Econometrics: a modern introduction
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boston ; Munich [u.a.]
Pearson Addison-Wesley
2006
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| Edition: | Internat. ed. |
| Series: | The Addison-Wesley series in economics
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| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXXVI, 929 S. graph. Darst. 24 cm |
| ISBN: | 0321223284 |
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MARC
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| 100 | 1 | |a Murray, Michael P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Econometrics |b a modern introduction |c Michael P. Murray |
| 250 | |a Internat. ed. | ||
| 264 | 1 | |a Boston ; Munich [u.a.] |b Pearson Addison-Wesley |c 2006 | |
| 300 | |a XXXVI, 929 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The Addison-Wesley series in economics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Econometrics | |
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| _version_ | 1804135157900247040 |
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| adam_text | Contents on the Web xxiv
Preface for Students xxv
Preface for Teachers xxvii
Part I The Linear Regression Model 1
1 What Is Econometrics? 1
1.1 A First Example of Econometric Modeling: Financial Aid and Income 3
Example 1: Income and Financial Aid 3
What Example 1 Illustrates About Econometrics 9
REGRESSION S GREATEST HITS An Econometric Top 40—Golden Oldies,
Classical Favorites, Pop Tunes 9
An Econometric Top 40—A Pop Tune: Paying for College 10
1.2 A Second Example of Econometric Modeling: Consumption and Income 11
Example 2: Income and Food Expenditure 12
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
How Income Influences Demand—Engel s Law 15
What Example 2 Illustrates About Econometrics 16
1.3 Organizing Econometrics 17
What Do We Assume About Where the Data Come From? 17
What Makes a Good Estimator? 18
How Do We Create an Estimator? 18
What Are an Estimator s Properties? 18
How Do We Test Hypotheses? 18
How Do We Forecast? 19
Summary 19
Concepts for Review 20
Questions for Discussion 21
Problems for Analysis 21
Endnotes 22
2 Choosing Estimators: Intuition and Monte Carlo Methods 24
2.1 How to Sell Econometrics 25
2.2 Estimating a Population s Mean 28
The Need for a Precise Statement of Assumptions 29
Sampling and Randomness 29
Precise Assumptions—the Data Generating Process 30
Interpreting the DGP 31
Estimating Means as Estimating Intercepts 32
2.3 Estimating the Slope of a Line with No Intercept: Families of Means 33
Economic Theory and Lines Through the Origin 33
Families of Means 34
2.4 Natural Estimators for the Slope of a Line Through the Origin 35
A First Natural Estimator 36
A Second Natural Estimator 37
A Third Natural Estimator 38
A Surfeit of Riches 40
2.5 The Data Generating Process 40
The New Assumptions 41
Are Fixed X s Realistic? 41
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
Engel on Price Elasticity 42
2.6 Monte Carlo Comparisons 43
Building a Roulette Wheel 44
What Must the Roulette Wheel Do? 45
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Friedman s Permanent Income Hypothesis 46
Building a Roulette Wheel of Your Own: MC Builder I 49
Spinning the Roulette Wheel 50
2.7 Picking £, s and the Real World 51
2.8 Comparing f}gu pg2, and /3g3 52
A Monte Carlo Exercise 52
What a Monte Carlo Analysis Can Say About Unbiasedness 55
2.9 Alternative Comparisons of pgi, fig2, and fig3 56
Additional Monte Carlo Exercises 57
2.10 Graphical Lessons from the Monte Carlo Exercises 60
What DGPs Do We Study? 61
What Do We Find? 61
Summary 65
Concepts for Review 66
Questions for Discussion 67
Problems for Analysis 67
Endnotes 69
3 Linear Estimators and the Gauss Markov Theorem 70
3.1 Linear Estimators 71
Linear Estimators and Their Weights 71
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Capital Asset Pricing Model 74
3.2 Unbiased Linear Estimators 76
The DGP 76
Unbiasedness and the Algebra of Expectations 76
Are Our Intuitive Estimators Unbiased? 78
3.3 The Variance of a Linear Estimator 79
Linear Estimators and the Algebra of Variances 80
Relative Variances of Linear Estimators 82
Revisiting Monte Carlo Exercises 82
3.4 A More Efficient Linear Estimator 84
Why Is pg2 More Efficient Than /3g] ? 85
What Estimator Might Be More Efficient Than /3g2? 86
Is p^ Unbiased? 87
The Variance of figA 88
Is There a Linear Estimator More Efficient Than /3g4? 90
3.5 A First Gauss Markov Theorem 90
The Gauss Markov Assumptions 91
Finding the Best Weights 91
3.6 Replacing Fixed X s with Stochastic X s 93
Extending the Reach of the Gauss Markov Assumptions 93
The Conditional and Population Properties of /3?4 94
3.7 Application: A U.S. Production Function 96
Estimating the Cobb Douglas Production Function with (5g , pLgi, pgi, and /3g4 96
Is Ours the Correct DGP for These U.S. Data? 98
3.8 Econometric Software Output 99
Summary 101
Concepts for Review 102
Questions for Discussion 102
Problems for Analysis 103
Endnotes 108
Appendix 3.A Finding the BLUE Estimator of a Straight Line Through
the Origin 109
3.A.1 The Gauss Markov Theorem 109
The Mathematical Problem 109
3.A.2 BLUE Estimation of |3 When n = 2 110
Finding the BLUE Estimator 110
3.A.3 BLUE Estimation of /3 When n 2 111
Solving the Constrained Minimization Problem 111
Appendix 3.B A Matrix Algebra Representation of Regressions,
Linear Estimators, and Linear Unbiased Estimators 112
3.B.I An Alternative to Summation Notation 112
Column Vectors and Row Vectors 113
Matrix Multiplication 114
Appendix 3.B Concepts for Review 118
4 BLUE Estimators for the Slope and Intercept of a Straight Line 119
4.1 The DGP for a Straight Line with Unknown Intercept 120
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Phillips Curve 121
4.2 The Expected Value and Variance of Linear Estimators 123
Conditions for Unbiasedness 123
The Variance of a Linear Estimator 125
4.3 BLUE Estimation of the Slope and Intercept of a Straight Line 126
A BLUE Estimator for the Slope, /3i 126
An Estimator for {So 128
An Often Used Property of Certain Sums 129
A Relationship Between j8i and /3g4 129
An Example: The Phillips Curve 130
4.4 /3o and /3i Are Intuitively Appealing Estimators 132
The First Intuition 132
The Second Intuition 133
The Third Intuition 133
A Further Insight About BLUE Estimators 134
4.5 Logarithms in Econometrics 136
The Attraction of Logarithms 136
Double Logarithmic Specifications and Elasticities 136
An Example: The Phillips Curve Revisited 137
Semilog Specifications and Percentage Changes 139
An Example: The Phillips Curve Yet Again 139
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
How Price Influences Demand 141
Summary 142
Concepts for Review 143
Questions for Discussion 143
Problems for Analysis 144
Endnotes 152
Appendix 4.A Finding the BLUE Estimator for the Slope of a Straight Line
with an Unknown Intercept 153
4.A.1 The Lagrangian Approach for the Case of n Observations 154
Appendix 4.B Matrix Algebra and Estimating the Slope of a Straight Line
with an Unknown Intercept 155
4.B.1 Constructing Appealing Linear Estimators of fi and /3o 156
A Matrix Representation of a Regression Model Including an Intercept 156
Multiplying Matrices Revisited 157
A Computational Path to Building /3i and ;3o 158
Multiplying Matrices When Neither Is a Vector 159
Extending the Notion of an Inverse Matrix 159
The Estimators /3o and j3i 160
Concepts for Review 162
4.C A Commonly Used Property of Certain Sums 162
5 Residuals 164
5.1 Estimating a2 165
An Intuitive Estimator of a1 165
An Unbiased Estimator of a2 166
5.2 The Variances and Covariance of /3i and /3o 167
The Variances of p and po 167
The Covariance Between /3o and 0 169
Estimators of Var(J30), Var(/3i), and Cov(/30, Pi) 170
5.3 The Gauss Markov Theorem and the Expected Value of Y, Given X 172
5.4 Confidence Intervals and Prediction Intervals 173
Confidence Intervals for the Slope, Intercept, and E(Y|X) 173
Prediction Intervals for Future Values of Y 175
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Cobb Douglas Production Function 176
5.5 Application: A U.S. Production Function 177
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The CES Production Function 180
5.6 The Goodness of Fit of an Estimated Line 182
Decomposing the Variance of the Y, Within a Sample 182
The Coefficient of Determination, R2 185
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The World s Surprisingly Immobile Capital Markets 189
5.7 Two Properties of the BLUE Estimators Residuals 190
The Sum of the Residuals 191
The Sum of the X s Times the Residuals 191
5.8 Ordinary Least Squares 192
Summary 194
Concepts for Review 195
Questions for Discussion 196
Problems for Analysis 196
Endnotes 203
Appendix 5.A The Unbiasedness of s2 204
5.A.I Estimating the Variance of the Disturbances 205
An Infeasible Alternative Estimator 205
Some Preliminaries 205
The Unbiasedness of s2 206
Appendix 5.B The Variance of /3o and the Covariance Between
Linear Estimators 208
5.B.I The Variance of the OLS Intercept Estimator 208
A Special Expression for the Sum of the X2 208
The Variance of j30 209
5.B.2 The Covariance of Linear Estimators 210
Appendix 5.C Matrix Algebra and the Properties of OLS Residuals 211
6 Multiple Regression 212
6.1 The DGP for the Regression Model 212
Polynomials 213
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
College Students Misbehavior and the Price of Beer 215
6.2 BLUE Estimation in a Multiple Regression Model 216
What Is Required for Unbiased Linear Estimation? 216
What Is the Variance of a Linear Estimator in This DGP? 218
What Are the BLUE Estimators of p0, /3i, . . ., /3K in This DGP? 218
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
The Demand for Drugs 219
A More General Gauss Markov Theorem 221
6.3 An Application: Earnings Equations 221
BLUE Estimates for Black Women 221
Using Dummy Variables to Capture Categories 222
6.4 Estimating a1 227
Using the Residuals to Mimic the Disturbances 228
6.5 Ordinary Least Squares 229
A Visual Approach to OLS 229
An Implication of OLS 229
6.6 R2 in the Multiple Regression Model 231
R2—the Coefficient of Determination Revisited 231
Adjusted R2 231
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Solow Model, Old and New 232
6.7 Four Uses of Linear in Econometrics 235
Summary 238
Concepts for Review 239
Questions for Discussion 239
Problems for Analysis 239
Endnotes 250
Appendix 6.A Blue Estimation in a DGP with Stochastic Regressors 252
6.A.1 Unbiasedness Conditions of Linear Estimators 252
Adapted Gauss Markov Assumptions 255
OLS BLUE in This DGP 255
Appendix 6.B Matrix Algebra and Multiple Regressions 256
6.B.1 A Matrix Representation of the Multiple Regression Model 256
The Multiple Regression Model in Matrix Form 257
The Gauss Markov Assumptions in Matrix Form 257
6.B.2 Estimating the Multiple Regression Model s Coefficients 258
An Intuitive Approach to Estimating /3 258
Ordinary Least Squares 259
Linear Estimators in the Multiple Regression Model 261
Unbiasedness Conditions for Linear Estimators 261
The Variance of Linear Estimators 262
The Variances and Covariances of the OLS Estimator 262
OLS Is BLUE Under the Gauss Markov Assumptions 263
A Relationship Among Explanators and Residuals for the OLS Estimator 264
6.B.3 Estimating a1
Appendix 6.B Concepts for Review 266
rt II Specification and Hypothesis Testing 267
7 Testing Single Hypotheses in Regression Models 267
7.1 Rejecting and Failing to Reject Hypotheses 269
7.2 Six Steps to Hypothesis Testing 270
Framing the Null and Alternative Hypotheses 271
Choosing a Test Statistic 272
The ^ Statistic 273
Choosing a Significance Level 275
Choosing a Critical Region 276
The Power of a Test 278
Critical Regions and Complex Null Hypotheses 279
Computing the Test Statistic and Drawing a Conclusion 280
A Caveat About Maintained Hypotheses 282
Tests Undermined 283
7. 3 Degrees of Freedom Revisited 284
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Capital Asset Model Revisited 286
7.4 An Application: The Capital Asset Pricing Model Revisited 287
7.5 Tests About a Linear Combination of Coefficients 289
Another f Statistic 290
Two Examples of Testing for a Relationship Among Regression Coefficients 291
A Special Case: the Expected Value of Y, Given X 292
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
A Deeper Look at Discrimination 293
Summary 297
Concepts for Review 297
Questions for Discussion 297
Problems for Analysis 298
Endnotes 307
8 Superfluous and Omitted Variables, Multicollinearity, and Binary Variables 308
8.1 Including Superfluous Variables 308
Superfluous Variables and Lost Efficiency 309
A MONTE CARLO EXPERIMENT Prelude to Omitted Variables 310
8.2 Omitting Relevant Variables 311
Omitted Variable Bias 311
A Formula for Omitted Variable Bias 312
What to Include, What to Exclude 315
When Omitted Relevant Variables Are Acceptable 315
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Expectations Augmented Phillips Curve 316
8.3 Multicollinearity 320
Correlated Explanators 321
The Consequences of Multicollinearity 322
Perfect Multicollinearity 323
Coping with Multicollinearity 324
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
Who Needs SAT Scores? 325
8.4 The Earnings Example Extended—More About Dummy Variables 328
Using Multiple Dummy Variables to Estimate Means 328
Using Multiple Dummies to Estimate Intercepts 330
Using Multiple Dummies to Categorize Along Several Dimensions 331
Using Dummy Variables to Allow Different Slopes for Different Groups 332
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Rational Expectations Revolution 333
Summary 335
Concepts for Review 336
Questions for Discussion 336
Problems for Analysis 336
Endnotes 342
Appendix 8.A Matrix Algebra, Omitted Variables, and Perfect Collinearity
8.A.1 A Matrix Representation of Omitted Variables Bias 343
8.A.2 Matrix Representation of Perfect Collinearity 343
Concepts for Review 343
9 Testing Multiple Hypotheses
9.1 The Error of Combining ^ Statistics 344
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
Life Is Too Short to Drink Bad Wine! 345
9.2 F Tests: The Intuition 347
9.3 F Tests for Multiple Linear Restrictions on Regression Coefficients 350
The Distribution of the F Statistic 351
A Special Case Commonly Encountered 352
9.4 Relaxing Assumptions 353
Letting Go of Normality 353
Letting Go of Fixed Regressors 354
A Caveat About Multiple Tests 354
9.5 An Application: Linear Coefficient Constraints and the Earnings of Blacks 355
9.6 An Application: Linear Coefficient Constraints in a Model of Deficits 361
9.7 Two Additional Tests for Regime Shifts 363
Chow Tests 363
Using Dummy Variables to Test for Regime Shifts 364
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Unanticipated Money 365
Summary 368
Concepts for Review 368
Questions for Discussion 369
Problems for Analysis 369
Endnotes 377
Appendix 9.A Matrix Algebra and Hypothesis Testing 379
9.A.1 The Case of a Straight Line Through the Origin Revisited 379
9.A.2 Testing Linear Constraints on Both the Slope and Intercept 380
9.A.3 Any Linear Constraint Can Be Expressed with R/3 = c 382
9.A.4 Goodness of Fit and Deviations from the Null Hypothesis 383
9.A.5 A General Gauss Markov Theorem 383
Concepts for Review 384
till Further Topics In Regression 385
10 Heteroskedastic Disturbances 385
10.1 Visualizing Heteroskedasticity 386
A MONTE CARLO EXPERIMENT: Prelude to Heteroskedasticity 389
10.2 The Consequences of Heteroskedasticity for the OLS Estimators 390
Unchanged Unbiasedness Conditions 391
The Changed Variance of a Linear Estimator 391
10.3 Tests for Heteroskedasticity 394
The White Test 394
The Breusch Pagan Test 397
An Example Comparing the White Test and the Breusch Pagan Test 398
The Goldfeld Quandt Test 401
An Example of the Goldfeld Quandt Test 402
Omitted Variables and Heteroskedasticity Tests 402
The RESET Specification Test 405
10.4 BLUE Estimation When Disturbances Are Heteroskedastic 406
Transforming the Data to Account for Heteroskedasticity 406
Weighting Observations with Larger of 408
Two Special Cases of Heteroskedastic Disturbances 409
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
Complete Systems of Demand Equations 410
10.5 An Application: GLS Estimation of the Rent Income Relationship 412
Disturbances with Variances Proportional to Income Squared 412
Disturbances with Variances Proportional to Income 414
A Need for Caution 416
10.6 Feasible Generalized Least Squares 416
FGLS and the Rent Income Relationship 417
10.7 White s Heteroskedasticity Consistent Standard Errors 418
10.8 Logarithms and Heteroskedasticity 420
Summary 422
Concepts for Review 424
Questions for Discussion 424
Problems for Analysis 425
Endnotes 431
Appendix 10.A Matrix Algebra and Generalized Least Squares I 432
10.A.1 The Heteroskedastic Variance Covariance Matrix 432
The Disturbances Variance Covariance Matrix 432
The Heteroskedastic Variance Covariance Matrix 433
10.A.2 OLS, GLS, and Heteroskedasticity 434
Heteroskedasticity and OLS 434
Heteroskedasticity and GLS 434
Concepts for Review 435
11 Autoregressive Disturbances 436
11.1 The Serially Correlated DGP 437
Visualizing Serial Correlation 437
The DGP 439
Stationarity 439
11.2 The Consequences of Serial Correlation for the OLS Estimators 441
The Unchanged Unbiasedness Conditions 441
The Changed Variance of a Linear Estimator 442
The Biased Standard Estimator of Var(jSi) 443
The Newey West Serial Correlation Consistent Standard Error Estimator 444
11.3 Tests for Serial Correlation 446
The Durbin Watson Test 446
Critical Values for the Durbin Watson Statistic 447
The Breusch Godfrey Test 452
An Example of Checking for Serial Correlation 453
Omitted Variables and Serial Correlation Tests 455
11.4 A DGP with First Order Autoregressive Disturbances 457
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Is Public Expenditure Productive? 458
Visualizing First Order Autoregressive Disturbances 459
The DGP 461
How the Disturbances Are Correlated 461
The Mean and Variance of the Disturbances 462
More Covariances Among Disturbances 463
An Alternative Expression of the New DGP 464
11.5 BLUE Estimation if Disturbances Are First Order Autoregressive 464
Constrained Minimization to Obtain BLUE Estimators 465
Transforming the Data to Obtain BLUE Estimators 466
Estimation When p Is Unknown 468
Iterating the Estimators 469
Nonlinear Estimation of Models with Autoregressive Disturbances 469
Serial Correlation Corrections and Omitted Variables 470
Testing Hypotheses 470
An Example of Estimation with Autoregressive Disturbances 471
Newey West Serial Correlation Consistent Variances 472
11.6 Serial Correlation and Heteroskedasticity Together 473
Generalized Least Squares 473
Autoregressive Conditional Heteroskedasticity 473
Conditional and Unconditional Variances 474
Testing for ARCH 475
Summary 477
Concepts for Review 478
Questions for Discussion 479
Problems for Analysis 479
Endnotes 486
Appendix ll.A Matrix Algebra and Generalized Least Squares II 487
11.A.I The Serial Correlation Variance Covariance Matrix 487
The Disturbances Variance Covariance Matrix 487
The Serial Correlation Variance Covariance Matrix 488
11.A.2 OLS, GLS, and Serial Correlation 489
Serial Correlation and OLS 490
Serial Correlation and GLS 490
12 Large Sample Properties of Estimators: Consistency and Asymptotic Efficiency 492
12.1 The Large Sample, or Asymptotic, Perspective 493
Picturing Consistency and Asymptotic Distributions 494
12.2 Asymptotic Unbiasedness, Consistency, and Probability Limits 497
Asymptotic Unbiasedness 497
Consistency 498
Probability Limits 499
12.3 The Consistency of /3^4 and fax 500
The Consistency of /3g4 Under the Gauss Markov Assumptions 501
Manipulating Probability Limits 502
The Consistency of /3i 502
Consistent Estimators and Specifying DGPs 504
An Example: Haavelmo and the Consumption Function 505
12.4 Replacing Fixed Jfs with Stochastic JCs 507
Assumptions About the Disturbances and Stochastic X s 507
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Marginal Propensity to Consume 508
OLS: Sometimes Consistent, Sometimes Not 511
The Finite Sample Bias in OLS When E(xi e, ) = 0 511
Multiple Regression Models, GLS, and FGLS 512
A MONTE CARLO EXPERIMENT: Prelude to Asymptotic Efficiency 513
12.5 Asymptotic Efficiency and Asymptotic Distributions 514
Asymptotic Efficiency 514
The Rate of Convergence of /3g4 515
The Root n Consistency and Asymptotic Normality of /3g , /3g2, Pg3, and (3g4 516
Hypothesis Testing 517
Alternatives to BLUE Estimation 520
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Making Music 521
Summary 524
Concepts for Review 524
Questions for Discussion 525
Problems for Analysis 525
Endnotes 530
Appendix 12.A Probability Limits and Consistency 531
12.A.1 Defining Probability Limits and Consistency 531
12.B Asymptotic Normality and OLS 533
13 Instrumental Variables Estimation 535
13.1 Friedman and the Consumption Function Revisited 535
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Heart Attacks and Heart Treatments 536
Consumption and Permanent Income 538
OLS s Measurement Error Bias 539
The Consistency of )3g2 541
13.2 Instrumental Variables Estimation 543
Improving on /3g2 543
Illustrative Instruments 543
The Instrumental Variables Estimator 544
The Bias of an IV Estimator 546
The Consistency of an IV Estimator 546
The Variance of an IV Estimator 547
The Multiple Regression Case 548
Identification 548
13.3 Sources of Contemporaneous Correlation 549
Instrumental Variables and Omitted Variables Bias 549
Instrumental Variables Estimation and Lagged Dependent Variables 550
Instrumental Variables and Jointly Determined Variables 551
Lagged Dependent Variables and Identification 553
13.4 An Application: Wage Equations and IV Estimation 553
Using Twins to Overcome Omitted Variable Bias 554
The Extent of Omitted Variables Bias in Wage Equations 555
13.5 Instrumental Variables and Two Stage Least Squares 559
Combining Multiple Candidate Instruments 559
Two Stage Least Squares 561
Testing Hypotheses Using 2SLS 562
Weak Instruments 564
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
Are Public Housing Projects Bad for Kids? 565
13.6 Testing Whether E(X, e,) Equals Zero 568
A Test for Troublesome Explanators 568
Testing Whether the Difference in Twins Education Is Troublesome 570
Summary 572
Concepts for Review 572
Questions for Discussion 573
Problems for Analysis 573
Appendix 13.A The Magnitude of Measurement Error Bias 581
13 .A. 1 The Measurement Error DGP 581
13.A.2 The Magnitude of Measurement Error Bias 582
13.A.3 Mismeasured Explanators in Multiple Regression 585
Appendix 13.B Matrix Representations of Instrumental Variables
and 2SLS Estimators 587
13.B.1 The DGP 587
13.B.2 The OLS and IV Estimators 588
Consistency 588
The Variation of j§rv About f3 589
13.B.3 2SLS and IV 589
2SLS in Matrix Form 589
2SLS in IV Estimation 590
The Special Nature of 2SLS 591
14 Systems of Equations 593
14.1 Endogenous and Exogenous Variables in Simultaneous Equations 594
Endogenous and Exogenous Variables 595
14.2 The Simultaneity Bias of OLS 596
Estimating the Demand for Personal Computers 596
Structural Equations and Reduced Form Equations 596
Simultaneity Bias 598
Recursive Systems 599
14.3 The Identification Problem 600
Indirect Least Squares 600
Underidentified, Exactly Identified, and Overidentified Parameters 601
Identification in the Supply and Demand Example 601
A Graphical Depiction of the Identification Problem 602
14.4 An Application: The Fulton Fish Market 604
14.5 ILS, Overidentification and Underidentification 606
Identification and the DGP 606
A Surfeit of Riches: Overidentification 607
Overidentification in the Supply and Demand Model 607
Underidentification in the Supply and Demand Model 608
14.6 Instrumental Variables and Simultaneity Bias 609
Instrumental Variables and Simultaneous Equations 609
Instrumental Variables and the Demand for Personal Computers 611
More Fish: IV Estimation and the Fulton Fish Market 612
REGRESSION S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Supply and Demand for Watermelons 613
14.7 Optimal Instruments and Two Stage Least Squares 614
Choosing Optimal Instruments 614
Two Stage Least Squares 615
14.8 Order and Rank Conditions for Identification 616
The Order Condition for Identification 616
Exclusion Restrictions and Covariance Restrictions 617
The Rank Condition for Identification 617
Some Rules of Thumb for Identification 619
Hausman s Test of Overidentifying Restrictions 619
14.9 An Application: 2SLS at the Fulton Fish Market 621
Testing the Overidentifying Restrictions in the Whiting Market 624
Serially Correlated Disturbances in Simultaneous Equations 626
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
Incarceration and Crime 627
Summary 628
Concepts for Review 630
Questions for Discussion 630
Problems for Analysis 630
Endnotes 638
15 Randomized Experiments and Natural Experiments 640
15.1 Estimating Means and Interpreting Differences in Means 641
Estimation versus Interpretation 641
The Neighborhood Poverty Example 642
15.2 Controlled and Randomized Experiments 644
Controlled Experiments 644
Randomized Experiments 646
The Neighborhood Poverty Example Revisited 647
Sources of Bias in Randomized Experiments 648
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Social Experiments: Labor Supply, Housing Allowances, and
Health Insurance 649
15.3 Natural Experiments 652
The Gautreaux Experiment 652
Differences in Means in the Gautreaux Experience 653
15.4 Difference in Differences Estimation 656
The Difference in Differences Estimator 656
The Variance of the Diff in Diffs Estimator 658
A Regression Formulation of Diff in Diffs 659
The Achilles Heel of Diff in Diffs 660
REGRESSION S GREATEST HITS An Econometric Top 40—A Pop Tune:
Fast Food and the Minimum Wage 661
The Strength of Randomized Experiments 664
15.5 Average and Marginal Treatment Effects 665
Average Treatment Effects on the Treated 665
Early Results from the Moving to Opportunity Experiment 666
Experimental Effects on the Treated and on Those We Intend to Treat 666
Randomized versus Natural Experiments 669
Summary 670
Concepts for Review 670
Questions for Discussion 671
Problems for Analysis 671
Endnotes 676
16 Analyzing Panel Data 678
16.1 Panel Data 679
Distinct Intercepts DGPs 680
Error Components Models 681
Choosing a Fixed or Error Components DGP 684
16.2 Estimation with Panel Data 684
Estimation in the Distinct Intercepts DGP 684
REGRESSION S GREATEST HITS An Econometric Top 40—Two Golden Oldies:
The Early Panel Studies 685
Fixed Effects Estimation as Within Estimation 689
Estimation in the First Error Components DGP 691
Implementing the FGLS Random Effects Estimator 692
Estimation in the Second Error Components DGP 692
An Example of Estimation with Panel Data: Manufacturing Firms 693
16.3 Related DGPs 696
An Example of a Clustered Data Set: Children in Russian Households in 1995 697
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Specification Tests and an Earnings Function 698
16.4 Distinguishing Among Panel Data DGPs 700
Testing for Correlation Between Individual Error Components and Explanators 701
Two Examples: Manufacturing Firms and Russian Households 703
What We Do and Don t Learn from Hausman s Test 704
Testing for Unobserved Heterogeneity 705
Summary 706
Concepts for Review 708
Questions for Discussion 708
Problems for Analysis 708
Endnotes 714
17 Forecasting 716
17.1 Conditional Forecasting 716
Conditional Forecasts and Prediction Intervals 717
Linear Time Trends 718
Exponential Growth Trends 719
Polynomial Trends 720
Information Criteria for Choosing Among Models 721
An Example of Model Choice: Forecasting Railroad Revenues 723
Seasonal Dummies 725
REGRESSION S GREATEST HITS An Econometric Top 40—Golden Oldies:
The Early Macroeconometric Modelers—Tinbergen and Klein 111
17.2 Univariate Forecasting 730
Forecasting with First Order Autoregressions 730
Forecasting with Higher Order Autoregressions 731
Estimating Autoregressive Models 732
Forecasting with Moving Averages 735
Estimating Moving Average Models 736
Forecasting with ARMA Models 736
17.3 Multivariate Forecasting with Vector Autoregression (VAR) 742
Vector Autoregressions 742
Granger Causality 743
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Money, Income, and Causality 744
Summary 746
Concepts for Review 747
Questions for Discussion 747
Problems for Analysis 748
Endnotes 752
18 Stochastically Trending Variables 753
18.1 Time Trends 753
Deterministic Trends 754
Macroeconomic Variables and Deterministic Trends 757
Stochastic Trends 757
Random Walks 760
18.2 Stochastic Trends in Regression Models 764
Stochastic Trends and Reversion to Trend 765
When an Explanator Trends Stochastically and Disturbances Don t 766
18.3 The Consequences of Stochastic Trends for Regression 768
Spurious Regressions: An Example 770
18.4 Testing for Unit Roots 773
Allowing for Both Deterministic and Stochastic Trends 773
The Dickey Fuller Test for a Unit Root 775
The Spurious Regression Example Continued 777
18.5 How to Overcome the Spuriousness of Spurious Regressions 781
Granger and Newbold s Strategy 781
Integrated Variables 782
Money Illusion Revisited 784
Integration and Forecasting 787
18.6 Common or Shared Trends 788
Cointegration and Error Correction 789
Testing for Cointegration 793
18.7 Estimating Cointegrated Relationships 793
Stock and Watson s Dynamic OLS Estimator 794
An Example of Dynamic OLS: Interest Rates and Deficits 795
Estimating an Error Correction Model 797
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Rational Expectations, Permanent Income, and the Consumption Function 799
Lessons About Time Trends 801
Summary 803
Concepts for Review 803
Questions for Discussion 804
Problems for Analysis 804
Endnotes 810
19 Logit and Probit Models: Truncated and Censored Samples 811
19.1 The Linear Probability Model 812
OLS Estimation of the Linear Probability Model 813
An Example of Linear Probability Models: National Football League Victory 814
Maximum Likelihood Estimation of the Linear Probability Model 816
19.2 Probit and Logit Models 817
Latent Variables That Determine Binary Outcomes 817
Probit and Logit Models 819
The Probit Model 820
An Example of the Probit Model: The Decision to Hold
Interest Bearing Assets 821
The Logit Model 823
An Example: The NFL and Point Spreads Once More 824
Comparing the Probit and Logit Models 826
RFX;rf.SS1ON s GREATEST HITS An Econometric Top 40—A Classical Favorite:
The National Health Insurance Experiment 827
19.3 Truncated and Censored Samples 829
Estimation with a Truncated Sample 831
Estimation with a Censored Sample 835
REGRESSION S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Women s Wages and Women s Choice to Work 836
Summary 840
Concepts for Review 841
Questions for Discussion 841
Problems for Analysis 841
Endnotes 847
Statistical Appendix: A Review of Probability and Statistics 849
SA.l Probability 849
Simple and Joint Probabilities 849
Conditional Probability 852
Statistical Independence 854
Bayes s Rule 854
The Probability Rules 855
Random Variables and Their Probability Functions 855
Conditional Probability Functions 857
Graphically Depicting Probability Functions 858
The Binomial Probability Function 858
Statistically Independent Random Variables 860
Continuous Random Variables and Their Zero Probabilities 861
Continuous Random Variables and Probability Densities 862
The Normal Probability Density Function 864
The Standard Normal Distribution 864
SA.2 Statistics 866
Descriptive Statistics for a Single Variable 866
Descriptive Statistics for Two Variables 867
Populations and Samples 868
Descriptive Statistics and Populations 868
The Algebra of Expectations 871
The Algebra of Variances 872
Estimation of the Population Mean by the Sample Mean 874
Distribution of the Sample Mean 876
Estimation of the Population Variance 877
Deriving the Bias of or as an Estimator of a2 877
Whence the Bias of a1 in Estimating a1 879
An Unbiased Estimator of a1 880
Confidence Intervals 880
Confidence Intervals Using s2 to Estimate a1: Step 1 881
The t and Chi Square Distributions 882
Confidence Intervals Using s2 to Estimate a2: Step 2 884
Across Sample Properties of Estimators 885
The Relationship Among Variance, Bias, and Mean Square Error 885
Testing Hypotheses About the Population Mean 887
The ^ Statistic 887
The Significance Level of a Test 888
Critical Regions and the Power of a Test 888
Rejecting and Failing to Reject Hypotheses 891
Hypothesis Tests About a Population Variance 891
The F Test 892
Asymptotic Unbiasedness and the Consistency of Estimators 892
The Law of Large Numbers 894
The Central Limit Theorem 894
Summary 895
Concepts for Review 856
Endnote 857
Glossary 898
Index 918
|
| adam_txt |
Contents on the Web xxiv
Preface for Students xxv
Preface for Teachers xxvii
Part I The Linear Regression Model 1
1 What Is Econometrics? 1
1.1 A First Example of Econometric Modeling: Financial Aid and Income 3
Example 1: Income and Financial Aid 3
What Example 1 Illustrates About Econometrics 9
REGRESSION'S GREATEST HITS An Econometric Top 40—Golden Oldies,
Classical Favorites, Pop Tunes 9
An Econometric Top 40—A Pop Tune: Paying for College 10
1.2 A Second Example of Econometric Modeling: Consumption and Income 11
Example 2: Income and Food Expenditure 12
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
How Income Influences Demand—Engel's Law 15
What Example 2 Illustrates About Econometrics 16
1.3 Organizing Econometrics 17
What Do We Assume About Where the Data Come From? 17
What Makes a Good Estimator? 18
How Do We Create an Estimator? 18
What Are an Estimator's Properties? 18
How Do We Test Hypotheses? 18
How Do We Forecast? 19
Summary 19
Concepts for Review 20
Questions for Discussion 21
Problems for Analysis 21
Endnotes 22
2 Choosing Estimators: Intuition and Monte Carlo Methods 24
2.1 How to Sell Econometrics 25
2.2 Estimating a Population's Mean 28
The Need for a Precise Statement of Assumptions 29
Sampling and Randomness 29
Precise Assumptions—the Data Generating Process 30
Interpreting the DGP 31
Estimating Means as Estimating Intercepts 32
2.3 Estimating the Slope of a Line with No Intercept: Families of Means 33
Economic Theory and Lines Through the Origin 33
Families of Means 34
2.4 Natural Estimators for the Slope of a Line Through the Origin 35
A First Natural Estimator 36
A Second Natural Estimator 37
A Third Natural Estimator 38
A Surfeit of Riches 40
2.5 The Data Generating Process 40
The New Assumptions 41
Are Fixed X's Realistic? 41
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
Engel on Price Elasticity 42
2.6 Monte Carlo Comparisons 43
Building a Roulette Wheel 44
What Must the Roulette Wheel Do? 45
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Friedman's Permanent Income Hypothesis 46
Building a Roulette Wheel of Your Own: MC Builder I 49
Spinning the Roulette Wheel 50
2.7 Picking £,'s and the Real World 51
2.8 Comparing f}gu pg2, and /3g3 52
A Monte Carlo Exercise 52
What a Monte Carlo Analysis Can Say About Unbiasedness 55
2.9 Alternative Comparisons of pgi, fig2, and fig3 56
Additional Monte Carlo Exercises 57
2.10 Graphical Lessons from the Monte Carlo Exercises 60
What DGPs Do We Study? 61
What Do We Find? 61
Summary 65
Concepts for Review 66
Questions for Discussion 67
Problems for Analysis 67
Endnotes 69
3 Linear Estimators and the Gauss Markov Theorem 70
3.1 Linear Estimators 71
Linear Estimators and Their Weights 71
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Capital Asset Pricing Model 74
3.2 Unbiased Linear Estimators 76
The DGP 76
Unbiasedness and the Algebra of Expectations 76
Are Our Intuitive Estimators Unbiased? 78
3.3 The Variance of a Linear Estimator 79
Linear Estimators and the Algebra of Variances 80
Relative Variances of Linear Estimators 82
Revisiting Monte Carlo Exercises 82
3.4 A More Efficient Linear Estimator 84
Why Is pg2 More Efficient Than /3g] ? 85
What Estimator Might Be More Efficient Than /3g2? 86
Is p^ Unbiased? 87
The Variance of figA 88
Is There a Linear Estimator More Efficient Than /3g4? 90
3.5 A First Gauss Markov Theorem 90
The Gauss Markov Assumptions 91
Finding the Best Weights 91
3.6 Replacing Fixed X's with Stochastic X's 93
Extending the Reach of the Gauss Markov Assumptions 93
The Conditional and Population Properties of /3?4 94
3.7 Application: A U.S. Production Function 96
Estimating the Cobb Douglas Production Function with (5g\, pLgi, pgi, and /3g4 96
Is Ours the Correct DGP for These U.S. Data? 98
3.8 Econometric Software Output 99
Summary 101
Concepts for Review 102
Questions for Discussion 102
Problems for Analysis 103
Endnotes 108
Appendix 3.A Finding the BLUE Estimator of a Straight Line Through
the Origin 109
3.A.1 The Gauss Markov Theorem 109
The Mathematical Problem 109
3.A.2 BLUE Estimation of |3 When n = 2 110
Finding the BLUE Estimator 110
3.A.3 BLUE Estimation of /3 When n 2 111
Solving the Constrained Minimization Problem 111
Appendix 3.B A Matrix Algebra Representation of Regressions,
Linear Estimators, and Linear Unbiased Estimators 112
3.B.I An Alternative to Summation Notation 112
Column Vectors and Row Vectors 113
Matrix Multiplication 114
Appendix 3.B Concepts for Review 118
4 BLUE Estimators for the Slope and Intercept of a Straight Line 119
4.1 The DGP for a Straight Line with Unknown Intercept 120
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Phillips Curve 121
4.2 The Expected Value and Variance of Linear Estimators 123
Conditions for Unbiasedness 123
The Variance of a Linear Estimator 125
4.3 BLUE Estimation of the Slope and Intercept of a Straight Line 126
A BLUE Estimator for the Slope, /3i 126
An Estimator for {So 128
An Often Used Property of Certain Sums 129
A Relationship Between j8i and /3g4 129
An Example: The Phillips Curve 130
4.4 /3o and /3i Are Intuitively Appealing Estimators 132
The First Intuition 132
The Second Intuition 133
The Third Intuition 133
A Further Insight About BLUE Estimators 134
4.5 Logarithms in Econometrics 136
The Attraction of Logarithms 136
Double Logarithmic Specifications and Elasticities 136
An Example: The Phillips Curve Revisited 137
Semilog Specifications and Percentage Changes 139
An Example: The Phillips Curve Yet Again 139
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
How Price Influences Demand 141
Summary 142
Concepts for Review 143
Questions for Discussion 143
Problems for Analysis 144
Endnotes 152
Appendix 4.A Finding the BLUE Estimator for the Slope of a Straight Line
with an Unknown Intercept 153
4.A.1 The Lagrangian Approach for the Case of n Observations 154
Appendix 4.B Matrix Algebra and Estimating the Slope of a Straight Line
with an Unknown Intercept 155
4.B.1 Constructing Appealing Linear Estimators of fi\ and /3o 156
A Matrix Representation of a Regression Model Including an Intercept 156
Multiplying Matrices Revisited 157
A Computational Path to Building /3i and ;3o 158
Multiplying Matrices When Neither Is a Vector 159
Extending the Notion of an Inverse Matrix 159
The Estimators /3o and j3i 160
Concepts for Review 162
4.C A Commonly Used Property of Certain Sums 162
5 Residuals 164
5.1 Estimating a2 165
An Intuitive Estimator of a1 165
An Unbiased Estimator of a2 166
5.2 The Variances and Covariance of /3i and /3o 167
The Variances of p\ and po 167
The Covariance Between /3o and 0\ 169
Estimators of Var(J30), Var(/3i), and Cov(/30, Pi) 170
5.3 The Gauss Markov Theorem and the Expected Value of Y, Given X 172
5.4 Confidence Intervals and Prediction Intervals 173
Confidence Intervals for the Slope, Intercept, and E(Y|X) 173
Prediction Intervals for Future Values of Y 175
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Cobb Douglas Production Function 176
5.5 Application: A U.S. Production Function 177
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The CES Production Function 180
5.6 The Goodness of Fit of an Estimated Line 182
Decomposing the Variance of the Y, Within a Sample 182
The Coefficient of Determination, R2 185
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The World's Surprisingly Immobile Capital Markets 189
5.7 Two Properties of the BLUE Estimators' Residuals 190
The Sum of the Residuals 191
The Sum of the X's Times the Residuals 191
5.8 Ordinary Least Squares 192
Summary 194
Concepts for Review 195
Questions for Discussion 196
Problems for Analysis 196
Endnotes 203
Appendix 5.A The Unbiasedness of s2 204
5.A.I Estimating the Variance of the Disturbances 205
An Infeasible Alternative Estimator 205
Some Preliminaries 205
The Unbiasedness of s2 206
Appendix 5.B The Variance of /3o and the Covariance Between
Linear Estimators 208
5.B.I The Variance of the OLS Intercept Estimator 208
A Special Expression for the Sum of the X2 208
The Variance of j30 209
5.B.2 The Covariance of Linear Estimators 210
Appendix 5.C Matrix Algebra and the Properties of OLS Residuals 211
6 Multiple Regression 212
6.1 The DGP for the Regression Model 212
Polynomials 213
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
College Students' Misbehavior and the Price of Beer 215
6.2 BLUE Estimation in a Multiple Regression Model 216
What Is Required for Unbiased Linear Estimation? 216
What Is the Variance of a Linear Estimator in This DGP? 218
What Are the BLUE Estimators of p0, /3i, . . ., /3K in This DGP? 218
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
The Demand for Drugs 219
A More General Gauss Markov Theorem 221
6.3 An Application: Earnings Equations 221
BLUE Estimates for Black Women 221
Using Dummy Variables to Capture Categories 222
6.4 Estimating a1 227
Using the Residuals to Mimic the Disturbances 228
6.5 Ordinary Least Squares 229
A Visual Approach to OLS 229
An Implication of OLS 229
6.6 R2 in the Multiple Regression Model 231
R2—the Coefficient of Determination Revisited 231
Adjusted R2 231
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Solow Model, Old and New 232
6.7 Four Uses of "Linear" in Econometrics 235
Summary 238
Concepts for Review 239
Questions for Discussion 239
Problems for Analysis 239
Endnotes 250
Appendix 6.A Blue Estimation in a DGP with Stochastic Regressors 252
6.A.1 Unbiasedness Conditions of Linear Estimators 252
Adapted Gauss Markov Assumptions 255
OLS BLUE in This DGP 255
Appendix 6.B Matrix Algebra and Multiple Regressions 256
6.B.1 A Matrix Representation of the Multiple Regression Model 256
The Multiple Regression Model in Matrix Form 257
The Gauss Markov Assumptions in Matrix Form 257
6.B.2 Estimating the Multiple Regression Model's Coefficients 258
An Intuitive Approach to Estimating /3 258
Ordinary Least Squares 259
Linear Estimators in the Multiple Regression Model 261
Unbiasedness Conditions for Linear Estimators 261
The Variance of Linear Estimators 262
The Variances and Covariances of the OLS Estimator 262
OLS Is BLUE Under the Gauss Markov Assumptions 263
A Relationship Among Explanators and Residuals for the OLS Estimator 264
6.B.3 Estimating a1
Appendix 6.B Concepts for Review 266
rt II Specification and Hypothesis Testing 267
7 Testing Single Hypotheses in Regression Models 267
7.1 Rejecting and Failing to Reject Hypotheses 269
7.2 Six Steps to Hypothesis Testing 270
Framing the Null and Alternative Hypotheses 271
Choosing a Test Statistic 272
The ^ Statistic 273
Choosing a Significance Level 275
Choosing a Critical Region 276
The Power of a Test 278
Critical Regions and Complex Null Hypotheses 279
Computing the Test Statistic and Drawing a Conclusion 280
A Caveat About Maintained Hypotheses 282
Tests Undermined 283
7. 3 Degrees of Freedom Revisited 284
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Capital Asset Model Revisited 286
7.4 An Application: The Capital Asset Pricing Model Revisited 287
7.5 Tests About a Linear Combination of Coefficients 289
Another f Statistic 290
Two Examples of Testing for a Relationship Among Regression Coefficients 291
A Special Case: the Expected Value of Y, Given X 292
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
A Deeper Look at Discrimination 293
Summary 297
Concepts for Review 297
Questions for Discussion 297
Problems for Analysis 298
Endnotes 307
8 Superfluous and Omitted Variables, Multicollinearity, and Binary Variables 308
8.1 Including Superfluous Variables 308
Superfluous Variables and Lost Efficiency 309
A MONTE CARLO EXPERIMENT Prelude to Omitted Variables 310
8.2 Omitting Relevant Variables 311
Omitted Variable Bias 311
A Formula for Omitted Variable Bias 312
What to Include, What to Exclude 315
When Omitted Relevant Variables Are Acceptable 315
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Expectations Augmented Phillips Curve 316
8.3 Multicollinearity 320
Correlated Explanators 321
The Consequences of Multicollinearity 322
Perfect Multicollinearity 323
Coping with Multicollinearity 324
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
Who Needs SAT Scores? 325
8.4 The Earnings Example Extended—More About Dummy Variables 328
Using Multiple Dummy Variables to Estimate Means 328
Using Multiple Dummies to Estimate Intercepts 330
Using Multiple Dummies to Categorize Along Several Dimensions 331
Using Dummy Variables to Allow Different Slopes for Different Groups 332
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Rational Expectations Revolution 333
Summary 335
Concepts for Review 336
Questions for Discussion 336
Problems for Analysis 336
Endnotes 342
Appendix 8.A Matrix Algebra, Omitted Variables, and Perfect Collinearity
8.A.1 A Matrix Representation of Omitted Variables Bias 343
8.A.2 Matrix Representation of Perfect Collinearity 343
Concepts for Review 343
9 Testing Multiple Hypotheses
9.1 The Error of Combining ^ Statistics 344
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
Life Is Too Short to Drink Bad Wine! 345
9.2 F Tests: The Intuition 347
9.3 F Tests for Multiple Linear Restrictions on Regression Coefficients 350
The Distribution of the F Statistic 351
A Special Case Commonly Encountered 352
9.4 Relaxing Assumptions 353
Letting Go of Normality 353
Letting Go of Fixed Regressors 354
A Caveat About Multiple Tests 354
9.5 An Application: Linear Coefficient Constraints and the Earnings of Blacks 355
9.6 An Application: Linear Coefficient Constraints in a Model of Deficits 361
9.7 Two Additional Tests for Regime Shifts 363
Chow Tests 363
Using Dummy Variables to Test for Regime Shifts 364
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Unanticipated Money 365
Summary 368
Concepts for Review 368
Questions for Discussion 369
Problems for Analysis 369
Endnotes 377
Appendix 9.A Matrix Algebra and Hypothesis Testing 379
9.A.1 The Case of a Straight Line Through the Origin Revisited 379
9.A.2 Testing Linear Constraints on Both the Slope and Intercept 380
9.A.3 Any Linear Constraint Can Be Expressed with R/3 = c 382
9.A.4 Goodness of Fit and Deviations from the Null Hypothesis 383
9.A.5 A General Gauss Markov Theorem 383
Concepts for Review 384
till Further Topics In Regression 385
10 Heteroskedastic Disturbances 385
10.1 Visualizing Heteroskedasticity 386
A MONTE CARLO EXPERIMENT: Prelude to Heteroskedasticity 389
10.2 The Consequences of Heteroskedasticity for the OLS Estimators 390
Unchanged Unbiasedness Conditions 391
The Changed Variance of a Linear Estimator 391
10.3 Tests for Heteroskedasticity 394
The White Test 394
The Breusch Pagan Test 397
An Example Comparing the White Test and the Breusch Pagan Test 398
The Goldfeld Quandt Test 401
An Example of the Goldfeld Quandt Test 402
Omitted Variables and Heteroskedasticity Tests 402
The RESET Specification Test 405
10.4 BLUE Estimation When Disturbances Are Heteroskedastic 406
Transforming the Data to Account for Heteroskedasticity 406
Weighting Observations with Larger of 408
Two Special Cases of Heteroskedastic Disturbances 409
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
Complete Systems of Demand Equations 410
10.5 An Application: GLS Estimation of the Rent Income Relationship 412
Disturbances with Variances Proportional to Income Squared 412
Disturbances with Variances Proportional to Income 414
A Need for Caution 416
10.6 Feasible Generalized Least Squares 416
FGLS and the Rent Income Relationship 417
10.7 White's Heteroskedasticity Consistent Standard Errors 418
10.8 Logarithms and Heteroskedasticity 420
Summary 422
Concepts for Review 424
Questions for Discussion 424
Problems for Analysis 425
Endnotes 431
Appendix 10.A Matrix Algebra and Generalized Least Squares I 432
10.A.1 The Heteroskedastic Variance Covariance Matrix 432
The Disturbances' Variance Covariance Matrix 432
The Heteroskedastic Variance Covariance Matrix 433
10.A.2 OLS, GLS, and Heteroskedasticity 434
Heteroskedasticity and OLS 434
Heteroskedasticity and GLS 434
Concepts for Review 435
11 Autoregressive Disturbances 436
11.1 The Serially Correlated DGP 437
Visualizing Serial Correlation 437
The DGP 439
Stationarity 439
11.2 The Consequences of Serial Correlation for the OLS Estimators 441
The Unchanged Unbiasedness Conditions 441
The Changed Variance of a Linear Estimator 442
The Biased Standard Estimator of Var(jSi) 443
The Newey West Serial Correlation Consistent Standard Error Estimator 444
11.3 Tests for Serial Correlation 446
The Durbin Watson Test 446
Critical Values for the Durbin Watson Statistic 447
The Breusch Godfrey Test 452
An Example of Checking for Serial Correlation 453
Omitted Variables and Serial Correlation Tests 455
11.4 A DGP with First Order Autoregressive Disturbances 457
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Is Public Expenditure Productive? 458
Visualizing First Order Autoregressive Disturbances 459
The DGP 461
How the Disturbances Are Correlated 461
The Mean and Variance of the Disturbances 462
More Covariances Among Disturbances 463
An Alternative Expression of the New DGP 464
11.5 BLUE Estimation if Disturbances Are First Order Autoregressive 464
Constrained Minimization to Obtain BLUE Estimators 465
Transforming the Data to Obtain BLUE Estimators 466
Estimation When p Is Unknown 468
Iterating the Estimators 469
Nonlinear Estimation of Models with Autoregressive Disturbances 469
Serial Correlation Corrections and Omitted Variables 470
Testing Hypotheses 470
An Example of Estimation with Autoregressive Disturbances 471
Newey West Serial Correlation Consistent Variances 472
11.6 Serial Correlation and Heteroskedasticity Together 473
Generalized Least Squares 473
Autoregressive Conditional Heteroskedasticity 473
Conditional and Unconditional Variances 474
Testing for ARCH 475
Summary 477
Concepts for Review 478
Questions for Discussion 479
Problems for Analysis 479
Endnotes 486
Appendix ll.A Matrix Algebra and Generalized Least Squares II 487
11.A.I The Serial Correlation Variance Covariance Matrix 487
The Disturbances' Variance Covariance Matrix 487
The Serial Correlation Variance Covariance Matrix 488
11.A.2 OLS, GLS, and Serial Correlation 489
Serial Correlation and OLS 490
Serial Correlation and GLS 490
12 Large Sample Properties of Estimators: Consistency and Asymptotic Efficiency 492
12.1 The Large Sample, or Asymptotic, Perspective 493
Picturing Consistency and Asymptotic Distributions 494
12.2 Asymptotic Unbiasedness, Consistency, and Probability Limits 497
Asymptotic Unbiasedness 497
Consistency 498
Probability Limits 499
12.3 The Consistency of /3^4 and fax 500
The Consistency of /3g4 Under the Gauss Markov Assumptions 501
Manipulating Probability Limits 502
The Consistency of /3i 502
Consistent Estimators and Specifying DGPs 504
An Example: Haavelmo and the Consumption Function 505
12.4 Replacing Fixed Jfs with Stochastic JCs 507
Assumptions About the Disturbances and Stochastic X's 507
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Marginal Propensity to Consume 508
OLS: Sometimes Consistent, Sometimes Not 511
The Finite Sample Bias in OLS When E(xi e, ) = 0 511
Multiple Regression Models, GLS, and FGLS 512
A MONTE CARLO EXPERIMENT: Prelude to Asymptotic Efficiency 513
12.5 Asymptotic Efficiency and Asymptotic Distributions 514
Asymptotic Efficiency 514
The Rate of Convergence of /3g4 515
The Root n Consistency and Asymptotic Normality of /3g\, /3g2, Pg3, and (3g4 516
Hypothesis Testing 517
Alternatives to BLUE Estimation 520
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Making Music 521
Summary 524
Concepts for Review 524
Questions for Discussion 525
Problems for Analysis 525
Endnotes 530
Appendix 12.A Probability Limits and Consistency 531
12.A.1 Defining Probability Limits and Consistency 531
12.B Asymptotic Normality and OLS 533
13 Instrumental Variables Estimation 535
13.1 Friedman and the Consumption Function Revisited 535
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Heart Attacks and Heart Treatments 536
Consumption and Permanent Income 538
OLS's Measurement Error Bias 539
The Consistency of )3g2 541
13.2 Instrumental Variables Estimation 543
Improving on /3g2 543
Illustrative Instruments 543
The Instrumental Variables Estimator 544
The Bias of an IV Estimator 546
The Consistency of an IV Estimator 546
The Variance of an IV Estimator 547
The Multiple Regression Case 548
Identification 548
13.3 Sources of Contemporaneous Correlation 549
Instrumental Variables and Omitted Variables Bias 549
Instrumental Variables Estimation and Lagged Dependent Variables 550
Instrumental Variables and Jointly Determined Variables 551
Lagged Dependent Variables and Identification 553
13.4 An Application: Wage Equations and IV Estimation 553
Using Twins to Overcome Omitted Variable Bias 554
The Extent of Omitted Variables Bias in Wage Equations 555
13.5 Instrumental Variables and Two Stage Least Squares 559
Combining Multiple Candidate Instruments 559
Two Stage Least Squares 561
Testing Hypotheses Using 2SLS 562
Weak Instruments 564
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
Are Public Housing Projects Bad for Kids? 565
13.6 Testing Whether E(X, e,) Equals Zero 568
A Test for Troublesome Explanators 568
Testing Whether the Difference in Twins' Education Is Troublesome 570
Summary 572
Concepts for Review 572
Questions for Discussion 573
Problems for Analysis 573
Appendix 13.A The Magnitude of Measurement Error Bias 581
13 .A. 1 The Measurement Error DGP 581
13.A.2 The Magnitude of Measurement Error Bias 582
13.A.3 Mismeasured Explanators in Multiple Regression 585
Appendix 13.B Matrix Representations of Instrumental Variables
and 2SLS Estimators 587
13.B.1 The DGP 587
13.B.2 The OLS and IV Estimators 588
Consistency 588
The Variation of j§rv About f3 589
13.B.3 2SLS and IV 589
2SLS in Matrix Form 589
2SLS in IV Estimation 590
The Special Nature of 2SLS 591
14 Systems of Equations 593
14.1 Endogenous and Exogenous Variables in Simultaneous Equations 594
Endogenous and Exogenous Variables 595
14.2 The Simultaneity Bias of OLS 596
Estimating the Demand for Personal Computers 596
Structural Equations and Reduced Form Equations 596
Simultaneity Bias 598
Recursive Systems 599
14.3 The Identification Problem 600
Indirect Least Squares 600
Underidentified, Exactly Identified, and Overidentified Parameters 601
Identification in the Supply and Demand Example 601
A Graphical Depiction of the Identification Problem 602
14.4 An Application: The Fulton Fish Market 604
14.5 ILS, Overidentification and Underidentification 606
Identification and the DGP 606
A Surfeit of Riches: Overidentification 607
Overidentification in the Supply and Demand Model 607
Underidentification in the Supply and Demand Model 608
14.6 Instrumental Variables and Simultaneity Bias 609
Instrumental Variables and Simultaneous Equations 609
Instrumental Variables and the Demand for Personal Computers 611
More Fish: IV Estimation and the Fulton Fish Market 612
REGRESSION'S GREATEST HITS An Econometric Top 40—A Golden Oldie:
The Supply and Demand for Watermelons 613
14.7 Optimal Instruments and Two Stage Least Squares 614
Choosing Optimal Instruments 614
Two Stage Least Squares 615
14.8 Order and Rank Conditions for Identification 616
The Order Condition for Identification 616
Exclusion Restrictions and Covariance Restrictions 617
The Rank Condition for Identification 617
Some Rules of Thumb for Identification 619
Hausman's Test of Overidentifying Restrictions 619
14.9 An Application: 2SLS at the Fulton Fish Market 621
Testing the Overidentifying Restrictions in the Whiting Market 624
Serially Correlated Disturbances in Simultaneous Equations 626
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
Incarceration and Crime 627
Summary 628
Concepts for Review 630
Questions for Discussion 630
Problems for Analysis 630
Endnotes 638
15 Randomized Experiments and Natural Experiments 640
15.1 Estimating Means and Interpreting Differences in Means 641
Estimation versus Interpretation 641
The Neighborhood Poverty Example 642
15.2 Controlled and Randomized Experiments 644
Controlled Experiments 644
Randomized Experiments 646
The Neighborhood Poverty Example Revisited 647
Sources of Bias in Randomized Experiments 648
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
The Social Experiments: Labor Supply, Housing Allowances, and
Health Insurance 649
15.3 Natural Experiments 652
The Gautreaux Experiment 652
Differences in Means in the Gautreaux Experience 653
15.4 Difference in Differences Estimation 656
The Difference in Differences Estimator 656
The Variance of the Diff in Diffs Estimator 658
A Regression Formulation of Diff in Diffs 659
The Achilles Heel of Diff in Diffs 660
REGRESSION'S GREATEST HITS An Econometric Top 40—A Pop Tune:
Fast Food and the Minimum Wage 661
The Strength of Randomized Experiments 664
15.5 Average and Marginal Treatment Effects 665
Average Treatment Effects on the Treated 665
Early Results from the Moving to Opportunity Experiment 666
Experimental Effects on the Treated and on Those We Intend to Treat 666
Randomized versus Natural Experiments 669
Summary 670
Concepts for Review 670
Questions for Discussion 671
Problems for Analysis 671
Endnotes 676
16 Analyzing Panel Data 678
16.1 Panel Data 679
Distinct Intercepts DGPs 680
Error Components Models 681
Choosing a Fixed or Error Components DGP 684
16.2 Estimation with Panel Data 684
Estimation in the Distinct Intercepts DGP 684
REGRESSION'S GREATEST HITS An Econometric Top 40—Two Golden Oldies:
The Early Panel Studies 685
Fixed Effects Estimation as Within Estimation 689
Estimation in the First Error Components DGP 691
Implementing the FGLS Random Effects Estimator 692
Estimation in the Second Error Components DGP 692
An Example of Estimation with Panel Data: Manufacturing Firms 693
16.3 Related DGPs 696
An Example of a Clustered Data Set: Children in Russian Households in 1995 697
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Specification Tests and an Earnings Function 698
16.4 Distinguishing Among Panel Data DGPs 700
Testing for Correlation Between Individual Error Components and Explanators 701
Two Examples: Manufacturing Firms and Russian Households 703
What We Do and Don't Learn from Hausman's Test 704
Testing for Unobserved Heterogeneity 705
Summary 706
Concepts for Review 708
Questions for Discussion 708
Problems for Analysis 708
Endnotes 714
17 Forecasting 716
17.1 Conditional Forecasting 716
Conditional Forecasts and Prediction Intervals 717
Linear Time Trends 718
Exponential Growth Trends 719
Polynomial Trends 720
Information Criteria for Choosing Among Models 721
An Example of Model Choice: Forecasting Railroad Revenues 723
Seasonal Dummies 725
REGRESSION'S GREATEST HITS An Econometric Top 40—Golden Oldies:
The Early Macroeconometric Modelers—Tinbergen and Klein 111
17.2 Univariate Forecasting 730
Forecasting with First Order Autoregressions 730
Forecasting with Higher Order Autoregressions 731
Estimating Autoregressive Models 732
Forecasting with Moving Averages 735
Estimating Moving Average Models 736
Forecasting with ARMA Models 736
17.3 Multivariate Forecasting with Vector Autoregression (VAR) 742
Vector Autoregressions 742
Granger Causality 743
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Money, Income, and Causality 744
Summary 746
Concepts for Review 747
Questions for Discussion 747
Problems for Analysis 748
Endnotes 752
18 Stochastically Trending Variables 753
18.1 Time Trends 753
Deterministic Trends 754
Macroeconomic Variables and Deterministic Trends 757
Stochastic Trends 757
Random Walks 760
18.2 Stochastic Trends in Regression Models 764
Stochastic Trends and Reversion to Trend 765
When an Explanator Trends Stochastically and Disturbances Don't 766
18.3 The Consequences of Stochastic Trends for Regression 768
Spurious Regressions: An Example 770
18.4 Testing for Unit Roots 773
Allowing for Both Deterministic and Stochastic Trends 773
The Dickey Fuller Test for a Unit Root 775
The Spurious Regression Example Continued 777
18.5 How to Overcome the Spuriousness of Spurious Regressions 781
Granger and Newbold's Strategy 781
Integrated Variables 782
Money Illusion Revisited 784
Integration and Forecasting 787
18.6 Common or Shared Trends 788
Cointegration and Error Correction 789
Testing for Cointegration 793
18.7 Estimating Cointegrated Relationships 793
Stock and Watson's Dynamic OLS Estimator 794
An Example of Dynamic OLS: Interest Rates and Deficits 795
Estimating an Error Correction Model 797
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Rational Expectations, Permanent Income, and the Consumption Function 799
Lessons About Time Trends 801
Summary 803
Concepts for Review 803
Questions for Discussion 804
Problems for Analysis 804
Endnotes 810
19 Logit and Probit Models: Truncated and Censored Samples 811
19.1 The Linear Probability Model 812
OLS Estimation of the Linear Probability Model 813
An Example of Linear Probability Models: National Football League Victory 814
Maximum Likelihood Estimation of the Linear Probability Model 816
19.2 Probit and Logit Models 817
Latent Variables That Determine Binary Outcomes 817
Probit and Logit Models 819
The Probit Model 820
An Example of the Probit Model: The Decision to Hold
Interest Bearing Assets 821
The Logit Model 823
An Example: The NFL and Point Spreads Once More 824
Comparing the Probit and Logit Models 826
RFX;rf.SS1ON's GREATEST HITS An Econometric Top 40—A Classical Favorite:
The National Health Insurance Experiment 827
19.3 Truncated and Censored Samples 829
Estimation with a Truncated Sample 831
Estimation with a Censored Sample 835
REGRESSION'S GREATEST HITS An Econometric Top 40—A Classical Favorite:
Women's Wages and Women's Choice to Work 836
Summary 840
Concepts for Review 841
Questions for Discussion 841
Problems for Analysis 841
Endnotes 847
Statistical Appendix: A Review of Probability and Statistics 849
SA.l Probability 849
Simple and Joint Probabilities 849
Conditional Probability 852
Statistical Independence 854
Bayes's Rule 854
The Probability Rules 855
Random Variables and Their Probability Functions 855
Conditional Probability Functions 857
Graphically Depicting Probability Functions 858
The Binomial Probability Function 858
Statistically Independent Random Variables 860
Continuous Random Variables and Their Zero Probabilities 861
Continuous Random Variables and Probability Densities 862
The Normal Probability Density Function 864
The Standard Normal Distribution 864
SA.2 Statistics 866
Descriptive Statistics for a Single Variable 866
Descriptive Statistics for Two Variables 867
Populations and Samples 868
Descriptive Statistics and Populations 868
The Algebra of Expectations 871
The Algebra of Variances 872
Estimation of the Population Mean by the Sample Mean 874
Distribution of the Sample Mean 876
Estimation of the Population Variance 877
Deriving the Bias of or as an Estimator of a2 877
Whence the Bias of a1 in Estimating a1 879
An Unbiased Estimator of a1 880
Confidence Intervals 880
Confidence Intervals Using s2 to Estimate a1: Step 1 881
The t and Chi Square Distributions 882
Confidence Intervals Using s2 to Estimate a2: Step 2 884
Across Sample Properties of Estimators 885
The Relationship Among Variance, Bias, and Mean Square Error 885
Testing Hypotheses About the Population Mean 887
The ^ Statistic 887
The Significance Level of a Test 888
Critical Regions and the Power of a Test 888
Rejecting and Failing to Reject Hypotheses 891
Hypothesis Tests About a Population Variance 891
The F Test 892
Asymptotic Unbiasedness and the Consistency of Estimators 892
The Law of Large Numbers 894
The Central Limit Theorem 894
Summary 895
Concepts for Review 856
Endnote 857
Glossary 898
Index 918 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:03:50Z |
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| language | English |
| lccn | 2005018586 |
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| spelling | Murray, Michael P. Verfasser aut Econometrics a modern introduction Michael P. Murray Internat. ed. Boston ; Munich [u.a.] Pearson Addison-Wesley 2006 XXXVI, 929 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier The Addison-Wesley series in economics Includes bibliographical references and index Econometrics Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ökonometrie (DE-588)4132280-0 s DE-604 http://www.loc.gov/catdir/toc/ecip0515/2005018586.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014660513&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murray, Michael P. Econometrics a modern introduction Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4123623-3 |
| title | Econometrics a modern introduction |
| title_auth | Econometrics a modern introduction |
| title_exact_search | Econometrics a modern introduction |
| title_exact_search_txtP | Econometrics a modern introduction |
| title_full | Econometrics a modern introduction Michael P. Murray |
| title_fullStr | Econometrics a modern introduction Michael P. Murray |
| title_full_unstemmed | Econometrics a modern introduction Michael P. Murray |
| title_short | Econometrics |
| title_sort | econometrics a modern introduction |
| title_sub | a modern introduction |
| topic | Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Econometrics Ökonometrie Lehrbuch |
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