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.
Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University
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 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. Students will have also studied the application of the techniques using modeling tools familiar to researchers in the area. The home page for the course is
http://people.stern.nyu.edu/wgreene/FrontierModels2014.htm
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University
Course Outline This is a course in econometric analysis of technical and economic efficiency. The theoretical foundation is an extension of basic microeconomics of the firm and production/cost functions. The empirical centerpiece is the stochastic frontier model pioneered by Aigner et al. (1977). The course will consist of two days of discussions and laboratory sessions which will apply the techniques to ‘live’ data sets. 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.
Course Outline Day 1 1
2
Microeconomic Essentials and history of thought: Production functions, functional form, CobbDouglas, translog isoquants and efficiency measures, implications for least squares estimation of productionrRelationships Frontier Modeling: Programming estimators, the gamma frontier, modifying least squares, Lab 1: Software. LIMDEP, Regression Computation, COLS
3
4
The stochastic frontier model: Implications for OLS, the half normal model, maximum likelihood estimation, exponential and truncated normal models, estimating inefficiency, confidence intervals, model specification, semiparametric approach, nonparametric DEA approach Production, cost and other models: Cost frontiers, allocative inefficiency, the Greene problem, multiple outputs, distance functions, profit and revenue functions Lab 2: Estimating Stochastic Frontier Models and Technical Inefficiency, DEA, Model building, production and cost models, estimating inefficiency
Day 2 5 6
Heterogeneity: Estimating inefficiency, environmental variables, one and two step estimation, latent class models, random parameters, heteroscedasticity, the scaling model, sample selection Model extensions, Bayesian and maximum simulated likelihood normal-gamma model, normal-Weibull, normal-Rayleigh, discrete outcomes Lab 3: Estimating stochastic frontier models with heterogeneity and heteroscedasticity
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Panel Data: Fixed and random effects, true random and fixed effects, time variation, heterogeneity, time varying and time persistent inefficiency, distance functions, DEA and total factor productivity growth Applications from the Literature: Summary and closing observations Lab 4: Estimating stochastic frontier models with panel data. Model building. Studying production, cost, and economic inefficiency, TFP
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University Timetable Day 1
Class
Essentials of Frontier Modeling
___________________________________________________________________________________________________
09:30 – 10:00 10:00 – 11:00 11:00 – 11:15 11:15 – 12:15 12:15 – 12:30
(1.1) (1.2)
Registration and Setup Microeconomic Essentials, Regression Models, Frontier Functions [Coffee Break] Frontier Models Break, set up lab, initial tutorial
12:30 – 13:15
LAB 1 Software, Regression Modeling, Modifications of OLS, COLS
13:15 – 14:15 14:15 – 15:15
(1.3)
15:15 – 15:30 15:30 – 16:30
(1.4)
16:30 – 17:15
LAB 2 Stochastic Frontier Cost and Production Models
Day 2
Class
[Lunch] Stochastic Frontier Model, Frontier Model Extensions, DEA, semiparametric estimation [Coffee Break] Cost functions, allocative inefficiency, the Greene problem Allocative Inefficiency, Multiple Outputs
Frontier Model Extensions
___________________________________________________________________________________________________
09:00 – 09:15 09:15 – 10:15
(2.5)
Set up Heteroscedasticity, heterogeneity, simulation and Latent class models, sample selection [Coffee Break] Simulation based estimation; other models, Bayesian models Break, set up lab, get started
10:15 – 10:30 10:30 – 11:30 11:30 – 11:45
(2.6)
11:45 – 12:30
LAB 3 Heterogeneity, Heteroscedasticity, Alternative Models
12:30 – 13:30 13:30 – 14:30
(2.7)
[Lunch] Models for panel data, random and fixed effects, true RE and FE, time variation, Battese-Coelli models, random parameters, DEA and total factor productivity growth [Coffee Break] Applications from the literature, summary and conclusions Break, set up lab, get started
14:30 – 14:45 14:45 – 15:45 15:45 – 16:00
(2.8)
16:00 – 16:45
LAB 4 Stochastic Frontier Models for Panel Data
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University
Software I. Stochastic Frontier Estimation Only two of the large integrated econometrics programs currently in general use provide programs and routines for frontier and efficiency analysis, LIMDEP/NLOGIT and Stata. The freeware program, FRONTIER 4.1 by Tim Coelli (find it on the web) can also be used for a small range of stochastic frontier models. FRONTIER is now rather old (mid 1990s), however, and is not being updated or maintained. A version of FRONTIER 4.1 in R has been developed by Arne Henningsen (January, 2009).) Belotti et al. (see www.econometrics.it) have written some new routines for Stata. Chris Parmeter has written some additional code in R. LIMDEP has included an extensive package for frontier modeling since the mid 1980s. New features and models are added to LIMDEP on an ongoing basis. II. Data Envelopment Analysis There are several packages that specialize in Data Envelopment Analysis (DEA) – a search of the web for this topic will amply demonstrate the variety of tools available for this mini-industry. Some of them are quite extensive. Tim Coelli has also developed another, separate program, DEAP for data envelopment analysis. Like FRONTIER, however, DEAP is rather old – 1996, and is not current with methodological developments of the last decade. However, it is freeware, and it does provide the basic capabilities needed by the entry level analyst. LIMDEP also contains some capability for data envelopment analysis. LIMDEP provides both stochastic frontier and DEA capabilities in matched formats so that modelers in both frameworks can extensively compare the results.
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University References A major comprehensive reference work is Kumbhakar, S. and Lovell, K. Stochastic Frontier Analysis, Cambridge University Press, 2000. Surveys that describe the content of the course are Fried, H., K. Lovell and S. Schmidt, “Efficiency and Productivity,” to appear as Chapter 1 in The Measurement of Productivity Efficiency, Oxford University Press, Oxford, 2006. Greene, W., “The Econometric Approach to Efficiency Analysis,” Chapter 2 in The Measurement of Productivity Efficiency, Oxford University Press, Oxford, 2008. Sena, V., “The Frontier Approach to the Measurement of Productivity and Technical Efficiency,” LUBS, University of Leeds, 2003 Murillo-Zamorano, L., “Economic Efficiency and Frontier Techniques,” Journal of Economic Surveys, 18, 1, 2004, pp. 33-45. An appropriate econometrics text for this course is Greene, W., Econometric Analysis 7th Ed., Prentice Hall, 2012. (Selected chapters are posted on the course home page.) Additional articles that were used in constructing this course are: Aigner, D., K. Lovell and P. Schmidt, 1977, “Formulation and Estimation of Stochastic Frontier Production Function Models,” Journal of Econometrics, 6, pp. 21-37. Alvarez, A., C. Arias and W. Greene, 2005, “Accounting for Unobservables in Production Models: Management and Inefficiency,” Working Paper, Department of Economics, University of Oviedo, Spain. Atkinson, S. and J. Dorfman, 2005, “Bayesian Measurement of Productivity and Efficiency in the Presence of Undesirable Outputs: Crediting Electric Utilities for Reducing Air Pollution,” Journal of Econometrics, 126, pp. 445-468. Barrios, E. and Lovado, R., 2010, “Spatial Stochastic Frontier Models,” Phillipine Institute for Development Studies, Discussion Paper 2010-08. Battese, G. and T. Coelli, 1988, “Prediction of Firm-level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data,” Journal of Econometrics, 38, pp. 387-399. Battese, G., and T. Coelli, 1992, “Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India,” Journal of Productivity Analysis, 3, pp. 153-169. Battese, G. and T. Coelli, 1995, “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Model for Panel Data,” Empirical Economics, 20, pp. 325-332. Bera, A. and S. Sharma, 1999, “Estimating Production Uncertainty in Stochastic Frontier Production Function Models,” Journal of Productivity Analysis, 12, pp. 187-210. Besstremyannaya, G., 2011, “Managerial Performance and Cost Efficiency of Japanese Local Public Hospitals: A Latent Class Stochastic Frontier Model,” Health Economics, 20, pp. 19-34. Christensen, L. and W. Greene, 1976, “Economies of Scale in U.S. Electric Power Generation,” Journal of Political Economy, 84, pp. 655-676.
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University Farsi, M. and M. Filippini, 2003, “An Empirical Analysis of Cost Efficiency in Nonprofit and Public Nursing Homes,” Working Paper, Department of Economics, University of Lugano. Farsi, M., M. Filippini and M. Kuenzle, 2003, “Unobserved Heterogeneity in Stochastic Cost Frontier Models: A Comparative Analysis,” Working Paper 03-11, Department of Economics, University of Lugano. Greene, W., 1980, “Maximum Likelihood Estimation of Econometric Frontier Functions,” Journal of Econometrics, 13, pp. 27-56. Greene, W., 1990, “A Gamma Distributed Stochastic Frontier Model,” Journal of Econometrics, 46, pp. 141-163. Greene, W., 2003a, “Panel Data,” Chapter 11 in Greene, W., Econometric Analysis. Greene, W., 2003b, “Maximum Likelihood Estimation,” Chapter 14 in Greene, W., Econometric Analysis. Greene, W., 2003c, “Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function,” Journal of Productivity Analysis, 19, pp. 179-190. Greene, W., 2004a, “Fixed and Random Effects in Stochastic Frontier Models,” Journal of Productivity Analysis, 23, pp. 7-32. Greene, W., 2004b, “Distinguishing Between Heterogeneity and Inefficiency: Stochastic Frontier Analysis of the World Health Organization's Panel Data on National Health Care Systems,” Health Economics, 13, pp. 959-980. Greene, W., 2005, “Reconsidering Heterogeneity in Panel Data Estimators of the Stochastic Frontier Model,” Journal of Econometrics, 126, pp. 269-303. Greene, W., 2010, “A Stochastic Frontier Model with Correction for Sample Selection,” Journal of Productivity Analysis,” 34, pp. 15-24. Hadri, K., 1999, “Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function” Journal of Business and Economics and Statistics, 17, pp. 359-363. Holloway, G., D. Tomberlin and X. Irz, 2005, “Hierarchical Analysis of Production Efficiency in a Coastal Trawl Fishery,” in R. Scarpa and A. Alberini, ed., Simulation Methods in Environmental and Resource Economics, Kluwer, Nijoff Academic Publishers, forthcoming. Horrace, W. and P. Schmidt, 1996, “Confidence Statements for Efficiency Estimates from Stochastic Frontier Models,” Journal of Productivity Analysis, 7, pp. 257-282. Horrace, W. and P. Schmidt, 2000, “Multiple Comparisons with the Best, with Economic Applications,” Journal of Applied Econometrics, 15, pp. 1-26. Huang, R., 2004, “Estimation of Technical Inefficiencies with Heterogeneous Technologies,” Journal of Productivity Analysis, 21, pp. 277-296. Jondrow, J., K. Lovell, I. Materov and P. Schmidt, 1982, “On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model,” Journal of Econometrics, 19, pp. 233-238. Kathuria, V., S. Raj and K. Sen, 2013, “The Effects of Economic Reforms on Manufacturing Dualism: Evidence from India,” Journal of Comparative Econmics, 41, pp. 1240-1262. Kim, Y. and P. Schmidt, 2000, “A Review and Empirical Comparison of Bayesian and Classical Approaches to Inference on Efficiency Levels in Stochastic Frontier Models with Panel Data,” Journal of Productivity Analysis, 14, pp. 91-98. Kleit, A. and D. Terrell, 2001, “Measuring Potential Efficiency Gains from Deregulation of Electricity Generation: A Bayesian Approach,” The Review of Economics and Statistics, 83, pp. 523-530. Koop, G., J. Osiewalski, and M. Steel, 1997, “Bayesian Efficiency Analysis Through Individual Effects: Hospital Cost Frontiers,” Journal of Econometrics, 76, pp. 77-106.
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Stochastic Frontier Models and Economic Efficiency Estimation William Greene Stern School of Business, New York University Kumbhakar, S., G. Lien and J. Hardaker, “Technical Efficiency in Competing Panel Data Models: A Study of Norwegian Grain Farming,” Journal of Productivity Analysis, 2014, forthcoming. Kumbhakar, S. and H. Wang, 2005 “Estimation of Growth Convergence Using a Stochastic Production Frontier Approach,” Economics Letters, 88, pp. 300-305. Kumbhakar, S. and E. Tsionas, 2004, “Estimation of Technical and Allocative Inefficiency in a Translog Cost System: An Exact Maximum Likelihood Approach,” Working Paper, Department of Economics, State University of New York, Binghamton. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "The Joint Measurement of Technical and Allocative Inefficiencies: An Application of Bayesian Inference in Nonlinear RandomEffects Models,"Journal of the American Statistical Association, 100, pp 736-747 Kumbhakar, S., Parmeter, C., Tsionas, E., 2013. “A Zero Inefficiency Stochastic Frontier Model,” Journal of Econometrics, 172, pp. 66-76. Mutter, R., Greene, W., Spector, W., Rosko, M. and Mukamel, D’, “Investigating the Impact of Endogeneity on Inefficiency Estimates in the Application of Stochastic Frontier Analysis to Nursing Homes,” Journal of Productivity Analysis, 2012. Nemoto, J. and N. Fufumatsu, 2013, “Scale and Scope Economics of Japanese Private Universities Revisited with an Input Distance Function Approach, manuscript, Nagoya University. Orea, C. and S. Kumbhakar, 2004, “Efficiency Measurement Using a Latent Class Stochastic Frontier Model,” Empirical Economics, 29, pp. 169-184.
Pitt, M., and L. Lee, 1981, “The Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry,” Journal of Development Economics, 9, pp. 43-64. Schmidt, P., and R. Sickles, 1984, “Production Frontiers and Panel Data,” Journal of Business and Economic Statistics, 2, pp. 367-374. Tsionas, E., 2007, “Efficiency Measurement with the Weibull Stochastic Frontier,” Oxford Bulletin of Economics and Statistics, 69, pp. 693-706. Tsionas, E., 2012. “Maximum Likelihood Estimation of Stochastic Frontier Models by the Fourier Transform,” Journal of Econometrics, 170, pp. 234-248. Waldman, D., 1982, “A Stationary Point for the Stochastic Frontier Likelihood,” Journal of Econometrics, 18, pp. 275-279. Wang, J. and C. Ho, 2010, “Estimating Fixed Effect Panel Stochastic Frontier Models by Model Transformation,” Journal of Econometrics, 157, pp. 286-296. Wang, H. and P. Schmidt, 2002, “One Step and Two Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels,” Journal of Productivity Analysis, 18, pp. 129144.
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