Introductory Econometrics: A Modern Approach

Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 5
1.1 What Is Econometrics?......Page 22
1.2 Steps in Empirical Economic Analysis......Page 23
Cross-Sectional Data......Page 26
Time Series Data......Page 29
Pooled Cross Sections......Page 30
Panel or Longitudinal Data......Page 31
1.4 Causality and the Notion of Ceteris Paribus in Econometric Analysis......Page 33
Problems......Page 38
Computer Exercises......Page 39
PART 1 Regression Analysis with Cross-Sectional Data......Page 42
2.1 Definition of the Simple Regression Model......Page 43
2.2 Deriving the Ordinary Least Squares Estimates......Page 48
2.3 Properties of OLS on Any Sample of Data......Page 57
2.4 Units of Measurement and Functional Form......Page 62
2.5 Expected Values and Variances of the OLS Estimators......Page 67
2.6 Regression through the Origin......Page 79
Summary......Page 80
Key Terms......Page 81
Problems......Page 82
Computer Exercises......Page 85
Appendix 2A......Page 87
3.1 Motivation for Multiple Regression......Page 89
3.2 Mechanics and Interpretation of Ordinary Least Squares......Page 94
3.3 The Expected Value of the OLS Estimators......Page 105
3.4 The Variance of the OLS Estimators......Page 115
3.5 Efficiency of OLS: The Gauss-Markov Theorem......Page 123
Summary......Page 125
Problems......Page 126
Computer Exercises......Page 131
Appendix 3A......Page 134
4.1 Sampling Distributions of the OLS Estimators......Page 138
4.2 Testing Hypotheses about a Single Population Parameter: The t Test......Page 141
4.3 Confidence Intervals......Page 159
4.4 Testing Hypotheses about a Single Linear Combination of the Parameters......Page 161
4.5 Testing Multiple Linear Restrictions: The F Test......Page 164
4.6 Reporting Regression Results......Page 175
Summary......Page 177
Key Terms......Page 179
Problems......Page 180
Computer Exercises......Page 184
5.1 Consistency......Page 188
5.2 Asymptotic Normality and Large Sample Inference......Page 193
5.3 Asymptotic Efficiency of OLS......Page 200
Summary......Page 201
Computer Exercises......Page 202
Appendix 5A......Page 203
6.1 Effects of Data Scaling on OLS Statistics......Page 205
6.2 More on Functional Form......Page 210
6.3 More on Goodness-of-Fit and Selection of Regressors......Page 220
6.4 Prediction and Residual Analysis......Page 227
Key Terms......Page 236
Problems......Page 237
Computer Exercises......Page 239
Appendix 6A......Page 244
7.1 Describing Qualitative Information......Page 246
7.2 A Single Dummy Independent Variable......Page 247
7.3 Using Dummy Variables for Multiple Categories......Page 254
7.4 Interactions Involving Dummy Variables......Page 259
7.5 A Binary Dependent Variable: The Linear Probability Model......Page 267
7.6 More on Policy Analysis and Program Evaluation......Page 272
Summary......Page 275
Problems......Page 276
Computer Exercises......Page 279
8.1 Consequences of Heteroskedasticity for OLS......Page 285
8.2 Heteroskedasticity-Robust Inference after OLS Estimation......Page 286
8.3 Testing for Heteroskedasticity......Page 292
8.4 Weighted Least Squares Estimation......Page 297
8.5 The Linear Probability Model Revisited......Page 311
Summary......Page 314
Problems......Page 315
Computer Exercises......Page 317
9.1 Functional Form Misspecification......Page 321
9.2 Using Proxy Variables for Unobserved Explanatory Variables......Page 327
9.3 Models with Random Slopes......Page 334
9.4 Properties of OLS under Measurement Error......Page 336
9.5 Missing Data, Nonrandom Samples, and Outlying Observations......Page 343
9.6 Least Absolute Deviations Estimation......Page 351
Summary......Page 352
Problems......Page 353
Computer Exercises......Page 355
PART 2 Regression Analysis with Time Series Data......Page 360
10.1 The Nature of Time Series Data......Page 361
10.2 Examples of Time Series Regression Models......Page 363
10.3 Finite Sample Properties of OLS under Classical Assumptions......Page 366
10.4 Functional Form, Dummy Variables, and Index Numbers......Page 374
10.5 Trends and Seasonality......Page 381
Summary......Page 391
Problems......Page 392
Computer Exercises......Page 394
11.1 Stationary and Weakly Dependent Time Series......Page 398
11.2 Asymptotic Properties of OLS......Page 402
11.3 Using Highly Persistent Time Series in Regression Analysis......Page 409
11.4 Dynamically Complete Models and the Absence of Serial Correlation......Page 417
11.5 The Homoskedasticity Assumption for Time Series Models......Page 420
Summary......Page 421
Problems......Page 422
Computer Exercises......Page 425
12.1 Properties of OLS with Serially Correlated Errors......Page 429
12.2 Testing for Serial Correlation......Page 433
12.3 Correcting for Serial Correlation with Strictly Exogenous Regressors......Page 440
12.4 Differencing and Serial Correlation......Page 447
12.5 Serial Correlation-Robust Inference after OLS......Page 449
12.6 Heteroskedasticity in Time Series Regressions......Page 453
Key Terms......Page 458
Computer Exercises......Page 459
PART 3 Advanced Topics......Page 464
CHAPTER 13 Pooling Cross Sections across Time: Simple Panel Data Methods......Page 465
13.1 Pooling Independent Cross Sections across Time......Page 466
13.2 Policy Analysis with Pooled Cross Sections......Page 471
13.3 Two-Period Panel Data Analysis......Page 476
13.4 Policy Analysis with Two-Period Panel Data......Page 483
13.5 Differencing with More Than Two Time Periods......Page 486
Problems......Page 492
Computer Exercises......Page 494
Appendix 13A......Page 499
14.1 Fixed Effects Estimation......Page 502
14.2 Random Effects Models......Page 510
14.3 Applying Panel Data Methods to Other Data Structures......Page 515
Key Terms......Page 517
Problems......Page 518
Computer Exercises......Page 519
Appendix 14A......Page 524
CHAPTER 15 Instrumental Variables Estimation and Two Stage Least Squares......Page 527
15.1 Motivation: Omitted Variables in a Simple Regression Model......Page 528
15.2 IV Estimation of the Multiple Regression Model......Page 538
15.3 Two Stage Least Squares......Page 542
15.4 IV Solutions to Errors-in-Variables Problems......Page 546
15.5 Testing for Endogeneity and Testing Overidentifying Restrictions......Page 548
15.7 Applying 2SLS to Time Series Equations......Page 552
15.8 Applying 2SLS to Pooled Cross Sections and Panel Data......Page 555
Problems......Page 557
Computer Exercises......Page 560
Appendix 15A......Page 564
16.1 The Nature of Simultaneous Equations Models......Page 567
16.2 Simultaneity Bias in OLS......Page 571
16.3 Identifying and Estimating a Structural Equation......Page 573
16.4 Systems with More Than Two Equations......Page 580
16.5 Simultaneous Equations Models with Time Series......Page 581
16.6 Simultaneous Equations Models with Panel Data......Page 585
Summary......Page 587
Problems......Page 588
Computer Exercises......Page 591
CHAPTER 17 Limited Dependent Variable Models and Sample Selection Corrections......Page 595
17.1 Logit and Probit Models for Binary Response......Page 596
17.2 The Tobit Model for Corner Solution Responses......Page 608
17.3 The Poisson Regression Model......Page 616
17.4 Censored and Truncated Regression Models......Page 621
17.5 Sample Selection Corrections......Page 627
Summary......Page 633
Key Terms......Page 634
Problems......Page 635
Computer Exercises......Page 636
Appendix 17A......Page 641
Appendix 17B......Page 642
CHAPTER 18 Advanced Time Series Topics......Page 644
18.1 Infinite Distributed Lag Models......Page 645
18.2 Testing for Unit Roots......Page 651
18.3 Spurious Regression......Page 657
18.4 Cointegration and Error Correction Models......Page 658
18.5 Forecasting......Page 666
Summary......Page 681
Problems......Page 682
Computer Exercises......Page 684
19.1 Posing a Question......Page 689
19.2 Literature Review......Page 691
19.3 Data Collection......Page 692
19.4 Econometric Analysis......Page 696
19.5 Writing an Empirical Paper......Page 699
Sample Empirical Projects......Page 708
List of Journals......Page 713
Data Sources......Page 714
A.1 The Summation Operator and Descriptive Statistics......Page 716
A.2 Properties of Linear Functions......Page 718
A.3 Proportions and Percentages......Page 720
A.4 Some Special Functions and Their Properties......Page 723
A.5 Differential Calculus......Page 730
Problems......Page 732
B.1 Random Variables and Their Probability Distributions......Page 735
B.2 Joint Distributions, Conditional Distributions, and Independence......Page 740
B.3 Features of Probability Distributions......Page 743
B.4 Features of Joint and Conditional Distributions......Page 750
B.5 The Normal and Related Distributions......Page 758
Key Terms......Page 765
Problems......Page 766
C.1 Populations, Parameters, and Random Sampling......Page 768
C.2 Finite Sample Properties of Estimators......Page 769
C.3 Asymptotic or Larger Sample Properties of Estimators......Page 776
C.4 General Approaches to Parameter Estimation......Page 781
C.5 Interval Estimation and Confidence Intervals......Page 783
C.6 Hypothesis Testing......Page 791
C.7 Remarks on Notation......Page 802
Key Terms......Page 803
Problems......Page 804
D.1 Basic Definitions......Page 809
D.2 Matrix Operations......Page 810
D.4 Quadratic Forms and Positive Definite Matrices......Page 814
D.5 Idempotent Matrices......Page 815
D.7 Moments and Distributions of Random Vectors......Page 816
Key Terms......Page 818
Problems......Page 819
E.1 The Model and Ordinary Least Squares Estimation......Page 820
E.2 Finite Sample Properties of OLS......Page 822
E.3 Statistical Inference......Page 826
E.4 Some Asymptotic Analysis......Page 828
Summary......Page 831
Problems......Page 832
Appendix F: Answers to Chapter Questions......Page 834
Appendix G: Statistical Tables......Page 844
References......Page 851
Glossary......Page 856
Index......Page 870