دانلود کتاب Introduction to Econometrics, Update

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Cover......Page 1
Title Page......Page 6
Copyright......Page 7
Contents......Page 10
Preface......Page 32
PART ONE Introduction and Review......Page 47
1.1 Economic Questions We Examine......Page 48
Question #1: Does Reducing Class Size Improve Elementary School Education?......Page 49
Question #3: How Much Do Cigarette Taxes Reduce Smoking?......Page 50
Question #4: By How Much Will U.S. GDP Grow Next Year?......Page 51
1.2 Causal Effects and Idealized Experiments......Page 52
Estimation of Causal Effects......Page 53
Experimental Versus Observational Data......Page 54
Cross-Sectional Data......Page 55
Time Series Data......Page 56
Panel Data......Page 58
CHAPTER 2 Review of Probability......Page 61
Probabilities, the Sample Space, and Random Variables......Page 62
Probability Distribution of a Discrete Random Variable......Page 63
2.2 Expected Values, Mean, and Variance......Page 66
The Standard Deviation and Variance......Page 68
Mean and Variance of a Linear Function of a Random Variable......Page 69
Other Measures of the Shape of a Distribution......Page 70
Joint and Marginal Distributions......Page 73
Conditional Distributions......Page 74
Covariance and Correlation......Page 78
The Mean and Variance of Sums of Random Variables......Page 79
The Normal Distribution......Page 83
The Student t Distribution......Page 88
The F Distribution......Page 89
Random Sampling......Page 90
The Sampling Distribution of the Sample Average......Page 91
2.6 Large-Sample Approximations to Sampling Distributions......Page 94
The Law of Large Numbers and Consistency......Page 95
The Central Limit Theorem......Page 97
APPENDIX 2.1 Derivation of Results in Key Concept 2.3......Page 110
CHAPTER 3 Review of Statistics......Page 112
Estimators and Their Properties......Page 113
Properties of Y......Page 115
The Importance of Random Sampling......Page 117
Null and Alternative Hypotheses......Page 118
The p-Value......Page 119
Calculating the p-Value When sY Is Known......Page 120
The Sample Variance, Sample Standard Deviation, and Standard Error......Page 121
The t-Statistic......Page 123
Hypothesis Testing with a Prespecified Significance Level......Page 124
One-Sided Alternatives......Page 126
3.3 Confidence Intervals for the Population Mean......Page 127
Hypothesis Tests for the Difference Between Two Means......Page 129
3.5 Differences-of-Means Estimation of Causal Effects Using Experimental Data......Page 131
Estimation of the Causal Effect Using Differences of Means......Page 132
The t-Statistic and the Student t Distribution......Page 134
Use of the Student t Distribution in Practice......Page 136
Scatterplots......Page 138
Sample Covariance and Correlation......Page 139
APPENDIX 3.1 The U.S. Current Population Survey......Page 153
APPENDIX 3.2 Two Proofs That Y Is the Least Squares Estimator of ?Y......Page 154
APPENDIX 3.3 A Proof That the Sample Variance Is Consistent......Page 155
4.1 The Linear Regression Model......Page 156
4.2 Estimating the Coefficients of the Linear Regression Model......Page 161
The Ordinary Least Squares Estimator......Page 163
OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio......Page 165
Why Use the OLS Estimator?......Page 166
The R2......Page 168
The Standard Error of the Regression......Page 169
Application to the Test Score Data......Page 170
Assumption #1: The Conditional Distribution of ui Given Xi Has a Mean of Zero......Page 171
Assumption #2: (Xi, Yi), i = 1,…, n, Are Independently and Identically Distributed......Page 173
Assumption #3: Large Outliers Are Unlikely......Page 174
Use of the Least Squares Assumptions......Page 175
4.5 Sampling Distribution of the OLS Estimators......Page 176
The Sampling Distribution of the OLS Estimators......Page 177
4.6 Conclusion......Page 180
APPENDIX 4.2 Derivation of the OLS Estimators......Page 188
APPENDIX 4.3 Sampling Distribution of the OLS Estimator......Page 189
5.1 Testing Hypotheses About One of the Regression Coefficients......Page 193
Two-Sided Hypotheses Concerning β......Page 194
One-Sided Hypotheses Concerning β1......Page 197
Testing Hypotheses About the Intercept β0......Page 199
5.2 Confidence Intervals for a Regression Coefficient......Page 200
Interpretation of the Regression Coefficients......Page 202
5.4 Heteroskedasticity and Homoskedasticity......Page 204
What Are Heteroskedasticity and Homoskedasticity?......Page 205
Mathematical Implications of Homoskedasticity......Page 207
What Does This Mean in Practice?......Page 208
5.5 The Theoretical Foundations of Ordinary Least Squares......Page 210
Linear Conditionally Unbiased Estimators and the Gauss-Markov Theorem......Page 211
Regression Estimators Other Than OLS......Page 212
The t-Statistic and the Student t Distribution......Page 213
Use of the Student t Distribution in Practice......Page 214
5.7 Conclusion......Page 215
APPENDIX 5.1 Formulas for OLS Standard Errors......Page 224
APPENDIX 5.2 The Gauss-Markov Conditions and a Proof of the Gauss-Markov Theorem......Page 225
6.1 Omitted Variable Bias......Page 229
Definition of Omitted Variable Bias......Page 230
A Formula for Omitted Variable Bias......Page 232
Addressing Omitted Variable Bias by Dividing the Data into Groups......Page 234
The Population Regression Line......Page 236
The Population Multiple Regression Model......Page 237
6.3 The OLS Estimator in Multiple Regression......Page 239
The OLS Estimator......Page 240
Application to Test Scores and the Student-Teacher Ratio......Page 241
The R2......Page 243
The \"Adjusted R2\"......Page 244
Application to Test Scores......Page 245
Assumption #3: Large Outliers Are Unlikely......Page 246
Assumption #4: No Perfect Multicollinearity......Page 247
6.6 The Distribution of the OLS Estimators in Multiple Regression......Page 248
6.7 Multicollinearity......Page 249
Examples of Perfect Multicollinearity......Page 250
Imperfect Multicollinearity......Page 252
6.8 Conclusion......Page 253
APPENDIX 6.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors......Page 261
APPENDIX 6.3 The Frisch-Waugh Theorem......Page 262
Standard Errors for the OLS Estimators......Page 264
Hypothesis Tests for a Single Coefficient......Page 265
Confidence Intervals for a Single Coefficient......Page 266
Application to Test Scores and the Student-Teacher Ratio......Page 267
Testing Hypotheses on Two or More Coefficients......Page 269
The F-Statistic......Page 271
Application to Test Scores and the Student-Teacher Ratio......Page 273
The Homoskedasticity-Only F-Statistic......Page 274
7.3 Testing Single Restrictions Involving Multiple Coefficients......Page 276
7.4 Confidence Sets for Multiple Coefficients......Page 278
7.5 Model Specification for Multiple Regression......Page 279
Omitted Variable Bias in Multiple Regression......Page 280
The Role of Control Variables in Multiple Regression......Page 281
Model Specification in Theory and in Practice......Page 283
Interpreting the R2 and the Adjusted R2 in Practice......Page 284
7.6 Analysis of the Test Score Data Set......Page 285
7.7 Conclusion......Page 290
APPENDIX 7.1 The Bonferroni Test of a Joint Hypothesis......Page 298
APPENDIX 7.2 Conditional Mean Independence......Page 300
CHAPTER 8 Nonlinear Regression Functions......Page 303
Test Scores and District Income......Page 305
The Effect on Y of a Change in X in Nonlinear Specifications......Page 308
8.2 Nonlinear Functions of a Single Independent Variable......Page 313
Polynomials......Page 314
Logarithms......Page 316
Polynomial and Logarithmic Models of Test Scores and District Income......Page 324
8.3 Interactions Between Independent Variables......Page 325
Interactions Between Two Binary Variables......Page 326
Interactions Between a Continuous and a Binary Variable......Page 329
Interactions Between Two Continuous Variables......Page 333
Discussion of Regression Results......Page 340
Summary of Findings......Page 344
8.5 Conclusion......Page 345
APPENDIX 8.1 Regression Functions That Are Nonlinear in the Parameters......Page 356
APPENDIX 8.2 Slopes and Elasticities for Nonlinear Regression Functions......Page 360
9.1 Internal and External Validity......Page 362
Threats to Internal Validity......Page 363
Threats to External Validity......Page 364
Omitted Variable Bias......Page 366
Misspecification of the Functional Form of the Regression Function......Page 368
Measurement Error and Errors-in-Variables Bias......Page 369
Missing Data and Sample Selection......Page 372
Simultaneous Causality......Page 373
Sources of Inconsistency of OLS Standard Errors......Page 376
Using Regression Models for Forecasting......Page 378
External Validity......Page 379
Internal Validity......Page 386
Discussion and Implications......Page 388
9.5 Conclusion......Page 389
APPENDIX 9.1 The Massachusetts Elementary School Testing Data......Page 396
CHAPTER 10 Regression with Panel Data......Page 397
10.1 Panel Data......Page 398
Example: Traffic Deaths and Alcohol Taxes......Page 399
10.2 Panel Data with Two Time Periods: \"Before and After\" Comparisons......Page 401
The Fixed Effects Regression Model......Page 404
Estimation and Inference......Page 406
10.4 Regression with Time Fixed Effects......Page 408
Time Effects Only......Page 409
Both Entity and Time Fixed Effects......Page 410
The Fixed Effects Regression Assumptions......Page 412
Standard Errors for Fixed Effects Regression......Page 414
10.6 Drunk Driving Laws and Traffic Deaths......Page 415
10.7 Conclusion......Page 419
APPENDIX 10.2 Standard Errors for Fixed Effects Regression......Page 427
CHAPTER 11 Regression with a Binary Dependent Variable......Page 432
Binary Dependent Variables......Page 433
The Linear Probability Model......Page 435
Probit Regression......Page 438
Logit Regression......Page 443
11.3 Estimation and Inference in the Logit and Probit Models......Page 445
Nonlinear Least Squares Estimation......Page 446
Maximum Likelihood Estimation......Page 447
Measures of Fit......Page 448
11.4 Application to the Boston HMDA Data......Page 449
11.5 Conclusion......Page 456
APPENDIX 11.2 Maximum Likelihood Estimation......Page 465
APPENDIX 11.3 Other Limited Dependent Variable Models......Page 468
CHAPTER 12 Instrumental Variables Regression......Page 471
The IV Model and Assumptions......Page 472
The Two Stage Least Squares Estimator......Page 473
Why Does IV Regression Work?......Page 474
The Sampling Distribution of the TSLS Estimator......Page 478
Application to the Demand for Cigarettes......Page 480
12.2 The General IV Regression Model......Page 482
TSLS in the General IV Model......Page 484
Instrument Relevance and Exogeneity in the General IV Model......Page 485
The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator......Page 486
Inference Using the TSLS Estimator......Page 487
Application to the Demand for Cigarettes......Page 488
12.3 Checking Instrument Validity......Page 489
Assumption #1: Instrument Relevance......Page 490
Assumption #2: Instrument Exogeneity......Page 492
12.4 Application to the Demand for Cigarettes......Page 495
12.5 Where Do Valid Instruments Come From?......Page 500
Three Examples......Page 501
12.6 Conclusion......Page 505
APPENDIX 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4)......Page 514
APPENDIX 12.3 Large-Sample Distribution of the TSLS Estimator......Page 515
APPENDIX 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid......Page 516
APPENDIX 12.5 Instrumental Variables Analysis with Weak Instruments......Page 518
APPENDIX 12.6 TSLS with Control Variables......Page 520
CHAPTER 13 Experiments and Quasi-Experiments......Page 522
Potential Outcomes and the Average Causal Effect......Page 523
Econometric Methods for Analyzing Experimental Data......Page 525
Threats to Internal Validity......Page 526
Threats to External Validity......Page 530
13.3 Experimental Estimates of the Effect of Class Size Reductions......Page 531
Experimental Design......Page 532
Analysis of the STAR Data......Page 533
Comparison of the Observational and Experimental Estimates of Class Size Effects......Page 538
13.4 Quasi-Experiments......Page 540
Examples......Page 541
The Differences-in-Differences Estimator......Page 543
Instrumental Variables Estimators......Page 546
Regression Discontinuity Estimators......Page 547
Threats to Internal Validity......Page 549
13.6 Experimental and Quasi-Experimental Estimates in Heterogeneous Populations......Page 551
OLS with Heterogeneous Causal Effects......Page 552
IV Regression with Heterogeneous Causal Effects......Page 553
13.7 Conclusion......Page 556
APPENDIX 13.2 IV Estimation When the Causal Effect Varies Across Individuals......Page 565
APPENDIX 13.3 The Potential Outcomes Framework for Analyzing Data from Experiments......Page 567
CHAPTER 14 Introduction to Time Series Regression and Forecasting......Page 569
14.1 Using Regression Models for Forecasting......Page 570
Real GDP in the United States......Page 571
Lags, First Differences, Logarithms, and Growth Rates......Page 572
Autocorrelation......Page 575
Other Examples of Economic Time Series......Page 576
The First-Order Autoregressive Model......Page 578
The pth-Order Autoregressive Model......Page 581
Forecasting GDP Growth Using the Term Spread Stationarity......Page 584
Time Series Regression with Multiple Predictors......Page 588
Forecast Uncertainty and Forecast Intervals......Page 591
Determining the Order of an Autoregression......Page 594
Lag Length Selection in Time Series Regression with Multiple Predictors......Page 597
What Is a Trend?......Page 598
Problems Caused by Stochastic Trends......Page 601
Detecting Stochastic Trends: Testing for a Unit AR Root......Page 603
14.7 Nonstationarity II: Breaks......Page 608
Testing for Breaks......Page 609
Pseudo Out-of-Sample Forecasting......Page 614
14.8 Conclusion......Page 620
APPENDIX 14.1 Time Series Data Used in Chapter 14......Page 630
APPENDIX 14.2 Stationarity in the AR(1) Model......Page 631
APPENDIX 14.3 Lag Operator Notation......Page 632
APPENDIX 14.4 ARMA Models......Page 633
APPENDIX 14.5 Consistency of the BIC Lag Length Estimator......Page 634
CHAPTER 15 Estimation of Dynamic Causal Effects......Page 636
15.1 An Initial Taste of the Orange Juice Data......Page 637
Causal Effects and Time Series Data......Page 640
Two Types of Exogeneity......Page 643
15.3 Estimation of Dynamic Causal Effects with Exogenous Regressors......Page 644
The Distributed Lag Model Assumptions......Page 645
Autocorrelated ut, Standard Errors, and Inference......Page 646
Dynamic Multipliers and Cumulative Dynamic Multipliers......Page 647
15.4 Heteroskedasticity- and Autocorrelation-Consistent Standard Errors......Page 648
Distribution of the OLS Estimator with Autocorrelated Errors......Page 649
HAC Standard Errors......Page 651
15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors......Page 653
The Distributed Lag Model with AR(1) Errors......Page 654
OLS Estimation of the ADL Model......Page 657
GLS Estimation......Page 658
The Distributed Lag Model with Additional Lags and AR(p) Errors......Page 660
15.6 Orange Juice Prices and Cold Weather......Page 663
U.S. Income and Australian Exports......Page 671
Oil Prices and Inflation......Page 672
The Growth Rate of GDP and the Term Spread......Page 673
15.8 Conclusion......Page 674
APPENDIX 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation......Page 681
16.1 Vector Autoregressions......Page 685
The VAR Model......Page 686
A VAR Model of the Growth Rate of GDP and the Term Spread......Page 689
Iterated Multiperiod Forecasts......Page 690
Direct Multiperiod Forecasts......Page 692
Which Method Should You Use?......Page 695
Other Models of Trends and Orders of Integration......Page 696
The DF-GLS Test for a Unit Root......Page 698
Why Do Unit Root Tests Have Nonnormal Distributions?......Page 701
Cointegration and Error Correction......Page 703
How Can You Tell Whether Two Variables Are Cointegrated?......Page 705
Estimation of Cointegrating Coefficients......Page 706
Extension to Multiple Cointegrated Variables......Page 708
Application to Interest Rates......Page 709
Volatility Clustering......Page 711
Autoregressive Conditional Heteroskedasticity......Page 713
Application to Stock Price Volatility......Page 714
16.6 Conclusion......Page 717
CHAPTER 17 The Theory of Linear Regression with One Regressor......Page 723
The Extended Least Squares Assumptions......Page 724
17.2 Fundamentals of Asymptotic Distribution Theory......Page 726
Convergence in Probability and the Law of Large Numbers......Page 727
The Central Limit Theorem and Convergence in Distribution......Page 729
Slutsky\'s Theorem and the Continuous Mapping Theorem......Page 730
Application to the t-Statistic Based on the Sample Mean......Page 731
Consistency of Heteroskedasticity-Robust Standard Errors......Page 732
Distribution of β with Normal Errors......Page 734
Distribution of the Homoskedasticity-Only t-Statistic......Page 736
WLS with Known Heteroskedasticity......Page 737
WLS with Heteroskedasticity of Known Functional Form......Page 738
Heteroskedasticity-Robust Standard Errors or WLS?......Page 741
APPENDIX 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables......Page 747
APPENDIX 17.2 Two Inequalities......Page 750
CHAPTER 18 The Theory of Multiple Regression......Page 752
The Multiple Regression Model in Matrix Notation......Page 753
The Extended Least Squares Assumptions......Page 755
The OLS Estimator......Page 756
The Multivariate Central Limit Theorem......Page 757
Asymptotic Normality of β......Page 758
Heteroskedasticity-Robust Standard Errors......Page 759
18.3 Tests of Joint Hypotheses......Page 760
Asymptotic Distribution of the F-Statistic......Page 761
Confidence Sets for Multiple Coefficients......Page 762
Matrix Representations of OLS Regression Statistics......Page 763
Distribution of β with Normal Errors......Page 764
Homoskedasticity-Only Standard Errors......Page 765
Distribution of the F-Statistic......Page 766
Linear Conditionally Unbiased Estimators......Page 767
The Gauss-Markov Theorem for Multiple Regression......Page 768
18.6 Generalized Least Squares......Page 769
The GLS Assumptions......Page 770
GLS When Ω Is Known......Page 772
The Zero Conditional Mean Assumption and GLS......Page 773
18.7 Instrumental Variables and Generalized Method of Moments Estimation......Page 775
The IV Estimator in Matrix Form......Page 776
Asymptotic Distribution of the TSLS Estimator......Page 777
Properties of TSLS When the Errors Are Homoskedastic......Page 778
Generalized Method of Moments Estimation in Linear Models......Page 781
APPENDIX 18.1 Summary of Matrix Algebra......Page 793
APPENDIX 18.2 Multivariate Distributions......Page 796
APPENDIX 18.3 Derivation of the Asymptotic Distribution of ?......Page 798
APPENDIX 18.4 Derivations of Exact Distributions of OLS Test Statistics with Normal Errors......Page 799
APPENDIX 18.5 Proof of the Gauss-Markov Theorem for Multiple Regression......Page 800
APPENDIX 18.6 Proof of Selected Results for IV and GMM Estimation......Page 801
Appendix......Page 804
References......Page 812
Glossary......Page 818
C......Page 826
D......Page 828
F......Page 829
H......Page 830
K......Page 831
M......Page 832
O......Page 833
R......Page 834
S......Page 835
T......Page 836
Z......Page 837