TY - BOOK AU - Stock,James H. AU - Watson,Mark W. TI - Introduction to econometrics: 2nd edition SN - 0321442539 (alk. paper) U1 - 330.028 22 PY - 2007/// CY - Boston PB - Pearson/Addison Wesley KW - Econometrics N1 - Contents Preface xxvii Part One Introduction and Review 1 Chapter 1 Economic Questions and Data 3 1.1 Economic Questions We Examine 4 Question #1: Does Reducing Class Size Improve Elementary School Education? 4 Question #2: Is There Racial Discrimination in the Market for Home Loans? 5 Question #3: How Much Do Cigarette Taxes Reduce Smoking? 5 Question #4: What Will the Rate of Inflation Be Next Year? 6 Quantitative Questions, Quantitative Answers 7 1.2 Causal Effects and Idealized Experiments 8 Estimation of Causal Effects 8 Forecasting and Causality 9 1.3 Data: Sources and Types 10 Experimental versus Observational Data 10 Cross-Sectional Data 11 Time Series Data 11 Panel Data 13 Chapter 2 Review of Probability 17 2.1 Random Variables and Probability Distributions 18 Probabilities, the Sample Space, and Random Variables 18 Probability Distribution of a Discrete Random Variable 19 Probability Distribution of a Continuous Random Variable 21 2.2 Expected Values, Mean, and Variance 23 The Expected Value of a Random Variable 23 The Standard Deviation and Variance 24 Mean and Variance of a Linear Function of a Random Variable 25 Other Measures of the Shape of a Distribution 26 2.3 Two Random Variables 29 Joint and Marginal Distributions 29 Conditional Distributions 30 Independence 34 Covariance and Correlation 34 The Mean and Variance of Sums of Random Variables 32 2.4 The Normal, Chi-Squared,Student t and F Distributions 39 The Normal Distribution 39 The Chi-Squared Distributions 43 The Student t Distribution 44 F Distributions 44 2.5 Random Sampling and the Distribution of the Sample Average 45 Random Sampling 45 The Sampling Distribution of the Sample Average 46 2.6 Large-Sample Approximations to Sampling Distributions 48 The Law of Large Numbers and Consistency 49 The Central Limit Theorem 52 Appendix 2.1 Derivation of Results in Key Concept 2.3 63 Chapter 3 Review of Statistics 65 3.1 Estimation of the Population Mean 66 Estimators and Their Properties 67 Properties of C 68 The Importance of Random Sampling 70 3.2 Hypothesis Tests Concerning the Population Mean 71 Null and Alternative Hypotheses 71 The p-Value 71 Calculating the p-Value When sY Is Known 74 The Sample Variance, Sample Standard Deviation, and Standard Error 75 Calculating the p-Value When sY Is Unknown 76 The t-Statistic 77 Hypothesis Testing with a Prespecified Significance Level 78 One-Sided Alternatives 80 3.3 Confidence Intervals for the Population Mean 81 3.4 Comparing Means from Different Populations 83 Hypothesis Tests for the Difference Between Two Means 83 Confidence Intervals for the Difference Between Two Population Means 84 3.5 Differences-ofMeans Estimation of Causal Effects Using Experimental Data 85 The Causal Effect as a Difference of Conditional Expectations 85 Estimation of the Causal Efect Using Differences of Means 87 3.6 Unsing the t-Statistic When the Sample Size Is Small 88 Scatterplots, the Sample Covariance, and the Sample Correlation 92 Scatterplots 93 Sample Covariance and Correlation 94 Appendix 3.1 The U.S. Current Population Survey 105 Appendix 3.2 Two Proofs That Is the Least Squares Estimator of mY 106 Appendix 3.3 A Proof That the Sample Variance Is Consistent 107 Part Two Fundamentals of Regression Analysis 109 Chapter 4 Linear Regression with One Regressor 111 4.1 The Linear Regression Model 112 4.2 Estimating the Coefficients of the Linear Regression Model 116 The Ordinary Least Squares Estimator 118 OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio 120 Why Use the OLS Estimator? 121 4.3 Measure of Fit 123 The R2 123 The Standard Error of the Regression 124 Application to the Test Score Data 125 4.4 The Least Squares Assumptions 126 Assumption #1: The Conditional Distribution of ui Given Xi Has a Mean of Zero 126 Assumption #2: (Xi,Yi), i 5 1, . . . , n Are Independently and Identically Distributed 128 Assumption #3: Large Outliers Are Im;ole;y 129 Use of the Least Squares Assumptions 130 The Sampling Distribution of the OLS Estimators 132 4.5 Testing Hypotheses About One of the Regression Coefficients 110 Two-Sided Hypotheses Concerning b1 111 One-Sided Hypotheses Concerning b1 114 Testing Hypotheses About the Intercept b0 116 4.6 Conclusion 135 Appendix 4.1 The California Test Score Data Set 143 Appendix 4.2 Derivation of the OLS Estimators 143 Appendix 4.3 Sampling Distribution of the OLS Estimator 144 Chapter 5 Regression with a Single Regressors: Hypothesis Tests and Confidence Intervals 148 5.1 Testing Hypotheses About One of the Regression Coefficients 149 Two-Sides Conerning B1 149 One-Sided Hypotheses Concerning B1 153 Testing Hypotheses About the Intercept B0 155 5.2 Confidence Intervals for a Regression Coefficient 155 5.3 Regression When X Is a Binary Variable 158 Interpretation of the RegressionCoefficients 158 5.4 Heteroskedasticity and Homoskedasticity 160 What are Heteroskedasticity and Homoskedasticity? 160 Mathematical Implications of Homoskedasticity? 163 What Does This Mean in Practice? 164 5.5 The Theorectical Foundations of Ordinary Least Squares 166 Linear Conditionlly Unbiased Estimators and the Gauss-Markov Theorem 167 Regression Estimators Other Than OLS 168 5.6 Using the t-Statistic in Regression When the Sample Size Is Small 169 The t-Statistic and the Student t Distribution 170 Use of the Student t Distribution in Pratice 171 5.7 Conclusion 171 Appendix 5.1 Formulas for OLS Standard Errorsr 180 Heteroskedasticity-Robust Standard Errors 180 Homoskedassticity-Only Variances 181 Homoskedasticity-Only Standard Errors 181 Appendix 5.2 The Gauss-Markiv Conditions and a Proof of the Gauss-Markov Theorem 182 IThe Gauss-Markov Conditions 182 The OLS Estimator B1 Is a Linear Conditionally Unbiased Estimator. 183 Proof of the Gquss-Markov Theorem 183 The Gauss-Markov Theorem When X is Nonrandom 184 The Sample Average is the Efficient Linear Estimator of E(Y) Chapter 6 Linear Regression with Multiple Regressors 186 6.1 Omitted Variable Bias 186 Definition of Omitted Variable Bias 187 A Formula for Omitted Variable Bias 189 Addressing Omitted Variable Bias by Dividing the Data into Groups 191 6.2 The Multiple Regression Model 193 The Population Regression Line 193 The Population Multiple Regression Model 194 6.3 The OLS Estimator in Multiple Regression 196 The OLS Estimator 197 Application to Test Scores and the Student-Teacher Ratio 198 6.4 Measures of Fit in Multiple Regression 200 The Standard Error of the Regression (SER) 200 The R2 200 The "Adusted R2" 201 Application to Test Scores 202 6.5 The Least Squares Assumptions in Multiple Regression 202 Assumpion #1: The Conditional Distribution of ui Given X1i, X2i, . . . , Xki Has a Mean of Zero 203 Assumption #2: (X1i, X2i, . . . , Xki, Yi), i 5 1, . . . , n Are i.i.d. 203 Assumption #3: Large Outliers Are Unlikely 203 Assumption #4: No Perfect Multicollinearity 203 6.6 The Distribution of the OLS Estimators in Multiple Regression 205 6.7 Multicollinearity 206 Examples of Perfect Multicollinearity 206 Imperfect Multicollinearity 209 6.8 Conclusion 210 Appendix 5.1 Derivation of Equation (6.1) 218 Appendix 5.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors 218 Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression 220 7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient 221 Standard Errors for the OLS Estimators 221 Hypothesis Tests for a Single Coefficient 221 Confidence Intervals for a Single Coefficient 223 Application to Test Scores and the Student-Teacher Ratio 229 The Homoskedasticity-Only F-Statistic 230 7.2 Tests of Joint Hypotheses 225 Testing Hypotheses on Two or More Coefficients 225 The F-Statistic 227 Polynomial and Logarithmic Models of Test Scores and District Income 216 7.3 Testing Single Restrictions Involving Multiple Coefficients 232 7.4 Confidence Sets for Multiple Coefficients 230 7.5 Model Specification for Multiple Regression 235 Omitted Variable Bias in Multiple Regression 236 Model Specification in Theory and in Practice 236 Interpreting the R2 and the Adjusted R2 in Practice 237 7.6 Analysis of the Test Score Data Set 239 7.7 Conclusion 244 Appendix 7.1 The Bonerroni Test of a Joint Hypotheses 251 Bonferroni's Inequality 251 Bonifferroni Tests 252 Application to Test Scores 253 Chapter 8 Nonlinear Regression Functions 254 8.1 A General Strategy for Modeling Nonlinear Regression Functions 256 Test Scores and District Income 256 The Effect on Y of a Change in X in Nonlinear Specifications 260 A General Approach to Modeling Nonlinearities Using Multiple Regression 264 8.2 Nonlinear Functions of a Single Independent Variable 264 Polynomials 265 Logarithms 267 Polynomial and Logarithmic Models of Test Scores and District Income 275 8.3 Interactions Between Independent Variables 277 Interactions Between Two Binary Variables 277 Interactions Between a Continuous and a Binary Variable 280 Interactions Between Two Continuous Variables 286 8.4 Nonlinear Effects on Test Scores of the Student-Teacher Ratio 290 Discussion of Regression Results 291 Summary of Findings 295 8.5 Conclusion 296 Appendix 8.1 Regression Functions That Are Nonlinear in the Parameters 307 Functions That Are Nonlinear in the Parameters 307 Nonlinear Least Squares Estimation 309 Application to the Tet Score-Income Relation 310 Chapter 9 Assessing Studies Based on Multiple Regression 312 9.1 Internal and External Validity 313 Threats to Internal Validity 313 Threats to External Validity 314 9.2 Threats to Internal Validity of Multiple Regression Analysis 316 Omitted Variable Bias 316 Misspecification of the Functional Form of the Regression Function 319 Errors-in-Variables 319 Sample Selection 322 Simultaneous Causality 324 Sources of Inconsistency of OLS Standard Errors 325 9.3 Internal and External ValidityWhen the Regression Is Used for Forecasting 327 Using Regression Models for Forecasting 327 Assessing the Validity of Regression Models for Forecasting 328 9.4 Example: Test Scores and Class Size 329 External Validity 329 Internal Validity 336 Discussion and Implications 337 9.5 Conclusion 338 Appendix 9.1 The Massachusetts Elementary School Testing Data 344 Part Three Further Topics in Regression Analysis 347 Chapter 10 Regression with Panel Data 349 10.1 Panel Data 350 Example: Traffic Deaths and Alcohol Taxes 351 10.2 Panel Data with Two Time Periods: "Before and After" Comparisons 353 10.3 Fixed Effects Regression 356 The Fixed Effects Regression Model 356 Estimation and Inference 359 Application to Traffic Deaths 360 10.4 Regression with Time Fixed Effects 361 Time Effects Only 361 Both Entity and Time and Fixed Effects 362 10.5 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regresstion 364 The Fixed Effects Regression Assumptions 364 Standard Errors for Fixed Effects Regression 366 10.6 Drunk Driving Laws and Traffic Deaths 367 10.7 Conclusion 371 Appendix 10.1 The State Traffic Fatality Data Set 378 Appendix 10.2 Standard Errors for Fixed Effects Regression with Serially Correlated Errors 379 Chapter 11 Regression with a Binary Dependent Variable 383 11.1 Binary Dependent Variables and the Linear Probability Model 384 Binary Dependent Variables 385 The Linear Probability Model 387 11.2 Probit and Logit Regression 389 Probit Regression 389 Logit Regression 394 Comparing the Linear Probability, Probit, and Logit Models 396 11.3 Estimation and Inference in the Logit and Probit Models 396 Nonlinear Least Squares Estimation 397 Maximum Likelihood Estimation 398 Measures of Fit 399 11.4 Application to the Boston HMDA Data 400 11.5 Summary 408 Appendix 11.1 The Boston HMDA Data Set 415 Appendix 11.2 Maximum Likelihood Estimation 415 Appendix 11.3 Other Limited Dependent Variable Models 418 Chapter 12 Instrumental Variables Regression 421 12.1 The IV Estimator with a Single Regressor and a Single Instrument 422 The IV Model and Assumptions 422 The Two-Stage Least Squares Estimator 423 Why Does IV Regression Work? 424 The Sampling Distribution of the TSLS Estimator 428 Application to the Demand for Cigarettes 430 12.2 The General IV Regression Model 432 TSLS in the General IV Model 433 Instrument Relevance and Exogeneity in the General IV Model 434 The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator 434 Inference Using the TSLS Estimator 437 Application to the Demand for Cigarettes 437 12.3 Checking Instrument Validity 439 Assumption #1: Instrument Relevance 439 Assumption #2: Instrument Exogeneity 443 12.4 Application to the Demand for Cigarettes 445 12.5 Where Do Valid Instruments Come From? 450 Three Examples 451 12.6 Conclusion 455 Appendix 12.1 The Cigarette Consumption Panel Data Set 462 Appendix 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4) 462 Appendix 12.3 Large-Sample Distribution of the TSLS Estimator 463 Appendix 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid 464 Appendix 12.5 Instrumental Variables Analysis with Weak Instruments 466 Chapter 13 Experiments and Quasi-Experiments 468 13.1 Idealized Experiments and Causal Effects 470 Ideal Randomized Controlled Experiments 470 The Differences Estimator 471 13.2 Potential Problems with Experiments in Practice 472 Threats to Internal Validity 472 Threats to External Validity 475 13.3 Regression Estimators of Causal Effects Using Experimental Data 477 The Differences Estimator with Additional Regressors 477 The Differences-in-Differences Estimator 480 Estimation of Causal Effects for Different Groups 484 Estimation When There Is Partial Compliance 484 Testing for Randomization 485 13.4 Experimental Estimates of the Effect of Class Size Reductions 486 Experimental Design 486 Analysis of the STAR Data 487 Comparison of the Observational and Experimental Estimates of Class Size Effects 492 13.5 Quasi-Experiments 494 Examples 495 Econometric Methods for Analyzing Quasi-Experiments 497 13.6 Potential Problems with Quasi-Experiments 500 Threats to Internal Validity 500 Threats to External Validity 502 13.7 Experimental and Quasi-Experimental Estimates in Heterogeneous Populations 502 Population Heterogeneity: Whose Causal Effect? 502 OLS with Heterogeneous Causal Effects 503 IV Regression with Heterogeneous Causal Effects 504 13.8 Conclusion 507 Appendix 13.1 The Project STAR Data Set 516 Appendix 13.2 Extension of the Differences-in-Differences Estimator to Multiple Time Periods 517 Appendix 13.3 Conditional Mean Independence 518 Appendix 13.4 IV Estimation When the Causal Effect Varies Across Individuals 520 Part Four Regression Analysis of Economic Time Series Data 523 Chapter 14 Introduction to Time Series Regression and Forecasting 525 14.1 Using Regression Models for Forecasting 527 14.2 Introduction to Time Series Data and Serial Correlation 528 The Rates of Inflation and Unemployment in the United States 528 Lags, First Differences, Logarithms, and Growth Rates 528 Autocorrelation 532 Other Examples of Economic Time Series 533 14.3 Autoregressions 535 The First Order Autoregressive Model 535 The pth Order Autoregressive Model 538 14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model 540 Forecasting Changes in the Inflation Rate Using Past Unemployment Rates 540 Stationarity 544 Time Series Regression with Multiple Predictors 544 Forecast Uncertainty and Forecast Intervals 548 14.5 Lag Length Selection Using Information Criteria 549 Determining the Order of an Autoregression 551 Lag Length Selection in Time Series Regression with Multiple Predictors 553 14.6 Nonstationarity I: Trends 554 What Is a Trend? 555 Problems Caused by Stochastic Trends 557 Detecting Stochastic Trends: Testing for a Unit AR Root 560 Avoiding the Problems Caused by Stochastic Trends 565 14.7 Nonstationarity II: Breaks 565 What Is a Break? 565 Testing for Breaks 566 Pseudo Out-of-Sample Forecasting 571 Avoiding the Problems Caused by Breaks 576 14.8 Conclusion 577 Appendix 14.1 Time Series Data Used in Chapter 14 586 Appendix 14.2 Stationarity in the AR(1) Model 586 Appendix 14.3 Lag Operator Notation 588 Appendix 14.4 ARMA Models 589 Appendix 14.5 Consistency of the BIC Lag Length Estimator 589 Chapter 15 Estimation of Dynamic Causal Effects 591 15.1 An Initial Taste of the Orange Juice Data 592 15.2 Dynamic Causal Effects 595 Causal Effects and Time Series Data 596 Two Types of Exogeneity 598 15.3 Estimation of Dynamic Causal Effects with Exogenous Regressors 600 The Distributed Lag Model Assumptions 601 Autocorrelated ut, Standard Errors, and Inference 601 Dynamic Multipliers and Cumulative Dynamic Multipliers 602 15.4 Heteroskedasticity- and Autocorrelation-Consistent Standard Errors 604 Distribution of the OLS Estimator with Autocorrelated Errors 604 HAC Standard Errors 606 15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors 608 The Distributed Lag Model with AR(1) Errors 609 OLS Estimation of the ADL Model 612 GLS Estimation 613 The Distributed Lag Model with Additional Lags and AR(p) Errors 615 15.6 Orange Juice Prices and Cold Weather 618 15.7 Is Exogeneity Plausible? Some Examples 624 U.S. Income and Australian Exports 625 Oil Prices and Inflation 626 Monetary Policy and Inflation 626 The Phillips Curve 627 15.8 Conclusion 627 Appendix 15.1 The Orange Juice Data Set 634 Appendix 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation 634 Chapter 16 Additional Topics in Time Series Regression 533 16.1 Vector Autoregressions 534 The VAR Model 534 A VAR Model of the Rates of Inflation and Unemployment 537 16.2 Multiperiod Forecasts 538 Multiperiod Forecasting: Univariate Autoregressions 539 Multiperiod Forecasting: Multivariate Forecasts 542 Which Method Should You Use? 544 16.3 Orders of Integration and Another Unit Root Test 545 Other Models of Trends and Orders of Integration 546 The DF-GLS Test for a Unit Root 547 Why Do Unit Root Tests Have Nonnormal Distributions? 551 16.4 Cointegration 552 Cointegration and Error Correction 552 How Can You Tell Whether Two Variables Are Cointegrated? 554 Estimation of Cointegrating Coefficients 556 Extension to Multiple Cointegrated Variables 558 Application to Interest Rates 559 16.5 Conditional Heteroskedasticity 561 Volatility Clustering 562 Autoregressive Conditional Heteroskedasticity 563 Application to Inflation Forecasts 564 16.6 Conclusion 566 Appendix 16.1 U.S. Financial Data Used in Chapter 14 569 Part Five The Econometric Theory of Regression Analysis 571 Chapter 17 The Theory of Linear Regression with One Regressor 573 17.1 The Extended Least Squares Assumptions and the OLS Estimator 575 The Extended Least Squares Assumptions 575 The OLS Estimator 576 17.2 Fundamentals of Asymptotic Distribution Theory 577 Convergence in Probability and the Law of Large Numbers 577 The Central Limit Theorem and Convergence in Distribution 580 Slutsky's Theorem and the Continuous Mapping Theorem 581 Application to the t-Statistic Based on the Sample Mean 582 17.3 Asymptotic Distribution of the OLS Estimator and t-Statistic 582 Consistency and Asymptotic Normality of the OLS Estimators 583 Consistency of Heteroskedasticity-Robust Standard Errors 583 Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic 584 17.4 Exact Sampling Distributions When the Errors Are Normally Distributed 585 Distribution of with Normal Errors 585 Distribution of the Homoskedasticity-only t-Statistic 586 17.5 Efficiency of the OLS Estimator with Homoskedastic Errors 588 The Gauss-Markov Conditions 588 Linear Conditionally Unbiased Estimators 589 The Gauss-Markov Theorem 590 17.6 Weighted Least Squares 591 WLS with Known Heteroskedasticity 592 WLS with Heteroskedasticity of Known Functional Form 593 Heteroskedasticity-Robust Standard Errors or WLS? 596 Appendix 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables 600 Appendix 17.2 Two Inequalities 603 Appendix 17.3 Proof of the Gauss-Markov Theorem 604 Chapter 18 The Theory of Multiple Regression 606 18.1 The Linear Multiple Regression Model and OLS Estimator in Matrix Form 607 The Multiple Regression Model in Matrix Notation 607 The Extended Least Squares Assumptions 609 The OLS Estimator 610 18.2 Asymptotic Distribution of the OLS Estimator and t-Statistic 611 The Multivariate Central Limit Theorem 612 Asymptotic Normality of 612 Heteroskedasticity-Robust Standard Errors 613 Confidence Intervals for Predicted Effects 614 Asymptotic Distribution of the t-Statistic 615 18.3 Tests of Joint Hypotheses 615 Joint Hypotheses in Matrix Notation 615 Asymptotic Distribution of the F-Statistic 616 Confidence Sets for Multiple Coefficients 616 18.4 Distribution of Regression Statistics with Normal Errors 617 Matrix Representations of OLS Regression Statistics 617 Distribution of with Normal Errors 619 Distribution of 619 Homoskedasticity-Only Standard Errors 619 Distribution of the t-Statistic 621 Distribution of the F-Statistic 621 18.5 Efficiency of the OLS Estimator with Homoskedastic Errors 621 The Gauss-Markov Conditions for Multiple Regression 621 Linear Conditionally Unbiased Estimators 622 The Gauss-Markov Theorem for Multiple Regression 622 18.6 Generalized Least Squares 623 The GLS Assumptions 624 GLS When W Is Known 626 GLS When W Contains Unknown Parameters 627 The Zero Conditional Mean Assumption and GLS 628 Appendix 18.1 Summary of Matrix Algebra 634 Appendix 18.2 Multivariate Distributions 637 Appendix 18.3 Derivation of the Asymptotic Distribution of 638 Appendix 18.4 Derivations of Exact Distributions of OLS Test Statistics with Normal Errors 639 Appendix 18.5 Proof of the Gauss-Markov Theorem for Multiple Regression 640 Appendix 642 References 651 Answers to "Review the Concepts" Questions 657 Glossary 672 Index 686 Includes bibliographical references (p. 359) and index UR - http://www.loc.gov/catdir/toc/ecip075/2006039352.html ER -