Productivity and Efficiency Analysis: An Economic Approach to Measuring and Explaining Managerial Performance

434 Pages·2018·7.32 MB·English

by  Christopher J. O'Donnell

Christopher J. O’Donnell
Productivity
and Efficiency
Analysis
An Economic Approach to Measuring
and Explaining Managerial Performance
fi
Productivity and Ef ciency Analysis
’
Christopher J. O Donnell
fi
Productivity and Ef ciency
Analysis
An Economic Approach to Measuring
and Explaining Managerial Performance
123
Christopher J.O’Donnell
University of Queensland
Brisbane, QLD,Australia
Additional material tothis bookcanbedownloaded from http://extras.springer.com.
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To the memory of my parents, Brian James
and Arkley Jean.
Preface
This book provides a coherent description of the main economic concepts and
statisticalmethodsusedtoanalysemanagerialperformance.Itisprimarilyaimedat
researchers, statisticians, accountants and economists working in regulatory
authorities, government departments and private firms. The target audience also
includes graduate students and academics. All readers are expected to have com-
pleted introductory university courses in economics, mathematics and statistics.
The book contains nine chapters. Chapter 1 provides a summary of the main
ideas presented later in the book. Among other things, it explains exactly what is
meant by the terms ‘production technology’, ‘production environment’, ‘produc-
tivity’ and ‘efficiency’. Chapter 2 discusses various sets and functions that can be
used to represent the input–output combinations that are possible using different
technologies indifferent environments. Thefocusisondistance, revenue,costand
profit functions. Chapter 3 explains how to measure productivity change. In this
book, measures of productivity change are defined as measures of output quantity
change divided by measures of input quantity change. To explain changes in out-
putsandinputs,andthereforechangesinproductivity,weneedtoknowsomething
about managerial behaviour. Chapter 4explainsthat firm managers tend tobehave
differentlydependingonwhattheyvalue,andonwhattheycanandcannotchoose.
It then discusses some of the simplest optimisation problems faced by managers
(e.g. profit maximisation). Chapter 5 defines various measures of efficiency.
Measures of efficiency can be viewed as ex post measures of how well managers
have solved different optimisation problems. Estimating and predicting levels of
efficiency involves estimating production frontiers. Chapter 6 explains how to
estimate the parameters of piecewise frontiers. The focus of this chapter is on data
envelopment analysis (DEA) estimators. Chapter 7 explains how to estimate the
parameters of deterministic frontiers. Here, the focus is on least squares
(LS) estimators. Chapter 8 explains how to estimate the parameters of stochastic
frontiers. Here, the focus is on maximum likelihood (ML) estimators. Finally,
Chap. 9 provides a practical step-by-step guide to analysing managerial perfor-
mance. It also considers government policies that can be used to target the main
drivers of performance.
vii
viii Preface
ThereisenoughmaterialinChap.1foraone-ortwo-dayintroductorycourseon
productivity and efficiency analysis. There is enough material in the remaining
chapters to build courses that can run over one or two semesters. Approximately
eighthoursoflecturesandfourhoursinthecomputerlaboratoryshouldbeenough
tocovermostofthematerialinChaps.2–5.Approximatelytwentyhoursoflectures
and another fifteen hours in the computer laboratoty should be enough to cover
most of the material in Chaps. 6–8. A one-hour lecture and another hour in the
computer laboratory is enough to cover the material in Chap. 9. These time esti-
mates assume that students have little or no experience with computer program-
ming. The empirical results reported in this book were obtained by running R
Version 3.3.3 (2017-03-06) on a MacBookPro with an OS X 10.10.5 (Yosemite)
operating system. The datasets and computer codes are available at http://extras.
springer.com/2018. Slightly different results may be obtained by running different
software packages (including more recent versions of R) on computers with dif-
ferent operating systems.
Partsofthebookaresomewhatrepetitive.Somereadersmayfindthisannoying.
However, it should help other readers see patterns in, and make connections
between, seemingly unrelated concepts and techniques. It should also help some
readers commit new material to memory. It also means that most chapters are
reasonably self-contained, which should make thebook more useful as areference
text.
Finally,some acknowledgementsaredue.Many ofthedefinitionsandconcepts
presented in the book were first developed while I was on sabbatical at the
Universitat Autónoma de Barcelona in 2008. I would like to thank Emili
Grifell-Tatjéforhostingmeduringthatvisit,andalsotheGeneralitatdeCatalunya
for providing financial support. In the last decade, I have been refining the main
ideasandbringingthemtogetherintheformofthisbook.Duringthistime,Ihave
received enormous encouragement from my wife, Adrienne, and my children,
Benjamin, Lachlan, Joshua and Courtney; I cannot thank them enough for their
patience and unwavering support. On an academic level, I am grateful for con-
structivecomments providedbystaff,studentsandacademicvisitorstotheSchool
of Economics at the University of Queensland. I am also grateful for feedback
receivedduringshortcoursesdeliveredattheAustralianDepartmentofHealthand
Ageing(DoHA),theAustralianConsumerandCompetitionCommission(ACCC),
the Independent Hospital Pricing Authority (IHPA), the Victorian Department of
Education and Early Childhood Development (DEECD), the University of
Queensland,theUniversityofWaikato,andtheAustralianDefenceForceAcademy
(ADFA). Individuals who deserve special mention include (in alphabetical order)
Julian Alston, Boris Bravo-Ureta, Cinzia Daraio, Rolf Färe, Finn Førsund, Bill
Greene, Kristiaan Kerstens, Chris Parmeter, Antonio Peyrache, Victor Podinovski,
Marshall Reinsdorf and Peter Schmidt. None of these individuals are in any way
responsible for any errors in the book.
Brisbane, Australia Christopher J. O’Donnell
August 2018
Contents
1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Basic Concepts and Terminology . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Production Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Output Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Input Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Production Possibilities Sets . . . . . . . . . . . . . . . . . . . . . 6
1.2.4 Output Distance Functions . . . . . . . . . . . . . . . . . . . . . . 8
1.2.5 Input Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.6 Other Sets and Functions . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Measures of Productivity Change . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Output Quantity Indices . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Input Quantity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.3 Productivity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 Other Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Managerial Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.1 Output Maximisation . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.2 Input Minimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4.3 Productivity Maximisation . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.4 Other Types of Behaviour . . . . . . . . . . . . . . . . . . . . . . . 21
1.5 Measures of Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.1 Output-Oriented Measures . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.2 Input-Oriented Measures . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.3 Productivity-Oriented Measures . . . . . . . . . . . . . . . . . . . 24
1.5.4 Other Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.6 Piecewise Frontier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.6.1 Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6.2 Productivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.6.3 Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
ix
x Contents
1.7 Deterministic Frontier Analysis . . . . . . . . . . . . . . . . . . . . . . . . 37
1.7.1 Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.7.2 Least Squares Estimation . . . . . . . . . . . . . . . . . . . . . . . . 38
1.7.3 Productivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.7.4 Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.8 Stochastic Frontier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.8.1 Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.8.2 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . . . 46
1.8.3 Productivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.8.4 Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.9 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.9.1 The Main Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.9.2 Government Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.10 Summary and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 52
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2 Production Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.1 Output Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.1.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.1.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Input Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.3 Production Possibilities Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.4 Output Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.4.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.4.2 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.4.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.5 Input Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.2 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.5.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.6 Revenue Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.6.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.6.2 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.6.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.7 Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.7.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.7.2 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.7.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Contents xi
2.8 Profit Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.8.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.8.2 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.8.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.9 Other Sets and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.9.1 Production Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.9.2 Input Requirement Functions . . . . . . . . . . . . . . . . . . . . . 80
2.9.3 Directional Distance Functions . . . . . . . . . . . . . . . . . . . 82
2.9.4 Hyperbolic Distance Functions . . . . . . . . . . . . . . . . . . . 83
2.9.5 Technology-and-Environment-Specific Sets and
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.9.6 Period-Specific Sets and Functions . . . . . . . . . . . . . . . . . 85
2.9.7 State-Contingent Sets and Functions . . . . . . . . . . . . . . . 86
2.10 Summary and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 86
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3 Measures of Productivity Change . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.1 Output Quantity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.1.1 Additive Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1.2 Multiplicative Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.1.3 Primal Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.1.4 Dual Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.1.5 Benefit-of-the-Doubt Indices . . . . . . . . . . . . . . . . . . . . . 98
3.1.6 Other Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.1.7 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.2 Input Quantity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.2.1 Additive Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.2.2 Multiplicative Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.2.3 Primal Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.2.4 Dual Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.2.5 Benefit-of-the-Doubt Indices . . . . . . . . . . . . . . . . . . . . . 109
3.2.6 Other Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.2.7 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.3 Productivity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.3.1 Additive Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.3.2 Multiplicative Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.3.3 Primal Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.3.4 Dual Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.3.5 Benefit-of-the-Doubt Indices . . . . . . . . . . . . . . . . . . . . . 119
3.3.6 Other Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.3.7 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123