Productivity and Efficiency Analysis (eBook)

Christopher J. O’Donnell is a Professor in Econometrics at the University of Queensland.  He is a co-editor of the Journal of Productivity Analysis, an associate editor of Empirical Economics, and a Distinguished Fellow of the Australian Agricultural and Resource Economics Society. His research interests focus on mathematical programming and statistical methods for measuring and explaining productivity and efficiency change. His work has been published in leading economics and econometrics journals, including the American Journal of Agricultural Economics, the Journal of Econometrics, the Journal of Applied Econometrics, and Econometric Reviews. He has provided in-house training and/or been a consultant for organisations including the World Bank, the International Rice Research Institute, the Australian Energy Regulator, the NSW Independent Pricing and Regulatory Tribunal, and the Australian Independent Hospital Pricing Authority.

Preface 6
Contents 8
Acronyms 16
Notation 20
1 Overview 21
1.1 Basic Concepts and Terminology 21
1.2 Production Technologies 23
1.2.1 Output Sets 24
1.2.2 Input Sets 25
1.2.3 Production Possibilities Sets 26
1.2.4 Output Distance Functions 28
1.2.5 Input Distance Functions 30
1.2.6 Other Sets and Functions 31
1.3 Measures of Productivity Change 31
1.3.1 Output Quantity Indices 32
1.3.2 Input Quantity Indices 34
1.3.3 Productivity Indices 34
1.3.4 Other Indices 37
1.4 Managerial Behaviour 37
1.4.1 Output Maximisation 37
1.4.2 Input Minimisation 39
1.4.3 Productivity Maximisation 40
1.4.4 Other Types of Behaviour 41
1.5 Measures of Efficiency 41
1.5.1 Output-Oriented Measures 41
1.5.2 Input-Oriented Measures 43
1.5.3 Productivity-Oriented Measures 44
1.5.4 Other Measures 46
1.6 Piecewise Frontier Analysis 47
1.6.1 Basic Models 48
1.6.2 Productivity Analysis 53
1.6.3 Other Models 57
1.7 Deterministic Frontier Analysis 57
1.7.1 Basic Models 57
1.7.2 Least Squares Estimation 58
1.7.3 Productivity Analysis 62
1.7.4 Other Models 63
1.8 Stochastic Frontier Analysis 64
1.8.1 Basic Models 65
1.8.2 Maximum Likelihood Estimation 66
1.8.3 Productivity Analysis 68
1.8.4 Other Models 71
1.9 Practical Considerations 71
1.9.1 The Main Steps 71
1.9.2 Government Policies 72
1.10 Summary and Further Reading 72
References 73
2 Production Technologies 75
2.1 Output Sets 75
2.1.1 Assumptions 76
2.1.2 Example 79
2.2 Input Sets 79
2.2.1 Assumptions 79
2.2.2 Example 81
2.3 Production Possibilities Sets 81
2.3.1 Assumptions 82
2.3.2 Example 83
2.4 Output Distance Functions 83
2.4.1 Properties 84
2.4.2 Marginal Effects 85
2.4.3 Example 86
2.5 Input Distance Functions 87
2.5.1 Properties 87
2.5.2 Marginal Effects 89
2.5.3 Example 89
2.6 Revenue Functions 90
2.6.1 Properties 91
2.6.2 Marginal Effects 92
2.6.3 Example 93
2.7 Cost Functions 93
2.7.1 Properties 94
2.7.2 Marginal Effects 95
2.7.3 Example 95
2.8 Profit Functions 96
2.8.1 Properties 97
2.8.2 Marginal Effects 97
2.8.3 Example 98
2.9 Other Sets and Functions 98
2.9.1 Production Functions 99
2.9.2 Input Requirement Functions 100
2.9.3 Directional Distance Functions 102
2.9.4 Hyperbolic Distance Functions 103
2.9.5 Technology-and-Environment-Specific Sets and Functions 103
2.9.6 Period-Specific Sets and Functions 105
2.9.7 State-Contingent Sets and Functions 106
2.10 Summary and Further Reading 106
References 111
3 Measures of Productivity Change 113
3.1 Output Quantity Indices 113
3.1.1 Additive Indices 115
3.1.2 Multiplicative Indices 116
3.1.3 Primal Indices 117
3.1.4 Dual Indices 118
3.1.5 Benefit-of-the-Doubt Indices 118
3.1.6 Other Indices 119
3.1.7 Toy Example 122
3.2 Input Quantity Indices 125
3.2.1 Additive Indices 126
3.2.2 Multiplicative Indices 126
3.2.3 Primal Indices 127
3.2.4 Dual Indices 128
3.2.5 Benefit-of-the-Doubt Indices 129
3.2.6 Other Indices 129
3.2.7 Toy Example 132
3.3 Productivity Indices 135
3.3.1 Additive Indices 136
3.3.2 Multiplicative Indices 136
3.3.3 Primal Indices 137
3.3.4 Dual Indices 138
3.3.5 Benefit-of-the-Doubt Indices 139
3.3.6 Other Indices 139
3.3.7 Toy Example 143
3.4 Other Indices 145
3.4.1 Output Price Indices 146
3.4.2 Input Price Indices 148
3.4.3 Terms-of-Trade Indices 151
3.4.4 Implicit Output Indices 152
3.4.5 Implicit Input Indices 153
3.4.6 Implicit Productivity Indices 155
3.5 Summary and Further Reading 156
References 160
4 Managerial Behaviour 164
4.1 Output Maximisation 164
4.1.1 Output Mix Predetermined 164
4.1.2 Outputs Chosen Freely 166
4.1.3 Example 167
4.2 Input Minimisation 167
4.2.1 Input Mix Predetermined 167
4.2.2 Inputs Chosen Freely 169
4.2.3 Example 170
4.3 Revenue Maximisation 170
4.3.1 Price Setters in Output Markets 170
4.3.2 Price Takers in Output Markets 172
4.3.3 Example 173
4.4 Cost Minimisation 174
4.4.1 Price Setters in Input Markets 174
4.4.2 Price Takers in Input Markets 176
4.4.3 Example 177
4.5 Profit Maximisation 177
4.5.1 Price Setters in Output and Input Markets 178
4.5.2 Price Takers in Output and Input Markets 179
4.5.3 Example 181
4.6 Productivity Maximisation 182
4.6.1 Output and Input Mixes Predetermined 182
4.6.2 Outputs and Inputs Chosen Freely 183
4.6.3 Example 184
4.7 Other Types of Behaviour 184
4.7.1 Choosing Technologies 185
4.7.2 Maximising Net Output 186
4.7.3 Maximising Return to the Dollar 187
4.7.4 Behaviour in the Face of Environmental Uncertainty 187
4.7.5 Behaviour in the Face of Other Types of Uncertainty 189
4.7.6 Bounded Rationality 190
4.8 Summary and Further Reading 190
References 192
5 Measures of Efficiency 193
5.1 Output-Oriented Measures 193
5.1.1 Output-Oriented Technical Efficiency 194
5.1.2 Output-Oriented Technical and Mix Efficiency 195
5.1.3 Output-Oriented Mix Efficiency 196
5.1.4 Example 199
5.2 Input-Oriented Measures 199
5.2.1 Input-Oriented Technical Efficiency 200
5.2.2 Input-Oriented Technical and Mix Efficiency 201
5.2.3 Input-Oriented Mix Efficiency 203
5.2.4 Example 204
5.3 Revenue-Oriented Measures 205
5.3.1 Revenue Efficiency 206
5.3.2 Output-Oriented Allocative Efficiency 207
5.3.3 Example 209
5.4 Cost-Oriented Measures 210
5.4.1 Cost Efficiency 210
5.4.2 Input-Oriented Allocative Efficiency 211
5.4.3 Example 213
5.5 Profit-Oriented Measures 214
5.5.1 Profit Efficiency 214
5.5.2 Output-Oriented Scale and Allocative Efficiency 216
5.5.3 Input-Oriented Scale and Allocative Efficiency 217
5.5.4 Example 218
5.6 Productivity-Oriented Measures 218
5.6.1 Technical and Scale Efficiency 218
5.6.2 Technical, Scale and Mix Efficiency 219
5.6.3 Residual Mix Efficiency 220
5.6.4 Example 221
5.7 Other Measures 222
5.7.1 Output-Oriented Scale Efficiency 222
5.7.2 Output-Oriented Scale and Mix Efficiency 223
5.7.3 Residual Output-Oriented Scale Efficiency 224
5.7.4 Input-Oriented Scale Efficiency 225
5.7.5 Input-Oriented Scale and Mix Efficiency 226
5.7.6 Residual Input-Oriented Scale Efficiency 228
5.7.7 Metatechnology Ratios 229
5.7.8 Nonradial Measures 231
5.8 Summary and Further Reading 232
References 235
6 Piecewise Frontier Analysis 237
6.1 Basic Models 237
6.1.1 Output-Oriented Models 238
6.1.2 Input-Oriented Models 241
6.1.3 Revenue-Oriented Models 243
6.1.4 Cost-Oriented Models 244
6.1.5 Profit-Oriented Models 247
6.1.6 Productivity-Oriented Models 247
6.2 Models with Stronger Assumptions 253
6.2.1 No Technical Change 253
6.2.2 Nonincreasing Returns to Scale 254
6.2.3 Constant Returns to Scale 255
6.2.4 Nondecreasing Returns to Scale 257
6.2.5 Toy Example 258
6.3 Models with Weaker Assumptions 258
6.3.1 Inputs Not Strongly Disposable 259
6.3.2 Outputs Not Strongly Disposable 260
6.3.3 Environmental Variables Not Strongly Disposable 261
6.3.4 Production Possibilities Sets Not Convex 262
6.3.5 Toy Example 263
6.4 Inference 263
6.4.1 PDFs Known 265
6.4.2 PDFs Unknown 268
6.5 Productivity Analysis 271
6.5.1 Measuring Changes in TFP 272
6.5.2 Explaining Changes in TFP 273
6.6 Other Models 282
6.6.1 Metafrontier Models 282
6.6.2 Inefficiency Models 288
6.7 Summary and Further Reading 290
References 294
7 Deterministic Frontier Analysis 299
7.1 Basic Models 299
7.1.1 Output-Oriented Models 299
7.1.2 Input-Oriented Models 301
7.1.3 Revenue-Oriented Models 303
7.1.4 Cost-Oriented Models 304
7.1.5 Profit-Oriented Models 305
7.2 Growth Accounting Estimation 307
7.2.1 Assumptions 307
7.2.2 Estimation 307
7.2.3 Toy Example 308
7.3 Least Squares Estimation 308
7.3.1 Assumptions 310
7.3.2 Estimation 310
7.3.3 Prediction 311
7.3.4 Hypothesis Tests 312
7.3.5 Toy Example 317
7.4 Maximum Likelihood Estimation 319
7.4.1 Assumptions 319
7.4.2 Estimation 320
7.4.3 Prediction 321
7.4.4 Hypothesis Tests 321
7.4.5 Toy Example 321
7.5 Productivity Analysis 323
7.5.1 Measuring Changes in TFP 323
7.5.2 Explaining Changes in TFP 326
7.6 Other Models 330
7.6.1 Metafrontier Models 330
7.6.2 Output Supply Systems 334
7.6.3 Input Demand Systems 336
7.7 Summary and Further Reading 338
References 340
8 Stochastic Frontier Analysis 343
8.1 Basic Models 343
8.1.1 Output-Oriented Models 343
8.1.2 Input-Oriented Models 345
8.1.3 Revenue-Oriented Models 346
8.1.4 Cost-Oriented Models 347
8.1.5 Profit-Oriented Models 349
8.2 Least Squares Estimation 350
8.2.1 Assumptions 350
8.2.2 Estimation 350
8.2.3 Prediction 351
8.2.4 Hypothesis Tests 352
8.2.5 Toy Example 353
8.3 Maximum Likelihood Estimation 355
8.3.1 Assumptions 355
8.3.2 Estimation 356
8.3.3 Prediction 356
8.3.4 Hypothesis Tests 357
8.3.5 Toy Example 359
8.4 Bayesian Estimation 361
8.4.1 Bayes's Theorem 362
8.4.2 The Likelihood Function 363
8.4.3 The Prior PDF 363
8.4.4 Marginal Posterior PDFs 364
8.4.5 Point Estimation 365
8.4.6 Interval Estimation 365
8.4.7 Assessing Alternative Hypotheses 365
8.4.8 Simulation 366
8.4.9 Toy Example 366
8.5 Productivity Analysis 367
8.5.1 Measuring Changes in TFP 367
8.5.2 Explaining Changes in TFP 371
8.6 Other Models 376
8.6.1 Metafrontier Models 377
8.6.2 Output Supply Systems 380
8.6.3 Input Demand Systems 381
8.6.4 Inefficiency Models 383
8.7 Summary and Further Reading 385
References 387
9 Practical Considerations 391
9.1 The Main Steps 391
9.2 Government Policies 399
9.3 Rice Example 401
References 409
A 410
A.1 Propositions 410
A.2 Rates of Growth 414
A.3 Exponential Random Variables 415
A.4 Gamma Random Variables 417
A.5 Normal Random Variables 418
A.6 Half-Normal Random Variables 419
A.7 Truncated-Normal Random Variables 420
A.8 The Maximum of Bivariate-Normal Random Variables 421
A.9 The Maximum of Independent Normal Random Variables 422
References 422
Author Index 423
Subject Index 429