Heteroscedasticity Heterogeneity in the distribution of u i  Normal-Gamma Classical vs. Bayesian applications Flexible functional forms for inefficiency

Modeling Settings  Production and Cost Models  Multiple output models Cost functions Distance functions, profits and revenue functions

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

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