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[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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
[Part 8] 7/27
Stochastic FrontierModelsApplications
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]
[Part 8] 8/27
Stochastic FrontierModelsApplications
Estimated Model
First order production coefficients (standard errors). Quadratic terms not shown.
[Part 8] 9/27
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
Energy Consumption
Derived input to household and community production
Cost analogy
Panel data, statewide electricity consumption: Filippini, Farsi, et al.
[Part 8] 15/27
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
[Part 8] 17/27
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
Stochastic FrontierModelsApplications
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
[Part 8] 21/27
Stochastic FrontierModelsApplications
Summary
[Part 8] 22/27
Stochastic FrontierModelsApplications
Inefficiency
[Part 8] 23/27
Stochastic FrontierModelsApplications
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
[Part 8] 24/27
Stochastic FrontierModelsApplications
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
[Part 8] 25/27
Stochastic FrontierModelsApplications
Modeling Settings
Production and Cost Models Multiple output models
Cost functions Distance functions, profits and revenue
functions
[Part 8] 26/27
Stochastic FrontierModelsApplications
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
[Part 8] 27/27
Stochastic FrontierModelsApplications
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