1 The Geometry of Least Square
1.1 Introduction
1.2 The Geometry of Least Squares
1.3 Restrictions and Reparametrizations
1.4 The Frisch-Waugh-Lovell Theorem
1.5 Computing OLS Estimates
1.6 Influential Observations and Leverage
1.7 Further Reading and Conclusion
2 Nonlinear Regression Models and Nonlinear Least Squares
2.1 Introduction
2.2 The Geometry of Nonlinear Least Squares
2.3 Identification in Nonlinear Regression Models
2.4 Models and Data-Generating Processes
2.5 Linear and Nonlinear Regression Functions
2.6 Error Terms
2.7 Conclusion
3 Inference in Nonlinear Regression Models
3.1 Introduction
3.2 Covariance Matrix Estimation
3.3 Confidence Intervals and Confidence Regions
3.4 Hypothesis Testing: Introduction
3.5 Hypothesis Testing in Linear Regression Models
3.6 Hypothesis Testing in Nonlinear Regression Models
3.7 Restrictions and Pretest Estimators
Conclusion
4 Introduction to Asymptotic Theory and Methods
4.1 Introduction
4.2 Sequences, Limits, and Convergence
4.3 Rates of Convergence
4.4 Data-Generating Processes and Asymptotic Theory
4.5 Consistency and Laws of Large Numbers
4.6 Asymptotic Normality and Central Limit Theorems
4.7 Some Useful Results
4.8 Conclusion
5 Asymptotic Methods and Nonlinear Least Squares
5.1 Introduction
5.2 Asymptotic Identifiability
5.3 Consistency of the NLS Estimator
5.4 Asymptotic Normality of the NLS Estimator
5.5 Asymptotic Efficiency of Nonlinear Least Squares
5.6 Properties of Nonlinear Least Squares Residuals
5.7 Test Statistics Based on NLS Estimates
5.8 Further Reading and Conclusion
6 The Gauss–Newton Regression
6.1 Introduction
6.2 Computing Covariance Matrices
6.3 Collinearity in Nonlinear Regression Models
6.4 Testing Restrictions
6.5 Diagnostic Tests for Linear Regression Models
6.6 One-Step Efficient Estimation
6.7 Hypothesis Tests Using Any Consistent Estimates
6.8 Nonlinear Estimation Using the GNR
6.9 Further Reading
7 Instrumental Variables
7.1 Introduction
7.2 Errors in Variables
7.3 Simultaneous Equations
7.4 Instrumental Variables: The Linear Case
7.5 Two-Stage Least Squares
7.6 Instrumental Variables: The Nonlinear Case
7.7 Hypothesis Tests Based on the GNR
7.8 Identification and Overidentifying Restrictions
7.9 Durbin-Wu-Hausman Tests
7.10 Conclusion
8 The Method of Maximum Likelihood
8.1 Introduction
8.2 Fundamental Concepts and Notation
8.3 Transformations and Reparametrizations
8.4 Consistency
8.5 The Asymptotic Distribution of the ML Estimator
8.6 The Information Matrix Equality
8.7 Concentrating the Loglikelihood Function
8.8 Asymptotic Efficiency of the ML Estimator
8.9 The Three Classical Test Statistics
8.10 Nonlinear Regression Models
8.11 Conclusion
9 Maximum Likelihood and Generalized Least Squares
9.1 Introduction
9.2 Generalized Least Squares
9.3 The Geometry of GLS
9.4 The Gauss-Newton Regression
9.5 Feasible Generalized Least Squares
9.6 Maximum Likelihood and GNLS
9.7 Introduction to Multivariate Regression Models
9.8 GLS Estimation of Multivariate Regression Models
9.9 ML Estimation of Multivariate Regression Models
9.10 Modeling Time-Series/Cross-Section Data
9.11 Conclusion
10 Serial Correlation
10.1 Introduction
10.2 Serial Correlation and Least Squares Estimation
10.3 Estimating Regression Models with AR(1) Errors
10.4 Standard Errors and Covariance Matrices
10.5 Higher-Order AR Processes
10.6 Initial Observations in Models with AR Errors
10.7 Moving Average and ARMA Processes
10.8 Testing for Serial Correlation
10.9 Common Factor Restrictions
10.10 Instrumental Variables and Serial Correlation
10.11 Serial Correlation and Multivariate Models
10.12 Conclusion
11 Tests Based on the Gauss-Newton Regression
11.1 Introduction
11.2 Tests for Equality of Two Parameter Vectors
11.3 Testing Nonnested Regression Models
11.4 Tests Based on Comparing Two Sets of Estimates
11.5 Testing for Heteroskedasticity
11.6 A Heteroskedasticity-Robust Version of the GNR
11.7 Conclusion
12 Interpreting Tests in Regression Directions
12.1 Introduction
12.2 Size and Power
12.3 Drifting DGPs
12.4 The Asymptotic Distribution of Test Statistics
12.5 The Geometry of Test Power
12.6 Asymptotic Relative Efficiency
12.7 Interpreting Test Statistics that Reject the Null
12.8 Test Statistics that Do Not Reject the Null
12.9 Conclusion
13 The Classical Hypothesis Tests
13.1 Introduction
13.2 The Geometry of the Classical Test Statistics
13.3 Asymptotic Equivalence of the Classical Tests
13.4 Classical Tests and Linear Regression Models
13.5 Alternative Covariance Matrix Estimators
13.6 Classical Test Statistics
13.7 The Outer-Product-of-the-Gradient Regression
13.8 Further Reading and Conclusion
14 Transforming the Dependent Variable
14.1 Introduction
14.2 The Box-Cox Transformation
14.3 The Role of Jacobian Terms in ML Estimation
14.4 Double-Length Artificial Regressions
14.5 The DLR and Models Involving Transformations
14.6 Testing Linear and Loglinear Regression Models
14.7 Other Transformations
14.8 Conclusion
15 Qualitative and Limited Dependent Variables
15.1 Introduction
15.2 Binary Response Models
15.3 Estimation of Binary Response Models
15.4 An Artificial Regression
15.5 Models for More than Two Discrete Responses
15.6 Models for Truncated Data
15.7 Models for Censored Data
15.8 Sample Selectivity
15.9 Conclusion
16 Heteroskedasticity and Related Topics
16.1 Introduction
16.2 Least Squares and Heteroskedasticity
16.3 Covariance Matrix Estimation
16.4 Autoregressive Conditional Heteroskedasticity
16.5 Testing for Heteroskedasticity
16.6 Skedastic Directions and Regression Directions
16.7 Tests for Skewness and Excess Kurtosis
16.8 Conditional Moment Tests
16.9 Information Matrix Tests
16.10 Conclusion
17 The Generalized Method of Moments
17.1 Introduction and Definitions
17.2 Criterion Functions and M-Estimators
17.3 Efficient GMM Estimators
17.4 Estimation with Conditional Moments
17.5 Covariance Matrix Estimation
17.6 Inference with GMM Models
17.7 Conclusion
18 Simultaneous Equations Models
18.1 Introduction
18.2 Exogeneity and Causality
18.3 Identification in Simultaneous Equations Models
18.4 Full-Information Maximum Likelihood
18.5 Limited-Information Maximum Likelihood
18.6 Three-Stage Least Squares
18.7 Nonlinear Simultaneous Equations Models
18.8 Conclusion
19 Regression Models for Time-Series Data
19.1 Introduction
19.2 Spurious Regressions
19.3 Distributed Lags
19.4 Dynamic Regression Models
19.5 Vector Autoregressions
19.6 Seasonal Adjustment
19.7 Modeling Seasonality
19.8 Conclusion
20 Unit Roots and Cointegration
20.1 Introduction
20.2 Testing for Unit Roots
20.3 Asymptotic Theory for Unit Root Tests
20.4 Serial Correlation and Other Problems
20.5 Cointegration
20.6 Testing for Cointegration
20.7 Model-Building with Cointegrated Variables
20.8 Vector Autoregressions and Cointegration
20.9 Conclusion
21 Monte Carlo Experiments
21.1 Introduction
21.2 Generating Pseudo-Random Numbers
21.3 Generating Pseudo-Random Variates
21.4 Designing Monte Carlo Experiments
21.5 Variance Reduction: Antithetic Variates
21.6 Variance Reduction: Control Variates
21.7 Response Surfaces
21.8 The Bootstrap and Related Methods
21.9 Conclusion
Appendices
A Matrix Algebra
A.1 Introduction
A.2 Elementary Facts about Matrices
A.3 The Geometry of Vectors
A.4 Matrices as Mappings of Linear Spaces
A.5 Partitioned Matrices
A.6 Determinants
A.7 Positive Definite Matrices
A.8 Eigenvalues and Eigenvectors
B Results from Probability Theory
B.1 Introduction
B.2 Random Variables and Probability Distributions
B.3 Moments of Random Variables
B.4 Some Standard Probability Distributions
References
Author Index
Subject Index
