[part 8] 1/27 stochastic frontiermodels applications stochastic frontier models william greene stern...

[Part 8] 1/27

Stochastic FrontierModelsApplications

Stochastic Frontier ModelsWilliam Greene

Stern School of Business

New York University

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

[Part 8] 2/27


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…

[Part 8] 3/27


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…”)

[Part 8] 4/27


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.

[Part 8] 5/27


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

[Part 8] 6/27


Fixed Management as an Input Implies Time Variation in Inefficiency

2 21 1=

2 2ln ln (ln ) lnit x xx m mm xmit it i i it i ity x x m m x m v

2* 2 * * *1 1= ( )

2 2ln ln (ln ) lnx xx m mm xmit it it i i it i ity x x m m x m v

2 *2

*

* ½ 0

=

ln -ln

= ln i i

it

it it it

m xm mmit i i m m

u

TE y y

x m m

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Random Coefficients Frontier Model

* *212

*121

12 1 1

ln

ln

ln ln

it m i mm i

K

k km i itkk

K K

kl itk itlk l

it it

y m m

m x

x x

v u

*

1

ln K

i k k ik

m x w

[Chamberlain/Mundlak: Correlation mi* (not mi-mi*) with xit]

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Estimated Model

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

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Inefficiency Distributions

U IN O MG T

1.26

2.51

3.77

5.02

6.28

.00.10 .21 .31 .42 .52.00

K er nel density estim ate for U IN O MG T

Density

U IMG T

3.89

7.78

11.67

15.57

19.46

.00.10 .21 .31 .42 .52.00

K er nel density estim ate for U IMG T

Density

Without Fixed Management

With Fixed Management

[Part 8] 10/27


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

[Part 8] 11/27


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)

[Part 8] 12/27


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

[Part 8] 13/27


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

[Part 8] 14/27


Energy Consumption

Derived input to household and community production

Cost analogy

Panel data, statewide electricity consumption: Filippini, Farsi, et al.

[Part 8] 15/27


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.

[Part 8] 16/27


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

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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

[Part 8] 18/27


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

[Part 8] 19/27


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

[Part 8] 20/27


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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Summary

[Part 8] 22/27


Inefficiency

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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

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SFA Models

Normal – Half Normal Truncation Heteroscedasticity Heterogeneity in the distribution of ui

Normal-Gamma, Exponential, Rayleigh Classical vs. Bayesian applications Flexible functional forms for inefficiency There are yet others in the literature

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Modeling Settings

Production and Cost Models Multiple output models

Cost functions Distance functions, profits and revenue

functions

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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

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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

[part 8] 1/27 stochastic frontiermodels applications stochastic frontier models william greene stern...

Documents

stochastic frontiers

inefficiency slide

fixed management slide

mixture model

fun slide

normal model

poisson model

model extensions