Stochastic Frontier Models - PowerPoint Presentation

Slide1

Stochastic Frontier Models

William GreeneStern School of BusinessNew York University

0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 ApplicationsSlide2

Range of Applications

Regulated industries – railroads, electricity, public servicesHealth care delivery – nursing homes, hospitals, health care systems (WHO)Banking and FinanceMany, many (many) other industries. See Lovell and Schmidt survey…Slide3

Discrete Variables

Count data frontierOutcomes inside the frontier: Preserve discrete outcomePatents (Hofler, R. “A Count Data Stochastic Frontier Model,”Infant Mortality (Fe, E., “On the Production of Economic Bads…”)Slide4

Count Frontier

P(y*|x)=Poisson Model for optimal outcomeEffects the distribution: P(y|y*,x)=P(y*-u|x)= a different count model for the mixture of two count variablesEffects the mean:E[y*|x]=λ

(x) while E[y|x]=u λ(x) with 0 < u < 1. (A mixture model)Other formulations.Slide5

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 modelEstimated by simulationApplication to Spanish dairy farmsSlide6

Fixed Management as an Input Implies Time Variation in InefficiencySlide7

Random Coefficients Frontier Model

[Chamberlain/Mundlak:

Correlation mi* (not mi-mi*) with xit]Slide8

Estimated Model

First order production coefficients (standard errors).

Quadratic terms not shown.Slide9

Inefficiency Distributions

Without Fixed Management

With Fixed ManagementSlide10

Holloway, Tomberlin, Irz: Coastal Trawl Fisheries

Application of frontier to coastal fisheriesHierarchical Bayes estimationTruncated normal model and exponentialPanel data applicationTime varying inefficiencyThe “good captain” effect vs. inefficiencySlide11

Sports

Kahane: Hiring practices in hockeyOutput=payroll, Inputs=coaching, franchise measuresEfficiency in payroll related to team performanceBattese/Coelli panel data translog modelKoop: Performance of baseball playersAggregate output: singles, doubles, etc.Inputs = year, league, teamPolicy relevance? (Just for fun)Slide12

Macro Performance Koop et al.

Productivity Growth in a stochastic frontier modelCountry, year, Yit = ft(Kit,Lit)Eit

witBayesian estimationOECD Countries, 1979-1988Slide13

Mutual Fund Performance

Standard CAPMStochastic frontier addedExcess return=a+b*Beta +v – uSub-model for determinants of inefficiencyBayesian frameworkPooled various different distribution estimatesSlide14

Energy Consumption

Derived input to household and community productionCost analogyPanel data, statewide electricity consumption: Filippini, Farsi, et al.Slide15

Hospitals

Usually cost studiesMultiple outputs – case mix“Quality” is a recurrent theme Complexity – unobserved variableEndogeneityRosko: 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.Slide16

Law Firms

Stochastic frontier applied to service industryOutput=RevenueInputs=Lawyers, associates/partners ratio, paralegals, average legal experience, national firmAnalogy drawn to hospitals literature – quality aspect of output is a difficult problemSlide17

Farming

Hundreds of applicationsMajor proving ground for new techniquesMany high quality, very low level micro data setsO’Donnell/Griffiths – Philippine rice farmsLatent class – favorable or unfavorable climatePanel data production modelBayesian – has a difficult time with latent class models. Classical is a better approachSlide18

Railroads and other Regulated Industries

Filippini – Maggi: Swiss railroads, scale effects etc. Also studied effect of different panel data estimatorsCoelli – Perelman, European railroads. Distance function. Developed methodology for distance functionsMany authors: Electricity (C&G). Used as the standard test data for Bayesian estimatorsSlide19

Banking

Dozens of studiesWheelock and Wilson, U.S. commercial banksTurkish Banking systemBanks in transition countriesU.S. Banks – Fed studies (hundreds of studies)Typically multiple output cost functions

Development area for new techniques Many countries have very high quality data availableSlide20

Sewers

New York State sewage treatment plants200+ statewide, several thousand employeesUsed fixed coefficients technologylnE = 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 interestSlide21

SummarySlide22

InefficiencySlide23

Methodologies

Data Envelopment AnalysisHUGE User baseLargely atheoreticalApplications in management, consulting, etc.Stochastic Frontier ModelingMore theoretically based – “model” based

More active technique development literatureEqually large applications poolSlide24

SFA Models

Normal – Half NormalTruncationHeteroscedasticityHeterogeneity in the distribution of uiNormal-Gamma, Exponential, RayleighClassical vs. Bayesian applicationsFlexible functional forms for inefficiencyThere are yet others in the literatureSlide25

Modeling Settings

Production and Cost ModelsMultiple output modelsCost functionsDistance functions, profits and revenue functionsSlide26

Modeling Issues

Appropriate model frameworkCost, production, etc.Functional formHow to handle observable heterogeneity – “where do we put the zs?”Panel dataIs inefficiency time invariant?Separating heterogeneity from inefficiencyDealing with endogeneity

Allocative inefficiency and the Greene problemSlide27

Range of Applications

Regulated industries – railroads, electricity, public servicesHealth care delivery – nursing homes, hospitals, health care systems (WHO, AHRQ)Banking and FinanceMany other industries. See Lovell and Schmidt “Efficiency and Productivity” 27 page bibliography.

Table of over 200 applications since 2000