# Introductory Econometrics: A Modern Approach, 7th Edition PDF by Jeffrey M Wooldridge

## Introductory Econometrics: A Modern Approach, 7th Edition

By Jeffrey M. Wooldridge

Content:

Preface xii
chapter 1 The Nature of Econometrics
and Economic Data 1
1-1 What Is Econometrics? 1
1-2 Steps in Empirical Economic Analysis 2
1-3 The Structure of Economic Data 5
1-3a Cross-Sectional Data 5
1-3b Time Series Data 7
1-3c Pooled Cross Sections 8
1-3d Panel or Longitudinal Data 9
1-3e A Comment on Data Structures 10
1-4 Causality, Ceteris Paribus, and Counterfactual
Reasoning 10
Summary 14
Key Terms 15
Problems 15
Computer Exercises 15
Part 1
Regression Analysis with
Cross- Sectional Data 19
chapter 2 The Simple Regression Model 20
2-1 Definition of the Simple Regression Model 20
2-2 Deriving the Ordinary Least Squares Estimates 24
2-2a A Note on Terminology 31
2-3 Properties of OLS on Any Sample of Data 32
2-3a Fitted Values and Residuals 32
2-3b Algebraic Properties of OLS Statistics 32
2-3c Goodness-of-Fit 35
2-4 Units of Measurement and Functional Form 36
2-4a The Effects of Changing Units of Measurement
on OLS Statistics 36
2-4b Incorporating Nonlinearities in Simple
Regression 37
2-4c The Meaning of “Linear” Regression 40
2-5 Expected Values and Variances of the OLS
Estimators 40
2-5a Unbiasedness of OLS 40
2-5b Variances of the OLS Estimators 45
2-5c Estimating the Error Variance 48
2-6 Regression through the Origin and Regression on a Constant 50
2-7 Regression on a Binary Explanatory Variable 51
2-7a Counterfactual Outcomes, Causality, and Policy
Analysis 53
Summary 56
Key Terms 57
Problems 58
Computer Exercises 62
chapter 3 Multiple Regression Analysis: Estimation 66
3-1 Motivation for Multiple Regression 67
3-1a The Model with Two Independent Variables 67
3-1b The Model with k Independent Variables 69
3-2 Mechanics and Interpretation of Ordinary Least
Squares 70
3-2a Obtaining the OLS Estimates 70
3-2b Interpreting the OLS Regression Equation 71
3-2c On the Meaning of “Holding Other Factors Fixed”
in Multiple Regression 73
3-2d Changing More Than One Independent Variable
Simultaneously 74
3-2e OLS Fitted Values and Residuals 74
3-2f A “Partialling Out” Interpretation of Multiple
Regression 75
3-2g Comparison of Simple and Multiple Regression
Estimates 75
3-2h Goodness-of-Fit 76
3-2i Regression through the Origin 79
3-3 The Expected Value of the OLS Estimators 79
3-3a Including Irrelevant Variables in a Regression
Model 83
3-3b Omitted Variable Bias: The Simple Case 84
3-3c Omitted Variable Bias: More General Cases 87
3-4 The Variance of the OLS Estimators 87
3-4a The Components of the OLS Variances:
Multicollinearity 89
3-4b Variances in Misspecified Models 92
3-4c Estimating s2: Standard Errors of the OLS
Estimators 93
3-5 Efficiency of OLS: The Gauss-Markov
Theorem 95
3-6 Some Comments on the Language of Multiple
Regression Analysis 96
3-7 Several Scenarios for Applying Multiple
Regression 97
3-7a Prediction 98
3-7b Efficient Markets 98
3-7c Measuring the Tradeoff between Two
Variables 99
3-7d Testing for Ceteris Paribus Group
Differences 99
3-7e Potential Outcomes, Treatment Effects, and Policy
Analysis 100
Summary 102
Key Terms 104
Problems 104
Computer Exercises 109
chapter 4 Multiple Regression Analysis:
Inference 117
4-1 Sampling Distributions of the OLS
Estimators 117
4-2 Testing Hypotheses about a Single Population
Parameter: The t Test 120
4-2a Testing against One-Sided Alternatives 122
4-2b Two-Sided Alternatives 126
4-2c Testing Other Hypotheses about bj 128
4-2d Computing p-Values for t Tests 130
4-2e A Reminder on the Language of Classical
Hypothesis Testing 132
4-2f Economic, or Practical, versus Statistical Significance 132
4-3 Confidence Intervals 134
4-4 Testing Hypotheses about a Single Linear
Combination of the Parameters 136
4-5 Testing Multiple Linear Restrictions: The F Test 139
4-5a Testing Exclusion Restrictions 139
4-5b Relationship between F and t Statistics 144
4-5c The R-Squared Form of the F Statistic 145
4-5d Computing p-values for F Tests 146
4-5e The F Statistic for Overall Significance of a
Regression 147
4-5f Testing General Linear Restrictions 148
4-6 Reporting Regression Results 149
4-7 Revisiting Causal Effects and Policy
Analysis 151
Summary 152
Key Terms 154
Problems 154
Computer Exercises 159
chapter 5 Multiple Regression Analysis: OLS
Asymptotics 163
5-1 Consistency 164
5-1a Deriving the Inconsistency in OLS 167
5-2 Asymptotic Normality and Large Sample
Inference 168
5-2a Other Large Sample Tests: The Lagrange
Multiplier Statistic 172
5-3 Asymptotic Efficiency of OLS 175
Summary 176
Key Terms 176
Problems 176
Computer Exercises 178
chapter 6 Multiple Regression Analysis:
Further Issues 181
6-1 Effects of Data Scaling on OLS Statistics 181
6-1a Beta Coefficients 184
6-2 More on Functional Form 186
6-2a More on Using Logarithmic Functional
Forms 186
6-2c Models with Interaction Terms 192
6-2d Computing Average Partial Effects 194
6-3 More on Goodness-of-Fit and Selection of
Regressors 195
6-3b Using Adjusted R-Squared to Choose between
Nonnested Models 197
6-3c Controlling for Too Many Factors in Regression
Analysis 199
6-3d Adding Regressors to Reduce the Error
Variance 200
6-4 Prediction and Residual Analysis 201
6.4a Confidence Intervals for Predictions 201
6-4b Residual Analysis 205
6-4c Predicting y When log(y) Is the Dependent
Variable 205
6-4d Predicting y When the Dependent Variable Is
log(y) 207
Summary 209
Key Terms 211
Problems 211
Computer Exercises 214
chapter 7 Multiple Regression Analysis with
Qualitative Information 220
7-1 Describing Qualitative Information 221
7-2 A Single Dummy Independent
Variable 222
7-2a Interpreting Coefficients on Dummy
Explanatory Variables When the Dependent
Variable Is log(y) 226
7-3 Using Dummy Variables for Multiple
Categories 228
7-3a Incorporating Ordinal Information by Using
Dummy Variables 230
7-4 Interactions Involving Dummy Variables 232
7-4a Interactions among Dummy Variables 232
7-4b Allowing for Different Slopes 233
7-4c Testing for Differences in Regression Functions
across Groups 237
7-5 A Binary Dependent Variable: The Linear
Probability Model 239
7-6 More on Policy Analysis and Program
Evaluation 244
7-6a Program Evaluation and Unrestricted Regression
7-7 Interpreting Regression Results with Discrete
Dependent Variables 249
Summary 250
Key Terms 251
Problems 251
Computer Exercises 256
chapter 8 Heteroskedasticity 262
8-1 Consequences of Heteroskedasticity for OLS 262
8-2 Heteroskedasticity-Robust Inference after OLS
Estimation 263
8-2a Computing Heteroskedasticity-Robust LM
Tests 267
8-3 Testing for Heteroskedasticity 269
8-3a The White Test for Heteroskedasticity 271
8-4 Weighted Least Squares Estimation 273
8-4a The Heteroskedasticity Is Known up to a
Multiplicative Constant 273
8-4b The Heteroskedasticity Function
Must Be Estimated: Feasible GLS 278
8-4c What If the Assumed Heteroskedasticity Function Is
Wrong? 281
8-4d Prediction and Prediction Intervals with
Heteroskedasticity 283
8-5 The Linear Probability Model Revisited 284
Summary 286
Key Terms 287
Problems 287
Computer Exercises 290
chapter 9 More on Specification and
Data Issues 294
9-1 Functional Form Misspecification 295
9-1a RESET as a General Test for Functional
Form Misspecification 297
9-1b Tests against Nonnested Alternatives 298
9-2 Using Proxy Variables for Unobserved Explanatory
Variables 299
9-2a Using Lagged Dependent Variables as Proxy
Variables 303
9-2b A Different Slant on Multiple Regression 304
9-2c Potential Outcomes and Proxy Variables 305
9-3 Models with Random Slopes 306
9-4 Properties of OLS under Measurement Error 308
9-4a Measurement Error in the Dependent Variable 308
9-4b Measurement Error in an Explanatory
Variable 310
9-5 Missing Data, Nonrandom Samples, and Outlying
Observations 313
9-5a Missing Data 313
9-5b Nonrandom Samples 315
9-5c Outliers and Influential Observations 317
9-6 Least Absolute Deviations Estimation 321
Summary 323
Key Terms 324
Problems 324
Computer Exercises 328
Pa r t 2
Regression Analysis with Time
Series Data 333
chapter 10 Basic Regression Analysis with
Time Series Data 334
10-1 The Nature of Time Series Data 334
10-2 Examples of Time Series Regression
Models 335
10-2a Static Models 336
10-2b Finite Distributed Lag Models 336
10-2c A Convention about the Time Index 338
10-3 Finite Sample Properties of OLS under Classical
Assumptions 339
10-3a Unbiasedness of OLS 339
10-3b The Variances of the OLS Estimators and the
Gauss-Markov Theorem 342
10-3c Inference under the Classical Linear Model
Assumptions 344
10-4 Functional Form, Dummy Variables, and Index
Numbers 345
10-5 Trends and Seasonality 351
10-5a Characterizing Trending Time Series 351
10-5b Using Trending Variables in Regression
Analysis 354
10-5c A Detrending Interpretation of Regressions
with a Time Trend 356
10-5d Computing R-Squared When the Dependent
Variable Is Trending 357
10-5e Seasonality 358
Summary 360
Key Terms 361
Problems 361
Computer Exercises 363
chapter 11 Further Issues in Using OLS with
Time Series Data 366
11-1 Stationary and Weakly Dependent Time
Series 367
11-1a Stationary and Nonstationary Time Series 367
11-1b Weakly Dependent Time Series 368
11-2 Asymptotic Properties of OLS 370
11-3 Using Highly Persistent Time Series in Regression
Analysis 376
11-3a Highly Persistent Time Series 376
11-3b Transformations on Highly Persistent Time
Series 380
11-3c Deciding Whether a Time Series Is I(1) 381
11-4 Dynamically Complete Models and the Absence of
Serial Correlation 382
11-5 The Homoskedasticity Assumption for Time
Series Models 385
Summary 386
Key Terms 387
Problems 387
Computer Exercises 390
chapter 12 Serial Correlation and
Heteroskedasticity in Time Series
Regressions 394
12-1 Properties of OLS with Serially Correlated
Errors 395
12-1a Unbiasedness and Consistency 395
12-1b Efficiency and Inference 395
12-1c Goodness-of-Fit 396
12-1d Serial Correlation in the Presence
of Lagged Dependent Variables 396
12-2 Serial Correlation–Robust Inference
after OLS 398
12-3 Testing for Serial Correlation 401
12-3a A t Test for AR(1) Serial Correlation with
Strictly Exogenous Regressors 402
12-3b The Durbin-Watson Test under Classical
Assumptions 403
12-3c Testing for AR(1) Serial Correlation without
Strictly Exogenous Regressors 404
12-3d Testing for Higher-Order Serial Correlation 406
12-4 Correcting for Serial Correlation with Strictly
Exogenous Regressors 407
12-4a Obtaining the Best Linear Unbiased
Estimator in the AR(1) Model 408
12-4b Feasible GLS Estimation with AR(1)
Errors 409
12-4c Comparing OLS and FGLS 411
12-4d Correcting for Higher-Order Serial
Correlation 413
12-4e What if the Serial Correlation Model Is
Wrong? 413
12-5 Differencing and Serial Correlation 414
12-6 Heteroskedasticity in Time Series
Regressions 415
12-6a Heteroskedasticity-Robust Statistics 416
12-6b Testing for Heteroskedasticity 416
12-6c Autoregressive Conditional
Heteroskedasticity 417
12-6d Heteroskedasticity and Serial Correlation in
Regression Models 418
Summary 419
Key Terms 420
Problems 420
Computer Exercises 421
Pa r t 3
chapter 13 Pooling Cross Sections across
Time: Simple Panel Data Methods 426
13-1 Pooling Independent Cross Sections across
Time 427
13-1a The Chow Test for Structural Change across
Time 431
13-2 Policy Analysis with Pooled Cross Sections 431
13-2b A General Framework for Policy Analysis
with Pooled Cross Sections 437
13-3 Two-Period Panel Data Analysis 439
13-3a Organizing Panel Data 444
13-4 Policy Analysis with Two-Period Panel
Data 444
13-5 Differencing with More Than Two Time
Periods 447
13-5a Potential Pitfalls in First Differencing Panel
Data 451
Summary 451
Key Terms 452
Problems 452
Computer Exercises 453
Data Methods 462
14-1 Fixed Effects Estimation 463
14-1a The Dummy Variable Regression 466
14-1b Fixed Effects or First Differencing? 467
14-1c Fixed Effects with Unbalanced Panels 468
14-2 Random Effects Models 469
14-2a Random Effects or Pooled OLS? 473
14-2b Random Effects or Fixed Effects? 473
14-3 The Correlated Random Effects Approach 474
14-3a Unbalanced Panels 476
14-4 General Policy Analysis with Panel Data 477
Analysis 478
14-5 Applying Panel Data Methods to Other Data
Structures 480
Summary 483
Key Terms 484
Problems 484
Computer Exercises 486
chapter 15 Instrumental Variables Estimation
and Two-Stage Least Squares 495
15-1 Motivation: Omitted Variables in a Simple
Regression Model 496
15-1a Statistical Inference with the IV
Estimator 500
15-1b Properties of IV with a Poor Instrumental
Variable 503
15-1c Computing R-Squared after IV Estimation 505
15-2 IV Estimation of the Multiple Regression
Model 505
15-3 Two-Stage Least Squares 509
15-3a A Single Endogenous Explanatory
Variable 509
15-3b Multicollinearity and 2SLS 511
15-3c Detecting Weak Instruments 512
15-3d Multiple Endogenous Explanatory
Variables 513
15-3e Testing Multiple Hypotheses after 2SLS
Estimation 513
15-4 IV Solutions to Errors-in-Variables Problems 514
15-5 Testing for Endogeneity and Testing Overidentifying
Restrictions 515
15-5a Testing for Endogeneity 515
15-5b Testing Overidentification Restrictions 516
15-6 2SLS with Heteroskedasticity 518
15-7 Applying 2SLS to Time Series Equations 519
15-8 Applying 2SLS to Pooled Cross Sections
and Panel Data 521
Summary 522
Key Terms 523
Problems 523
Computer Exercises 526
chapter 16 Simultaneous Equations
Models 534
16-1 The Nature of Simultaneous Equations
Models 535
16-2 Simultaneity Bias in OLS 538
16-3 Identifying and Estimating a Structural
Equation 539
16-3a Identification in a Two-Equation System 540
16-3b Estimation by 2SLS 543
16-4 Systems with More Than Two Equations 545
16-4a Identification in Systems with Three or More
Equations 545
16-4b Estimation 546
16-5 Simultaneous Equations Models with Time
Series 546
16-6 Simultaneous Equations Models with Panel
Data 549
Summary 551
Key Terms 552
Problems 552
Computer Exercises 555
chapter 17 Limited Dependent Variable Models
and Sample Selection Corrections 559
17-1 Logit and Probit Models for Binary
Response 560
17-1a Specifying Logit and Probit Models 560
17-1b Maximum Likelihood Estimation of Logit and
Probit Models 563
17-1c Testing Multiple Hypotheses 564
17-1d Interpreting the Logit and Probit Estimates 565
17-2 The Tobit Model for Corner Solution
Responses 571
17-2a Interpreting the Tobit Estimates 572
17-2b Specification Issues in Tobit Models 578
17-3 The Poisson Regression Model 578
17-4 Censored and Truncated Regression Models 582
17-4a Censored Regression Models 583
17-4b Truncated Regression Models 586
17-5 Sample Selection Corrections 588
17-5a When Is OLS on the Selected Sample
Consistent? 588
17-5b Incidental Truncation 589
Summary 593
Key Terms 593
Problems 594
Computer Exercises 596
chapter 18 Advanced Time Series Topics 604
18-1 Infinite Distributed Lag Models 605
18-1a The Geometric (or Koyck) Distributed Lag
Model 607
18-1b Rational Distributed Lag Models 608
18-2 Testing for Unit Roots 610
18-3 Spurious Regression 614
18-4 Cointegration and Error Correction Models 616
18-4a Cointegration 616
18-4b Error Correction Models 620
18-5 Forecasting 622
18-5a Types of Regression Models Used for
Forecasting 623
18-5e Forecasting Trending, Seasonal, and Integrated
Processes 631
Summary 635
Key Terms 636
Problems 636
Computer Exercises 638
chapter 19 Carrying Out an Empirical
Project 642
19-1 Posing a Question 642
19-2 Literature Review 644
19-3 Data Collection 645
19-3a Deciding on the Appropriate Data Set 645
19-3b Entering and Storing Your Data 646
19-3c Inspecting, Cleaning, and Summarizing Your
Data 647
19-4 Econometric Analysis 648
19-5 Writing an Empirical Paper 651
19-5a Introduction 651
19-5b Conceptual (or Theoretical)
Framework 652
19-5c Econometric Models and Estimation
Methods 652
19-5d The Data 654
19-5e Results 655
19.5f Conclusions 656
19-5g Style Hints 656
Summary 658
Key Terms 658
Sample Empirical Projects 658
List of Journals 664
Data Sources 665
Math Refresher A Basic Mathematical
Tools 666
A-1 The Summation Operator and Descriptive
Statistics 666
A-2 Properties of Linear Functions 668
A-3 Proportions and Percentages 671
A-4 Some Special Functions and Their
Properties 672
A-4b The Natural Logarithm 674
A-4c The Exponential Function 677
A-5 Differential Calculus 678
Summary 680
Key Terms 681
Problems 681
Math Refresher B Fundamentals of
Probability 684
B-1 Random Variables and Their Probability
Distributions 684
B-1a Discrete Random Variables 685
B-1b Continuous Random Variables 687
B-2 Joint Distributions, Conditional Distributions,
and Independence 688
B-2a Joint Distributions and Independence 688
B-2b Conditional Distributions 690
B-3 Features of Probability Distributions 691
B-3a A Measure of Central Tendency: The Expected
Value 691
B-3b Properties of Expected Values 692
B-3c Another Measure of Central Tendency: The
Median 694
B-3d Measures of Variability: Variance and Standard
Deviation 695
B-3e Variance 695
B-3f Standard Deviation 696
B-3g Standardizing a Random Variable 696
B-3h Skewness and Kurtosis 697
B-4 Features of Joint and Conditional
Distributions 697
B-4a Measures of Association: Covariance and
Correlation 697
B-4b Covariance 697
B-4c Correlation Coefficient 698
B-4d Variance of Sums of Random Variables 699
B-4e Conditional Expectation 700
B-4f Properties of Conditional Expectation 702
B-4g Conditional Variance 704
B-5 The Normal and Related Distributions 704
B-5a The Normal Distribution 704
B-5b The Standard Normal Distribution 705
B-5c Additional Properties of the Normal
Distribution 707
B-5d The Chi-Square Distribution 708
B-5e The t Distribution 708
B-5f The F Distribution 709
Summary 711
Key Terms 711
Problems 711
Math Refresher C Fundamentals of
Mathematical Statistics 714
C-1 Populations, Parameters, and Random
Sampling 714
C-1a Sampling 714
C-2 Finite Sample Properties of Estimators 715
C-2a Estimators and Estimates 715
C-2b Unbiasedness 716
C-2c The Sampling Variance of Estimators 718
C-2d Efficiency 719
C-3 Asymptotic or Large Sample Properties of
Estimators 721
C-3a Consistency 721
C-3b Asymptotic Normality 723
C-4 General Approaches to Parameter Estimation 724
C-4a Method of Moments 725
C-4b Maximum Likelihood 725
C-4c Least Squares 726
C-5 Interval Estimation and Confidence Intervals 727
C-5a The Nature of Interval Estimation 727
C-5b Confidence Intervals for the Mean from a Normally
Distributed Population 729
C-5c A Simple Rule of Thumb for a 95% Confidence
Interval 731
C-5d Asymptotic Confidence Intervals for Nonnormal
Populations 732
C-6 Hypothesis Testing 733
C-6a Fundamentals of Hypothesis Testing 733
C-6b Testing Hypotheses about the Mean in a Normal
Population 735
C-6c Asymptotic Tests for Nonnormal
Populations 738
C-6d Computing and Using p-Values 738
C-6e The Relationship between Confidence Intervals
and Hypothesis Testing 741
C-6f Practical versus Statistical Significance 742
C-7 Remarks on Notation 743
Summary 743
Key Terms 744
Problems 744
Advanced Treatment D Summary of Matrix
Algebra 749
D-1 Basic Definitions 749
D-2 Matrix Operations 750
D-2b Scalar Multiplication 750
D-2c Matrix Multiplication 751
D-2d Transpose 752
D-2e Partitioned Matrix Multiplication 752
D-2f Trace 753
D-2g Inverse 753
D-3 Linear Independence and Rank of a
Matrix 754
D-4 Quadratic Forms and Positive Definite
Matrices 754
D-5 Idempotent Matrices 755
D-6 Differentiation of Linear and Quadratic
Forms 755
D-7 Moments and Distributions of Random
Vectors 756
D-7a Expected Value 756
D-7b Variance-Covariance Matrix 756
D-7c Multivariate Normal Distribution 756
D-7d Chi-Square Distribution 757
D-7e t Distribution 757
D-7f F Distribution 757
Summary 757
Key Terms 757
Problems 758
Advanced Treatment E The Linear Regression
Model in Matrix Form 760
E-1 The Model and Ordinary Least
Squares Estimation 760
E-1a The Frisch-Waugh Theorem 762
E-2 Finite Sample Properties of OLS 763
E-3 Statistical Inference 767
E-4 Some Asymptotic Analysis 769
E-4a Wald Statistics for Testing Multiple
Hypotheses 771
Summary 771
Key Terms 771
Problems 772
Answers to Going Further Questions 775
Statistical Tables 784
References 791
Glossary 797
Index 812
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