An introduction to classical econometric theory:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Oxford Univ. Press
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 951 S. graph. Darst. |
| ISBN: | 0195111648 9780195111644 |
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| 100 | 1 | |a Ruud, Paul A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to classical econometric theory |c Paul A. Ruud |
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 2000 | |
| 300 | |a XXIV, 951 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| _version_ | 1804127863065018368 |
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| adam_text | Titel: An introduction to classical econometric theory
Autor: Ruud, Paul A.
Jahr: 2000
CONTENTS
List of Figures xvii
List of Tables xxi
Preface xxiv
PART 1 ORDINARY LEAST SQUARES 1
Chapter 1 The Least-Squares Linear Fit 3
1.1 Earnings and Attributes of Workers 3
1.2 Generalizing the Sample Average 7
1.3 OLS Regression 14
1.4 Overview 15
1.5 Exercises 16
1.6 Appendix: Data Collection 17
Chapter 2 The Geometry of Least Squares 19
2.1 Introductory Example 19
2.2 Ordinary Least Squares 21
2.3 Examples of OLS 25
2.4 Orthogonal Projection 28
2.4.1 The Projection Theorem 31
2.4.2 Orthogonal Projectors 31
2.5 Exact Multicollinearity 34
2.6 Mathematical Notes 36
2.6.1 Gram-Schmidt Orthonormalization 36
2.6.2 Properties of Orthogonal Projectors 37
2.6.3 Proofs 38
2.7 Overview 40
2.8 Exercises 41
2.8.1 Review 41
2.8.2 Extensions 44
iv Contents
Chapter 3 Partitioned Fit 47
3.1 Introductory Example 47
3.2 Partitioned Fit 54
3.3 Projection 61
3.4 Projectors 66
3.5 Overview 68
3.6 Exercises 69
3.6.1 Review 69
3.6.2 Extensions 72
Chapter 4 Restricted Least Squares 74
4.1 Introduction 74
4.2 Linear Restrictions 77
4.3 Restricted Least Squares 79
4.4 Generalized Distance 84
4.4.1 Translation 87
4.5 Generalized Projection 88
4.6 Overview 91
4.7 Exercises 92
4.7.1 Review 92
4.7.2 Extensions 94
Chapter 5 Overview of Ordinary Least Squares
5.1 Geometric Theory 97
5.2 Econometric Specifications 99
5.3 Econometric Method 100
97
PART II LINEAR REGRESSION 101
Chapter 6 Linear Unbiased Estimation 105
6.1 Experimental Example 105
6.2 First Moments 110
6.3 Conditional Means 113
6.4 Projection of Random Variables 114
6.5 Mathematical Notes 118
6.6 Methodological Notes 120
6.7 Overview 121
6.8 Exercises 122
6.8.1 Review 122
6.8.2 Extensions 123
Chapter 7 Variances and Covariances 125
7.1 Introduction 125
7.2 Second Moments 129
Contents v
7.3 Spherical Distributions 131
7.4 The Variance Ellipse 133
7.5 Minimum MSE Linear Prediction 135
7.6 Mathematical Notes 140
7.6.1 A Square Root of the Variance Matrix 140
7.6.2 The Cauchy-Schwarz Inequality 143
7.6.3 Linear Transformation of Variance Ellipses 144
7.6.4 A Quadratic Decomposition 146
7.7 Overview 148
7.8 Exercises 149
7.8.1 Review 149
7.8.2 Extensions 152
Chapter 8 Variances and Covariances of Ordinary Least Squares 154
8.1 Experimental Example 154
8.2 Second-Moment Properties 157
8.3 Variance and Covariance Matrices 159
8.4 Estimation of the Variance Parameter 163
8.5 Methodological Note 167
8.6 Overview 168
8.7 Exercises 168
8.7.1 Review 168
8.7.2 Extensions 170
Chapter 9 Efficient Estimation 173
9.1 Introduction 173
9.2 Design and Precision 175
9.2.1 Dispersion 177
9.2.2 Sample Size 177
9.2.3 Near Multicollinearity 178
9.2.4 Forecast Variance 180
9.3 Restricted Estimation 182
9.4 The Gauss-Markov Theorem 186
9.4.1 Geometry of the Gauss-Markov Theorem 187
9.4.2 Proof of the Gauss-Markov Theorem 188
9.5 Mathematical Notes 189
9.6 Overview 190
9.7 Exercises 191
9.7.1 Review 191
9.7.2 Extensions 193
Chapter 10 Normal Distribution Theory 195
10.1 Introduction 195
10.2 Distribution Theory for OLS Estimators 198
vi Contents
10.3 Interval Estimators 200
10.3.1 Variance 200
10.3.2 Coefficient Vector with Known Variance 201
10.3.3 Coefficient Vector with Unknown Variance 203
10.3.4 Linear Functions of Coefficients 204
10.4 Efficiency of OLS 205
10.5 Basic Distribution Theory 205
10.5.1 The Multivariate Normal Distribution 206
10.5.2 The Chi-Square and F Distributions 210
10.5.3 Singular Variances and Generalized Inverses 211
10.5.4 Singular Multivariate Normal Distributions 214
10.6 Methodological Notes 215
10.7 Overview 216
10.8 Exercises 217
10.8.1 Review 217
10.8.2 Extensions 219
Chapter 11 Hypothesis Testing 222
11.1 Introduction 222
11.2 Hypothesis Testing 224
11.3 Statistical Power 228
Ð .3.1 Power Comparisons for Tests 229
11.3.2 t Statistics 229
11.3.3 Optimal Power and the F Test 231
11.4 Basic Distribution Theory 232
11.5 Methodological Notes 236
11.6 Overview 237
11.7 Exercises 238
11.7.1 Review 238
11.7.2 Extensions 239
Chapter 12 Overview of Linear Regression 240
12.1 Statistical Theory 240
12.2 Probability Distribution Theory 241
Chapter 13 Nonnormal Distribution Theory 245
13.1 Introduction 245
13.2 Nonnormal Parametric Distributions 246
13.2.1 The Student t Distribution 247
13.2.2 Laplace (Double Exponential) Distribution 249
13.2.3 Logistic Distribution 250
13.2.4 Power Exponential Distribution 250
Contents v¡¡
13.3 LAD Estimation 251
13.3.1 The Sample Median 252
13.3.2 LAD Linear Regression 253
13.4 Asymptotic Distribution Theory 256
13.4.1 Convergence in Distribution 259
13.4.2 Law of Large Numbers 262
13.4.3 Central Limit Theorem 265
13.4.4 Sample Size 267
13.5 Mathematical Notes 270
13.5.1 The Density of an Order Statistic 270
13.5.2 Properties of LAD Fit 271
13.5.3 Convergence Proofs 273
13.6 Overview 278
13.7 Exercises 279
13.7.1 Review 279
13.7.2 Extensions 281
Chapter 14 Maximum Likelihood Estimation 284
14.1 Introduction 284
14.2 Probability Model Specification 285
14.3 The Likelihood Function 288
14.4 The Maximum Likelihood Estimator 293
14.5 Identification 295
14.6 The Score Function 300
14.7 The Information Matrix 302
14.8 The Cramér-Rao Lower Bound 305
14.9 Mathematical Notes 311
14.10 Overview 312
14.11 Exercises 314
14.11.1 Review 314
14.11.2 Extensions 315
Chapter 15 Maximum Likelihood Asymptotic Distribution Theory 318
15.1 Introduction 318
15.2 Consistency 320
15.3 Asymptotic Normality 324
15.3.1 Score 325
15.3.2 Information 326
15.3.3 Asymptotic Distribution 327
15.4 Variance Estimation 329
15.5 Efficiency 331
15.6 Linearized M LE 333
15.7 Restricted Estimation 334
vüi Contents
15.8 Mathematical Notes 336
15.9 Overview 340
15.10 Exercises 342
15.10.1 Review 342
15.10.2 Extensions 343
Chapter 16 Maximum Likelihood Computation 347
16.1 Introduction 347
16.2 Grid Search 349
16.3 Polynomial Approximation 349
16.4 Line Searches 351
16.4.1 The Method of Steepest Ascent 353
16.4.2 Quadratic Methods 355
16.4.3 Quadratic Methods and the MLE 357
16.4.4 LMLE 361
16.5 Convergence Criteria 362
16.6 Transformations of Parameters 364
16.7 Concentrating the Likelihood Function 368
16.8 The Gauss-Seidel Algorithm 371
16.9 Mathematical Notes 372
16.9.1 Proofs 372
16.9.2 Stochastic Order 374
16.9.3 Uniqueness of the MLE 375
16.10 Overview 376
16.11 Exercises 377
16.11.1 Review 377
16.11.2 Extensions 379
Chapter 17 Maximum Likelihood Statistical Inference 380
17.1 Introduction 380
17.2 The Classical Hypothesis Test Statistics 384
17.2.1 The Wald Test 384
17.2.2 The Score Test 385
17.2.3 The Likelihood Ratio Test 388
17.2.4 A Graphic Description of the Test Statistics 389
17.3 Asymptotic Distribution Theory 393
17.3.1 The Likelihood Ratio Test 394
17.3.2 The Score Test 395
17.3.3 The Wald Test 395
17.3.4 The C(a) Test 396
17.3.5 Limiting Distribution 396
17.4 Parameter Transformations and Invariance 397
17.5 Power 402
17.5.1 Local Power 403
Contents ¡x
17.5.2 Neyman-Pearson Lemma 406
17.6 Interval Estimation 408
17.7 Overview 409
17.8 Exercises 410
17.8.1 Review 410
17.8.2 Extensions 412
Chapter 18 Heteroskedasticity 416
18.1 Heteroskedasticity in Wages 417
18.2 Heteroskedasticity and OLS 421
18.3 Testing for Heteroskedasticity 423
18.3.1 The Goldfeld-Quandt F Test 424
18.3.2 The Breusch-Pagan Score Test 424
18.4 Adjustments to OLS 427
18.5 Heteroskedasticity and WLS/GLS 429
18.5.1 Maximum Likelihood 433
18.5.2 FGLS 435
18.5.3 Adaptive Estimation 440
18.6 Methodological Notes 442
18.7 Mathematical Notes 443
18.7.1 Score and Information 444
18.7.2 The Maximum Likelihood Estimator 444
18.7.3 The Breusch-Pagan Score Test 446
18.7.4 Regularity 447
18.7.5 Asymptotic Theory for Heteroskedasticity 448
18.8 Overview 451
18.9 Exercises 452
18.9.1 Review 452
18.9.2 Extensions 453
Chapter 19 Serial Correlation 455
19.1 The Phillips Curve 455
19.2 The Basic Autoregressive Model 458
19.2.1 The Autocorrelation Function 458
19.2.2 The Log-Likelihood Function 460
19.3 Autocorrelation and OLS 462
19.4 Testing for Autocorrelation 464
19.4.1 Breusch-Godfrey Score Test 464
19.4.2 The Durbin-Watson Test 466
19.5 Variance Estimation for OLS 466
19.6 Serial Correlation and GLS 468
19.6.1 Maximum Likelihood Estimation 469
19.6.2 FGLS 471
19.7 Prediction 471
÷ Contents
19.8 Methodological Notes 472
19.9 Mathematical Notes 475
19.9.1 Score and Information 475
19.9.2 Breusch-Godfrey Score Test 476
19.9.3 Asymptotic Distribution Theory 477
19.9.4 OLS versus GLS 480
19.10 Overview 481
19.11 Exercises 482
19.11.1 Review 482
19.11.2 Extensions 483
Chapter 20 Instrumental Variables Estimation 486
20.1 The Phillips Curve Revisited 487
20.2 Latent Variable Models 491
20.3 Omitted Explanatory Variables 493
20.4 Consistent Estimation 499
20.5 Two-Stage Least Squares 502
20.6 Two-Step Variance Estimation 505
20.7 Efficiency 509
20.7.1 Simultaneous Equations 509
20.7.2 Dynamic Regression 511
20.7.3 IV and GLS 512
20.8 Issues in Small Samples 514
20.9 Methodological Notes 515
20.10 Mathematical Notes 516
20.10.1 Covariance Stationarity 517
20.10.2 Dynamic Regression Log-Likelihood 518
20.10.3 Hatanaka s Estimator 518
20.10.4 Two-Step Estimation 519
20.10.5 Optimal Instruments 520
20.11 Overview 521
20.12 Exercises 522
20.12.1 Review 522
20.12.2 Extensions 526
Chapter 21 The Generalized Method of Moments 531
21.1 A Random Walk 532
21.2 Definition of GMM 536
21.2.1 Turning Moments into Estimators 537
21.2.2 Nonlinear Least Squares 539
21.2.3 Two-Stage Least Squares 541
21.3 Identification 542
21.4 Distribution Theory 545
21.4.1 Proof of Consistency 546
Contents xi
21.4.2 Proof of Asymptotic Normality 547
21.4.3 Variance Matrix Estimation 548
21.4.4 Efficiency 550
21.5 Methodological Notes 555
21.6 Mathematical Notes 555
21.6.1 Uniform Convergence of the GMM Criterion Function 555
21.6.2 Nonsingularity of the GMM Hessian 556
21.6.3 GMM Efficiency 557
21.7 Overview 557
21.8 Exercises 558
21.8.1 Review 558
21.8.2 Extensions 561
21.9 Appendix: Data Collection 562
Chapter 22 Generalized Method of Moments Hypothesis Tests 564
22.1 Tests of Parameter Restrictions 565
22.1.1 Wald Test 566
22.1.2 Gradient Test 567
22.1.3 Distance Difference Test 567
22.1.4 Minimum Chi-Square Test 568
22.1.5 Special identities 569
22.1.6 Generalizing Likelihood-Based Diagnostics 570
22.2 Tests of Moment Restrictions 572
22.2.1 Overidentifying Restrictions Tests 576
22.3 Hausman Specification Tests 578
22.4 Equivalence among Test Statistics 585
22.4.1 A Trinity of GMM Test Statistics 586
22.4.2 Minimum Chi-Square 587
22.5 Statistical Power 590
22.6 Sequential Testing 592
22.7 Minimum Distance Estimation 594
22.8 Mathematical Notes 597
22.9 Methodological Notes 601
22.10 Overview 601
22.11 Exercises 602
22.11.1 Review 602
22.11.2 Extensions 605
Chapter 23 Overview 608
PART IV LATENT VARIABLE MODELS 613
Chapter 24 Panel Data Models 615
24.1 Introduction 615
xii Contents
24.2 Fixed Individual Effects 616
24.3 Random Individual Effects 618
24.4 Fixed versus Random Effects 622
24.5 Generalizations 623
24.5.1 Individual-Specific Explanatory Variables 624
24.5.2 Time-Specific Effects 625
24.5.3 Dynamic Models 626
24.6 Specification Tests 628
24.7 Linear Projection 630
24.7.1 Identification and OLS 631
24.7.2 Efficient Estimation 632
24.7.3 Diagnostic Tests 634
24.8 Additional Moment Restrictions 635
24.8.1 Identification 635
24.8.2 Estimation 636
24.9 Mathematical Notes 638
24.10 Overview 640
24.11 Exercises 641
24.11.1 Review 641
24.11.2 Extensions 643
Chapter 25 Autoregressive Moving-Average Time Series Models 645
25.1 Introduction 645
25.2 Autoregressive Processes 649
25.2.1 Stationarity 651
25.2.2 Restricted Estimation 656
25.2.3 Sequential Testing for Order 657
25.3 Moving-Average Processes 658
25.3.1 Identification 660
25.3.2 Kalman Filter 663
25.3.3 Estimation 667
25.3.4 Testing Serial Correlation 670
25.4 ARMA Processes 673
25.4.1 Identification and Invertibility 675
25.4.2 Kalman Filter and Estimation 679
25.4.3 Hypothesis Tests 679
25.5 Wold Decomposition 680
25.5.1 Linearly Deterministic Processes 681
25.5.2 Wold Decomposition Theorem 682
25.6 Methodological Notes 684
25.7 Mathematical Notes 685
25.7.1 Yule-Walker Equations 685
25.7.2 Kalman Filter 686
25.7.3 MAfø) Identification 689
Contents x¡¡¡
25.7.4 Score Test Equivalence 690
25.8 Overview 691
25.9 Exercises 693
25.9.1 Review 693
25.9.2 Extensions 696
Chapter 26 Simultaneous Equations 697
26.1 Introduction 697
26.2 Seemingly Unrelated Regressions 698
26.2.1 Estimation of a Cost Function 699
26.2.2 Assumptions 700
26.2.3 OLS versus GLS 701
26.2.4 Feasible GLS Estimation 704
26.2.5 Maximum Likelihood Estimation 705
26.3 Simultaneous Equations 706
26.3.1 Definitions 709
26.3.2 Assumptions 710
26.4 Identification 711
26.4.1 Equation Identification 714
26.4.2 System Identification 717
26.5 Estimation 718
26.5.1 Limited Information 719
26.5.2 Full Information 721
26.5.3 Maximum Likelihood 723
26.6 Hypothesis Tests 727
26.7 Mathematical Notes 730
26.7.1 Score Functions 730
26.7.2 Information Matrix 732
26.8 Overview 734
26.9 Exercises 736
26.9.1 Review 736
26.9.2 Extensions 742
Chapter 27 Discrete Dependent Variables 747
27.1 Bernoulli Dependent Variables 748
27.1.1 Bernoulli Regression 748
27.1.2 Estimation 750
27.1.3 A Latent Variable Interpretation 755
27.2 Additional Univariate Models 757
27.2.1 Ordered Data 758
27.2.2 Count Data 761
27.3 Multivariate Models 764
27.3.1 Multiple Choice 764
27.3.2 Rank-Ordered Multiple Choice 770
xiv Contents
27.4 Latent Variables and Computation 771
27.4.1 Score Functions 772
27.4.2 Hessian and Information Functions 773
27.4.3 EM Algorithm 774
27.4.4 Simulation 775
27.5 Methodological Notes 777
27.6 Mathematical Notes 778
27.6.1 Katz Family of Distributions 779
27.6.2 Logit Probabilities 780
27.6.3 EM Algorithm 782
27.6.4 Simulation 784
27.7 Overview 784
27.8 Exercises 786
27.8.1 Review 786
27.8.2 Extensions 788
Chapter 28 Censored and Truncated Variables 791
28.1 Labor Supply 791
28.2 Mixed Probability Functions 794
28.3 Censored Moments 798
28.4 Estimation 800
28.5 Prediction and Truncated Means 802
28.6 Truncated Regression 803
28.7 Nonrandom Sample Selection 806
28.7.1 Log-Likelihood 807
28.7.2 Moments 808
28.7.3 Estimation 809
28.8 Specification of Distribution 810
28.8.1 Censored Regression 810
28.8.2 Truncated Regression 814
28.9 Mathematical Notes 817
28.9.1 Integrals 817
28.9.2 Censored Moments 819
28.9.3 Nonrandom Sample Selection 822
28.10 Overview 824
28.11 Exercises 824
28.11.1 Review 824
28.11.2 Extensions 827
Chapter 29 Overview 831
Appendix A Abbreviations and Acronyms 835
Appendix  Notation 837
Contents xv
B.I Limits 837
B.2 Sets 838
B.3 Functions 838
B.4 Linear Vector Spaces 838
B.5 Matrices 839
B.6 Random Variables 840
B.7 Optima and Roots 840
Appendix C Linear Algebra and Matrix Theory 841
C.1 Linear Vector Spaces 841
C.2 Linear Transformations 847
C3 Inner Products and Orthogonality 851
C.4 Normed Linear Vector Spaces 855
C.5 Determinants 856
C.5.1 Volume of a Parallelogram 857
C.5.2 Determinant of a Matrix 860
C.5.3 The Cofactor Expansion 862
C6 Eigenvalues and Eigenvectors 865
Appendix D Probability 867
D.I Fundamental Concepts 867
D.2 Random Variables 868
D.2.1 Mathematical Notes 875
D.3 Joint and Conditional Probability 879
D.3.1 Mathematical Notes 883
D.4 Special Distributions 884
D.5 Limiting Approximations 891
D.5.1 A Sequence of Densities 893
D.5.2 Sequences of Moments 895
D.5.3 Sequences of cf.s 896
D.5.4 Mathematical Notes 898
Appendix E Classical Statistics 902
E.I Sampling 902
E.2
904
Appendix F
Appendix G
Classical Statistical Inference
E.2.1 Estimation 904
E.2.2 Hypothesis Tests 906
E.2.3 Estimation Methods 907
E.2.4 Asymptotic Distribution Theory
Noncentral Distributions 916
Multivaríate Differentiation 922
G.I Basic Notation 922
G.2 Vectorization and Kronecker Products
913
924
xvi Contents
G.2.1 Kronecker Products 925
G.3 Derivative Vectors 926
G.4 Derivative Matrices 927
G.5 The Normal Log-Likelihood Function 928
Appendix H Characteristic Functions 931
Bibliography 935
Index 945
|
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| discipline | Wirtschaftswissenschaften |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV013163164 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:40:06Z |
| institution | BVB |
| isbn | 0195111648 9780195111644 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008968386 |
| oclc_num | 43050273 |
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| physical | XXIV, 951 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Ruud, Paul A. Verfasser aut An introduction to classical econometric theory Paul A. Ruud New York [u.a.] Oxford Univ. Press 2000 XXIV, 951 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Econometria larpcal Econometrie gtt Économétrie Économétrie ram Econometrics Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ökonometrie (DE-588)4132280-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008968386&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ruud, Paul A. An introduction to classical econometric theory Econometria larpcal Econometrie gtt Économétrie Économétrie ram Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4123623-3 |
| title | An introduction to classical econometric theory |
| title_auth | An introduction to classical econometric theory |
| title_exact_search | An introduction to classical econometric theory |
| title_full | An introduction to classical econometric theory Paul A. Ruud |
| title_fullStr | An introduction to classical econometric theory Paul A. Ruud |
| title_full_unstemmed | An introduction to classical econometric theory Paul A. Ruud |
| title_short | An introduction to classical econometric theory |
| title_sort | an introduction to classical econometric theory |
| topic | Econometria larpcal Econometrie gtt Économétrie Économétrie ram Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Econometria Econometrie Économétrie Econometrics Ökonometrie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008968386&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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