Introduction to Econometrics

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Acknowledgments......Page 41
Contents......Page 8
Preface......Page 30
1.1 Economic Questions We Examine......Page 46
1.2 Causal Effects and Idealized Experiments......Page 50
1.3 Data: Sources and Types......Page 52
CHAPTER 2 Review of Probability......Page 59
2.1 Random Variables and Probability Distributions......Page 60
2.2 Expected Values, Mean, and Variance......Page 64
2.3 Two Random Variables......Page 71
2.4 The Normal, Chi-Squared, Student t, and F Distributions......Page 81
2.5 Random Sampling and the Distribution of the Sample Average......Page 88
2.6 Large-Sample Approximations to Sampling Distributions......Page 92
APPENDIX 2.1 Derivation of Results in Key Concept 2.3......Page 108
CHAPTER 3 Review of Statistics......Page 110
3.1 Estimation of the Population Mean......Page 111
3.2 Hypothesis Tests Concerning the Population Mean......Page 116
3.3 Confidence Intervals for the Population Mean......Page 125
3.4 Comparing Means from Different Populations......Page 127
3.5 Differences-of-Means Estimation of Causal Effects Using Experimental Data......Page 129
3.6 Using the t-Statistic When the Sample Size Is Small......Page 132
3.7 Scatterplots, the Sample Covariance, and the Sample Correlation......Page 136
APPENDIX 3.1 The U.S. Current Population Survey......Page 151
APPENDIX 3.2 Tow Proofs That (Omitted) Is the Least Squares Estimator of μ(sub[(γ)]......Page 152
APPENDIX 3.3 A Proof That the Sample Variance Is Consistent......Page 153
4.1 The Linear Regression Model......Page 154
4.2 Estimating the Coefficients of the Linear Regression Model......Page 159
4.3 Measures of Fit......Page 166
4.4 The Least Squares Assumptions......Page 169
4.5 Sampling Distribution of the OLS Estimators......Page 174
4.6 Conclusion......Page 178
APPENDIX 4.2 Derivation of the OLS Estimators......Page 186
APPENDIX 4.3 Sampling Distribution of the OLS Estimator......Page 187
5.1 Testing Hypotheses About One of the Regression Coefficients......Page 191
5.2 Confidence Intervals for a Regression Coefficient......Page 198
5.3 Regression When X Is a Binary Variable......Page 200
5.4 Heteroskedasticity and Homoskedasticity......Page 202
5.5 The Theoretical Foundations of Ordinary Least Squares......Page 208
5.6 Using the t-Statistic in Regression When the Sample Size Is Small......Page 211
5.7 Conclusion......Page 213
APPENDIX 5.1 Formulas for OLS Standard Errors......Page 222
APPENDIX 5.2 The Gauss–Markov Conditions and a Proof of the Gauss–Markov Theorem......Page 223
6.1 Omitted Variable Bias......Page 227
6.2 The Multiple Regression Model......Page 234
6.3 The OLS Estimator in Multiple Regression......Page 237
6.4 Measures of Fit in Multiple Regression......Page 241
6.5 The Least Squares Assumptions in Multiple Regression......Page 244
6.6 The Distribution of the OLS Estimators in Multiple Regression......Page 246
6.7 Multicollinearity......Page 247
6.8 Conclusion......Page 251
APPENDIX 6.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors......Page 259
APPENDIX 6.3 The Frisch–Waugh Theorem......Page 260
7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient......Page 262
7.2 Tests of Joint Hypotheses......Page 267
7.3 Testing Single Restrictions Involving Multiple Coefficients......Page 274
7.4 Confidence Sets for Multiple Coefficients......Page 276
7.5 Model Specification for Multiple Regression......Page 277
7.6 Analysis of the Test Score Data Set......Page 283
7.7 Conclusion......Page 288
APPENDIX 7.1 The Bonferroni Test of a Joint Hypothesis......Page 296
APPENDIX 7.2 Conditional Mean Independence......Page 298
CHAPTER 8 Nonlinear Regression Functions......Page 301
8.1 A General Strategy for Modeling Nonlinear Regression Functions......Page 303
8.2 Nonlinear Functions of a Single Independent Variable......Page 311
8.3 Interactions Between Independent Variables......Page 323
8.4 Nonlinear Effects on Test Scores of the Student–Teacher Ratio......Page 338
8.5 Conclusion......Page 343
APPENDIX 8.1 Regression Functions That Are Nonlinear in the Parameters......Page 354
APPENDIX 8.2 Slopes and Elasticities for Nonlinear Regression Functions......Page 358
9.1 Internal and External Validity......Page 360
9.2 Threats to Internal Validity of Multiple Regression Analysis......Page 364
9.3 Internal and External Validity When the Regression Is Used for Forecasting......Page 376
9.4 Example: Test Scores and Class Size......Page 377
9.5 Conclusion......Page 387
APPENDIX 9.1 The Massachusetts Elementary School Testing Data......Page 394
CHAPTER 10 Regression with Panel Data......Page 395
10.1 Panel Data......Page 396
10.2 Panel Data with Two Time Periods: "Before and After" Comparisons......Page 399
10.3 Fixed Effects Regression......Page 402
10.4 Regression with Time Fixed Effects......Page 406
10.5 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression......Page 410
10.6 Drunk Driving Laws and Traffic Deaths......Page 413
10.7 Conclusion......Page 417
APPENDIX 10.2 Standard Errors for Fixed Effects Regression......Page 425
CHAPTER 11 Regression with a Binary Dependent Variable......Page 430
11.1 Binary Dependent Variables and the Linear Probability Model......Page 431
11.2 Probit and Logit Regression......Page 436
11.3 Estimation and Inference in the Logit and Probit Models......Page 443
11.4 Application to the Boston HMDA Data......Page 447
11.5 Conclusion......Page 454
APPENDIX 11.2 Maximum Likelihood Estimation......Page 463
APPENDIX 11.3 Other Limited Dependent Variable Models......Page 466
CHAPTER 12 Instrumental Variables Regression......Page 469
12.1 The IV Estimator with a Single Regressor and a Single Instrument......Page 470
12.2 The General IV Regression Model......Page 480
12.3 Checking Instrument Validity......Page 487
12.4 Application to the Demand for Cigarettes......Page 493
12.5 Where Do Valid Instruments Come From?......Page 498
12.6 Conclusion......Page 503
APPENDIX 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4)......Page 512
APPENDIX 12.3 Large-Sample Distribution of the TSLS Estimator......Page 513
APPENDIX 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid......Page 514
APPENDIX 12.5 Instrumental Variables Analysis with Weak Instruments......Page 516
APPENDIX 12.6 TSLS with Control Variables......Page 518
CHAPTER 13 Experiments and Quasi-Experiments......Page 520
13.1 Potential Outcomes, Causal Effects, and Idealized Experiments......Page 521
13.2 Threats to Validity of Experiments......Page 524
13.3 Experimental Estimates of the Effect of Class Size Reductions......Page 529
13.4 Quasi-Experiments......Page 538
13.5 Potential Problems with Quasi-Experiments......Page 547
13.6 Experimental and Quasi-Experimental Estimates in Heterogeneous Populations......Page 549
13.7 Conclusion......Page 554
APPENDIX 13.2 IV Estimation When the Causal Effect Varies Across Individuals......Page 563
APPENDIX 13.3 The Potential Outcomes Framework for Analyzing Data from Experiments......Page 565
CHAPTER 14 Introduction to Time Series Regression and Forecasting......Page 567
14.1 Using Regression Models for Forecasting......Page 568
14.2 Introduction to Time Series Data and Serial Correlation......Page 569
14.3 Autoregressions......Page 576
14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model......Page 582
14.5 Lag Length Selection Using Information Criteria......Page 592
14.6 Nonstationarity I: Trends......Page 596
14.7 Nonstationarity II: Breaks......Page 606
14.8 Conclusion......Page 618
APPENDIX 14.1 Time Series Data Used in Chapter 14......Page 628
APPENDIX 14.2 Stationarity in the AR(1) Model......Page 629
APPENDIX 14.3 Lag Operator Notation......Page 630
APPENDIX 14.4 ARMA Models......Page 631
APPENDIX 14.5 Consistency of the BIC Lag Length Estimator......Page 632
CHAPTER 15 Estimation of Dynamic Causal Effects......Page 634
15.1 An Initial Taste of the Orange Juice Data......Page 635
15.2 Dynamic Causal Effects......Page 638
15.3 Estimation of Dynamic Causal Effects with Exogenous Regressors......Page 642
15.4 Heteroskedasticity- and Autocorrelation-Consistent Standard Errors......Page 646
15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors......Page 651
15.6 Orange Juice Prices and Cold Weather......Page 661
15.7 Is Exogeneity Plausible? Some Examples......Page 669
15.8 Conclusion......Page 672
APPENDIX 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation......Page 679
16.1 Vector Autoregressions......Page 683
16.2 Multiperiod Forecasts......Page 688
16.3 Orders of Integration and the DF-GLS Unit Root Test......Page 694
16.4 Cointegration......Page 701
16.5 Volatility Clustering and Autoregressive Conditional Heteroskedasticity......Page 709
16.6 Conclusion......Page 715
CHAPTER 17 The Theory of Linear Regression with One Regressor......Page 721
17.1 The Extended Least Squares Assumptions and the OLS Estimator......Page 722
17.2 Fundamentals of Asymptotic Distribution Theory......Page 724
17.3 Asymptotic Distribution of the OLS Estimator and t-Statistic......Page 730
17.4 Exact Sampling Distributions When the Errors Are Normally Distributed......Page 732
17.5 Weighted Least Squares......Page 735
APPENDIX 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables......Page 745
APPENDIX 17.2 Two Inequalities......Page 748
CHAPTER 18 The Theory of Multiple Regression......Page 750
18.1 The Linear Multiple Regression Model and OLS Estimator in Matrix Form......Page 751
18.2 Asymptotic Distribution of the OLS Estimator and t-Statistic......Page 755
18.3 Tests of Joint Hypotheses......Page 758
18.4 Distribution of Regression Statistics with Normal Errors......Page 761
18.5 Efficiency of the OLS Estimator with Homoskedastic Errors......Page 765
18.6 Generalized Least Squares......Page 767
18.7 Instrumental Variables and Generalized Method of Moments Estimation......Page 773
APPENDIX 18.1 Summary of Matrix Algebra......Page 791
APPENDIX 18.2 Multivariate Distributions......Page 794
APPENDIX 18.3 Derivation of the Asymptotic Distribution of (Omitted)......Page 796
APPENDIX 18.4 Derivations of Exact Distributions of OLS Test Statistics
with Normal Errors......Page 797
APPENDIX 18.5 Proof of the Gauss–Markov theorem for Multiple regression......Page 798
APPENDIX 18.6 Proof of Selected Results for IV and GMM Estimation......Page 799
Appendix......Page 802
References......Page 810
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