Hayashi - Econometrics




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
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
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