William Greene
Stern School of Business
New York University
Stochastic Frontier
and
Efficiency Estimation
Professor
Professor William. Greene
e-mail: wgreene@stern.nyu.edu
Home Page: http://people.stern.nyu.edu/wgreene
Abstract
This course will
present the methodology of econometric estimation of economic efficiency. We
will examine the stochastic frontier model as an econometric extension of the
classical microeconomic theory of production and cost at the individual
producer level. Basic models for production, cost and distance will be
examined. We will examine major extensions of the models to provide scope for
cross firm heterogeneity (such as heteroscedasticity) as well as unobserved
heterogeneity captured by the stochastic specification of the model. The second
day of the course will turn to more advanced applications, such as Bayesian and
classical methods of estimation and, especially, panel data models. In addition
to the examination of theoretical and econometric methods, we will study
several applications from the recent literature.
The course will
include lectures that develop the relevant theory and extensive practical, laboratory
applications. Emphasis in the laboratory sessions will be on estimation of
stochastic frontier models and using them to compute measures of economic
efficiency. Course participants will apply the techniques on their own
computers using the LIMDEP/NLOGIT computer program and several real data sets
that have been used in applications already in the literature.
Prior knowledge
is assumed to include a course in microeconomics, calculus at the level assumed
in the first year of a Ph.D. program in economics and a course in econometrics
at the beginning Ph.D. level out of a textbook such as Greene, W., Econometric Analysis, 7th
edition. Familiarity with LIMDEP will be helpful, but is not necessary.
Students in this
course will obtain background in both the theory and methods of estimation for
stochastic frontier modeling. This course will provide a gateway to the
professional literature as well as practical application of the methods at the
level of the contemporary research in the field.
Prerequisites
Students are assumed to have had a
previous course in Econometrics at the graduate level, using a text at the
level of Greene, W., Econometric
Analysis.
Course Outline
This is a course in efficiency and productivity
analysis. There are a huge variety of models that are used in this context. We
will focus on, the fundamental normal-half normal model that began the field
then examine a long list of extensions that have accommodated different
situations and data. The course will consist of discussions and laboratory
sessions which will apply the techniques to live data sets and some time
devoted to topics, discussions and laboratory work on student projects.
Discussions will cover the topics listed below. Lab sessions will apply the
techniques discussed in the preceding sessions. Practicals will consist of
directed exercises and student assignments to be completed singly or in groups.
No specific textbook is assigned
for the course. A useful reference is
Kumbhakar, S. and K. Lovell, Stochastic
Frontier Modeling, Cambridge University Press, 2000, monograph.
A foundation work that contains
broad surveys of the field is
Fried, H., K. Lovell and S. Schmidt, The Measurement of Productive Efficiency and Productivity, Oxford
University Press, 2007, the Red Book.
Some of the presentation will be
based on Econometric Analysis, 7th
ed., by Greene, W. (Prentice Hall, 2011). Some chapters are included with
the course materials: Left click to
activate. Right click to download
Greene, W., Econometric
Analysis, 7th Ed.
Greene 11-Panel data methods
Greene 12-Estimation methods
Greene 14-Maximum likelihood estimation
Greene 15-Simulation based estimation and inference
Greene 19-Censoring and truncation (see Section 19.2.4 on stochastic
frontiers)
The received literature on
frontier models is vast - one could easily compose a list of thousands of
articles. Your course materials include a small handful of survey articles:
Recent Developments and
Methodology of Stochastic Frontier Analysis,Parmeter and
Kumbhakar Survey
The Econometric Approach to
Efficiency Estimation Greene Survey (one of the chapters in the
Red Book)
Efficiency Analysis
Fried,
Lovell and Schmidt Survey (Chapter 1 in the Red Book)
Efficiency Analysis, Sena survey
(article)
Economic Efficiency and
Frontier Techniques Luis R. Murillo-Zamorano
Course
Materials and Resources
I. Class Notes: These
are Powerpoint slide presentations and background readings (pdf). Left click to activate. Right click to
download.
Part 0: Introduction
Part 1:
Modeling Efficiency
Microeconomic essentials:
Production functions; Functional form, Cobb-Douglas and translog; Isoquants and
efficiency measures; implications for least squares estimation of production
relationships
Greene
(2007 survey, Red Book)
Fried,
Lovell, Schmidt (2007 Red Book),
Kumbhakar
and Lovell (2000 monograph)
Part 2:
Production Frontiers
Frontier modeling; programming
estimators; The gamma frontier; modifying least squares; Data envelopment
analysis
Greene (1980) gamma frontier, one sided errors
Greene (1990) gamma frontier, maximum likelihood
Part 3:
The Stochastic Frontier Model
The stochastic frontier model;
Implications for OLS; The half normal model; Maximum likelihood estimation;
Exponential and truncated distributions; estimating inefficiency; Confidence
intervals; Model specification
Aigner,
Lovell, Schmidt (1977), original proposal for stochastic frontier model
Jondrow,
Lovell, Materov, Schmidt (1982), how to compute inefficiency
Waldman (1982), wrongward leaning residuals
Greene (1990), MLE for gamma model
Greene
(2003b), the last gamma frontier paper
Bera
and Sharma (1999), confidence intervals for inefficiency
Tsionas (2012), continues developing the gamma frontier model
Tsionas (2013), Weibull model
Part 4:
Production and Cost and Allocative Inefficiency
Production, cost and other models;
Cost frontiers; Allocative inefficiency; The Greene problem; Multiple outputs;
Distance functions; Profit and revenue functions
Christensen and Greene (1976), translog form for cost function
Tsionas
and Kumbhakar (2004), Bayesian solution to the Greene problem
Atkinson and Dorfman (2005), multiple outputs, one undesirable
Tsionas
and Kumbhakar (2005), banking industry
Part 5:
Modeling Heterogeneity
Review of stochastic frontier
modeling; Estimating inefficiency; functional form Heterogeneity in the
stochastic frontier model; model extensions; heteroscedasticity; One and two
step estimation; A latent class model; Random parameters; Sample Selection
Greene
survey (2007, Red Book)
Greene
(2004a), Health Economics, heterogeneity
Hadri
(1999), heteroscedasticity
Wang and Schmidt (2002), one step vs. two step estimation of inefficiency
Orea and Kumbhakar (2004), a latent class model
Greene (2005), modeling
heterogeneity in frontier functions
Besstremyannaya (2011), latent
class stochastic frontier model, health economics
Mutter et al., AHRQ (2012),
omitted endogenous quality in an SF model
Greene (2010) Sample selection model; maximum simulated
likelihood
Kathuria, Raj, Sen (2013)
Application of sample selection model
Kumbhakar, Parmeter, Tsionas (2013), latent class
stochastic frontier
Part 6:
Model Extensions
Bayesian and Maximum simulated
likelihood estimation; The normal-gamma, Weibull and Rayleigh models; Discrete
outcomes
Greene (2003b), MSL estimation of the gamma model
Kim and Schmidt (2000), Bayesian vs. classical estimation
Kleit and Terrell (2001), Bayesian application to
electricity
Huang (2004), Bayesian estimation of gamma frontier model
Koop, Osiewalski and Steel (1997), Bayesian estimation of the frontier
model
Nemoto and Furumatsu (2013),
distance function approach
Part 7:
Panel Data
(Part 9: True Fixed Effects:
Discussion of a Panel Data Frontier Model)
Panel data; Fixed and random
effects; FE and RE in the stochastic frontier model; True random and fixed
effects models, spatial effects
Pitt
and Lee (1981), original random effects model
Schmidt
and Sickles (1984), fixed effects models
Koop, Osiewalski and Steel (1997), Bayesian treatment of fixed effects
Greene
(2005), fixed and random effects models
Battese
and Coelli (1988,
1992,
1995),
time
variation in inefficiency models
Greene
2004b, heterogeneity
Farsi,
Fillipini, Kuenzle (2003), true random and fixed effects models
Wang and Ho (2010), more on
fixed effects
Kumbhakar Lien Hardaker
(2013), Survey of panel data approaches
Filippini and Greene (2015),
Stochastic Frontier Model with Time Varying and Time Invariant Inefficiency
Faust and Baranzini (2014)
True Random Effects Cost Frontier Analysis
Greene (2014) Discussion of
Estimation of True Random Effects Models
Glass-Kenjegalievay-Sickles(2013)
Spatial Stochastic Frontier Model for U.S. States
Glass-Kenjegalievay-Sickles(2013)
Spatial Stochastic Frontier Model for European Countries
Part 8:
Applications; Summary and Conclusions
Applications from the literature
Alvarez,
Arias, Greene (2005), latent variable model, management
Farsi, Filippini, Kuenzle
(2003), fixed and random effects, railways
Holloway (2005), Bayesian
application, hierarchical analysis fishing trawlers
Kumbhakar and Wang (2005) Macro application - cross
country growth
Kleit and Terrell (2001), electricity market
II. Lab Exercises
Assignments:
Exercises and Practicals for Stochastic Frontier Modeling. Left click to activate. Right click to
download. Note there are two parts to each, the .pdf file for the
assignment and the .lim file that contains the NLOGIT commands. Each will also
use one or more of the data sets.
Assignment
1: (NLOGIT Commands for Assignment 1)
Assignment
2: (NLOGIT Commands for Assignment 2)
Assignment
3: (NLOGIT Commands for Assignment 3)
Assignment
4: (NLOGIT Commands for Assignment 4)
Data
Sets: These are NLOGIT project (.lpj) files. Each
is accompanied by a corresponding NLOGIT command (.lim) file that contains a
description of the variables in the file. Left
click to activate. Right click to download.
Airlines
data
Banking
data
Dairy Farms data
Electricity data
Swiss Railways data
WHO Health Systems data
III. Program Notes:
These are Powerpoint slide presentations that explain using NLOGIT
and how to do the assignments with NLOGIT. Left
click to activate. Right click to download.
Lab 1:
Getting Started
Lab 2:
Stochastic Frontier Models and Technical Inefficiency; Model Building,
Production and Cost Models, Estimating Efficiency
Lab 3:
Stochastic Frontier Models with Heterogeneity
Lab 4:
Frontier Models and Panel Data
IV. LIMDEP/NLOGIT
Software:: The short introduction is a getting started. The LIMDEP manual explains the basics of using
LIMDEP and NLOGIT. (LIMDEP is embedded in NLOGIT). The setup file contains an
installation kit for installing a copy of NLOGIT made specially for this course
on your own computer. You should download the setup file to your own computer
and execute it there, rather than launching it from your web browser. Left click to activate. Right click to
download.
These chapters from the
LIMDEP/NLOGIT manual are specifically for frontier estimation and efficiency
analysis.
Chapter E62: Estimating
Stochastic Frontier Models
Chapter E63:
Heteroscedasticity and Truncation
Chapter E64: Panel Data
Stochastic Frontier Models
Chapter E65: Data Envelopment
Analysis
These are descriptions of new
frontier and efficiency estimation tools that were added to LIMDEP and NLOGIT
in 2013
New
Stochastic Frontier Specifications
Extensions of the Data
Envelopment Analysis Program
These are short
manuals that document how to use the program:
Quickstart Introduction to NLOGIT (Command script file to use with Quickstart) (Data file to use with
Quickstart)
Short Introduction to NLOGIT
LIMDEP
Student User Manual
NLOGIT
Student User Manual
This is the
installation kit for installing the program. Download this file to your
computer before you use it to install NLOGIT on your computer.
NLOGIT Software Setup for Installing NLOGIT on Your
Computer