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Preface | |

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Introduction and Review | |

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Economic Questions and Data | |

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Economic Questions We Examine | |

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Does Reducing Class Size Improve Elementary School Education? | |

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Is There Racial Discrimination in the Market for Home Loans? | |

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How Much Do Cigarette Taxes Reduce Smoking? | |

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What Will the Rate of Inflation Be Next Year? | |

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Quantitative Questions, Quantitative Answers | |

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Causal Effects and Idealized Experiments | |

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Estimation of Causal Effects | |

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Forecasting and Causality | |

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Data: Sources and Types | |

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Experimental versus Observational Data | |

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Cross-Sectional Data | |

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Time Series Data | |

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Panel Data | |

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Review of Probability | |

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Random Variables and Probability Distributions | |

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Probabilities, the Sample Space, and Random Variables | |

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Probability Distribution of a Discrete Random Variable | |

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Probability Distribution of a Continuous Random Variable | |

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Expected Values, Mean, and Variance | |

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The Expected Value of a Random Variable | |

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The Standard Deviation and Variance | |

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Mean and Variance of a Linear Function of a Random Variable | |

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Other Measures of the Shape of a Distribution | |

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Two Random Variables | |

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Joint and Marginal Distributions | |

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Conditional Distributions | |

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Independence | |

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Covariance and Correlation | |

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The Mean and Variance of Sums of Random Variables | |

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The Normal, Chi-Squared, Student t, and F Distributions | |

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The Normal Distribution | |

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The Chi-Squared Distribution | |

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The Student t Distribution | |

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The F Distribution | |

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Random Sampling and the Distribution of the Sample Average | |

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Random Sampling | |

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The Sampling Distribution of the Sample Average | |

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Large-Sample Approximations to Sampling Distributions | |

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The Law of Large Numbers and Consistency | |

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The Central Limit Theorem | |

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Derivation of Results in Key Concept 2.3 | |

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Review of Statistics | |

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Estimation of the Population Mean | |

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Estimators and Their Properties | |

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Properties of Y | |

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The Importance of Random Sampling | |

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Hypothesis Tests Concerning the Population Mean | |

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Null and Alternative Hypotheses | |

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The p-Value | |

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Calculating the p-Value When [sigma subscript Y] is Known | |

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The Sample Variance, Sample Standard Deviation, and Standard Error | |

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Calculating the p-Value When [sigma subscript Y] Is Unknown | |

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The t-Statistic | |

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Hypothesis Testing with a Prespecified Significance Level | |

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One-Sided Alternatives | |

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Confidence Intervals for the Population Mean | |

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Comparing Means from Different Populations | |

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Hypothesis Tests for the Difference Between Two Means | |

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Confidence Intervals for the Difference Between Two Population Means | |

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Differences-of-Means Estimation of Causal Effects Using Experimental Data | |

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The Causal Effect as a Difference of Conditional Expectations | |

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Estimation of the Causal Effect Using Differences of Means | |

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Using the t-Statistic When the Sample Size Is Small | |

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The t-Statistic and the Student t Distribution | |

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Use of the Student t Distribution in Practice | |

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Scatterplot, the Sample Covariance, and the Sample Correlation | |

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Scatterplots | |

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Sample Covariance and Correlation | |

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The U.S. Current Population Survey | |

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Two Proofs That Y Is the Least Squares Estimator of [mu subscript Y] | |

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A Proof That the Sample Variance Is Consistent | |

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Fundamentals of Regression Analysis | |

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Linear Regression with One Regressor | |

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The Linear Regression Model | |

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Estimating the Coefficients of the Linear Regression Model | |

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The Ordinary Least Squares Estimator | |

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OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio | |

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Why Use the OLS Estimator? | |

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Measures of Fit | |

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The R[superscript 2] | |

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The Standard Error of the Regression | |

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Application to the Test Score Data | |

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The Least Squares Assumptions | |

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The Conditional Distribution of u[subscript i] Given X[subscript i] Has a Mean of Zero | |

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(X[subscript i], Y[subscript i]), = 1,..., n Are Independently and Identically Distributed | |

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Large Outliers Are Unlikely | |

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Use of the Least Squares Assumptions | |

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The Sampling Distribution of the OLS Estimators | |

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The Sampling Distribution of the OLS Estimators | |

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Conclusion | |

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The California Test Score Data Set | |

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Derivation of the OLS Estimators | |

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Sampling Distribution of the OLS Estimator | |

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Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals | |

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Testing Hypotheses About One of the Regression Coefficients | |

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Two-Sided Hypotheses Concerning [Beta subscript 1] | |

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One-Sided Hypotheses Concerning [Beta subscript 1] | |

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Testing Hypotheses About the Intercept [Beta subscript 0] | |

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Confidence Intervals for a Regression Coefficient | |

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Regression When X Is a Binary Variable | |

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Interpretation of the Regression Coefficients | |

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Heteroskedasticity and Homoskedasticity | |

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What Are Heteroskedasticity and Homoskedasticity? | |

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Mathematical Implications of Homoskedasticity | |

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What Does This Mean in Practice? | |

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The Theoretical Foundations of Ordinary Least Squares | |

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Linear Conditionally Unbiased Estimators and the Gauss-Markov Theorem | |

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Regression Estimators Other Than OLS | |

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Using the t-Statistic in Regression When the Sample Size Is Small | |

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The t-Statistic and the Student t Distribution | |

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Use of the Student t Distribution in Practice | |

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Conclusion | |

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Formulas for OLS Standard Errors | |

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The Gauss-Markov Conditions and a Proof of the Gauss-Markov Theorem | |

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Linear Regression with Multiple Regressors | |

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Omitted Variable Bias | |

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Definition of Omitted Variable Bias | |

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A Formula for Omitted Variable Bias | |

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Addressing Omitted Variable Bias by Dividing the Data into Groups | |

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The Multiple Regression Model | |

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The Population Regression Line | |

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The Population Multiple Regression Model | |

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The OLS Estimator in Multiple Regression | |

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The OLS Estimator | |

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Application to Test Scores and the Student-Teacher Ratio | |

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Measures of Fit in Multiple Regression | |

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The Standard Error of the Regression (SER) | |

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The R[superscript 2] | |

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The "Adjusted R[superscript 2]" | |

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Application to Test Scores | |

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The Least Squares Assumptions in Multiple Regression | |

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The Conditional Distribution of u[subscript i] Given X[subscript 1i], X[subscript 2i],..., X[subscript ki] Has a Mean of Zero | |

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(X[subscript 1i], X[subscript 2i],..., X[subscript ki], Y[subscript i]) i = 1,..., n Are i.i.d. | |

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Large Outliers Are Unlikely | |

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No Perfect Multicollinearity | |

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The Distribution of the OLS Estimators in Multiple Regression | |

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Multicollinearity | |

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Examples of Perfect Multicollinearity | |

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Imperfect Multicollinearity | |

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Conclusion | |

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Derivation of Equation (6.1) | |

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Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors | |

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Hypothesis Tests and Confidence Intervals in Multiple Regression | |

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Hypothesis Tests and Confidence Intervals for a Single Coefficient | |

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Standard Errors for the OLS Estimators | |

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Hypothesis Tests for a Single Coefficient | |

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Confidence Intervals for a Single Coefficient | |

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Application to Test Scores and the Student-Teacher Ratio | |

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Tests of Joint Hypotheses | |

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Testing Hypotheses on Two or More Coefficients | |

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The F-Statistic | |

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Application to Test Scores and the Student-Teacher Ratio | |

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The Homoskedasticity-Only F-Statistic | |

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Testing Single Restrictions Involving Multiple Coefficients | |

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Confidence Sets for Multiple Coefficients | |

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Model Specification for Multiple Regression | |

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Omitted Variable Bias in Multiple Regression | |

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Model Specification in Theory and in Practice | |

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Interpreting the R[superscript 2] and the Adjusted R[superscript 2] in Practice | |

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Analysis of the Test Score Data Set | |

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Conclusion | |

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The Bonferroni Test of a Joint Hypotheses | |

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Nonlinear Regression Functions | |

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A General Strategy for Modeling Nonlinear Regression Functions | |

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Test Scores and District Income | |

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The Effect on Y of a Change in X in Nonlinear Specifications | |

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A General Approach to Modeling Nonlinearities Using Multiple Regression | |

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Nonlinear Functions of a Single Independent Variable | |

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Polynomials | |

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Logarithms | |

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Polynomial and Logarithmic Models of Test Scores and District Income | |

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Interactions Between Independent Variables | |

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Interactions Between Two Binary Variables | |

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Interactions Between a Continuous and a Binary Variable | |

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Interactions Between Two Continuous Variables | |

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Nonlinear Effects on Test Scores of the Student-Teacher Ratio | |

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Discussion of Regression Results | |

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Summary of Findings | |

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Conclusion | |

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Regression Functions That Are Nonlinear in the Parameters | |

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Assessing Studies Based on Multiple Regression | |

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Internal and External Validity | |

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Threats to Internal Validity | |

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Threats to External Validity | |

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Threats to Internal Validity of Multiple Regression Analysis | |

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Omitted Variable Bias | |

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Misspecification of the Functional Form of the Regression Function | |

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Errors-in-Variables | |

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Sample Selection | |

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Simultaneous Causality | |

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Sources of Inconsistency of OLS Standard Errors | |

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Internal and External Validity When the Regression Is Used for Forecasting | |

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Using Regression Models for Forecasting | |

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Assessing the Validity of Regression Models for Forecasting | |

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Example: Test Scores and Class Size | |

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External Validity | |

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Internal Validity | |

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Discussion and Implications | |

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Conclusion | |

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The Massachusetts Elementary School Testing Data | |

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Further Topics in Regression Analysis | |

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Regression with Panel Data | |

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Panel Data | |

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Example: Traffic Deaths and Alcohol Taxes | |

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Panel Data with Two Time Periods: "Before and After" Comparisons | |

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Fixed Effects Regression | |

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The Fixed Effects Regression Model | |

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Estimation and Inference | |

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Application to Traffic Deaths | |

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Regression with Time Fixed Effects | |

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Time Effects Only | |

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Both Entity and Time Fixed Effects | |

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The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression | |

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The Fixed Effects Regression Assumptions | |

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Standard Errors for Fixed Effects Regression | |

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Drunk Driving Laws and Traffic Deaths | |

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Conclusion | |

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The State Traffic Fatality Data Set | |

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Standard Errors for Fixed Effects Regression with Serially Correlated Errors | |

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Regression with a Binary Dependent Variable | |

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Binary Dependent Variables and the Linear Probability Model | |

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Binary Dependent Variables | |

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The Linear Probability Model | |

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Probit and Logit Regression | |

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Probit Regression | |

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Logit Regression | |

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Comparing the Linear Probability, Probit, and Logit Models | |

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Estimation and Inference in the Logit and Probit Models | |

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Nonlinear Least Squares Estimation | |

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Maximum Likelihood Estimation | |

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Measures of Fit | |

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Application to the Boston HMDA Data | |

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Summary | |

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The Boston HMDA Data Set | |

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Maximum Likelihood Estimation | |

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Other Limited Dependent Variable Models | |

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Instrumental Variables Regression | |

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The IV Estimator with a Single Regressor and a Single Instrument | |

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The IV Model and Assumptions | |

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The Two Stage Least Squares Estimator | |

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Why Does IV Regression Work? | |

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The Sampling Distribution of the TSLS Estimator | |

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Application to the Demand for Cigarettes | |

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The General IV Regression Model | |

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TSLS in the General IV Model | |

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Instrument Relevance and Exogeneity in the General IV Model | |

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The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator | |

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Inference Using the TSLS Estimator | |

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Application to the Demand for Cigarettes | |

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Checking Instrument Validity | |

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Instrument Relevance | |

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Instrument Exogeneity | |

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Application to the Demand for Cigarettes | |

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Where Do Valid Instruments Come From? | |

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Three Examples | |

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Conclusion | |

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The Cigarette Consumption Panel Data Set | |

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Derivation of the Formula for the TSLS Estimator in Equation (12.4) | |

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Large-Sample Distribution of the TSLS Estimator | |

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Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid | |

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Instrumental Variables Analysis with Weak Instruments | |

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Experiments and Quasi-Experiments | |

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Idealized Experiments and Causal Effects | |

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Ideal Randomized Controlled Experiments | |

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The Differences Estimator | |

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Potential Problems with Experiments in Practice | |

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Threats to Internal Validity | |

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Threats to External Validity | |

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Regression Estimators of Causal Effects Using Experimental Data | |

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The Differences Estimator with Additional Regressors | |

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The Differences-in-Differences Estimator | |

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Estimation of Causal Effects for Different Groups | |

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Estimation When There Is Partial Compliance | |

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Testing for Randomization | |

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Experimental Estimates of the Effect of Class Size Reductions | |

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Experimental Design | |

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Analysis of the STAR Data | |

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Comparison of the Observational and Experimental Estimates of Class Size Effects | |

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Quasi-Experiments | |

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Examples | |

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Econometric Methods for Analyzing Quasi-Experiments | |

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Potential Problems with Quasi-Experiments | |

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Threats to Internal Validity | |

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Threats to External Validity | |

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Experimental and Quasi-Experimental Estimates in Heterogeneous Populations | |

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Population Heterogeneity: Whose Causal Effect? | |

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OLS with Heterogeneous Causal Effects | |

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IV Regression with Heterogeneous Causal Effects | |

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Conclusion | |

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The Project STAR Data Set | |

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Extension of the Differences-in-Differences Estimator to Multiple Time Periods | |

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Conditional Mean Independence | |

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IV Estimation When the Causal Effect Varies Across Individuals | |

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Regression Analysis of Economic Time Series Data | |

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Introduction to Time Series Regression and Forecasting | |

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Using Regression Models for Forecasting | |

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Introduction to Time Series Data and Serial Correlation | |

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The Rates of Inflation and Unemployment in the United States | |

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Lags, First Differences, Logarithms, and Growth Rates | |

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Autocorrelation | |

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Other Examples of Economic Time Series | |

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Autoregressions | |

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The First Order Autoregressive Model | |

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The p[superscript th] Order Autoregressive Model | |

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Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model | |

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Forecasting Changes in the Inflation Rate Using Past Unemployment Rates | |

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Stationarity | |

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Time Series Regression with Multiple Predictors | |

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Forecast Uncertainty and Forecast Intervals | |

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Lag Length Selection Using Information Criteria | |

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Determining the Order of an Autoregression | |

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Lag Length Selection in Time Series Regression with Multiple Predictors | |

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Nonstationarity I: Trends | |

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What Is a Trend? | |

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Problems Caused by Stochastic Trends | |

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Detecting Stochastic Trends: Testing for a Unit AR Root | |

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Avoiding the Problems Caused by Stochastic Trends | |

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Nonstationarity II: Breaks | |

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What Is a Break? | |

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Testing for Breaks | |

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Pseudo Out-of-Sample Forecasting | |

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Avoiding the Problems Caused by Breaks | |

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Conclusion | |

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Time Series Data Used in Chapter 14 | |

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Stationarity in the AR(1) Model | |

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Lag Operator Notation | |

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ARMA Models | |

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Consistency of the BIC Lag Length Estimator | |

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Estimation of Dynamic Causal Effects | |

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An Initial Taste of the Orange Juice Data | |

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Dynamic Causal Effects | |

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Causal Effects and Time Series Data | |

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Two Types of Exogeneity | |

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Estimation of Dynamic Causal Effects with Exogenous Regressors | |

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The Distributed Lag Model Assumptions | |

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Autocorrelated u[subscript t], Standard Errors, and Inference | |

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Dynamic Multipliers and Cumulative Dynamic Multipliers | |

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Heteroskedasticity- and Autocorrelation-Consistent Standard Errors | |

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Distribution of the OLS Estimator with Autocorrelated Errors | |

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HAC Standard Errors | |

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Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors | |

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The Distributed Lag Model with AR(1) Errors | |

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OLS Estimation of the ADL Model | |

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GLS Estimation | |

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The Distributed Lag Model with Additional Lags and AR(p) Errors | |

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Orange Juice Prices and Cold Weather | |

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Is Exogeneity Plausible? Some Examples | |

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U.S. Income and Australian Exports | |

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Oil Prices and Inflation | |

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Monetary Policy and Inflation | |

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The Phillips Curve | |

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Conclusion | |

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The Orange Juice Data Set | |

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The ADL Model and Generalized Least Squares in Lag Operator Notation | |

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Additional Topics in Time Series Regression | |

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Vector Autoregressions | |

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The VAR Model | |

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A VAR Model of the Rates of Inflation and Unemployment | |

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Multiperiod Forecasts | |

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Iterated Muliperiod Forecasts | |

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Direct Multiperiod Forecasts | |

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Which Method Should You Use? | |

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Orders of Integration and the DF-GLS Unit Root Test | |

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Other Models of Trends and Orders of Integration | |

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The DF-GLS Test for a Unit Root | |

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Why Do Unit Root Tests Have Non-normal Distributions? | |

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Cointegration | |

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Cointegration and Error Correction | |

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How Can You Tell Whether Two Variables Are Cointegrated? | |

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Estimation of Cointegrating Coefficients | |

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Extension to Multiple Cointegrated Variables | |

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Application to Interest Rates | |

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Volatility Clustering and Autoregressive Conditional Heteroskedasticity | |

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Volatility Clustering | |

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Autoregressive Conditional Heteroskedasticity | |

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Application to Stock Price Volatility | |

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Conclusion | |

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U.S. Financial Data Used in Chapter 16 | |

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The Econometric Theory of Regression Analysis | |

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The Theory of Linear Regression with One Regressor | |

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The Extended Least Squares Assumptions and the OLS Estimator | |

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The Extended Least Squares Assumptions | |

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The OLS Estimator | |

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Fundamentals of Asymptotic Distribution Theory | |

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Convergence in Probability and the Law of Large Numbers | |

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The Central Limit Theorem and Convergence in Distribution | |

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Slutsky's Theorem and the Continuous Mapping Theorem | |

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Application to the t-Statistic Based on the Sample Mean | |

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Asymptotic Distribution of the OLS Estimator and t-Statistic | |

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Consistency and Asymptotic Normality of the OLS Estimators | |

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Consistency of Heteroskedasticity-Robust Standard Errors | |

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Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic | |

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Exact Sampling Distributions When the Errors Are Normally Distributed | |

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Distribution of [Beta subscript 1] with Normal Errors | |

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Distribution of the Homoskedasticity-only t-Statistic | |

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Weighted Least Squares | |

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WLS with Known Heteroskedasticity | |

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WLS with Heteroskedasticity of Known Functional Form | |

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Heteroskedasticity-Robust Standard Errors or WLS? | |

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The Normal and Related Distributions and Moments of Continuous Random Variables | |

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Two Inequalities | |

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The Theory of Multiple Regression | |

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The Linear Multiple Regression Model and OLS Estimator in Matrix Form | |

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The Multiple Regression Model in Matrix Notation | |

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The Extended Least Squares Assumptions | |

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The OLS Estimator | |

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Asymptotic Distribution of the OLS Estimator and t-Statistic | |

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The Multivariate Central Limit Theorem | |

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Asymptotic Normality of [Beta] | |

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Heteroskedasticity-Robust Standard Errors | |

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Confidence Intervals for Predicted Effects | |

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Asymptotic Distribution of the t-Statistic | |

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Tests of Joint Hypotheses | |

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Joint Hypotheses in Matrix Notation | |

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Asymptotic Distribution of the F-Statistic | |

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Confidence Sets for Multiple Coefficients | |

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Distribution of Regression Statistics with Normal Errors | |

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Matrix Representations of OLS Regression Statistics | |

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Distribution of [Beta] with Normal Errors | |

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Distribution of [Characters not reproducible] | |

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Homoskedasticity-Only Standard Errors | |

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Distribution of the t-Statistic | |

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Distribution of the F-Statistic | |

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Efficiency of the OLS Estimator with Homoskedastic Errors | |

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The Gauss-Markov Conditions for Multiple Regression | |

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Linear Conditionally Unbiased Estimators | |

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The Gauss-Markov Theorem for Multiple Regression | |

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Generalized Least Squares | |

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The GLS Assumptions | |

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GLS When [Omega] Is Known | |

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GLS When [Omega] Contains Unknown Parameters | |

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The Zero Conditional Mean Assumption and GLS | |

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Instrumental Variables and Generalized Method of Moments Estimation | |

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The IV Estimator in Matrix Form | |

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Asymptotic Distribution of the TSLS Estimator | |

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Properties of TSLS When the Errors Are Homoskedastic | |

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Generalized Method of Moments Estimation in Linear Models | |

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Summary of Matrix Algebra | |

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Multivariate Distributions | |

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Derivation of the Asymptotic Distribution of [Beta] | |

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Derivations of Exact Distributions of OLS Test Statistics with Normal Errors | |

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Proof of the Gauss-Markov Theorem for Multiple Regression | |

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Proof of Selected Results for IV and GMM Estimation | |

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Appendix | |

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References | |

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Answers to "Review the Concepts" Questions | |

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Glossary | |

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Index | |