CONTENTS
List of Figures = xxiii
List of Tables = xxvii
Preface = xxix
Ⅰ Concepts, Models, and Processes in Econometrics = 1
1 Introduction = 3
1.1 Empirical econometrics modelling = 3
1.2 The problems of econometrics = 5
1.3 The aims of this book = 6
1.4 Constructive and destructive approaches = 7
1.5 A brief discourse on scientific method = 9
1.6 Theories, instruments, and evidence = 11
1.7 Economic analysis and statistical theory = 13
1.8 Four levels of knowledge = 16
1.8.1 Probability theory = 16
1.8.2 Estimation theory = 16
1.8.3 Modelling theory = 17
1.8.4 Forecasting theory = 17
1.8.5 The origins of the methodological crisis = 18
1.9 Some economic time series = 19
1.10 A first data-generation process = 21
1.11 Empirical models as derived entities = 27
1.12 Exercises = 29
2 Econometrics Concepts = 31
2.1 Parameter = 31
2.2 Constancy = 32
2.3 Structure = 33
2.4 Distributional shape = 34
2.5 Identification and observational equivalence = 36
2.6 Interdependence = 37
2.7 Stochastic process = 38
2.8 Conditioning = 39
2.9 White noise = 39
2.10 Autocorrelation = 40
2.11 Stationarity = 42
2.12 Integratedness = 43
2.13 Co-integration = 44
2.14 Trend = 44
2.15 Heteroscedasticity = 45
2.16 Dimensionality = 46
2.17 Aggregation = 46
2.18 Marginalization = 48
2.19 A general formulation = 49
2.20 A static solved example = 51
2.21 Models, mechanisms, and DGPs = 55
2.22 Factorizations = 56
2.23 Innovation processes = 58
2.24 Empirical models = 60
2.25 White noise and innovations = 63
2.26 Auto-correlated. shocks = 64
2.27 Sequential factorization = 65
2.28 Model design = 67
2.29 A dynamic solved example = 68
2.30 Exercises = 72
3 Econometrics Tools and Techniques = 75
3.1 Review = 75
3.2 Estimating unknown parameters = 76
3.2.1 An empirical example = 76
3.2.2 Recursive estimation = 78
3.2.3 A solved recursive example = 82
3.3 Methods for evaluating models = 85
3.4 Statistical theory = 86
3.5 Asymptotic distribution theory = 87
3.6 Monte Carlo = 87
3.6.1 Distribution sampling = 88
3.6.2 Antithetic variate = 90
3.6.3 Control variables = 93
3.6.4 Response surfaces = 94
3.6.5 Invariance = 95
3.6.6 Recursive Monte Carlo = 97
3.7 Ergodicity = 98
3.8 Non-stationarity * = 100
3.9 A solved example * = 104
3.10 Vector Brownian motion * = 111
3.11 A Monte Carlo study = 115
3.12 Exercises = 118
4 Dynamics and Interdependence = 122
4.1 Nonsense regressions = 122
4.2 Analysing nonsense regressions * = 130
4.3 Spurious de-trending * = 133
4.4 First-order autoregressive dynamics = 134
4.5 Reduction and dynamics = 138
4.6 Interdependence = 140
4.7 Co-integration = 143
4.8 Bivariate dynamics = 143
4.9 A solved example = 145
4.10 Exercises = 150
5 Exogeneity and Causality = 156
5.1 What are 'exogenous variables'? = 156
5.2 Two counter-examples = 157
5.2.1 An expectations counter-example = 158
5.2.2 A fixed-regressor counter-example = 161
5.3 Weak exogeneity = 162
5.4 A cobweb model = 164
5.5 The counter-examples reconsidered = 166
5.6 An ambiguity in strict exogeneity = 167
5.7 Can the model mis-specification be detected? = 168
5.7.1 ζ t is not an innovation relative to X t-1 = 169
5.7.2 tζ t is white noise = 169
5.8 Strong exogeneity = 170
5.9 Super exogeneity = 172
5.10 An illustration of super exogeneity = 173
5.11 Causality = 175
5.11.1 Granger non-causality = 175
5.11.2 Invariance under interventions = 176
5.12 Two solved examples = 177
5.13 Weak exogeneity and unit roots * = 181
5.13.1 A bivariate cointegrated system = 182
5.13.2 Six cases of interest = 183
5.13.3 Limiting distributions = 184
5.13.4 Inference = 187
5.13.5 A Monte Carlo study = 188
5.14 Exercises = 191
6 Interpreting Linear Models = 195
6.1 Four interpretations of Y t = β 'Z t + ε t = 195
6.1.1 Regression = 196
6.1.2 Linear least-squares approximation = 197
6.1.3 Contingent plan = 198
6.1.4 Behavioral model = 200
6.2 Expectations formation = 202
6.2.1 Rational expectations = 202
6.2.2 Unbiased expectations = 204
6.2.3 Data-based expectations = 205
6.3 Autocorrelation corrections = 207
6.4 A simple dynamic model : AD(l, ,l) = 211
6.5 Lags and their measurement = 212
6.5.1 Static solutions = 212
6.5.2 Lag distributions = 214
6.5.3 Interpreting empirical lag distributions = 217
6.6 A Monte Carlo study of the AD(l, 1) model = 219
6.6.1 Coefficient biases = 220
6.6.2 Coefficient standard errors = 221
6.6.3 Parameter constancy tests = 223
6.7 An empirical illustration = 223
6.8 A solved example = 227
6.9 Exercises = 229
7 A Typology of Linear Dynamic Equations = 231
7.1 Introduction = 231
7.2 Static regression = 233
7.3 Auto-regression = 241
7.4 Differenced-data model = 247
7.5 Leading indicator = 252
7.6 Partial adjustment = 256
7.7 Common factor = 266
7.8 Finite distributed lags = 273
7.9 Dead-start models = 283
7.10 Equilibrium correction = 286
7.10.1 Co-integration = 288
7.10.2 Servo-mechanistic control = 290
7.10.3 Empirical success of ECMs = 291
7.11 Solved examples = 294
7.11.1 Partial adjustment and equilibrium correction = 294
7.11.2 Testing co-integration = 297
7.11.3 Co-integration representations = 303
7.12 Summary and conclusion = 304
7.12.1 Goodness of fit = 304
7.12.2 Distributed-lag shapes = 304
7.13 Exercises = 306
8 Dynamic Systems = 309
8.1 Introduction = 309
8.2 Statistical formulation = 310
8.3 Theoretical formulation = 311
8.4 Closed linear systems = 313
8.4.1 Formulation = 313
8.4.2 Invariance under linear transformations = 313
8.4.3 Co-integration = 315
8.5 Open linear systems = 316
8.5.1 Conditional systems = 316
8.5.2 Simultaneous equations = 317
8.5.3 Co-integration = 317
8.6 Modelling dynamic systems = 318
8.6.1 The economy is a system = 319
8.6.2 To test marginalization = 319
8.6.3 Simultaneity = 319
8.6.4 To test weak exogeneity = 320
8.6.5 To check identification = 320
8.6.6 Co-integration is a system property = 320
8.6.7 To test cross-equation dependencies = 320
8.6.8 To investigate system dynamics = 321
8.7 A typology of open linear dynamic systems = 321
8.7.1 Vector equilibrium-correction system = 322
8.7.2 Static system = 323
8.7.3 Vector auto-regression = 323
8.7.4 .Differenced. system = 323
8.7.5 Leading indicator = 323
8.7.6 Partial adjustment = 324
8.7.7 Common factor = 324
8.7.8 Finite distributed lag = 324
8.7.19 Dead start = 324
8.7.10 An empirical illustration = 325
8.8 Models of linear systems = 329
8.8.1 Vector autoregressive representation = 329
8.8.2 Vector equilibrium correction = 330
8.8.3 Simultaneous-equations model = 331
8.8.4 Conditional model = 332
8.8.5 Conditional simultaneous model = 333
8.8.6 Causal chain = 333
8.8.7 Block-recursive representation = 334
8.8.8 Triangular representation = 335
8.8.9 Empirical illustrations = 335
8.9 Analysing dynamic systems = 337
8.9.1 Dynamic multipliers = 339
8.9.2 Final forms = 340
8.9.3 Non-linearity = 340
8.9.4 Dynamic simulation = 341
8.10 Exercises = 343
9 The Theory of Reduction = 344
9.1 Introduction = 344
9.2 Data transformations and aggregation = 346
9.3 Parameters of interest = 347
9.4 Data partition = 350
9.5 Marginalization = 350
9.6 Sequential factorization = 352
9.6.1 Sequential factorization of W 1 T = 352
9.6.2 Marginalizing with respect to V T 1 = 352
9.7 Mapping to 1(0) = 353
9.8 Conditional factorization = 354
9.9 Constancy = 355
9.10 Lag truncation = 356
9.11 Functional form = 356
9.12 The derived model = 357
9.13 Econometrics concepts as measures of no information loss = 359
9.14 Implicit model design = 361
9.15 Explicit model design = 361
9.16 A taxonomy of evaluation information = 362
9.16.1 Past data = 363
9.16.2 Present data = 363
9.16.3 Future data = 363
9.16.4 Theory information = 363
9.16.5 Measurement information = 364
9.16.6 Rival models = 364
9.17 Exercises = 367
Ⅱ Statistical Tools for Econometrics Analysis = 369
10 Likelihood = 371
10.1 Review of Part Ⅰ = 371
10.2 The statistical model = 373
10.3 Estimation criteria and estimation methods = 374
10.4 The likelihood function = 377
10.5 Maximum likelihood estimation = 378
10.6 Properties of the score = 379
10.7 Properties of maximum likelihood estimators = 382
10.8 Large-sample properties of MLEs = 384
10.9 Two solved examples = 387
10.10 Misleading inference when V ≠ X - 1 = 391
10.11 Derived distributions = 393
10.12 Asymptotic equivalence = 394
10.13 Concentrated likelihood functions = 395
10.14 Marginal and conditional distributions = 396
10.15 Estimator generating equations = 397
10.16 An EG E for common-factor dynamics = 398
10.17 Exercises = 399
11 Simultaneous Equations Systems = 405
11.1 Introduction = 405
11.2 The statistical system = 406
11.3 System dynamic specification = 407
11.4 System estimation = 409
11.5 System co-integration estimation = 412
11.6 System evaluation = 418
11.7 Empirical co-integration illustration = 419
11.8 The econometrics model = 421
11.9 Identification = 422
11.10 An EGE for simultaneous equations estimation = 423
11.10.1 Non-linear parameters = 428
11.10.2 Vector autoregressive errors = 429
11.11 A solved example = 430
11.12 Simultaneous equations modelling = 433
11.13 Derived statistics = 434
11.14 Empirical model estimates = 436
11.15 Exercises = 440
12 Measurement Problems in Econometrics = 442
12.1 Introduction = 442
12.2 Errors in variables = 443
12.2.1 Analysing the errors-Lin-variables model = 445
12.2.2 Instrumental variables = 449
12.3 Dynamic latent-variables models = 451
12.3.1 Method of simulated moments = 453
12.3.2 Simulated likelihood functions = 455
12.3.3 A dynamic min-condition model = 456
12.3.4 Exogeneity issues = 458
12.4 Revisions to 1(1) data = 459
12.4.1 Revisions to price indices = 459
12.4.2 An empirical illustration = 461
12.5 The impact of measurement errors on ECMs = 463
12.6 Exercises = 466
13 Testing and Evaluation = 468
13.1 The statistical framework = 468
13.2 Non-central X 2 distributions = 470
13.3 Large-sample properties of tests = 472
13.4 Understanding the non-central X 2 distribution = 474
13.5 Test power = 476
13.6 Likelihood-ratio, Wald, and Lagrange-multiplier tests = 477
13.6.1 Likelihood-ratio tests = 478
13.6.2 Wald tests = 479
13.6.3 Lagrange-multiplier or efficient-score tests = 480
13.7 Comparing the tests = 480
13.8 A solved example = 482
13.9 Non-linear restrictions = 485
13.10 Some methodological considerations = 487
13.10.1 The null hypothesis = 487
13.10.2 The alternative hypothesis = 488
13.10.3 The test statistics = 488
13.10.4 The significance level = 490
13.10.5 Multiple testing = 490
13.11 Exercises = 492
Ⅲ Empirical Modelling = 499
14 Encompassing = 501
14.1 Introduction = 501
14.2 Augmenting the conventional testing strategy = 503
14.2.1 Rejection is not final = 503
14.2.2 Corroboration is not definitive = 504
14.3 Encompassing and mis-specification analysis = 505
14.4 Formalizing encompassing = 506
14.5 Levels of analysis = 509
14.5.1 Specification encompassing = 510
14.5.2 Mis-specification encompassing = 510
14.5.3 Selection encompassing = 510
14.6 Parsimonious encompassing = 511
14.7 A simple example = 512
14.7.1 Can M 1 ? M 2 ? = 513
14.7.2 Can M 2 ? M 1 ? = 514
14.8 Nesting and encompassing = 514
14.9 Encompassing in linear regression = 516
14.10 Encompassing in stationary stochastic processes = 520
14.11 A solved example = 523
14.12 An empirical illustration = 525
14.13 Encompassing the VAR = 527
14.14 Testing the Lucas critique529
14.15 The applicability of the critique = 531
14.16 Tests for. super exogeneity = 532
14.17 Encompassing implications of feedback versus feed forward models = 534
14.17.1 Does H b ? H e ? = 535
14.17.2 Does H e ? H b ? = 535
14.17.3 Incomplete information = 536
14.17.4 Implications = 536
14.18 Empirical testing of invariance = 536
14.18.1 Testing super-exogeneity = 537
14.18.2 Testing encompassing = 538
14.19 Exercises = 539
15 Modelling Issues = 544
15.1 Data mining = 544
15.2 Theory dependence versus sample dependence = 546
15.2.1 Theory-driven approaches = 546
15.2.2 Data-driven approaches = 547
15.2.3 Bayesian approaches = 547
15.2.4 Data modelling using economic theory guidelines = 547
15.3 Progressive research strategies = 550
15.3.1 Identified cointegration vector = 550
15.3.2 Orthogonal parameters = 552
15.3.3 Inappropriate estimation = 553
15.3.4 Common trends = 553
15.3.5 Residual analysis = 553
15.3.6 Expectations and structure = 553
15.4 Pyrrho's lemma = 554
15.5 Dummy variables = 557
15.6 Seasonal adjustment = 559
15.6.1 Seasonal filters = 561
15.6.2 Properties of seasonal filters = 562
15.6.3 Co-integration = 563
15.7 Approximating moving-average processes = 565
15.8 A solved example : modelling second moments = 568
15.9 Populations and samples = 574
15.10 Exercises = 576
16 Econometrics in Action = 577
16.1 The transactions demand for money = 577
16.2 Economic theories of money demand = 579
16.3 Econometrics formulation = 581
16.4 Financial innovation = 583
16.5 Data description = 585
16.6 A small monetary system = 591
16.7 Cointegration analysis = 597
16.8 Modelling the Ⅰ(0) PVAR = 600
16.9 Evaluating the model = 604
16.10 A single-equation money-demand model = 606
16.11 Transformation and reduction = 611
16.12 Post-modelling evaluation = 614
16.12.1 Learning adjustment = 615
16.12.2 Constancy = 615
16.12.3 Encompassing = 616
16.13 Testing the Lucas critique = 616
16.14 Post-sample evaluation = 618
16.15 Policy implications = 618
16.16 Data definitions = 619
Ⅳ Appendices = 621
Al Matrix Algebra = 623
A1.1 Summary of the appendix chapters = 623
A1.2 Matrices = 625
A1.3 Matrix operations = 627
Al.4 Relations between operations = 633
A1.5 Partitioned inverse = 634
A1.6 Polynomial matrices = 635
A2 Probability and Distributions = 639
A2.1 Introduction = 639
A2.1.1 Chance = 639
A2.1.2 Empirical distributions and histograms = 639
A2.2 Events = 641
A2.2.1 Random experiments, sets, and sample spaces = 641
A2.2.2 Complements, unions, and intersections = 642
A2.2.3 Event space = 644
A2.2.4 Measurability = 646
A2.3 Probability = 646
A2.3.1 Probability spaces = 647
A2.3.2 Conditional probability = 648
A2.3.3 Stochastic independence = 651
A2.4 Random variables = 653
A2.4.1 Mapping events to numbers = 653
A2.4.2 Image sets = 654
A2.4.3 Functions of random variables = 655
A2.5 Distribution and density functions = 656
A2.5.1 Cumulative distribution function = 656
A2.5.2 Density function = 656
A2.5.3 Change of variable = 657
A2.5.4 Normal distribution = 657
A2.5.5 Parameters, probability models, and distributions = 658
A2.6 Joint distributions = 659
A2.6.1 Joint distribution functions = 659
A2.6.2 Marginal distributions = 659
A2.6.3 Conditional distributions = 661
A2.7 Expectations = 662
A2.7.1 Expectations, moments, and correlations = 662
A2.7.2 Conditional expectations and minimum variance = 663
A2.7.3 Indicator functions = 665
A2.7.4 Chibychev's inequality = 666
A2.8 Bivariate normal distribution = 666
A2.8.1 Change of variable = 666
A2.8.2 The bivariate normal density = 667
A2.8.3 Conditional normal = 668
A2.8.4 Regression = 669
A2.9 Multivariate normal = 670
A2.9.1 Multivariate normal density = 670
A2.9.2 Multiple regression = 670
A2.9.3 Multivariate regression = 671
A2.9.4 Functions of normal variables : X 2 , t and F distributions = 672
A2.10 Exercises = 674
A3 Statistical Theory = 677
A3.1 Sampling distributions = 677
A3.1.1 Statistics = 677
A3.1.2 Derived distributions = 678
A3.1.3 χ2 , t, and F distributions = 680
A3.1.4 Sufficiency = 681
A3.1.5 Estimation criteria = 683
A3.1.6 Consistency and asymptotic efficiency = 684
A3.2 Likelihood = 684
A3.2.1 Likelihood function = 684
A3.2.2 Log-likelihood = 685
A3.2.3 Estimation = 685
A3.2.4 The score and the Hessian = 686
A3.3 Maximum-likelihood estimation = 687
A3.3.1 Efficiency and the information matrix = 687
A3.3.2 Cram e r-Rao bound = 688
A3.3.3 Properties of the information matrix = 689
A3.3.4 Estimating the information matrix = 689
A3.4Statistical inference and testing = 690
A3.4.1 Null and alternative hypotheses = 690
A3.4.2 Critical regions, error types, and power = 690
A3.4.3 Significance level = 691
A3.5 Powerful tests = 692
A3.5.1 Neyman-Pearson lemma = 692
A3.5.2 Likelihood-ratio, Wald, and efficient-score tests = 693
A3.6 Non-parametric density estimation = 694
A3.7 Multiple regression = 695
A3.7.1 The multiple-regression model = 695
A3.7.2 Ordinary least squares = 696
A3.7.3 The Gauss-Markov theorem = 698
A3.7.4 Distributional results = 698
A3.7.5 Subsets of parameters = 700
A3.7.6 Partitioned inversion = 702
A3.7.7 Regression and inversion = 703
A3.7.8 Multiple correlation = 703
A3.7.9 Partial correlation = 704
A3.7.10 Maximum-likelihood estimation = 705
A3.9 Exercises = 706
A4 Asymptotic Distribution Theory = 707
A4.1 Introduction = 707
A4.2 Orders of magnitude = 710
A4.2.1 Deterministic sequences = 710
A4.2.2 Stochastic sequences = 711
A4.3 Stochastic convergence = 712
A4.4 Laws of large numbers = 714
A4.4.1 Weak law of large numbers = 714
A4.4.2 Strong law of large numbers = 714
A4.5 Central-limit theorems = 715
A4.6 Vector random variables = 718
A4.7 Solved examples = 719
A4.7.1 Example 1 : an I ID process = 719
A4.7.2 Example 2 : A trend model = 720
A4.8 Stationary dynamic processes = 722
A4.8.1 Vector autoregressive representations = 722
A4.8.2 Mann and Wald's theorem = 723
A4.8.3 Hannan's theorem = 724
A4.8.4 Limiting distribution of OLS for a linear equation = 725
A4.9 Instrumental variables = 728
A4.10 Mixing processes = 730
A4.10.1 Mixing and ergodicity = 730
A4.10.2 Uniform mixing and α-mixing processes = 731
A4.10.3 Laws of large numbers and central-limit theorems = 732
4.11 Martingale difference sequences = 733
A4.11.1 Constructing martingales = 733
A4.11.2 Properties of martingale-difference sequences = 734
A4.11.3 Applications to maximum-likelihood estimation = 736
A4.12 A solved autoregressive example = 738
A4.13 Ifigher-order approximations = 741
A4.13.1 Delta method = 741
A4.13.2 Asymptotic expansions = 742
A4.13.3 Power-series expansions = 744
A4.13.4 Addendum = 746
A4.14 Exercises = 748
A.5 Numerical Optimization Methods = 751
A5.1 Introduction = 751
A5.2 An overview of numerical optimization = 753
A5.3 Maximizing likelihood functions = 757
A5.4 Scalar optimization = 759
A5.4.1 Search methods = 761
A5.4.2 Gradient methods = 765
A5.5 Multivariate optimization = 767
A5.5.1 Gradient methods = 767
A5.5.2 Step-wise optimization = 771
A5.5.3 Conjugate directions = 773
A5.5.4 Variable metric or quasi-Newton methods = 776
A5.6 Conclusion = 779
A5.7 Exercises = 780
A6 Macro-Econometrics Models = 781
A6.1 Introduction = 781
A6.2 The skeletal structure of macro models = 782
A6.2.1 Modelled variables = 782
A6.2.2 Time lags = 783
A6.2.3 Error terms = 784
A6.2.4 Time aggregation = 784
A6.2.5 Interdependence = 785
A6.2.6 Size = 785
A6.2.7 The economy as a system = 785
A6.3 The national income accounts = 786
A6.3.1 Commodity flows = 786
A6.3.2 Aggregating economic transactions = 786
A6.3.3 Reconciling nominal and real magnitudes = 786
A6.4 The components of macro models = 787
A6.4.1 Kinds of variables = 787
A6.4.2 Kinds of equations = 788
A6.4.3 Behavioral equations = 789
A6.4.4 Identity equations = 789
A6.4.5 Technical equations = 790
A6.4.6 Equilibrium conditions = 790
A6.4.7 Stock-flow equations = 791
A6.4.8 Adjustment equations = 791
A6.4.9 Expectations formation = 791
A6.4.10 Observation equations = 792
A6.5 A simultaneous system of equations = 792
A6.5.1 Price dynamics = 792
A6.5.2 Simultaneity = 793
A6.6 Sectors and markets = 794
A6.6.1 Households = 795
A6.6.2 Firms = 796
A6.6.3 Static-equilibrium solutions = 798
A6.6.4 Dynamic adjustment = 800
A6.7 Additional aspects of the first model = 801
A6.7.1 Financial markets = 801
A6.7.2 Government sector = 801
A6.7.3 Foreign sector = 802
A6.7.4 Completing equations = 803
A6.7.5 Revised National Income identities = 805
A6.8 Industrial disaggregation = 805
A6.9 A general framework = 807
A6.9.1 Stable process = 809
A6.9.2 Trending process = 809
A6.9.3 Difference stable process = 809
A6.9.4 Quadratic trend process = 809
A6.9.5 Integrated process = 810
A6.9.6 Co-integrated process = 810
A6.10 Forecasting = 810
A6.10.1 Forecast standard errors = 811
A6.10.2 Model evaluation = 811
A6.11 An example = 812
A6.12 Addendum : static-model solution = 815
A6.13 Macro-model notation = 817
References = 819
Common Acronyms = 847
Glossary = 848
Author Index = 853
Subject Index = 859
