Introduction to econometrics

Title:

Author:

Stock, James H.

ISBN:

9780321278876

9780321442536

Personal Author:

Stock, James H.

Edition:

2nd ed.

Publication Information:

Boston : Pearson/Addison Wesley, 2007.

Physical Description:

xlii, 796 pages : illustrations ; 24 cm.

Series:

The Addison-Wesley series in economics.

Addison-Wesley series in economics.

Subject Term:

Econometrics.

Ekonometri.

Added Author:

Watson, Mark W.

Available:*

Library	Material Type	Item Barcode	Shelf Number	Status
Searching... Pamukkale Central Library	Book	0104196	HB139 S765 2007	Searching... Unknown

To make econometrics relevant in an introductory course, interesting applications must motivate the theory and the theory must match the applications. This text aims to motivate the need for tools with concrete applications, providing simple assumptions that match the application.

Preface	p. xxvii
Part 1 Introduction and Review	p. 1
Chapter 1 Economic Questions and Data	p. 3
1.1 Economic Questions We Examine	p. 4
Question #1 Does Reducing Class Size Improve Elementary School Education?	p. 4
Question #2 Is There Racial Discrimination in the Market for Home Loans?	p. 5
Question #3 How Much Do Cigarette Taxes Reduce Smoking?	p. 5
Question #4 What Will the Rate of Inflation Be Next Year?	p. 6
Quantitative Questions, Quantitative Answers	p. 7
1.2 Causal Effects and Idealized Experiments	p. 8
Estimation of Causal Effects	p. 8
Forecasting and Causality	p. 9
1.3 Data: Sources and Types	p. 10
Experimental versus Observational Data	p. 10
Cross-Sectional Data	p. 11
Time Series Data	p. 11
Panel Data	p. 13
Chapter 2 Review of Probability	p. 17
2.1 Random Variables and Probability Distributions	p. 18
Probabilities, the Sample Space, and Random Variables	p. 18
Probability Distribution of a Discrete Random Variable	p. 19
Probability Distribution of a Continuous Random Variable	p. 21
2.2 Expected Values, Mean, and Variance	p. 23
The Expected Value of a Random Variable	p. 23
The Standard Deviation and Variance	p. 24
Mean and Variance of a Linear Function of a Random Variable	p. 25
Other Measures of the Shape of a Distribution	p. 26
2.3 Two Random Variables	p. 29
Joint and Marginal Distributions	p. 29
Conditional Distributions	p. 30
Independence	p. 34
Covariance and Correlation	p. 34
The Mean and Variance of Sums of Random Variables	p. 35
2.4 The Normal, Chi-Squared, Student t, and F Distributions	p. 39
The Normal Distribution	p. 39
The Chi-Squared Distribution	p. 43
The Student t Distribution	p. 44
The F Distribution	p. 44
2.5 Random Sampling and the Distribution of the Sample Average	p. 45
Random Sampling	p. 45
The Sampling Distribution of the Sample Average	p. 46
2.6 Large-Sample Approximations to Sampling Distributions	p. 48
The Law of Large Numbers and Consistency	p. 49
The Central Limit Theorem	p. 52
Appendix 2.1 Derivation of Results in Key Concept 2.3	p. 63
Chapter 3 Review of Statistics	p. 65
3.1 Estimation of the Population Mean	p. 66
Estimators and Their Properties	p. 67
Properties of Y	p. 68
The Importance of Random Sampling	p. 70
3.2 Hypothesis Tests Concerning the Population Mean	p. 71
Null and Alternative Hypotheses	p. 72
The p-Value	p. 72
Calculating the p-Value When [sigma subscript Y] is Known	p. 74
The Sample Variance, Sample Standard Deviation, and Standard Error	p. 75
Calculating the p-Value When [sigma subscript Y] Is Unknown	p. 76
The t-Statistic	p. 77
Hypothesis Testing with a Prespecified Significance Level	p. 78
One-Sided Alternatives	p. 80
3.3 Confidence Intervals for the Population Mean	p. 81
3.4 Comparing Means from Different Populations	p. 83
Hypothesis Tests for the Difference Between Two Means	p. 83
Confidence Intervals for the Difference Between Two Population Means	p. 84
3.5 Differences-of-Means Estimation of Causal Effects Using Experimental Data	p. 85
The Causal Effect as a Difference of Conditional Expectations	p. 85
Estimation of the Causal Effect Using Differences of Means	p. 87
3.6 Using the t-Statistic When the Sample Size Is Small	p. 88
The t-Statistic and the Student t Distribution	p. 88
Use of the Student t Distribution in Practice	p. 92
3.7 Scatterplot, the Sample Covariance, and the Sample Correlation	p. 92
Scatterplots	p. 93
Sample Covariance and Correlation	p. 94
Appendix 3.1 The U.S. Current Population Survey	p. 105
Appendix 3.2 Two Proofs That Y Is the Least Squares Estimator of [mu subscript Y]	p. 106
Appendix 3.3 A Proof That the Sample Variance Is Consistent	p. 107
Part 2 Fundamentals of Regression Analysis	p. 109
Chapter 4 Linear Regression with One Regressor	p. 111
4.1 The Linear Regression Model	p. 112
4.2 Estimating the Coefficients of the Linear Regression Model	p. 116
The Ordinary Least Squares Estimator	p. 118
OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio	p. 120
Why Use the OLS Estimator?	p. 121
4.3 Measures of Fit	p. 123
The R[superscript 2]	p. 123
The Standard Error of the Regression	p. 124
Application to the Test Score Data	p. 125
4.4 The Least Squares Assumptions	p. 126
Assumption #1 The Conditional Distribution of u[subscript i] Given X[subscript i] Has a Mean of Zero	p. 126
Assumption #2 (X[subscript i], Y[subscript i]), = 1,..., n Are Independently and Identically Distributed	p. 128
Assumption #3 Large Outliers Are Unlikely	p. 129
Use of the Least Squares Assumptions	p. 130
4.5 The Sampling Distribution of the OLS Estimators	p. 131
The Sampling Distribution of the OLS Estimators	p. 132
4.6 Conclusion	p. 135
Appendix 4.1 The California Test Score Data Set	p. 143
Appendix 4.2 Derivation of the OLS Estimators	p. 143
Appendix 4.3 Sampling Distribution of the OLS Estimator	p. 144
Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals	p. 148
5.1 Testing Hypotheses About One of the Regression Coefficients	p. 149
Two-Sided Hypotheses Concerning [Beta subscript 1]	p. 149
One-Sided Hypotheses Concerning [Beta subscript 1]	p. 153
Testing Hypotheses About the Intercept [Beta subscript 0]	p. 155
5.2 Confidence Intervals for a Regression Coefficient	p. 155
5.3 Regression When X Is a Binary Variable	p. 158
Interpretation of the Regression Coefficients	p. 158
5.4 Heteroskedasticity and Homoskedasticity	p. 160
What Are Heteroskedasticity and Homoskedasticity?	p. 160
Mathematical Implications of Homoskedasticity	p. 163
What Does This Mean in Practice?	p. 164
5.5 The Theoretical Foundations of Ordinary Least Squares	p. 166
Linear Conditionally Unbiased Estimators and the Gauss-Markov Theorem	p. 167
Regression Estimators Other Than OLS	p. 168
5.6 Using the t-Statistic in Regression When the Sample Size Is Small	p. 169
The t-Statistic and the Student t Distribution	p. 170
Use of the Student t Distribution in Practice	p. 170
5.7 Conclusion	p. 171
Appendix 5.1 Formulas for OLS Standard Errors	p. 180
Appendix 5.2 The Gauss-Markov Conditions and a Proof of the Gauss-Markov Theorem	p. 182
Chapter 6 Linear Regression with Multiple Regressors	p. 186
6.1 Omitted Variable Bias	p. 186
Definition of Omitted Variable Bias	p. 187
A Formula for Omitted Variable Bias	p. 189
Addressing Omitted Variable Bias by Dividing the Data into Groups	p. 191
6.2 The Multiple Regression Model	p. 193
The Population Regression Line	p. 193
The Population Multiple Regression Model	p. 194
6.3 The OLS Estimator in Multiple Regression	p. 196
The OLS Estimator	p. 197
Application to Test Scores and the Student-Teacher Ratio	p. 198
6.4 Measures of Fit in Multiple Regression	p. 200
The Standard Error of the Regression (SER)	p. 200
The R[superscript 2]	p. 200
The "Adjusted R[superscript 2]"	p. 201
Application to Test Scores	p. 202
6.5 The Least Squares Assumptions in Multiple Regression	p. 202
Assumption #1 The Conditional Distribution of u[subscript i] Given X[subscript 1i], X[subscript 2i],..., X[subscript ki] Has a Mean of Zero	p. 203
Assumption #2 (X[subscript 1i], X[subscript 2i],..., X[subscript ki], Y[subscript i]) i = 1,..., n Are i.i.d.	p. 203
Assumption #3 Large Outliers Are Unlikely	p. 203
Assumption #4 No Perfect Multicollinearity	p. 203
6.6 The Distribution of the OLS Estimators in Multiple Regression	p. 205
6.7 Multicollinearity	p. 206
Examples of Perfect Multicollinearity	p. 206
Imperfect Multicollinearity	p. 209
6.8 Conclusion	p. 210
Appendix 6.1 Derivation of Equation (6.1)	p. 218
Appendix 6.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors	p. 218
Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression	p. 220
7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient	p. 221
Standard Errors for the OLS Estimators	p. 221
Hypothesis Tests for a Single Coefficient	p. 221
Confidence Intervals for a Single Coefficient	p. 223
Application to Test Scores and the Student-Teacher Ratio	p. 223
7.2 Tests of Joint Hypotheses	p. 225
Testing Hypotheses on Two or More Coefficients	p. 225
The F-Statistic	p. 227
Application to Test Scores and the Student-Teacher Ratio	p. 229
The Homoskedasticity-Only F-Statistic	p. 230
7.3 Testing Single Restrictions Involving Multiple Coefficients	p. 232
7.4 Confidence Sets for Multiple Coefficients	p. 234
7.5 Model Specification for Multiple Regression	p. 235
Omitted Variable Bias in Multiple Regression	p. 236
Model Specification in Theory and in Practice	p. 236
Interpreting the R[superscript 2] and the Adjusted R[superscript 2] in Practice	p. 237
7.6 Analysis of the Test Score Data Set	p. 239
7.7 Conclusion	p. 244
Appendix 7.1 The Bonferroni Test of a Joint Hypotheses	p. 251
Chapter 8 Nonlinear Regression Functions	p. 254
8.1 A General Strategy for Modeling Nonlinear Regression Functions	p. 256
Test Scores and District Income	p. 256
The Effect on Y of a Change in X in Nonlinear Specifications	p. 260
A General Approach to Modeling Nonlinearities Using Multiple Regression	p. 264
8.2 Nonlinear Functions of a Single Independent Variable	p. 264
Polynomials	p. 265
Logarithms	p. 267
Polynomial and Logarithmic Models of Test Scores and District Income	p. 275
8.3 Interactions Between Independent Variables	p. 277
Interactions Between Two Binary Variables	p. 277
Interactions Between a Continuous and a Binary Variable	p. 280
Interactions Between Two Continuous Variables	p. 286
8.4 Nonlinear Effects on Test Scores of the Student-Teacher Ratio	p. 290
Discussion of Regression Results	p. 291
Summary of Findings	p. 295
Conclusion	p. 296
Appendix 8.1 Regression Functions That Are Nonlinear in the Parameters	p. 307
Chapter 9 Assessing Studies Based on Multiple Regression	p. 312
9.1 Internal and External Validity	p. 313
Threats to Internal Validity	p. 313
Threats to External Validity	p. 314
9.2 Threats to Internal Validity of Multiple Regression Analysis	p. 316
Omitted Variable Bias	p. 316
Misspecification of the Functional Form of the Regression Function	p. 319
Errors-in-Variables	p. 319
Sample Selection	p. 322
Simultaneous Causality	p. 324
Sources of Inconsistency of OLS Standard Errors	p. 325
9.3 Internal and External Validity When the Regression Is Used for Forecasting	p. 327
Using Regression Models for Forecasting	p. 327
Assessing the Validity of Regression Models for Forecasting	p. 328
9.4 Example: Test Scores and Class Size	p. 329
External Validity	p. 329
Internal Validity	p. 336
Discussion and Implications	p. 337
9.5 Conclusion	p. 338
Appendix 9.1 The Massachusetts Elementary School Testing Data	p. 344
Part 3 Further Topics in Regression Analysis	p. 347
Chapter 10 Regression with Panel Data	p. 349
10.1 Panel Data	p. 350
Example: Traffic Deaths and Alcohol Taxes	p. 351
10.2 Panel Data with Two Time Periods: "Before and After" Comparisons	p. 353
10.3 Fixed Effects Regression	p. 356
The Fixed Effects Regression Model	p. 356
Estimation and Inference	p. 359
Application to Traffic Deaths	p. 360
10.4 Regression with Time Fixed Effects	p. 361
Time Effects Only	p. 361
Both Entity and Time Fixed Effects	p. 362
10.5 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression	p. 364
The Fixed Effects Regression Assumptions	p. 364
Standard Errors for Fixed Effects Regression	p. 366
10.6 Drunk Driving Laws and Traffic Deaths	p. 367
10.7 Conclusion	p. 371
Appendix 10.1 The State Traffic Fatality Data Set	p. 378
Appendix 10.2 Standard Errors for Fixed Effects Regression with Serially Correlated Errors	p. 379
Chapter 11 Regression with a Binary Dependent Variable	p. 383
11.1 Binary Dependent Variables and the Linear Probability Model	p. 384
Binary Dependent Variables	p. 385
The Linear Probability Model	p. 387
11.2 Probit and Logit Regression	p. 389
Probit Regression	p. 389
Logit Regression	p. 394
Comparing the Linear Probability, Probit, and Logit Models	p. 396
11.3 Estimation and Inference in the Logit and Probit Models	p. 396
Nonlinear Least Squares Estimation	p. 397
Maximum Likelihood Estimation	p. 398
Measures of Fit	p. 399
11.4 Application to the Boston HMDA Data	p. 400
11.5 Summary	p. 407
Appendix 11.1 The Boston HMDA Data Set	p. 415
Appendix 11.2 Maximum Likelihood Estimation	p. 415
Appendix 11.3 Other Limited Dependent Variable Models	p. 418
Chapter 12 Instrumental Variables Regression	p. 421
12.1 The IV Estimator with a Single Regressor and a Single Instrument	p. 422
The IV Model and Assumptions	p. 422
The Two Stage Least Squares Estimator	p. 423
Why Does IV Regression Work?	p. 424
The Sampling Distribution of the TSLS Estimator	p. 428
Application to the Demand for Cigarettes	p. 430
12.2 The General IV Regression Model	p. 432
TSLS in the General IV Model	p. 433
Instrument Relevance and Exogeneity in the General IV Model	p. 434
The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator	p. 434
Inference Using the TSLS Estimator	p. 437
Application to the Demand for Cigarettes	p. 437
12.3 Checking Instrument Validity	p. 439
Assumption #1 Instrument Relevance	p. 439
Assumption #2 Instrument Exogeneity	p. 443
12.4 Application to the Demand for Cigarettes	p. 445
12.5 Where Do Valid Instruments Come From?	p. 450
Three Examples	p. 451
12.6 Conclusion	p. 455
Appendix 12.1 The Cigarette Consumption Panel Data Set	p. 462
Appendix 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4)	p. 462
Appendix 12.3 Large-Sample Distribution of the TSLS Estimator	p. 463
Appendix 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid	p. 464
Appendix 12.5 Instrumental Variables Analysis with Weak Instruments	p. 466
Chapter 13 Experiments and Quasi-Experiments	p. 468
13.1 Idealized Experiments and Causal Effects	p. 470
Ideal Randomized Controlled Experiments	p. 470
The Differences Estimator	p. 471
13.2 Potential Problems with Experiments in Practice	p. 472
Threats to Internal Validity	p. 472
Threats to External Validity	p. 475
13.3 Regression Estimators of Causal Effects Using Experimental Data	p. 477
The Differences Estimator with Additional Regressors	p. 477
The Differences-in-Differences Estimator	p. 480
Estimation of Causal Effects for Different Groups	p. 484
Estimation When There Is Partial Compliance	p. 484
Testing for Randomization	p. 485
13.4 Experimental Estimates of the Effect of Class Size Reductions	p. 486
Experimental Design	p. 486
Analysis of the STAR Data	p. 487
Comparison of the Observational and Experimental Estimates of Class Size Effects	p. 492
13.5 Quasi-Experiments	p. 494
Examples	p. 495
Econometric Methods for Analyzing Quasi-Experiments	p. 497
13.6 Potential Problems with Quasi-Experiments	p. 500
Threats to Internal Validity	p. 500
Threats to External Validity	p. 502
13.7 Experimental and Quasi-Experimental Estimates in Heterogeneous Populations	p. 502
Population Heterogeneity: Whose Causal Effect?	p. 502
OLS with Heterogeneous Causal Effects	p. 503
IV Regression with Heterogeneous Causal Effects	p. 504
13.8 Conclusion	p. 507
Appendix 13.1 The Project STAR Data Set	p. 516
Appendix 13.2 Extension of the Differences-in-Differences Estimator to Multiple Time Periods	p. 517
Appendix 13.3 Conditional Mean Independence	p. 518
Appendix 13.4 IV Estimation When the Causal Effect Varies Across Individuals	p. 520
Part 4 Regression Analysis of Economic Time Series Data	p. 523
Chapter 14 Introduction to Time Series Regression and Forecasting	p. 525
14.1 Using Regression Models for Forecasting	p. 527
14.2 Introduction to Time Series Data and Serial Correlation	p. 528
The Rates of Inflation and Unemployment in the United States	p. 528
Lags, First Differences, Logarithms, and Growth Rates	p. 528
Autocorrelation	p. 532
Other Examples of Economic Time Series	p. 533
14.3 Autoregressions	p. 535
The First Order Autoregressive Model	p. 535
The p[superscript th] Order Autoregressive Model	p. 538
14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model	p. 541
Forecasting Changes in the Inflation Rate Using Past Unemployment Rates	p. 541
Stationarity	p. 544
Time Series Regression with Multiple Predictors	p. 545
Forecast Uncertainty and Forecast Intervals	p. 548
14.5 Lag Length Selection Using Information Criteria	p. 549
Determining the Order of an Autoregression	p. 551
Lag Length Selection in Time Series Regression with Multiple Predictors	p. 553
14.6 Nonstationarity I: Trends	p. 554
What Is a Trend?	p. 555
Problems Caused by Stochastic Trends	p. 557
Detecting Stochastic Trends: Testing for a Unit AR Root	p. 560
Avoiding the Problems Caused by Stochastic Trends	p. 564
14.7 Nonstationarity II: Breaks	p. 565
What Is a Break?	p. 565
Testing for Breaks	p. 566
Pseudo Out-of-Sample Forecasting	p. 571
Avoiding the Problems Caused by Breaks	p. 576
14.8 Conclusion	p. 577
Appendix 14.1 Time Series Data Used in Chapter 14	p. 586
Appendix 14.2 Stationarity in the AR(1) Model	p. 586
Appendix 14.3 Lag Operator Notation	p. 588
Appendix 14.4 ARMA Models	p. 589
Appendix 14.5 Consistency of the BIC Lag Length Estimator	p. 589
Chapter 15 Estimation of Dynamic Causal Effects	p. 591
15.1 An Initial Taste of the Orange Juice Data	p. 593
15.2 Dynamic Causal Effects	p. 595
Causal Effects and Time Series Data	p. 596
Two Types of Exogeneity	p. 598
15.3 Estimation of Dynamic Causal Effects with Exogenous Regressors	p. 600
The Distributed Lag Model Assumptions	p. 601
Autocorrelated u[subscript t], Standard Errors, and Inference	p. 601
Dynamic Multipliers and Cumulative Dynamic Multipliers	p. 602
15.4 Heteroskedasticity- and Autocorrelation-Consistent Standard Errors	p. 604
Distribution of the OLS Estimator with Autocorrelated Errors	p. 604
HAC Standard Errors	p. 606
15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors	p. 608
The Distributed Lag Model with AR(1) Errors	p. 609
OLS Estimation of the ADL Model	p. 612
GLS Estimation	p. 613
The Distributed Lag Model with Additional Lags and AR(p) Errors	p. 615
15.6 Orange Juice Prices and Cold Weather	p. 618
15.7 Is Exogeneity Plausible? Some Examples	p. 624
U.S. Income and Australian Exports	p. 625
Oil Prices and Inflation	p. 626
Monetary Policy and Inflation	p. 626
The Phillips Curve	p. 627
15.8 Conclusion	p. 627
Appendix 15.1 The Orange Juice Data Set	p. 634
Appendix 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation	p. 634
Chapter 16 Additional Topics in Time Series Regression	p. 637
16.1 Vector Autoregressions	p. 638
The VAR Model	p. 638
A VAR Model of the Rates of Inflation and Unemployment	p. 641
16.2 Multiperiod Forecasts	p. 642
Iterated Muliperiod Forecasts	p. 643
Direct Multiperiod Forecasts	p. 645
Which Method Should You Use?	p. 647
16.3 Orders of Integration and the DF-GLS Unit Root Test	p. 648
Other Models of Trends and Orders of Integration	p. 648
The DF-GLS Test for a Unit Root	p. 650
Why Do Unit Root Tests Have Non-normal Distributions?	p. 653
16.4 Cointegration	p. 655
Cointegration and Error Correction	p. 655
How Can You Tell Whether Two Variables Are Cointegrated?	p. 658
Estimation of Cointegrating Coefficients	p. 660
Extension to Multiple Cointegrated Variables	p. 661
Application to Interest Rates	p. 662
16.5 Volatility Clustering and Autoregressive Conditional Heteroskedasticity	p. 664
Volatility Clustering	p. 665
Autoregressive Conditional Heteroskedasticity	p. 666
Application to Stock Price Volatility	p. 667
16.6 Conclusion	p. 669
Appendix 16.1 U.S. Financial Data Used in Chapter 16	p. 674
Part 5 The Econometric Theory of Regression Analysis	p. 675
Chapter 17 The Theory of Linear Regression with One Regressor	p. 677
17.1 The Extended Least Squares Assumptions and the OLS Estimator	p. 678
The Extended Least Squares Assumptions	p. 678
The OLS Estimator	p. 680
17.2 Fundamentals of Asymptotic Distribution Theory	p. 680
Convergence in Probability and the Law of Large Numbers	p. 681
The Central Limit Theorem and Convergence in Distribution	p. 683
Slutsky's Theorem and the Continuous Mapping Theorem	p. 685
Application to the t-Statistic Based on the Sample Mean	p. 685
17.3 Asymptotic Distribution of the OLS Estimator and t-Statistic	p. 686
Consistency and Asymptotic Normality of the OLS Estimators	p. 686
Consistency of Heteroskedasticity-Robust Standard Errors	p. 686
Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic	p. 688
17.4 Exact Sampling Distributions When the Errors Are Normally Distributed	p. 688
Distribution of [Beta subscript 1] with Normal Errors	p. 688
Distribution of the Homoskedasticity-only t-Statistic	p. 690
17.5 Weighted Least Squares	p. 691
WLS with Known Heteroskedasticity	p. 691
WLS with Heteroskedasticity of Known Functional Form	p. 692
Heteroskedasticity-Robust Standard Errors or WLS?	p. 695
Appendix 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables	p. 700
Appendix 17.2 Two Inequalities	p. 702
Chapter 18 The Theory of Multiple Regression	p. 704
18.1 The Linear Multiple Regression Model and OLS Estimator in Matrix Form	p. 706
The Multiple Regression Model in Matrix Notation	p. 706
The Extended Least Squares Assumptions	p. 707
The OLS Estimator	p. 708
18.2 Asymptotic Distribution of the OLS Estimator and t-Statistic	p. 710
The Multivariate Central Limit Theorem	p. 710
Asymptotic Normality of [Beta]	p. 710
Heteroskedasticity-Robust Standard Errors	p. 711
Confidence Intervals for Predicted Effects	p. 712
Asymptotic Distribution of the t-Statistic	p. 713
18.3 Tests of Joint Hypotheses	p. 713
Joint Hypotheses in Matrix Notation	p. 713
Asymptotic Distribution of the F-Statistic	p. 714
Confidence Sets for Multiple Coefficients	p. 714
18.4 Distribution of Regression Statistics with Normal Errors	p. 715
Matrix Representations of OLS Regression Statistics	p. 715
Distribution of [Beta] with Normal Errors	p. 716
Distribution of [Characters not reproducible]	p. 717
Homoskedasticity-Only Standard Errors	p. 717
Distribution of the t-Statistic	p. 718
Distribution of the F-Statistic	p. 718
18.5 Efficiency of the OLS Estimator with Homoskedastic Errors	p. 719
The Gauss-Markov Conditions for Multiple Regression	p. 719
Linear Conditionally Unbiased Estimators	p. 719
The Gauss-Markov Theorem for Multiple Regression	p. 720
18.6 Generalized Least Squares	p. 721
The GLS Assumptions	p. 722
GLS When [Omega] Is Known	p. 724
GLS When [Omega] Contains Unknown Parameters	p. 725
The Zero Conditional Mean Assumption and GLS	p. 725
18.7 Instrumental Variables and Generalized Method of Moments Estimation	p. 727
The IV Estimator in Matrix Form	p. 728
Asymptotic Distribution of the TSLS Estimator	p. 729
Properties of TSLS When the Errors Are Homoskedastic	p. 730
Generalized Method of Moments Estimation in Linear Models	p. 733
Appendix 18.1 Summary of Matrix Algebra	p. 743
Appendix 18.2 Multivariate Distributions	p. 747
Appendix 18.3 Derivation of the Asymptotic Distribution of [Beta]	p. 748
Appendix 18.4 Derivations of Exact Distributions of OLS Test Statistics with Normal Errors	p. 749
Appendix 18.5 Proof of the Gauss-Markov Theorem for Multiple Regression	p. 751
Appendix 18.6 Proof of Selected Results for IV and GMM Estimation	p. 752
Appendix	p. 755
References	p. 763
Answers to "Review the Concepts" Questions	p. 767
Glossary	p. 775
Index	p. 783

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