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Introduction to Econometrics, Third Edition 

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Comment from the Stata technical groupIntroduction to Econometrics, Third Edition, by James H. Stock and Mark W. Watson, is a real pageturner. By ingeniously introducing statistical methods as a means of answering four interesting empirical questions, the authors have written a rigorous text that makes you want to keep reading to find out how the story ends. The authors use the excitement generated by the questions as a springboard for an excellent introduction to estimation, inference, and interpretation in econometrics. The text makes advanced statistical concepts easily understandable. For instance, the current econometric approach to analyzing linear models combines assumptions on the conditional moments of random variables and largesample theory to derive estimators and their properties. This textbook provides an accessible introduction to this technique and its application to crosssectional data, paneldata, and timeseries regression. The coverage and level of this text make it an excellent choice for undergraduate study or as a supplement to advanced courses. The third edition includes new material on the potentialoutcomes framework, regression discontinuity design methods, and missingdata problems. These new sections provide a steppingstone into modern econometrics because they use the same firstprinciples logic applied in much of modern econometrics. 

Table of contentsView table of contents >> Preface
PART ONE Introduction and Review
CHAPTER 1 Economic Questions and Data
1.1 Economic Questions We Examine
Question #1: Does Reducing Class Size Improve Elementary School Education?
1.2 Causal Effects and Idealized ExperimentsQuestion #2: Is There Racial Discrimination in the Market for Home Loans? Question #3: How Much Do Cigarette Taxes Reduce Smoking? Question #4: What Will the Rate of Inflation Be Next Year? Quantitative Questions, Quantitative Answers
Estimation of Causal Effects
1.3 Data: Sources and TypesForecasting and Causality
Experimental Versus Observational Data
CrossSectional Data Time Series Data Panel Data CHAPTER 2 Review of Probability
2.1 Random Variables and Probability Distributions
Probabilities, the Sample Space, and Random Variables
2.2 Expected Values, Mean, and VarianceProbability Distribution of a Discrete Random Variable Probability Distribution of a Continuous Random Variable
The Expected Value of a Random Variable
2.3 Two Random VariablesThe Standard Deviation and Variance Mean and Variance of a Linear Function of a Random Variable Other Measures of the Shape of a Distribution
Joint and Marginal Distributions
2.4 The Normal, ChiSquared, Student t, and F DistributionsConditional Distributions Independence Covariance and Correlation The Mean and Variance of Sums of Random Variables
The Normal Distributions
2.5 Random Sampling and the Distribution of the Sample AverageThe ChiSquared Distribution The Student t Distribution The F Distribution
Random Sampling
2.6 LargeSample Approximations to the Sampling DistributionsThe Sampling Distribution of the Sample Average
The Law of Large Numbers and Consistency
The Central Limit Theorem APPENDIX 2.1 Derivation of Results in Key Concept 2.3 CHAPTER 3 Review of Statistics
3.1 Estimation of the Population Mean
Estimators and Their Properties
3.2 Hypothesis Tests Concerning the Population MeanProperties of Ybar The Importance of Random Sampling
Null and Alternative Hypotheses
3.3 Confidence Intervals for the Population MeanThe pValue Calculating the pValue When σ_{ϒ} Is Known The Sample Variance, Sample Standard Deviation, and Standard Error Calculating the pValue When σ_{ϒ} Is Unknown The tStatistic Hypothesis Testing with a Prespecified Significance Level OneSided Alternatives 3.4 Comparing Means from Different Populations
Hypothesis Tests for the Difference Between Two Means
3.5 DifferencesofMeans Estimation of Causal Effects Using Experimental DataConfidence Intervals for the Difference Between Two Population Means
The Causal Effect as a Difference of Conditional Expectations
3.6 Using the tStatistic When the Sample Size Is SmallEstimation of the Causal Effect Using Differences of Means
The tStatistic and the Student t Distribution
3.7 Scatterplots, the Sample Covariance, and the Sample CorrelationUse of the Student t Distribution in Practice
Scatterplots
Sample Covariance and Correlation APPENDIX 3.1 The U.S. Current Population Survey APPENDIX 3.2 Two Proofs That Ybar Is the Least Squares Estimator of μ_{ϒ} APPENDIX 3.3 A Proof That the Sample Variance is Consistent PART TWO Fundamentals of Regression Analysis
CHAPTER 4 Linear Regression with One Regressor
4.1 The Linear Regression Model
4.2 Estimating the Coefficients of the Linear Regression Model
The Ordinary Least Squares Estimator
4.3 Measures of FitOLS Estimates of the Relationship Between Test Scores and the Student–Teacher Ratio Why Use the OLS Estimator?
The R^{2}
4.4 The Least Squares AssumptionsThe Standard Error of the Regression Application to the Test Score Data
Assumption #1: The Conditional Distribution of u_{i}
Given X_{i} Has a Mean of Zero
4.5 Sampling Distribution of the OLS EstimatorsAssumption #2: (X_{i}, X_{i}) i = 1,…, n, Are Independently and Identically Distributed Assumption #3: Large Outliers Are Unlikely Use of the Least Squares Assumptions
The Sampling Distribution of the OLS Estimators
4.6 Conclusion
APPENDIX 4.1 The California Test Score Data Set
APPENDIX 4.2 Derivation of the OLS Estimators APPENDIX 4.3 Sampling Distribution of the OLS Estimator CHAPTER 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
5.1 Testing Hypotheses About One of the Regression Coefficients
TwoSided Hypotheses Concerning Β_{1}
5.2 Confidence Intervals for a Regression CoefficientOneSided Hypotheses Concerning Β_{1} Testing Hypotheses About the Intercept Β_{0} 5.3 Regression When X is a Binary Variable
Interpretation of the Regression Coefficients
5.4 Heteroskedasticity and Homoskedasticity
What Are Heteroskedasticity and Homoskedasticity?
5.5 The Theoretical Foundations of Ordinary Least SquaresMathematical Implications of Homoskedasticity What Does This Mean in Practice
Linear Conditionally Unbiased Estimators and the Gauss–Markov Theorem
5.6 Using the tStatistic in Regression When the Sample Size Is SmallRegression Estimators Other Than OLS
The tStatistic and the Student t Distribution
5.7 ConclusionUse of the Student t Distribution in Practice
APPENDIX 5.1 Formulas for OLS Standard Errors
APPENDIX 5.2 The Gauss–Markov Conditions and a Proof of the Gauss–Markov Theorem CHAPTER 6 Linear Regression with Multiple Regressors
6.1 Omitted Variable Bias
Definition of Omitted Variable Bias
6.2 The Multiple Regression ModelA Formula for Omitted Variable Bias Addressing Omitted Variable Bias by Dividing the Data into Groups
The Population Regression Line
6.3 The OLS Estimator in Multiple RegressionThe Population Multiple Regression Model
The OLS Estimator
6.4 Measures of Fit in Multiple RegressionApplication to Test Scores and the Student–Teacher Ratio
The Standard Error of the Regression (SER)
6.5 The Least Squares Assumptions in Multiple RegressionThe R^{2} The “Adjusted R^{2}” Application to Test Scores
Assumption #1: The Conditional Distribution of u_{i}
Given X_{1i ′},
X_{2i ′},…,
X_{ki} Has a Mean of Zero
6.6 The Distribution of OLS Estimators in Multiple RegressionAssumption #2: (X_{1i ′}, X_{2i ′},…, X_{ki},Y_{i}), i = 1,…,n, Are i.i.d. Assumption #3: Large Outliers Are Unlikely Assumption #4: No Perfect Multicollinearity 6.7 Multicollinearity
Examples of Perfect Multicollinearity
6.8 ConclusionImperfect Multicollinearity
APPENDIX 6.1 Derivation of Equation (6.1)
APPENDIX 6.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors APPENDIX 6.3 The Frisch–Waugh Theorem CHAPTER 7: Hypothesis Tests and Confidence Intervals in Multiple Regression
7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient
Standard Errors for the OLS Estimators
7.2 Tests of Joint HypothesesHypothesis Tests for a Single Coefficient Confidence Intervals for a Single Coefficient Application to Test Scores and the Student–Teacher Ratio
Testing Hypotheses on Two or More Coefficients
7.3 Testing Single Restrictions Involving Multiple CoefficientsThe FStatistic Application to Test Scores and the Student–Teacher Ratio The HomoskedasticityOnly FStatistic 7.4 Confidence Sets for Multiple Coefficients 7.5 Model Specification for Multiple Regression
Omitted Variable Bias in Multiple Regression
7.6 Analysis of the Test Score Data SetThe Role of Control Variables in Multiple Regression Model Specification in Theory and Practice Interpreting the R^{2} and the Adjusted R^{2} in Practice 7.7 Conclusion
APPENDIX 7.1 The Bonferroni Test of a Joint Hypothesis
APPENDIX 7.2 Conditional Mean Independence CHAPTER 8 Nonlinear Regression Functions
8.1 A General Strategy for Modeling Nonlinear Regression Functions
Test Scores and District Income
8.2 Nonlinear Functions of a Single Independent VariableThe Effect on Y of a Change in X in Nonlinear Specifications A General Approach to Modeling Nonlinearities Using Multiple Regression
Polynomials
8.3 Interactions Between Independent VariablesLogarithms Polynomial and Logarithmic Models of Test Scores and District Income
Interactions Between Two Binary Variables
8.4 Nonlinear Effects on Test Scores of the Student–Teacher RatioInteractions Between a Continuous and a Binary Variable Interactions Between Two Continuous Variables
Discussion of Regression Results
8.5 ConclusionSummary of Findings
APPENDIX 8.1 Regression Functions That Are Nonlinear in the Parameters
APPENDIX 8.2 Slopes and Elasticities for Nonlinear Regression Functions CHAPTER 9 Assessing Studies Based on Multiple Regression
9.1 Internal and External Validity
Threats to Internal Validity
9.2 Threats to Internal Validity of Multiple Regression AnalysisThreats to External Validity
Omitted Variable Bias
9.3 Internal and External Validity When the Regression Is Used for ForecastingMisspecification of the Functional Form of the Regression Function Measurement Error and ErrorsinVariables Bias Missing Data and Sample Selection Simultaneous Causality Sources of Inconsistency of OLS Standard Errors
Using Regression Models for Forecasting
9.4 Example: Test Scores and Class SizeAssessing the Validity of Regression Models for Forecasting
External Validity
9.5 ConclusionInternal Validity Discussion and Implications
APPENDIX 9.1 The Massachusetts Elementary School Testing Data
PART THREE Further Topics in Regression Analysis
CHAPTER 10 Regression with Panel Data
10.1 Panel Data
Example: Traffic Deaths and Alcohol Taxes
10.2 Panel Data with Two Time Periods: “Before and After” Comparisons10.3 Fixed Effects Regression
The Fixed Effects Regression Model
10.4 Regression with Time Fixed EffectsEstimation and Inference Application to Traffic Deaths
Time Effects Only
10.5 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects RegressionBoth Entity and Time Fixed Effects
The Fixed Effects Regression Assumptions
10.6 Drunk Driving Laws and Traffic DeathsStandard Errors for Fixed Effects Regression 10.7 Conclusion
APPENDIX 10.1 The State Traffic Fatality Data Set
APPENDIX 10.2 Standard Errors for Fixed Effects Regression CHAPTER 11 Regression with a Binary Dependent Variable
11.1 Binary Dependent Variables and the Linear Probability Model
Binary Dependent Variables
11.2 Probit and Logit RegressionThe Linear Probability Model
Probit Regression
11.3 Estimation and Inference in the Logit and Probit ModelsLogit Regression Comparing the Linear Probability, Probit, and Logit Models
Nonlinear Least Squares Estimation
11.4 Application to the Boston HMDA DataMaximum Likelihood Estimation Measures of Fit 11.5 Conclusion
APPENDIX 11.1 The Boston HMDA Data Set
APPENDIX 11.2 Maximum Likelihood Estimation APPENDIX 11.3 Other Limited Dependent Variable Models CHAPTER 12 Instrumental Variables Regression
12.1 The IV Estimator with a Single Regressor and a Single Instrument
The IV Model and Assumptions
12.2 The General IV Regression ModelThe Two Stage Least Squares Estimator Why Does IV Regression Work? The Sampling Distribution of the TSLS Estimator Application to the Demand for Cigarettes
TSLS in the General IV Model
12.3 Checking Instrument ValidityInstrument Relevance and Exogeneity in the General IV Model The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator Inference Using the TSLS Estimator Application to the Demand for Cigarettes
Assumption #1: Instrument Relevance
12.4 Application to the Demand for CigarettesAssumption #2: Instrument Exogeneity 12.5 Where Do Valid Instruments Come From?
Three Examples
12.6 Conclusion
APPENDIX 12.1 The Cigarette Consumption Panel Data Set
APPENDIX 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4) APPENDIX 12.3 LargeSample Distribution of the TSLS Estimator APPENDIX 12.4 LargeSample Distribution of the TSLS Estimator When the Instrument Is Not Valid APPENDIX 12.5 Instrumental Variables Analysis with Weak Instruments APPENDIX 12.6 TSLS with Control Variables CHAPTER 13 Experiments and QuasiExperiments
13.1 Potential Outcomes, Causal Effects, and Idealized Experiments
Potential Outcomes and the Average Causal Effect
13.2 Threats to Validity of ExperimentsEconometric Methods for Analyzing Experimental Data
Threats to Internal Validity
13.3 Experimental Estimates of the Effect of Class Size ReductionsThreats to External Validity
Experimental Design
13.4 QuasiExperimentsAnalysis of the STAR Data Comparison of the Observational and Experimental Estimates of Class Size Effects
Examples
13.5 Potential Problems with QuasiExperimentsThe DifferencesinDifferences Estimator Instrumental Variables Estimators Regression Discontinuity Estimators
Threats to Internal Validity
13.6 Experimental and QuasiExperimental Estimates in Heterogeneous PopulationsThreats to External Validity
OLS with Heterogeneous Causal Effects
13.7 ConclusionIV Regression with Heterogeneous Causal Effects
APPENDIX 13.1 The Project STAR Data Set
APPENDIX 13.2 IV Estimation When the Causal Effect Varies Across Individuals APPENDIX 13.3 The Potential Outcomes Framework for Analyzing Data from Experiments PART FOUR Regression Analysis of Economic Time Series Data
CHAPTER 14 Introduction to Time Series Regression and Forecasting
14.1 Using Regression Models for Forecasting
14.2 Introduction to Time Series Data and Serial Correlation
The Rates of Inflation and Unemployment in the United States
14.3 AutoregressionsLags, First Differences, Logarithms, and Growth Rates Autocorrelation Other Examples of Economic Time Series
The First Order Autoregressive Model
14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag ModelThe p^{th} Order Autoregressive Model
Forecasting Changes in the Inflation Rate Using Past Unemployment Rates
14.5 Lag Length Selection Using Information CriteriaStationarity Time Series Regression with Multiple Predictors Forecast Uncertainty and Forecast Intervals
Determining the Order of an Autoregression
14.6 Nonstationarity I: TrendsLag Length Selection in Time Series Regression with Multiple Predictors
What Is a Trend?
14.7 Nonstationarity II: BreaksProblems Caused by Stochastic Trends Detecting Stochastic Trends: Testing for a Unit AR Root Avoiding the Problems Caused by Stochastic Trends
What Is a Break?
14.8 ConclusionTesting for Breaks Pseudo OutofSample Forecasting Avoiding the Problems Caused by Breaks
APPENDIX 14.1 Time Series Data Used in Chapter 14
APPENDIX 14.2 Stationarity in the AR(1) Model APPENDIX 14.3 Lag Operator Notation APPENDIX 14.4 ARMA Models APPENDIX 14.5 Consistency of the BIC Lag Length Estimator CHAPTER 15 Estimation of Dynamic Causal Effects
15.1 An Initial Taste of the Orange Juice Data
15.2 Dynamic Causal Effects
Causal Effects and Time Series Data
15.3 Estimation of Dynamic Causal Effects with Exogenous RegressorsTwo Types of Exogeneity
The Distributed Lag Model Assumptions
15.4 Heteroskedasticity and AutocorrelationConsistent Standard ErrorsAutocorrelated u_{t}, Standard Errors, and Inference Dynamic Multipliers and Cumulative Dynamic Multipliers
Distribution of the OLS Estimator with Autocorrelated Errors
15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous RegressorsHAC Standard Errors
The Distributed Lag Model with AR(1) Errors
15.6 Orange Juice Prices and Cold WeatherOLS Estimation of the ADL Model GLS Estimation The Distributed Lag Model with Additional Lags and AR(p) Errors 15.7 Is Exogeneity Plausible? Some Examples
U.S. Income and Australian Exports
15.8 ConclusionOil Prices and Inflation Monetary Policy and Inflation The Phillips Curve
APPENDIX 15.1 The Orange Juice Data Set
APPENDIX 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation CHAPTER 16 Additional Topics in Time Series Regression
16.1 Vector Autoregressions
The VAR Model
16.2 Multiperiod ForecastsA VAR Model of the Rates of Inflation and Unemployment
Iterated Multiperiod Forecasts
16.3 Orders of Integration and the DFGLS Unit Root TestDirect Multiperiod Forecasts Which Method Should You Use?
Other Models of Trends and Orders of Integration
16.4 CointegrationThe DFGLS Test for a Unit Root Why Do Unit Root Tests Have Nonnormal Distributions?
Cointegration and Error Correction
16.5 Volatility Clustering and Autoregressive Conditional HeteroskedasticityHow Can You Tell Whether Two Variables are Cointegrated? Estimation of Cointegrating Coefficients Extension to Multiple Cointegrated Variables Application to Interest Rates
Volatility Clustering
16.6 ConclusionAutoregressive Conditional Heteroskedasticity Application to Stock Price Volatility
APPENDIX 16.1 U.S. Financial Data Used in Chapter 16
PART FIVE The Econometric Theory of Regression Analysis
CHAPTER 17 The Theory of Linear Regression with One Regressor
17.1 The Extended Least Squares Assumptions and the OLS Estimator
The Extended Least Squares Assumptions
17.2 Fundamentals of Asymptotic Distribution TheoryThe OLS Estimator
Convergence in Probability and the Law of Large Numbers
17.3 Asymptotic Distribution of the OLS Estimator and tStatisticThe Central Limit Theorem and Convergence in Distribution Slutsky’s Theorem and the Continuous Mapping Theorem Application to the tStatistic Based on the Sample Mean
Consistency and Asymptotic Normality of the OLS Estimators
17.4 Exact Sampling Distributions When the Errors Are Normally DistributedConsistency of HeteroskedasticityRobust Standard Errors Asymptotic Normality of the HeteroskedasticityRobust tStatistic
Distribution of Βhat_{1} with Normal Errors
17.5 Weighted Least SquaresDistribution of the HomoskedasticityOnly tStatistic
WLS with Known Heteroskedasticity
WLS with Heteroskedasticity of Known Functional Form HeteroskedasticityRobust Standard Errors or WLS? APPENDIX 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables APPENDIX 17.2 Two Inequalities CHAPTER 18 The Theory of Multiple Regression
18.1 The Linear Multiple Regression Model and OLS Estimator in Matrix Form
The Multiple Regression Model in Matrix Notation
18.2 Asymptotic Distribution of the OLS Estimator and tStatisticThe Extended Least Squares Assumptions The OLS Estimator
The Multivariate Central Limit Theorem
18.3 Tests of Joint HypothesesAsymptotic Normality of Βhat HeteroskedasticityRobust Standard Errors Confidence Intervals for Predicted Effects Asymptotic Distribution of the tStatistic
Joint Hypotheses in Matrix Notation
18.4 Distribution of Regression Statistics with Normal ErrorsAsymptotic Distribution of the FStatistic Confidence Sets for Multiple Coefficients
Matrix Representations of OLS Regression Statistics
18.5 Efficiency of the OLS Estimator with Homoskedastic ErrorsDistribution of Βhat for Normal Errors Distribution of s^{2}_{û} HomoskedasticityOnly Standard Errors Distribution of the tStatistic Distribution of the FStatistic
The Gauss–Markov Conditions for Multiple Regression
18.6 Generalized Least SquaresLinear Conditionally Unbiased Estimators The Gauss–Markov Theorem for Multiple Regression
The GLS Assumptions
18.7 Instrumental Variables and Generalized Method of Moments EstimationGLS When Ω Is Known GLS When Ω Contains Unknown Parameters The Zero Conditional Mean Assumption and GLS
The IV Estimator in Matrix Form
Asymptotic Distribution of the TSLS Estimator Properties of TSLS When the Errors are Homoskedastic Generalized Method of Moments Estimation in Linear Models APPENDIX 18.1 Summary of Matrix Algebra APPENDIX 18.2 Multivariate Distributions APPENDIX 18.3 Derivation of the Asymptotic Distribution of Βhat APPENDIX 18.4 Derivations of Exact Distributions of OLS Test Statistics with Normal Errors APPENDIX 18.5 Proof of the Gauss–Markov Theorem for Multiple Regression APPENDIX 18.6 Proof of Selected Results for IV and GMM Estimation Appendix
References
Glossary
Index

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