Quantitative Methods in Regulation


 Curtis Green
 2 years ago
 Views:
Transcription
1 Quantitative Methods in Regulation (DEA) Data envelopment analysis is one of the methods commonly used in assessing efficiency for regulatory purposes, as an alternative to regression. The theoretical development of DEA is usually attributed to an economist, M.J. Farrell (1957) but became operational much later following work by OR specialists Charnes, Cooper and Rhodes (1978)(CCR). Consequently, the DEA technique is more associated with the operations research and management science literature, although applications in the economics literature are becoming fairly common. Two orientations are possible corresponding to the cost and output approaches respectively. Figure 1 shows the standard regressionbased approach. Figure 2 is a version of the original Farrell diagram for the cost (strictly, input) orientation. There are five companies (A to E), each producing a unit of single output (y) using two inputs (x1 and x2). Companies C, D and E are technically efficient. For example, C uses more of x1 and less of x2 compared with D, while company B is inefficient compared to D since it uses more of both x1 and x2. The efficient counterpart of B, i.e. D, is called B s reference group. Figure 1: Leastsquares regression Cost (C) A ^ C = o + 1X 1 OLS line x A Corrected OLS Line most efficient observation Size (X) The term data envelopment analysis arises because DEA can be thought of as fitting a frontier which envelopes the data. In Figure 2 the frontier is defined by CDE. Points C, D and E of the frontier represent real companies while points on the line segments linking the real companies represent hypothetical ones. The technical efficiency of a company such as A is measured by comparing it with its corresponding hypothetical benchmark which is A. The distance AA is a measure of the efficiency of company A. The general version of DEA allows for many inputs in order to calculate technical efficiency. In the management science literature DEA is typically represented as a generalised ratio: City University 1
2 weighted sum of outputs efficiency ratio = = weighted sum of inputs i j qy i px j i j (3) where ys and xs are outputs and inputs respectively while q s and p s are firm specific weights to be calculated by the DEA technique. (These are counterparts of the regression coefficients.) Each company is given a single efficiency measure from zero to one. The primal LP problem as defined by CCR is essentially to choose these q s and p s to maximise the efficiency score, subject to the constraint that, with these weights no company gets score higher than The closer the score to one the more efficient the firm. DEA allocates specific weights (q s and p s) for each company, on the basis of giving the highest possible score. This is sometimes expressed as putting a company in the best possible light. Here we consider the special case where inputs are aggregated by their prices with the aim of deriving overall cost efficiency for (potentially) multiple outputs. Furthermore, the following description is the dual of the approach described by Charnes and Cooper and much of the management science literature since it corresponds more closely to the economic interpretation of the frontier. As with COLS, DEA assumes that there is at least one efficient observation. As in the Farrell diagram, the cost frontier is a convex hull formed by joining adjacent efficient points together by hyperplanes. (Where there is only one x one y and no zs these can be represented by straight lines as in the diagram above.) A separate analysis is carried out for each observation. In the special case here where the inputs are aggregated into a single cost measure we can express the production correspondence as an explicit function c(y,z). c = f(y 0,z 0) A technically efficient company in an environment z 0 would produce the given output y 0 at minimum cost (c min ) while an inefficient company would under the same conditions, incur cost more than the maximum. (c>c min ). A measure of the company s technical efficiency could be therefore the ratio (c min /c). The closer this ratio to one the higher the company s efficiency. In the dual of the CCR approach, for each observation the algorithm searches for an efficient set E 0 which minimises the efficiency score K. We use the efficient set (or reference group) to construct an artificial observation which is a linear combination of the efficient set. Thus the cost of the artificial observation, c E is formed from c E = Σ λ I c i iεe The efficient set must produce at least as much of every output as observation 0: y E j = Σ λ I y ij y 0j for each output j iεe City University 2
3 Where there are additional noncontrollable factors z, these must also meet the weak inequality: z E j = Σ λ I z ij z 0j for each noncontrollable j iεe The efficiency score is then K = c e /c 0. (There are no noncontrollables in LAB7DEA Model1) Additional constraints are that the weight on any observation, λ i is nonnegative. In the original, constant returns to scale formulation, the λ i s are otherwise unconstrained. In the variable returns to scale approach, due to Banker, Charnes, and Cooper (1984), the sum of the λ i s is constrained to 1, which ensures that the artificial observation is not just a linear, but a convex combination of the efficient set. The shadow prices on each constraint represent the weights (ps and qs) on the normal, primal analysis. Roughly these correspond to the regression coefficients, except that each observation has its own weights depending on which facet of the convex hull the reference group defines. DEA also allows the inclusion not only of inputs and outputs but also of other variables describing a company s operating environment (often called noncontrollable or environmental variables), thus enabling like for like comparisons. In DEA one has to decide about the relative importance of competing explanatory factors prior to the analysis. The inputs and the outputs are entered into the DEA optimisation algorithm but there is no builtin test about their appropriateness. With DEA one has to decide also about the sign of these explanatory factors prior to the running of the DEA programme while with RA the signs of the explanatory variables are calculated by the OLS algorithm. Without any means for determining the appropriate specification DEA should not be used as the primary approach in comparative efficiency especially when RA is possible. DEA operates in one of two modes  input shrinkage (or minimisation) and output expansion (or maximisation.) Figure 2 shows how, in the input minimisation mode, DEA can use data on several inputs to produce a performance score that is independent of any imposed weighting system for the inputs. The unit under consideration, D, is producing the same City University 3
4 amount (or less) of every output as units A, B, and C. Figure 2: Input Efficiency: A Comparison of units Producing the Same Output Input 2 A, B, and C are all technically efficient G F A B E C D Input efficiency for D = OE/OD 0 Input 2 B and C are the `reference group' for unit D The fundamental assumption of DEA is that, if B and C are feasible then a linear combination such as E is also feasible. E represents a radial contraction of D, using proportionately less of every input. The ratio OE/OD is the Farrell measure of technical efficiency. B and C are said to be the reference group for unit D. Figure 3 shows the equivalent measure in the output expansion mode. Units I, J, and K are using the same (or less) of every input as branch G. I, J and K are regarded as technically efficient relative to the other points in the data set. City University 4
5 Figure 3: Output Efficiency: A Comparison Units Using the Same Inputs Output 2 I, J, and K are technically efficient I H J Efficiency score of G = OG/OH G K 0 Output 1 I and J are the reference group for G Constant and Variable Returns in DEA The difference between the constant and variable returns to scale cases is illustrated in Figure 4 using a singleinput, single output example. On this figure we have a single output on the vertical axis and a single input on the horizontal axis. Points A, B, C, D, E and F represent actual companies with varying outputinput ratios. Company C has the maximum outputinput ratio. Under CRS (constant returns) the fitted DEA frontier will be the ray OC. However under VRS (variable returns) the fitted DEA frontier will be the envelope line ABCDE. Figure 4: Constant and varying returns to scale in DEA Output D E F C B O A Input The companies below and to the left of company C are subject to increasing returns while the ones located above and the right are subject to decreasing returns. Therefore, if a CRS frontier like OC is fitted the companies on ABCDE which are not on ray OC will be City University 5
6 classified as inefficient, partly due to scale inefficiency, so that more companies are likely to be labelled as efficient under VRS compared to the CRS case. 3. RA versus DEA RA and DEA are widely regarded as equivalent alternative techniques for estimating or fitting an efficiency frontier. Both are the results of a minimisation process: RA uses the least squares algorithm to fit an average line while DEA uses linear programming to fit a convex hull. However, the two techniques have fundamental differences: 1) RA calculates a fixed number of parameters defined by the number of regressors k. The number of parameters calculated by DEA depends on the data set, and the number of factors used as reference sets. The upper limit is N k, where N is the number of observations and k the number of variables. By way of comparison a third approach, (known as parametric programming) combines the LP approach to minimisation with a fixed number of parameters, k.. 2) RA makes assumptions about the stochastic properties of the observed data. Under RA the observed data points are assumed to be realisations of random variables following certain distributions, usually normal, enabling the carrying out of hypothesis testing. This is an important advantage of RA over DEA as it is normally practised since it enables to check the statistical significance of competing explanatory variables as well as the appropriateness of the estimated functional form. Since DEA has been developed mainly in a nonstatistical framework, hypothesis testing is more problematic with DEA. Without hypothesis testing model selection is problematic. Consider for example the case of fitting a cost frontier. Economic theory predicts that the quantity of output and factor prices should be among the exogenous determinants of costs. While this is true, there are also other important factors influencing costs in the real world. RA provides an empirical test or a decision rule for identifying the important ones. The implied production possibility frontier for the two approaches is clearly different. In particular, whilst there is only one efficient observation in the econometric approach, DEA will tend to find many observations on the frontier. In order to carry out either of these methods an essential first step is to find out which factors affect the raw performance as reflected in the indicators. The econometric approach, with its statistical tests, is most useful in this process, and we used the results of our econometric analysis to inform our specification of the DEA model. In the econometric approach the benchmark cost level is derived from a statistical cost function which provides the best fit to the data. Implementing this approach requires an assumption to be made about the shape of the underlying cost function. On the other hand, (DEA) does not require an assumption about the shape of the cost function, and, in some ways provides a more convenient framework where there are many outputs and inputs. Finally, all attempts at calculating relative efficiency may be frustrated by difficulties in obtaining sufficient data of good enough quality. Remember GIGO. City University 6
Estimating most productive scale size in DEA with real and integer value data
Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 20085621) Vol. 6, No. 2, 2014 Article ID IJIM00342, 8 pages Research Article Estimating most productive scale size in
More informationSession 9 Case 3: Utilizing Available Software Statistical Analysis
Session 9 Case 3: Utilizing Available Software Statistical Analysis Michelle Phillips Economist, PURC michelle.phillips@warrington.ufl.edu With material from Ted Kury Session Overview With Data from Cases
More informationGautam Appa and H. Paul Williams A formula for the solution of DEA models
Gautam Appa and H. Paul Williams A formula for the solution of DEA models Working paper Original citation: Appa, Gautam and Williams, H. Paul (2002) A formula for the solution of DEA models. Operational
More informationNonlinear Arash Model in DEA
Research Journal of Applied Sciences, Engineering and Technology 5(17): 42684273, 2013 ISSN: 20407459; eissn: 20407467 Maxwell Scientific Organization, 2014 Submitted: July 27, 2012 Accepted: September
More informationDEA implementation and clustering analysis using the KMeans algorithm
Data Mining VI 321 DEA implementation and clustering analysis using the KMeans algorithm C. A. A. Lemos, M. P. E. Lins & N. F. F. Ebecken COPPE/Universidade Federal do Rio de Janeiro, Brazil Abstract
More informationA PRIMALDUAL APPROACH TO NONPARAMETRIC PRODUCTIVITY ANALYSIS: THE CASE OF U.S. AGRICULTURE. JeanPaul Chavas and Thomas L. Cox *
Copyright 1994 by JeanPaul Chavas and homas L. Cox. All rights reserved. Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that this copyright notice
More informationAN ASSESSMENT OF FINANCIAL RATIO ANALYSIS AND DATA ENVELOPMENT ANALYSIS IN COMPARING THE RELATIVE PROFITABILITY OF BANKS
AN ASSESSMENT OF FINANCIAL RATIO ANALYSIS AND DATA ENVELOPMENT ANALYSIS IN COMPARING THE RELATIVE PROFITABILITY OF BANKS JJL Cronje Curtin University of Technology, Perth WA Presented by PH Potgieter :
More informationTechnical Efficiency Accounting for Environmental Influence in the Japanese Gas Market
Technical Efficiency Accounting for Environmental Influence in the Japanese Gas Market Sumiko Asai Otsuma Women s University 271, Karakida, Tama City, Tokyo, 26854, Japan asai@otsuma.ac.jp Abstract:
More informationMeasuring the efficiency in the Czech banking industry: Data Envelopment Analysis and Malmquist index
Measuring the efficiency in the Czech banking industry: Data Envelopment Analysis and Malmquist index Iveta Řepková 1 1 Introduction Abstract. This paper estimates the technical efficiency and the efficiency
More informationData Envelopment Analysis: A Primer for Novice Users and Students at all Levels
Data Envelopment Analysis: A Primer for Novice Users and Students at all Levels R. Samuel Sale Lamar University Martha Lair Sale Florida Institute of Technology In the three decades since the publication
More informationChapter 14: Production Possibility Frontiers
Chapter 14: Production Possibility Frontiers 14.1: Introduction In chapter 8 we considered the allocation of a given amount of goods in society. We saw that the final allocation depends upon the initial
More informationThe CobbDouglas Production Function
171 10 The CobbDouglas Production Function This chapter describes in detail the most famous of all production functions used to represent production processes both in and out of agriculture. First used
More informationEvaluating Customer Service Representative Staff Allocation and Meeting Customer Satisfaction Benchmarks: DEA Bank Branch Analysis
Centre for Management of Technology and Entrepreneurship Faculty of Applied Science and Engineering University of Toronto Evaluating Customer Service Representative Staff Allocation and Meeting Customer
More informationIntroduction to Support Vector Machines. Colin Campbell, Bristol University
Introduction to Support Vector Machines Colin Campbell, Bristol University 1 Outline of talk. Part 1. An Introduction to SVMs 1.1. SVMs for binary classification. 1.2. Soft margins and multiclass classification.
More informationMethodology for analysing competitiveness, efficiency and economy of scale. Use and applications of DEA
FACEPA Farm Accountancy Cost Estimation and Policy Analysis of European Agriculture Methodology for analysing competitiveness, efficiency and economy of scale. Use and applications of DEA FACEPA Deliverable
More informationSUPPLEMENT TO CHAPTER
SUPPLEMENT TO CHAPTER 6 Linear Programming SUPPLEMENT OUTLINE Introduction and Linear Programming Model, 2 Graphical Solution Method, 5 Computer Solutions, 14 Sensitivity Analysis, 17 Key Terms, 22 Solved
More information1. The Classical Linear Regression Model: The Bivariate Case
Business School, Brunel University MSc. EC5501/5509 Modelling Financial Decisions and Markets/Introduction to Quantitative Methods Prof. Menelaos Karanasos (Room SS69, Tel. 018956584) Lecture Notes 3 1.
More informationLINEAR PROGRAMMING THE SIMPLEX METHOD
LINEAR PROGRAMMING THE SIMPLE METHOD () Problems involving both slack and surplus variables A linear programming model has to be extended to comply with the requirements of the simplex procedure, that
More informationChapter 15 Introduction to Linear Programming
Chapter 15 Introduction to Linear Programming An Introduction to Optimization Spring, 2014 WeiTa Chu 1 Brief History of Linear Programming The goal of linear programming is to determine the values of
More informationLINEAR PROGRAMMING P V Ram B. Sc., ACA, ACMA Hyderabad
LINEAR PROGRAMMING P V Ram B. Sc., ACA, ACMA 98481 85073 Hyderabad Page 1 of 19 Question: Explain LPP. Answer: Linear programming is a mathematical technique for determining the optimal allocation of resources
More informationDoes Ownership and Size Influence Bank Efficiency? Evidence from Sri Lankan Banking Sector J.M.R. Fernando and P.D. Nimal
Ruhuna Journal of Management and Finance Volume 1 Number 1  January 2014 ISSN 22359222 R JMF Does Ownership and Size Influence Bank Efficiency? Evidence from Sri Lankan Banking Sector J.M.R. Fernando
More informationEfficiency in Software Development Projects
Efficiency in Software Development Projects Aneesh Chinubhai Dharmsinh Desai University aneeshchinubhai@gmail.com Abstract A number of different factors are thought to influence the efficiency of the software
More informationEconometrics Simple Linear Regression
Econometrics Simple Linear Regression Burcu Eke UC3M Linear equations with one variable Recall what a linear equation is: y = b 0 + b 1 x is a linear equation with one variable, or equivalently, a straight
More informationLancaster University Management School Working Paper 2009/008. Costs and Efficiency of Higher Education Institutions in England: A DEA Analysis
Lancaster University Management School Working Paper 2009/008 Costs and Efficiency of Higher Education Institutions in England: A DEA Analysis E Thanassoulis, Mika Kortelainen, Geraint Johnes and Jill
More informationANNDEA Integrated Approach for Sensitivity Analysis in Efficiency Models
Iranian Journal of Operations Research Vol. 4, No. 1, 2013, pp. 1424 ANNDEA Integrated Approach for Sensitivity Analysis in Efficiency Models L. Karamali *,1, A. Memariani 2, G.R. Jahanshahloo 3 Here,
More informationData Envelopment Analysis
Data Envelopment Analysis Theory and Techniques for Economics and Operations Research SUBHASH C. RAY University of Connecticut PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building,
More informationAn Assessment of Comparative Efficiency Measurement Techniques
An Assessment of Comparative Efficiency Measurement Techniques By Vasilis Sarafidis October 2002 OCCASIONAL PAPER 2 OCCASIONAL PAPER 2 FOREWORD Europe Economics is an independent economics consultancy,
More informationStatistical Machine Learning
Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes
More information3y 1 + 5y 2. y 1 + y 2 20 y 1 0, y 2 0.
1 Linear Programming A linear programming problem is the problem of maximizing (or minimizing) a linear function subject to linear constraints. The constraints may be equalities or inequalities. 1.1 Example
More informationHow to deal with numbers of decision making units and variables in data envelopment analysis
How to deal with numbers of decision making units and variables in data envelopment analysis Dariush Khezrimotlagh * Department of Applied Statistics, Faculty of Economics and Administration, University
More informationChap 4 The Simplex Method
The Essence of the Simplex Method Recall the Wyndor problem Max Z = 3x 1 + 5x 2 S.T. x 1 4 2x 2 12 3x 1 + 2x 2 18 x 1, x 2 0 Chap 4 The Simplex Method 8 corner point solutions. 5 out of them are CPF solutions.
More informationSensitivity Analysis 3.1 AN EXAMPLE FOR ANALYSIS
Sensitivity Analysis 3 We have already been introduced to sensitivity analysis in Chapter via the geometry of a simple example. We saw that the values of the decision variables and those of the slack and
More informationHOW CAN WE USE THE RESULT FROM A DEA ANALYSIS? IDENTIFICATION OF FIRMRELEVANT REFERENCE UNITS JONAS MÅNSSON *
Journal of Applied Economics, Vol. VI, No. 1 (May 2003), 157175 HOW CAN WE USE THE RESULT FROM A DEA ANALYSIS? 157 HOW CAN WE USE THE RESULT FROM A DEA ANALYSIS? IDENTIFICATION OF FIRMRELEVANT REFERENCE
More informationThe efficiency of fleets in Serbian distribution centres
The efficiency of fleets in Serbian distribution centres Milan Andrejic, Milorad Kilibarda 2 Faculty of Transport and Traffic Engineering, Logistics Department, University of Belgrade, Belgrade, Serbia
More informationDEABASED INVESTMENT STRATEGY AND ITS APPLICATION IN THE CROATIAN STOCK MARKET
DEABASED INVESTMENT STRATEGY AND ITS APPLICATION IN THE CROATIAN STOCK MARKET Margareta Gardijan Faculty of Economics and Business, University of Zagreb Trg. J. F. Kennedyja 6, 10000 Zagreb Email: mgardijan@efzg.hr
More informationStochastic Inventory Control
Chapter 3 Stochastic Inventory Control 1 In this chapter, we consider in much greater details certain dynamic inventory control problems of the type already encountered in section 1.3. In addition to the
More informationPERFORMANCE MANAGEMENT AND COSTEFFECTIVENESS OF PUBLIC SERVICES:
PERFORMANCE MANAGEMENT AND COSTEFFECTIVENESS OF PUBLIC SERVICES: EMPIRICAL EVIDENCE FROM DUTCH MUNICIPALITIES Hans de Groot (Innovation and Governance Studies, University of Twente, The Netherlands, h.degroot@utwente.nl)
More informationAlternative Methods to Examine Hospital Efficiency: Data Envelopment Analysis and Stochastic Frontier Analysis
CENTRE FOR HEALTH ECONOMICS Alternative Methods to Examine Hospital Efficiency: Data Envelopment Analysis and Stochastic Frontier Analysis Rowena Jacobs DISCUSSION PAPER 177 ALTERNATIVE METHODS TO EXAMINE
More informationBy W.E. Diewert. July, Linear programming problems are important for a number of reasons:
APPLIED ECONOMICS By W.E. Diewert. July, 3. Chapter : Linear Programming. Introduction The theory of linear programming provides a good introduction to the study of constrained maximization (and minimization)
More information7.1 Modelling the transportation problem
Chapter Transportation Problems.1 Modelling the transportation problem The transportation problem is concerned with finding the minimum cost of transporting a single commodity from a given number of sources
More informationDefinition of a Linear Program
Definition of a Linear Program Definition: A function f(x 1, x,..., x n ) of x 1, x,..., x n is a linear function if and only if for some set of constants c 1, c,..., c n, f(x 1, x,..., x n ) = c 1 x 1
More informationLinear Programming I
Linear Programming I November 30, 2003 1 Introduction In the VCR/guns/nuclear bombs/napkins/star wars/professors/butter/mice problem, the benevolent dictator, Bigus Piguinus, of south Antarctica penguins
More informationLinear Programming. Solving LP Models Using MS Excel, 18
SUPPLEMENT TO CHAPTER SIX Linear Programming SUPPLEMENT OUTLINE Introduction, 2 Linear Programming Models, 2 Model Formulation, 4 Graphical Linear Programming, 5 Outline of Graphical Procedure, 5 Plotting
More informationBank Branch Grouping Strategy, an Unusual DEA Application
Journal of Service Science and Management, 2012, 5, 355364 http://dx.doi.org/10.4236/jssm.2012.54042 Published Online December 2012 (http://www.scirp.org/journal/jssm) 355 Bank Branch Grouping Strategy,
More informationRegression III: Advanced Methods
Lecture 5: Linear leastsquares Regression III: Advanced Methods William G. Jacoby Department of Political Science Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Simple Linear Regression
More informationAssessing Container Terminal Safety and Security Using Data Envelopment Analysis
Assessing Container Terminal Safety and Security Using Data Envelopment Analysis ELISABETH GUNDERSEN, EVANGELOS I. KAISAR, PANAGIOTIS D. SCARLATOS Department of Civil Engineering Florida Atlantic University
More informationModern Efficiency Analysis:
Timo Kuosmanen Modern Efficiency Analysis: Combining axiomatic nonparametric frontier with stochastic noise Outline Applications of efficiency analysis The classic DEA and SFA approaches Modern synthesis
More informationInternational Doctoral School Algorithmic Decision Theory: MCDA and MOO
International Doctoral School Algorithmic Decision Theory: MCDA and MOO Lecture 2: Multiobjective Linear Programming Department of Engineering Science, The University of Auckland, New Zealand Laboratoire
More informationmax cx s.t. Ax c where the matrix A, cost vector c and right hand side b are given and x is a vector of variables. For this example we have x
Linear Programming Linear programming refers to problems stated as maximization or minimization of a linear function subject to constraints that are linear equalities and inequalities. Although the study
More informationLecture 7  Linear Programming
COMPSCI 530: Design and Analysis of Algorithms DATE: 09/17/2013 Lecturer: Debmalya Panigrahi Lecture 7  Linear Programming Scribe: Hieu Bui 1 Overview In this lecture, we cover basics of linear programming,
More informationClusteringBased Method for Data Envelopment Analysis. Hassan Najadat, Kendall E. Nygard, Doug Schesvold North Dakota State University Fargo, ND 58105
ClusteringBased Method for Data Envelopment Analysis Hassan Najadat, Kendall E. Nygard, Doug Schesvold North Dakota State University Fargo, ND 58105 Abstract. Data Envelopment Analysis (DEA) is a powerful
More informationProject selection with limited resources in data envelopment analysis
Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 20085621) Vol. 7, No. 1, 2015 Article ID IJIM00564, 6 pages Research Article Project selection with limited resources
More informationAlternative Methods to Examine Hospital Efficiency Data Envelopment Analysis and Stochastic Frontier Analysis
Seminar (SEd) Nr. 417.069 Operations Research im Gesundheitswesen o.univ.prof. Dr. Kurt Heidenberger Alternative Methods to Examine Hospital Efficiency Data Envelopment Analysis and Stochastic Frontier
More informationSimultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the
Simultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the explanatory variables is jointly determined with the dependent
More informationC: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}
C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression
More informationDEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests
DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also
More informationStanford University CS261: Optimization Handout 6 Luca Trevisan January 20, In which we introduce the theory of duality in linear programming.
Stanford University CS261: Optimization Handout 6 Luca Trevisan January 20, 2011 Lecture 6 In which we introduce the theory of duality in linear programming 1 The Dual of Linear Program Suppose that we
More informationSolution Guide to Exercises for Chapter 5 Portfolio selection: the meanvariance model
THE ECONOMICS O INANCIAL MARKETS R. E. BAILEY Solution Guide to Exercises for Chapter 5 Portfolio selection: the meanvariance model 1. An investor uses the meanvariance criterion for selecting a portfolio
More informationFE670 Algorithmic Trading Strategies. Stevens Institute of Technology
FE670 Algorithmic Trading Strategies Lecture 6. Portfolio Optimization: Basic Theory and Practice Steve Yang Stevens Institute of Technology 10/03/2013 Outline 1 MeanVariance Analysis: Overview 2 Classical
More informationCOMPUTATIONS IN DEA. Abstract
ISSN 01017438 COMPUTATIONS IN DEA José H. Dulá School of Business Administration The University of Mississippi University MS 38677 Email: jdula@olemiss.edu Received November 2001; accepted October 2002
More informationAN ANALYSIS OF EFFICIENCY PATTERNS FOR A SAMPLE OF NORWEGIAN BUS COMPANIES
AN ANALYSIS OF EFFICIENCY PATTERNS FOR A SAMPLE OF NORWEGIAN BUS COMPANIES Torben Holvad Transport Studies Unit, University of Oxford INTRODUCTION In recent years significant progress has been made concerning
More informationA Guide to DEAP Version 2.1: A Data Envelopment Analysis (Computer) Program
A Guide to DEAP Version 2.1: A Data Envelopment Analysis (Computer) Program by Tim Coelli Centre for Efficiency and Productivity Analysis Department of Econometrics University of New England Armidale,
More informationMincost flow problems and network simplex algorithm
Mincost flow problems and network simplex algorithm The particular structure of some LP problems can be sometimes used for the design of solution techniques more efficient than the simplex algorithm.
More informationMinimize subject to. x S R
Chapter 12 Lagrangian Relaxation This chapter is mostly inspired by Chapter 16 of [1]. In the previous chapters, we have succeeded to find efficient algorithms to solve several important problems such
More informationThe aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree
PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and
More informationSimple Regression Theory I 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY I 1 Simple Regression Theory I 2010 Samuel L. Baker Regression analysis lets you use data to explain and predict. A simple regression line drawn through data points In Assignment
More informationChapter 11 STATISTICAL TESTS BASED ON DEA EFFICIENCY SCORES 1. INTRODUCTION
Chapter STATISTICAL TESTS BASED O DEA EFFICIECY SCORES Raiv D. Banker and Ram ataraan School of Management, The University of Texas at Dallas, Richardson, TX 750830688 USA email: rbanker@utdallas.edu
More informationLinear Programming Models: Graphical and Computer Methods
Linear Programming Models: Graphical and Computer Methods Learning Objectives Students will be able to: 1. Understand the basic assumptions and properties of linear programming (LP). 2. Graphically solve
More information1 Introduction. Linear Programming. Questions. A general optimization problem is of the form: choose x to. max f(x) subject to x S. where.
Introduction Linear Programming Neil Laws TT 00 A general optimization problem is of the form: choose x to maximise f(x) subject to x S where x = (x,..., x n ) T, f : R n R is the objective function, S
More informationBank efficiency evaluation using a neural networkdea method
Iranian Journal of Mathematical Sciences and Informatics Vol. 4, No. 2 (2009), pp. 3348 Bank efficiency evaluation using a neural networkdea method G. Aslani a,s.h.momenimasuleh,a,a.malek b and F. Ghorbani
More informationUnderstanding the Impact of Weights Constraints in Portfolio Theory
Understanding the Impact of Weights Constraints in Portfolio Theory Thierry Roncalli Research & Development Lyxor Asset Management, Paris thierry.roncalli@lyxor.com January 2010 Abstract In this article,
More informationLecture 1: Linear Programming Models. Readings: Chapter 1; Chapter 2, Sections 1&2
Lecture 1: Linear Programming Models Readings: Chapter 1; Chapter 2, Sections 1&2 1 Optimization Problems Managers, planners, scientists, etc., are repeatedly faced with complex and dynamic systems which
More informationStochastic Data Envelopment Analysis: Oriented and Linearized Models
Stochastic Data Envelopment Analysis: Oriented and Linearized Models František Brázdik January 2004 Abstract In this paper the chance constrained problems for DEA analysis are constructed. The goal is
More informationRelative Performance of Equity Markets: An Assessment in the Conventional and Downside Frameworks
INTERNATIONAL JOURNAL OF BUSINESS, 14(1), 2009 ISSN: 1083 4346 Relative Performance of Equity Markets: An Assessment in the Conventional and Downside Frameworks Carla Bainbridge a and Don U.A. Galagedera
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationCourse Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.
SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed
More informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationDistributed Generation in Electricity Networks
Distributed Generation in Electricity Networks Benchmarking Models and Revenue Caps MariaMagdalena Eden Robert Gjestland Hooper Endre Bjørndal Mette Bjørndal 2010 I Abstract The main focus of this report
More informationDEA investment strategy in the Brazilian stock market. Abstract. Department of Management, Santa Catarina South University
DEA investment strategy in the Brazilian stock market Ana Lopes Department of Management, Santa Catarina South University Marcus Lima Department of Management, Santa Catarina South University Edgar Lanzer
More informationThe Transportation Problem: LP Formulations
The Transportation Problem: LP Formulations An LP Formulation Suppose a company has m warehouses and n retail outlets A single product is to be shipped from the warehouses to the outlets Each warehouse
More information4.6 Linear Programming duality
4.6 Linear Programming duality To any minimization (maximization) LP we can associate a closely related maximization (minimization) LP. Different spaces and objective functions but in general same optimal
More informationWeighing Positive vs. Negative Factors: A Data Envelopment Analysis Technique
Eugenio María de Hostos Community College of The City University of New York Alexander Vaninsky avaninsky@hostos.cuny.edu Weighing Positive vs. Negative Factors: A Data Envelopment Analysis Technique Decision
More informationChapter 3 LINEAR PROGRAMMING GRAPHICAL SOLUTION 3.1 SOLUTION METHODS 3.2 TERMINOLOGY
Chapter 3 LINEAR PROGRAMMING GRAPHICAL SOLUTION 3.1 SOLUTION METHODS Once the problem is formulated by setting appropriate objective function and constraints, the next step is to solve it. Solving LPP
More informationInteractive Math Glossary Terms and Definitions
Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas
More informationRobust Data Envelopment Analysis
Robust Data Envelopment Analysis Tiziano Bellini Abstract Data envelopment analysis (DEA) is a nonstochastic and nonparametric linear programming technique where a set of units are evaluated according
More informationDuality in Linear Programming
Duality in Linear Programming 4 In the preceding chapter on sensitivity analysis, we saw that the shadowprice interpretation of the optimal simplex multipliers is a very useful concept. First, these shadow
More informationan introduction to Data Envelopment Analysis (DEA) for people unfamiliar with the technique.
Chapter 12 Data Envelopment Analysis Data Envelopment Analysis (DEA) is an increasingly popular management tool. This writeup is an introduction to Data Envelopment Analysis (DEA) for people unfamiliar
More informationMethods Of Measuring The Economy, Efficiency And Effectiveness Of Public Expenditure
Methods Of Measuring The Economy, Efficiency And Effectiveness Of Public Expenditure ANNEX 7: August 2015 1 P a g e TABLE OF CONTENTS 1 Introduction... 3 2 PER Context... 3 3 Necessity of the measures...
More informationLinear Programming Sensitivity Analysis
Linear Programming Sensitivity Analysis Massachusetts Institute of Technology LP Sensitivity Analysis Slide 1 of 22 Sensitivity Analysis Rationale Shadow Prices Definition Use Sign Range of Validity Opportunity
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More information2. Simple Linear Regression
Research methods  II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationCardiff Economics Working Papers
Cardiff Economics Working Papers Working Paper No. E2012/18 Bootstrap DEA and Hypothesis Testing Panagiotis Tziogkidis August 2012 Cardiff Business School Aberconway Building Colum Drive Cardiff CF10 3EU
More informationHybrid Data Envelopment Analysis and Neural Networks for Suppliers Efficiency Prediction and Ranking
1 st International Conference of Recent Trends in Information and Communication Technologies Hybrid Data Envelopment Analysis and Neural Networks for Suppliers Efficiency Prediction and Ranking Mohammadreza
More informationArrangements And Duality
Arrangements And Duality 3.1 Introduction 3 Point configurations are tbe most basic structure we study in computational geometry. But what about configurations of more complicated shapes? For example,
More informationDEA IN MUTUAL FUND EVALUATION
DEA IN MUTUAL FUND EVALUATION Email: funari@unive.it Dipartimento di Matematica Applicata Università Ca Foscari di Venezia ABSTRACT  In this contribution we illustrate the recent use of Data Envelopment
More informationLecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method
Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming
More informationDESCRIPTION OF COURSES
DESCRIPTION OF COURSES MGT600 Management, Organizational Policy and Practices The purpose of the course is to enable the students to understand and analyze the management and organizational processes and
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationPASS Sample Size Software. Linear Regression
Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes
More informationDecision Supporting Procedure for Strategic Planning: DEA Implementation for Regional Economy Efficiency Estimation
Decision Supporting Procedure for Strategic Planning: DEA Implementation for Regional Economy Efficiency Estimation Karine Mesropyan 1 1 Institute of SocioEconomic and Humanitarian Researches of Southern
More information