Efnisyfirlit

• Title Page
• Copyright Page
• Brief Contents
• Contents
• Key Concepts
• General Interest Boxes
• Preface
• Acknowledgments
• Global Acknowledgments
• Chapter 1: Economic Questions and Data
• 1.1. Economic Questions We Examine
• Question #1: Does Reducing Class Size Improve Elementary School Education?
• Question #2: Is There Racial Discrimination in the Market for Home Loans?
• Question #3: Does Healthcare Spending Improve Health Outcomes?
• Question #4: By How Much Will U.S. GDP Grow Next Year?
• Quantitative Questions, Quantitative Answers
• 1.2. Causal Effects and Idealized Experiments
• Estimation of Causal Effects
• Prediction, Forecasting, and Causality
• 1.3. Data: Sources and Types
• Experimental versus Observational Data
• Cross-Sectional 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
• Probability Distribution of a Discrete Random Variable
• Probability Distribution of a Continuous Random Variable
• 2.2. Expected Values, Mean, and Variance
• The Expected Value of a Random Variable
• The Standard Deviation and Variance
• Mean and Variance of a Linear Function of a Random Variable
• Other Measures of the Shape of a Distribution
• Standardized Random Variables
• 2.3. Two Random Variables
• Joint and Marginal Distributions
• Conditional Distributions
• Independence
• Covariance and Correlation
• The Mean and Variance of Sums of Random Variables
• 2.4. The Normal, Chi-Squared, Student t, and F Distributions
• The Normal Distribution
• The Chi-Squared Distribution
• The Student t Distribution
• The F Distribution
• 2.5. Random Sampling and the Distribution of the Sample Average
• Random Sampling
• The Sampling Distribution of the Sample Average
• 2.6. Large-Sample Approximations to Sampling Distributions
• The Law of Large Numbers and Consistency
• The Central Limit Theorem
• Appendix 2.1: Derivation of Results in Key Concept 2.3
• Appendix 2.2: The Conditional Mean as the Minimum Mean Squared Error Predictor
• Chapter 3: Review of Statistics
• 3.1. Estimation of the Population Mean
• Estimators and Their Properties
• Properties of Y
• The Importance of Random Sampling
• 3.2. Hypothesis Tests Concerning the Population Mean
• Null and Alternative Hypotheses
• The p-Value
• Calculating the p-Value When sY Is Known
• The Sample Variance, Sample Standard Deviation, and Standard Error
• Calculating the p-Value When sY Is Unknown
• The t-Statistic
• Hypothesis Testing with a Prespecified Significance Level
• One-Sided Alternatives
• 3.3. Confidence Intervals for the Population Mean
• 3.4. Comparing Means from Different Populations
• Hypothesis Tests for the Difference Between Two Means
• Confidence Intervals for the Difference Between Two Population Means
• 3.5. Differences-of-Means Estimation of Causal Effects Using Experimental Data
• The Causal Effect as a Difference of Conditional Expectations
• Estimation of the Causal Effect Using Differences of Means
• 3.6. Using the t-Statistic When the Sample Size Is Small
• The t-Statistic and the Student t Distribution
• Use of the Student t Distribution in Practice
• 3.7. Scatterplots, the Sample Covariance, and the Sample Correlation
• Scatterplots
• Sample Covariance and Correlation
• Appendix 3.1: The U.S. Current Population Survey
• Appendix 3.2: Two Proofs That Y Is the Least Squares Estimator of µY
• Appendix 3.3: A Proof That the Sample Variance Is Consistent
• 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
• OLS Estimates of the Relationship Between Test Scores and the Student–Teacher Ratio
• Why Use the OLS Estimator?
• 4.3. Measures of Fit and Prediction Accuracy
• The R2
• The Standard Error of the Regression
• Prediction Using OLS
• Application to the Test Score Data
• 4.4. The Least Squares Assumptions for Causal Inference
• Assumption 1: The Conditional Distribution of ui Given Xi Has a Mean of Zero
• Assumption 2: (Xi, Yi), i = 1,
• Assumption 3: Large Outliers Are Unlikely
• Use of the Least Squares Assumptions
• 4.5. 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
• Appendix 4.4: The Least Squares Assumptions for Prediction
• Chapter 5: Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
• 5.1. Testing Hypotheses About One of the Regression Coefficients
• Two-Sided Hypotheses Concerning ß1
• One-Sided Hypotheses Concerning ß1
• Testing Hypotheses About the Intercept ß0
• 5.2. Confidence Intervals for a Regression Coefficient
• 5.3. Regression When X Is a Binary Variable
• Interpretation of the Regression Coefficients
• 5.4. Heteroskedasticity and Homoskedasticity
• What Are Heteroskedasticity and Homoskedasticity?
• Mathematical Implications of Homoskedasticity
• What Does This Mean in Practice?
• 5.5. The Theoretical Foundations of Ordinary Least Squares
• Linear Conditionally Unbiased Estimators and the Gauss–Markov Theorem
• Regression Estimators Other Than OLS
• 5.6. Using the t-Statistic in Regression When the Sample Size Is Small
• The t-Statistic and the Student t Distribution
• Use of the Student t Distribution in Practice
• 5.7. Conclusion
• 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
• A Formula for Omitted Variable Bias
• Addressing Omitted Variable Bias by Dividing the Data into Groups
• 6.2. The Multiple Regression Model
• The Population Regression Line
• The Population Multiple Regression Model
• 6.3. The OLS Estimator in Multiple Regression
• The OLS Estimator
• Application to Test Scores and the Student–Teacher Ratio
• 6.4. Measures of Fit in Multiple Regression
• The Standard Error of the Regression (SER)
• The R2
• The Adjusted R2
• Application to Test Scores
• 6.5. The Least Squares Assumptions for Causal Inference in Multiple Regression
• Assumption 1: The Conditional Distribution of ui Given X1i, X2i,
• Assumption 2: (X1i, X2i,
• Assumption 3: Large Outliers Are Unlikely
• Assumption 4: No Perfect Multicollinearity
• 6.6. The Distribution of the OLS Estimators in Multiple Regression
• 6.7. Multicollinearity
• Examples of Perfect Multicollinearity
• Imperfect Multicollinearity
• 6.8. Control Variables and Conditional Mean Independence
• Control Variables and Conditional Mean Independence
• 6.9. Conclusion
• Appendix 6.1: Derivation of Equation (6.1)
• Appendix 6.2: Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Err
• Appendix 6.3: The Frisch–Waugh Theorem
• Appendix 6.4: The Least Squares Assumptions for Prediction with Multiple Regressors
• Appendix 6.5: Distribution of OLS Estimators in Multiple Regression with Control Variables
• 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
• Hypothesis Tests for a Single Coefficient
• Confidence Intervals for a Single Coefficient
• Application to Test Scores and the Student–Teacher Ratio
• 7.2. Tests of Joint Hypotheses
• Testing Hypotheses on Two or More Coefficients
• The F-Statistic
• Application to Test Scores and the Student–Teacher Ratio
• The Homoskedasticity-Only F-Statistic
• 7.3. Testing Single Restrictions Involving Multiple Coefficients
• 7.4. Confidence Sets for Multiple Coefficients
• 7.5. Model Specification for Multiple Regression
• Model Specification and Choosing Control Variables
• Interpreting the R2 and the Adjusted R2 in Practice
• 7.6. Analysis of the Test Score Data Set
• 7.7. Conclusion
• Appendix 7.1: The Bonferroni Test of a Joint Hypothesis
• Chapter 8: Nonlinear Regression Functions
• 8.1. A General Strategy for Modeling Nonlinear Regression Functions
• Test Scores and District Income
• The Effect on Y of a Change in X in Nonlinear Specifications
• A General Approach to Modeling Nonlinearities Using Multiple Regression
• 8.2. Nonlinear Functions of a Single Independent Variable
• Polynomials
• Logarithms
• Polynomial and Logarithmic Models of Test Scores and District Income
• 8.3. Interactions Between Independent Variables
• Interactions Between Two Binary Variables
• Interactions Between a Continuous and a Binary Variable
• Interactions Between Two Continuous Variables
• 8.4. Nonlinear Effects on Test Scores of the Student–Teacher Ratio
• Discussion of Regression Results
• Summary of Findings
• 8.5. Conclusion
• 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
• Threats to External Validity
• 9.2. Threats to Internal Validity of Multiple Regression Analysis
• Omitted Variable Bias
• Misspecification of the Functional Form of the Regression Function
• Measurement Error and Errors-in-Variables Bias
• Missing Data and Sample Selection
• Simultaneous Causality
• Sources of Inconsistency of OLS Standard Errors
• 9.3. Internal and External Validity When the Regression Is Used for Prediction
• 9.4. Example: Test Scores and Class Size
• External Validity
• Internal Validity
• Discussion and Implications
• 9.5. Conclusion
• Appendix 9.1: The Massachusetts Elementary School Testing Data
• 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” Comparisons
• 10.3. Fixed Effects Regression
• The Fixed Effects Regression Model
• Estimation and Inference
• Application to Traffic Deaths
• 10.4. Regression with Time Fixed Effects
• Time Effects Only
• Both Entity and Time Fixed Effects
• 10.5. The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression
• The Fixed Effects Regression Assumptions
• Standard Errors for Fixed Effects Regression
• 10.6. Drunk Driving Laws and Traffic Deaths
• 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
• The Linear Probability Model
• 11.2. Probit and Logit Regression
• Probit Regression
• Logit Regression
• Comparing the Linear Probability, Probit, and Logit Models
• 11.3. Estimation and Inference in the Logit and Probit Models
• Nonlinear Least Squares Estimation
• Maximum Likelihood Estimation
• Measures of Fit
• 11.4. Application to the Boston HMDA Data
• 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
• The Two Stage Least Squares Estimator
• Why Does IV Regression Work?
• The Sampling Distribution of the TSLS Estimator
• Application to the Demand for Cigarettes
• 12.2. The General IV Regression Model
• TSLS in the General IV Model
• Instrument 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
• 12.3. Checking Instrument Validity
• Assumption 1: Instrument Relevance
• Assumption 2: Instrument Exogeneity
• 12.4. Application to the Demand for Cigarettes
• 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: Large-Sample Distribution of the TSLS Estimator
• Appendix 12.4: Large-Sample 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 Quasi-Experiments
• 13.1. Potential Outcomes, Causal Effects, and Idealized Experiments
• Potential Outcomes and the Average Causal Effect
• Econometric Methods for Analyzing Experimental Data
• 13.2. Threats to Validity of Experiments
• Threats to Internal Validity
• Threats to External Validity
• 13.3. Experimental Estimates of the Effect of Class Size Reductions
• Experimental Design
• Analysis of the STAR Data
• Comparison of the Observational and Experimental Estimates of Class Size Effects
• 13.4. Quasi-Experiments
• Examples
• The Differences-in-Differences Estimator
• Instrumental Variables Estimators
• Regression Discontinuity Estimators
• 13.5. Potential Problems with Quasi-Experiments
• Threats to Internal Validity
• Threats to External Validity
• 13.6. Experimental and Quasi-Experimental Estimates in Heterogeneous Populations
• OLS with Heterogeneous Causal Effects
• IV Regression with Heterogeneous Causal Effects
• 13.7. Conclusion
• 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
• Chapter 14: Prediction with Many Regressors and Big Data
• 14.1. What Is “Big Data”?
• 14.2. The Many-Predictor Problem and OLS
• The Mean Squared Prediction Error
• The First Least Squares Assumption for Prediction
• The Predictive Regression Model with Standardized Regressors
• The MSPE of OLS and the Principle of Shrinkage
• Estimation of the MSPE
• 14.3. Ridge Regression
• Shrinkage via Penalization and Ridge Regression
• Estimation of the Ridge Shrinkage Parameter by Cross Validation
• Application to School Test Scores
• 14.4. The Lasso
• Shrinkage Using the Lasso
• Application to School Test Scores
• 14.5. Principal Components
• Principals Components with Two Variables
• Principal Components with k Variables
• Application to School Test Scores
• 14.6. Predicting School Test Scores with Many Predictors
• 14.7. Conclusion
• Appendix 14.1: The California School Test Score Data Set
• Appendix 14.2: Derivation of Equation (14.4) for k = 1
• Appendix 14.3: The Ridge Regression Estimator When k = 1
• Appendix 14.4: The Lasso Estimator When k = 1
• Appendix 14.5: Computing Out-of-Sample Predictions in the Standardized Regression Model
• Chapter 15: Introduction to Time Series Regression and Forecasting
• 15.1. Introduction to Time Series Data and Serial Correlation
• Real GDP in the United States
• Lags, First Differences, Logarithms, and Growth Rates
• Autocorrelation
• Other Examples of Economic Time Series
• 15.2. Stationarity and the Mean Squared Forecast Error
• Stationarity
• Forecasts and Forecast Errors
• The Mean Squared Forecast Error
• 15.3. Autoregressions
• The First-Order Autoregressive Model
• The pth-Order Autoregressive Model
• 15.4. Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model
• Forecasting GDP Growth Using the Term Spread
• The Autoregressive Distributed Lag Model
• The Least Squares Assumptions for Forecasting with Multiple Predictors
• 15.5. Estimation of the MSFE and Forecast Intervals
• Estimation of the MSFE
• Forecast Uncertainty and Forecast Intervals
• 15.6. Estimating the Lag Length Using Information Criteria
• Determining the Order of an Autoregression
• Lag Length Selection in Time Series Regression with Multiple Predictors
• 15.7. Nonstationarity I: Trends
• What Is a Trend?
• Problems Caused by Stochastic Trends
• Detecting Stochastic Trends: Testing for a Unit AR Root
• Avoiding the Problems Caused by Stochastic Trends
• 15.8. Nonstationarity II: Breaks
• What Is a Break?
• Testing for Breaks
• Detecting Breaks Using Pseudo Out-of-Sample Forecasts
• Avoiding the Problems Caused by Breaks
• 15.9. Conclusion
• Appendix 15.1: Time Series Data Used in Chapter 15
• Appendix 15.2: Stationarity in the AR(1) Model
• Appendix 15.3: Lag Operator Notation
• Appendix 15.4: ARMA Models
• Appendix 15.5: Consistency of the BIC Lag Length Estimator
• Chapter 16: Estimation of Dynamic Causal Effects
• 16.1. An Initial Taste of the Orange Juice Data
• 16.2. Dynamic Causal Effects
• Causal Effects and Time Series Data
• Two Types of Exogeneity
• 16.3. Estimation of Dynamic Causal Effects with Exogenous Regressors
• The Distributed Lag Model Assumptions
• Autocorrelated ut, Standard Errors, and Inference
• Dynamic Multipliers and Cumulative Dynamic Multipliers
• 16.4. Heteroskedasticity- and Autocorrelation-Consistent Standard Errors
• Distribution of the OLS Estimator with Autocorrelated Errors
• HAC Standard Errors
• 16.5. Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors
• The Distributed Lag Model with AR(1) Errors
• OLS Estimation of the ADL Model
• GLS Estimation
• 16.6. Orange Juice Prices and Cold Weather
• 16.7. Is Exogeneity Plausible? Some Examples
• U.S. Income and Australian Exports
• Oil Prices and Inflation
• Monetary Policy and Inflation
• The Growth Rate of GDP and the Term Spread
• 16.8. Conclusion
• Appendix 16.1: The Orange Juice Data Set
• Appendix 16.2: The ADL Model and Generalized Least Squares in Lag Operator Notation
• Chapter 17: Additional Topics in Time Series Regression
• 17.1. Vector Autoregressions
• The VAR Model
• A VAR Model of the Growth Rate of GDP and the Term Spread
• 17.2. Multi-period Forecasts
• Iterated Multi-period Forecasts
• Direct Multi-period Forecasts
• Which Method Should You Use?
• 17.3. Orders of Integration and the Nonnormality of Unit Root Test Statistics
• Other Models of Trends and Orders of Integration
• Why Do Unit Root Tests Have Nonnormal Distributions?
• 17.4. Cointegration
• Cointegration and Error Correction
• How Can You Tell Whether Two Variables Are Cointegrated?
• Estimation of Cointegrating Coefficients
• Extension to Multiple Cointegrated Variables
• 17.5. Volatility Clustering and Autoregressive Conditional Heteroskedasticity
• Volatility Clustering
• Realized Volatility
• Autoregressive Conditional Heteroskedasticity
• Application to Stock Price Volatility
• 17.6. Forecasting with Many Predictors Using Dynamic Factor Models and Principal Components
• The Dynamic Factor Model
• The DFM: Estimation and Forecasting
• Application to U.S. Macroeconomic Data
• 17.7. Conclusion
• Appendix 17.1: The Quarterly U.S. Macro Data Set
• Chapter 18: The Theory of Linear Regression with One Regressor
• 18.1. The Extended Least Squares Assumptions and the OLS Estimator
• The Extended Least Squares Assumptions
• The OLS Estimator
• 18.2. Fundamentals of Asymptotic Distribution Theory
• Convergence in Probability and the Law of Large Numbers
• The Central Limit Theorem and Convergence in Distribution
• Slutsky’s Theorem and the Continuous Mapping Theorem
• Application to the t-Statistic Based on the Sample Mean
• 18.3. Asymptotic Distribution of the OLS Estimator and t-Statistic
• Consistency and Asymptotic Normality of the OLS Estimators
• Consistency of Heteroskedasticity-Robust Standard Errors
• Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic
• 18.4. Exact Sampling Distributions When the Errors Are Normally Distributed
• Distribution of b n 1 with Normal Errors
• Distribution of the Homoskedasticity-Only t-Statistic
• 18.5. Weighted Least Squares
• WLS with Known Heteroskedasticity
• WLS with Heteroskedasticity of Known Functional Form
• Heteroskedasticity-Robust Standard Errors or WLS?
• Appendix 18.1: The Normal and Related Distributions and Moments of Continuous Random Variables
• Appendix 18.2: Two Inequalities
• Chapter 19: The Theory of Multiple Regression
• 19.1. The Linear Multiple Regression Model and OLS Estimator in Matrix Form
• The Multiple Regression Model in Matrix Notation
• The Extended Least Squares Assumptions
• The OLS Estimator
• 19.2. Asymptotic Distribution of the OLS Estimator and t-Statistic
• The Multivariate Central Limit Theorem
• Asymptotic Normality of b n
• Heteroskedasticity-Robust Standard Errors
• Confidence Intervals for Predicted Effects
• Asymptotic Distribution of the t-Statistic
• 19.3. Tests of Joint Hypotheses
• Joint Hypotheses in Matrix Notation
• Asymptotic Distribution of the F-Statistic
• Confidence Sets for Multiple Coefficients
• 19.4. Distribution of Regression Statistics with Normal Errors
• Matrix Representations of OLS Regression Statistics
• Distribution of b n with Independent Normal Errors
• Distribution of su 2 N
• Homoskedasticity-Only Standard Errors
• Distribution of the t-Statistic
• Distribution of the F-Statistic
• 19.5. Efficiency of the OLS Estimator with Homoskedastic Errors
• The Gauss–Markov Conditions for Multiple Regression
• Linear Conditionally Unbiased Estimators
• The Gauss–Markov Theorem for Multiple Regression
• 19.6. Generalized Least Squares
• The GLS Assumptions
• GLS When O Is Known
• GLS When O Contains Unknown Parameters
• The Conditional Mean Zero Assumption and GLS
• 19.7. Instrumental Variables and Generalized Method of Moments Estimation
• 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 19.1: Summary of Matrix Algebra
• Appendix 19.2: Multivariate Distributions
• Appendix 19.3: Derivation of the Asymptotic Distribution of b n
• Appendix 19.4: Derivations of Exact Distributions of OLS Test Statistics with Normal Errors
• Appendix 19.5: Proof of the Gauss–Markov Theorem for Multiple Regression
• Appendix 19.6: Proof of Selected Results for IV and GMM Estimation
• Appendix 19.7: Regression with Many Predictors: MSPE, Ridge Regression, and Principal Components Ana
• Appendix
• References
• Glossary
• Index