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Preface | |

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Introduction | |

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Single-Equation Regression Models | |

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The Nature of Regression Analysis | |

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Historical Origin of the Term "Regression" | |

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The Modern Interpretation of Regression | |

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Examples | |

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Statistical vs. Deterministic Relationships | |

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Regression vs. Causation | |

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Regression vs. Correlation | |

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Terminology and Notation | |

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The Nature and Sources of Data for Econometric Analysis | |

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Types of Data | |

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The Sources of Data | |

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The Accuracy of Data | |

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Summary and Conclusions | |

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Exercises | |

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Appendix 1A | |

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Sources of Economic Data | |

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Sources of Financial Data | |

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Two-Variable Regression Analysis: Some Basic Ideas | |

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A Hypothetical Example | |

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The Concept of Population Regression Function (PRF) | |

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The Meaning of the Term "Linear" | |

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Linearity in the Variables | |

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Linearity in the Parameters | |

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Stochastic Specification of PRF | |

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The Significance of the Stochastic Disturbance Term | |

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The Sample Regression Function (SRF) | |

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Summary and Conclusions | |

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Exercises | |

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Two-Variable Regression Model: The Problem of Estimation | |

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The Method of Ordinary Least Squares | |

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The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares | |

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How Realistic Are These Assumptions? | |

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Precision or Standard Errors of Least-Squares Estimates | |

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Properties of Least-Squares Estimators: The Gauss-Markov Theorem | |

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The Coefficient of Determination r2: A Measure of "Goodness of Fit" | |

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A Numerical Example | |

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Illustrative Examples | |

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Coffee Consumption in the United States, 1970-1980 | |

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Keynesian Consumption Function for the United States, 1980-1991 | |

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Computer Output for the Coffee Demand Function | |

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A Note on Monte Carlo Experiments | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 3A | |

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Derivation of Least-Squares Estimates | |

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Linearity and Unbiasedness Properties of Least-Squares Estimators | |

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Variances and Standard Errors of Least-Squares Estimators | |

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Covariance between B1 and B2 | |

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The Least-Squares Estimator of o2 | |

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Minimum-Variance Property of Least-Squares Estimators | |

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SAS Output of the Coffee Demand Function (3.7.1) | |

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The Normality Assumption: Classical Normal Linear Regression Model (CNLRM) | |

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The Probability Distribution of Disturbances ui | |

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The Normality Assumption | |

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Properties of OLS Estimators under the Normality Assumption | |

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The Method of Maximum Likelihood (ML) | |

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Probability Distributions Related to the Normal Distribution: The t, Chi-square (X2), and F Distributions | |

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Summary and Conclusions | |

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Appendix 4A | |

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Maximum Likelihood Estimation of Two-Variable Regression Model | |

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Maximum Likelihood Estimation of the Consumption-Income Example | |

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Appendix 4A Exercises | |

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Two-Variable Regression: Interval Estimation and Hypothesis Testing | |

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Statistical Prerequisites | |

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Interval Estimation: Some Basic Ideas | |

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Confidence Intervals for Regression Coefficients B1 and B2 | |

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Confidence Interval for B2 | |

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Confidence Interval for B1 | |

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Confidence Interval for B1 and B2 Simultaneously | |

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Confidence Interval for o2 | |

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Hypothesis Testing: General Comments | |

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Hypothesis Testing: The Confidence-Interval Approach | |

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Two-Sided or Two-Tail Test | |

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One-Sided or One-Tail Test | |

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Hypothesis Testing: The Test-of-Significance Approach | |

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Testing the Significance of Regression Coefficients: The t-Test | |

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Testing the Significance of o2: the X2 Test | |

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Hypothesis Testing: Some Practical Aspects | |

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The Meaning of "Accepting" or "Rejecting" a Hypothesis | |

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The "Zero" Null Hypothesis and the "2-t" Rule of Thumb | |

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Forming the Null and Alternative Hypotheses | |

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Choosing a, the Level of Significance | |

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The Exact Level of Significance: The p Value | |

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Statistical Significance versus Practical Significance | |

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The Choice between Confidence-Interval and Test-of-Significance Approaches to Hypothesis Testing | |

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Regression Analysis and Analysis of Variance | |

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Application of Regression Analysis: The Problem of Prediction | |

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Mean Prediction | |

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Individual Prediction | |

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Reporting the Results of Regression Analysis | |

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Evaluating the Results of Regression Analysis | |

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Normality Test | |

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Other Tests of Model Adequacy | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 5A | |

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Derivation of Equation (5.3.2) | |

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Derivation of Equation (5.9.1) | |

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Derivation of Equations (5.10.2) and (5.10.6) | |

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Variance of Mean Prediction | |

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Variance of Individual Prediction | |

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Extensions of the Two-Variable Linear Regression Model | |

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Regression through the Origin | |

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r2 for Regression-through-Origin Model An Illustrative Example: The Characteristic Line of Portfolio Theory | |

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Scaling and Units of Measurement | |

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A Numerical Example: The Relationship between GPDI and GNP, United States, 1974-1983 | |

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A Word about Interpretation | |

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Functional Forms of Regression Models | |

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How to Measure Elasticity: The Log-Linear Model | |

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An Illustrative Example: The Coffee Demand Function Revisited | |

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Semilog Models: Log-Lin and Lin-Log Models | |

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How to Measure the Growth Rate: The Log-Lin Model | |

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The Lin-Log Model | |

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Reciprocal Models | |

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An Illustrative Example: The Phillips Curve for the United Kingdom, 1950-1966 | |

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Summary of Functional Forms | |

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A Note on the Nature of the Stochastic Error Term: Additive versus Multiplicative Stochastic Error Term | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 6A | |

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Derivation of Least-Squares Estimators for Regression through the Origin | |

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SAS Output of the Characteristic Line (6.1.12) | |

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SAS Output of the United Kingdom Phillips Curve Regression (6.6.2) | |

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Multiple Regression Analysis: The Problem of Estimation | |

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The Three-Variable Model: Notation and Assumptions | |

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Interpretation of Multiple Regression Equation | |

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The Meaning of Partial Regression Coefficients | |

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OLS and ML Estimation of the Partial Regression Coefficients | |

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OLS Estimators | |

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Variances and Standard Errors of OLS Estimators | |

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Properties of OLS Estimators | |

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Maximum Likelihood Estimators | |

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The Multiple Coefficient of Determination R2 and the Multiple Coefficient of Correlation R | |

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Example 7.1: The Expectations-Augmented Phillips Curve for the United States, 1970-1982 | |

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Simple Regression in the Context of Multiple Regression: Introduction to Specification Bias | |

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R2 and the Adjusted R2 | |

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Comparing Two R2 Values | |

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Example 7.2: Coffee Demand Function Revisited | |

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The "Game" of Maximizing R2 | |

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Partial Correlation Coefficients | |

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Explanation of Simple and Partial Correlation Coefficients | |

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Interpretation of Simple and Partial Correlation Coefficients | |

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Example 7.3: The Cobb-Douglas Production Function: More on Functional Form | |

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Polynomial Regression Models | |

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Example 7.4: Estimating the Total Cost Function | |

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Empirical Results | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 7A | |

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Derivation of OLS Estimators Given in Equations (7.4.3) and (7.4.5) | |

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Equality between a1 of (7.3.5) and B2 of (7.4.7) | |

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Derivation of Equation (7.4.19) | |

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Maximum Likelihood Estimation of the Multiple Regression Model | |

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The Proof that E(b12) = B2 + B3b32 (Equation 7.7.4) | |

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SAS Output of the Expectations-Augmented Phillips Curve (7.6.2) | |

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SAS Output of the Cobb-Douglas Production Function (7.10.4) | |

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Multiple Regression Analysis: The Problem of Inference | |

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The Normality Assumption Once Again | |

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Example 8.1: U.S. Personal Consumption and Personal Disposal Income Relation, 1956-1970 | |

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Hypothesis Testing in Multiple Regression: General Comments | |

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Hypothesis Testing about Individual Partial Regression Coefficients | |

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Testing the Overall Significance of the Sample Regression | |

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The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test | |

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An Important Relationship between R2 and F | |

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The "Incremental," or "Marginal," Contribution of an Explanatory Variable | |

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Testing the Equality of Two Regression Coefficients | |

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Example 8.2: The Cubic Cost Function Revisited | |

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Restricted Least Squares: Testing Linear Equality Restrictions | |

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The t Test Approach | |

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The F Test Approach: Restricted Least Squares | |

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Example 8.3: The Cobb-Douglas Production Function for Taiwanese Agricultural Sector, 1958-1972 | |

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General F Testing | |

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Comparing Two Regressions: Testing for Structural Stability of Regression Models | |

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Testing the Functional Form of Regression: Choosing between Linear and Log-Linear Regression Models | |

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Example 8.5: The Demand for Roses | |

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Prediction with Multiple Regression | |

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The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Tests | |

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Summary and Conclusions | |

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The Road Ahead | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 8A | |

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Likelihood Ratio (LR) Test | |

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The Matrix Approach to Linear Regression Model | |

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The k-Variable Linear Regression Model | |

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Assumptions of the Classical Linear Regression Model in Matrix Notation | |

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OLS Estimation | |

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An Illustration | |

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Variance-Covariance Matrix of B | |

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Properties of OLS Vector B | |

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The Coefficient of Determination R2 in Matrix Notation | |

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The Correlation Matrix | |

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Hypothesis Testing about Individual Regression Coefficients in Matrix Notation | |

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Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notation | |

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Testing Linear Restrictions: General F Testing Using Matrix Notation | |

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Prediction Using Multiple Regression: Matrix Formulation | |

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Mean Prediction | |

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Individual Prediction | |

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Variance of Mean Prediction | |

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Variance of Individual Prediction | |

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Summary of the Matrix Approach: An Illustrative Example | |

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Summary and Conclusions | |

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Exercises | |

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Appendix 9A | |

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Derivation of k Normal or Simultaneous Equations | |

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Matrix Derivation of Normal Equations | |

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Variance-Covariance Matrix of B | |

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Blue Property of OLS Estimators | |

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Relaxing the Assumptions of the Classical Model | |

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Multicollinearity and Micronumerosity | |

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The Nature of Multicollinearity | |

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Estimation in the Presence of Perfect Multicollinearity | |

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Estimation in the Presence of "High" but "Imperfect" Multicollinearity | |

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Multicollinearity: Much Ado about Nothing? Theoretical Consequences of Multicollinearity | |

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Practical Consequences of Multicollinearity | |

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Large Variances and Covariances of OLS Estimators | |

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Wider Confidence Intervals | |

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"Insignificant" t Ratios | |

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A High R2 but Few Significant t Ratios | |

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Sensitivity of OLS Estimators and Their Standard Errors to Small Changes in Data | |

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Consequences of Micronumerosity | |

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An Illustrative Example: Consumption Expenditure in Relation to Income and Wealth | |

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Detection of Multicollinearity | |

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Remedial Measures | |

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Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Only | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Heteroscedasticity | |

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The Nature of Heteroscedasticity | |

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OLS Estimation in the Presence of Heteroscedasticity | |

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The Method of Generalized Least Squares (GLS) | |

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Difference between OLS and GLS | |

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Consequences of Using OLS in the Presence of Heteroscedasticity | |

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OLS Estimation Allowing for Heteroscedasticity | |

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OLS Estimation Disregarding Heteroscedasticity | |

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Detection of Heteroscedasticity | |

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Informal Methods | |

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Formal Methods | |

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Remedial Measures | |

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When oi2 Is Known: The Method of Weighted Least Squares | |

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When o12 Is Not Known | |

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A Concluding Example | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 11A | |

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Proof of Equation (11.2.2) | |

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The Method of Weighted Least Squares | |

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Autocorrelation | |

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The Nature of the Problem | |

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OLS Estimation in the Presence of Autocorrelation | |

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The BLUE Estimator in the Presence of Autocorrelation | |

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Consequences of Using OLS in the Presence of Autocorrelation | |

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OLS Estimation Allowing for Autocorrelation | |

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OLS Estimation Disregarding Autocorrelation | |

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Detecting Autocorrelation | |

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Graphical Method | |

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The Runs Test | |

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Durbin-Watson d Test | |

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Additional Tests of Autocorrelation | |

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Remedial Measures | |

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When the Structure of Autocorrelation Is Known | |

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When p Is Not Known | |

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An Illustrative Example: The Relationship between Help-Wanted Index and the Unemployment Rate, United States: Comparison of the Methods | |

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Autoregressive Conditional Heteroscedasticity (ARCH) Model | |

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What to Do If ARCH Is Present? | |

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A Word on the Durbin-Watson d Statistic and the ARCH Effect | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 12A | |

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TSP Output of United States Wages (Y)-Productivity (X) Regression, 1960-1991 | |

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Econometric Modeling I: Traditional Econometric Methodology | |

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The Traditional View of Econometric Modeling: Average Economic Regression (AER) | |

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Types of Specification Errors | |

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Consequences of Specification Errors | |

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Omitting a Relevant Variable (Underfitting a Model) | |

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Inclusion of an Irrelevant Variable (Overfitting a Model) | |

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Tests of Specification Errors | |

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Detecting the Presence of Unnecessary Variables | |

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Tests for Omitted Variables and Incorrect Functional Form | |

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Errors of Measurement | |

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Errors of Measurement in the Dependent Variable Y | |

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Errors of Measurement in the Explanatory Variable X | |

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An Example | |

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Measurement Errors in the Dependent Variable Y Only | |

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Errors of Measurement in X | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 13A | |

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The Consequences of Including an Irrelevant Variable: The Unbiasedness Property | |

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Proof of (13.5.10) | |

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Econometric Modeling II: Alternative Econometric Methodologies | |

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Learner's Approach to Model Selection | |

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Hendry's Approach to Model Selection | |

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Selected Diagnostic Tests: General Comments | |

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Tests of Nonnested Hypothesis | |

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The Discrimination Approach | |

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The Discerning Approach | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Topics in Econometrics | |

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Regression on Dummy Variables | |

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The Nature of Dummy Variables | |

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Example 15.1: Professor's Salary by Sex | |

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Regression on One Quantitative Variable and One Qualitative Variable with Two Classes, or Categories | |

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Example 15.2: Are Inventories Sensitive to Interest Rates? | |

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Regression on One Quantitative Variable and One Qualitative Variable with More than Two Classes | |

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Regression on One Quantitative Variable and Two Qualitative Variables | |

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Example 15.3: The Economics of "Moonlighting" | |

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Testing for Structural Stability of Regression Models: Basic Ideas | |

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Example 15.4: Savings and Income, United Kingdom, 1946-1963 | |

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Comparing Two Regressions: The Dummy Variable Approach | |

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Comparing Two Regressions: Further Illustration | |

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Example 15.5: The Behavior of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971 | |

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Interaction Effects | |

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The Use of Dummy Variables in Seasonal Analysis | |

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Example 15.6: Profits-Sales Behavior in U.S. Manufacturing | |

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Piecewise Linear Regression | |

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Example 15.7: Total Cost in Relation to Output | |

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The Use of Dummy Variables in Combining Time Series and Cross-Sectional Data | |

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Pooled Regression: Pooling Time Series and Cross-Sectional Data | |

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Example 15.8: Investment Functions for General Motors and Westinghouse Companies | |

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Some Technical Aspects of Dummy Variable Technique | |

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The Interpretation of Dummy Variables in Semilogarithmic Regressions | |

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Example 15.9: Semilogarithmic Regression with Dummy Variable | |

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Another Method of Avoiding the Dummy Variable Trap | |

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Dummy Variables and Heteroscedasticity | |

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Dummy Variables and Autocorrelation | |

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Topics for Further Study | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 15A | |

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Data Matrix for Regression (15.8.2) | |

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Data Matrix for Regression (15.10.2) | |

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Regression on Dummy Dependent Variable: The LPM, Logit, Probit, and Tobit Models | |

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Dummy Dependent Variable | |

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The Linear Probability Model (LPM) | |

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Problems in Estimation of LPM | |

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Nonnormality of the Disturbances ui | |

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Heteroscedastic Variances of the Disturbances | |

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Nonfulfillment of 0 [= E(Yi\X) [= 1 | |

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Questionable Value of R2 as a Measure of Goodness of Fit | |

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LPM: A Numerical Example | |

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Applications of LPM | |

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Example 16.1: Cohen-Rea-Lerman study | |

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Example 16.2: Predicting a Bond Rating | |

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Example 16.3: Predicting Bond Defaults | |

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Alternatives to LPM | |

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The Logit Model | |

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Estimation of the Logit Model | |

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The Logit Model: A Numerical Example | |

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The Logit Model: Illustrative Examples | |

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Example 16.4: "An Application of Logit Analysis to Prediction of Merger Targets" | |

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Example 16.5: Predicting a Bond Rating | |

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The Probit Model | |

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The Probit Model: A Numerical Example | |

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Logit versus Probit | |

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Comparing Logit and Probit Estimates | |

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The Marginal Effect of a Unit Change in the Value of a Regressor | |

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The Probit Model: Example 16.5 | |

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The Tobit Model | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Dynamic Econometric Model: Autoregressive and Distributed-Lag Models | |

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The Role of "Time," or "Lag," in Economics | |

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The Reasons for Lags | |

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Estimation of Distributed-Lag Models | |

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Ad Hoc Estimation of Distributed-Lag Models | |

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The Koyck Approach to Distributed-Lag Models | |

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The Median Lag | |

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The Mean Lag | |

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Rationalization of the Koyck Model: The Adaptive Expectations Model | |

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Another Rationalization of the Koyck Model: The Stock Adjustment, or Partial Adjustment, Model | |

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Combination of Adaptive Expectations and Partial Adjustment Models | |

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Estimation of Autoregressive Models | |

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The Method of Instrumental Variables (IV) | |

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Detecting Autocorrelation in Autoregressive Models: Durbin h Test | |

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A Numerical Example: The Demand for Money in India | |

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Illustrative Examples | |

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Example 17.7: The Fed and the Real Rate of Interest | |

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Example 17.8: The Short- and Long-Run Aggregate Consumption Functions for the United States, 1946-1972 | |

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The Almon Approach to Distributed-Lag Models: The Almon or Polynomial Distributed Lag (PDL) | |

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Causality in Economics: The Granger Test | |

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The Granger Test | |

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Empirical Results | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Simultaneous-Equation Models | |

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Simultaneous-Equation Models | |

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The Nature of Simultaneous-Equation Models | |

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Examples of Simultaneous-Equation Models | |

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Example 18.1: Demand-and-Supply Model | |

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Example 18.2: Keynesian Model of Income Determination | |

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Example 18.3: Wage-Price Models | |

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Example 18.4: The IS Model of Macroeconomics | |

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Example 18.5: The LM Model | |

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Example 18.6: Econometric Models | |

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The Simultaneous-Equation Bias: Inconsistency of OLS Estimators | |

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The Simultaneous-Equation Bias: A Numerical Example | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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The Identification Problem | |

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Notations and Definitions | |

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The Identification Problem | |

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Underidentification | |

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Just, or Exact, Identification | |

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Overidentification | |

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Rules for Identification | |

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The Order Condition of Identifiability | |

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The Rank Condition of Identifiability | |

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A Test of Simultaneity | |

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Hausman Specification Test | |

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Example 19.5: Pindyck-Rubinfeld Model of Public Spending | |

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Tests for Exogeneity | |

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A Note on Causality and Exogeneity | |

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Summary and Conclusions | |

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Exercises | |

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Simultaneous-Equation Methods | |

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Approaches to Estimation | |

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Recursive Models and Ordinary Least Squares | |

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Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS) | |

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An Illustrative Example | |

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Properties of ILS Estimators | |

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Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS) | |

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2SLS: A Numerical Example | |

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Illustrative Examples | |

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Example 20.1: Advertising, Concentration, and Price Margins | |

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Example 20.2: Klein's Model I | |

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Example 20.3: The Capital Asset Pricing Model Expressed as a Recursive System | |

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Example 20.4: Revised Form of St. Louis Model | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 20A | |

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Bias in the Indirect Least-Squares Estimators | |

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Estimation of Standard Errors of 2SLS Estimators | |

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Time Series Econometrics | |

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Time Series Econometrics I: Stationarity, Unit Roots, and Cointegration | |

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A Look at Selected U.S. Economic Time Series | |

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Stationary Stochastic Process | |

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Test of Stationarity Based on Correlogram | |

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The Unit Root Test of Stationarity | |

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Is the U.S. GDP Time Series Stationary? | |

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Is the First-Differenced GDP Series Stationary? | |

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Trend-Stationary (TS) and Difference-Stationary (DS) Stochastic Process | |

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Spurious Regression | |

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Cointegration | |

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Engle-Granger (EG) or Augmented Engle-Granger (AEG) Test | |

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Cointegrating Regression Durbin-Watson (CRDW) Test | |

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Cointegration and Error Correction Mechanism (ECM) | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendix 21A | |

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A Random Walk Model | |

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Time Series Econometrics II: Forecasting with ARIMA and VAR Models | |

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Approaches to Economic Forecasting | |

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AR, MA, and ARIMA Modeling of Time Series Data | |

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An Autoregressive (AR) Process | |

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A Moving Average (MA) Process | |

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An Autoregressive and Moving Average (ARMA) Process | |

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An Autoregressive Integrated Moving Average (ARIMA) Process | |

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The Box-Jenkins (BJ) Methodology | |

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Identification | |

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Estimation of the ARIMA Model | |

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Diagnostic Checking | |

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Forecasting | |

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Further Aspects of the BJ Methodology | |

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Vector Autoregression (VAR) | |

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Estimation of VAR | |

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Forecasting with VAR | |

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Some Problems with VAR Modeling | |

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An Application of VAR: A VAR Model of the Texas Economy | |

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Summary and Conclusions | |

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Exercises | |

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Questions | |

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Problems | |

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Appendixes | |

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A Review of Some Statistical Concepts | |

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Rudiments of Matrix Algebra | |

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A List of Statistical Computer Packages | |

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Statistical Tables | |

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Areas under the Standardized Normal Distribution | |

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Percentage Points of the t Distribution | |

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Upper Percentage Points of the F Distribution | |

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Upper Percentage Points of the X2 Distribution | |

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Durbin-Watson d Statistic: Significant Points of dL and dU at 0.05 and 0.01 Levels of Significance | |

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Critical Values of Runs in the Runs Test | |

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Selected Bibliography | |

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Indexes | |

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Name Index | |

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Subject Index | |