Hayashi_2000_Econometrics

Hayashi_2000_Econometrics - Contents List of Figures xvii...

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Unformatted text preview: Contents List of Figures xvii Preface xix 1 Finite-Sample Properties of OLS 1.1 The Classical Linear Regression Model The Linearity Assumption Matrix Notation The Strict Exogeneity Assumption Implications of Strict Exogeneity Strict Exogeneity in Time-Series Models Other Assumptions of the Model The Classical Regression Model for Random Samples "Fixed" Regressors 1.2 The Algebra of Least Squares OLS Minimizes the Sum of Squared Residuals Normal Equations Two Expressions for the OLS Estimator More Concepts and Algebra Influential Analysis (optional) A Note on the Computation of OLS Estimates 1.3 Finite-Sample Properties of OLS Finite-Sample Distribution of b Finite-Sample Properties of s2 Estimate of Var(b 1 X) 1.4 Hypothesis Testing under Normality Normally Distributed Error Terms Testing Hypotheses about Individual Regression Coefficients Decision Rule for the t-Test Confidence Interval vi Contents p-Value 3 8 Linear Hypotheses 39 The F-Test 40 A More Convenient Expression for F 42 t versus F 43 An Example of a Test Statistic Whose Distribution Depends on X 45 1.5 Relation to Maximum Likelihood 47 The Maximum Likelihood Principle 47 Conditional versus Unconditional Likelihood 47 The Log Likelihood for the Regression Model 48 ML via Concentrated Likelihood 48 Cramer-Rao Bound for the Classical Regression Model 49 The F-Test as a Likelihood Ratio Test 52 Quasi-Maximum Likelihood 53 1.6 Generalized Least Squares (GLS) 54 Consequence of Relaxing Assumption 1.4 55 Efficient Estimation with Known V 55 A Special Case: Weighted Least Squares (WLS) 58 Limiting Nature of GLS 58 1.7 Application: Returns to Scale in Electricity Supply 60 The Electricity Supply Industry 60 The Data 60 Why Do We Need Econometrics? 61 The Cobb-Douglas Technology 62 How Do We Know Things Are Cobh-Douglas? 63 Are the OLS Assumptions Satisfied? 64 Restricted Least Squares 65 Testing the Homogeneity of the Cost Function 65 Detour: A Cautionary Note on R~ 67 Testing Constant Returns to Scale 67 Importance of Plotting Residuals 68 Subsequent Developments 68 Problem Set 7 1 Answers to Selected Questions 84 Large-Sample Theory 88 2.1 Review of Limit Theorems for Sequences of Random Variables 88 Various Modes of Convergence 89 Three Useful Results 92 Contents vii Viewing Estimators as Sequences of Random Variables Laws of Large Numbers and Central Limit Theorems 2.2 Fundamental Concepts in Time-Series Analysis Need for Ergodic Stationarity Various Classes of Stochastic Processes Different Formulation of Lack of Serial Dependence The CLT for Ergodic Stationary Martingale Differences Sequences 2.3 Large-Sample Distribution of the OLS Estimator The Model Asymptotic Distribution of the OLS Estimator s2 IS Consistent 2.4 Hypothesis Testing Testing Linear Hypotheses The Test Is Consistent Asymptotic Power Testing Nonlinear Hypotheses 2.5 Estimating E(E?x~x;) Consistently Using Residuals for the Errors Data Matrix Representation of S Finite-Sample Considerations 2.6 Implications of Conditional Homoskedasticity...
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Hayashi_2000_Econometrics - Contents List of Figures xvii...

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