Econometrics: Statistical Foundations and Applications

Abstract

1. Elementary Aspects of Multivariate Analysis.- 1.1 Preliminaries.- 1.2 Joint, Marginal, and Conditional Distributions.- 1.3 A Mathematical Digression.- 1.4 The Multivariate Normal Distribution.- 1.5 Correlation Coefficients and Related Topics.- 1.6 Estimators of the Mean Vector and Covariance Matrix and their Distribution.- 1.7 Tests of Significance.- 2. Applications of Multivariate Analysis.- 2.1 Canonical Correlations and Canonical Variables.- 2.2 Principal Components.- 2.3 Discriminant Analysis.- 2.4 Factor Analysis.- 3. Probability Limits, Asymptotic Distributions, and Properties of Maximum Likelihood Estimators.- 3.1 Introduction.- 3.2 Estimators and Probability Limits.- 3.3 Convergence to a Random Variable: Convergence in Distribution and Convergence of Moments.- 3.4 Central Limit Theorems and Related Topics.- 3.5 Miscellaneous Useful Convergence Results.- 3.6 Properties of Maximum Likelihood (ML) Estimators.- 3.7 Estimation for Distribution Admitting of Sufficient Statistics.- 3.8 Minimum Variance Estimation and Sufficient Statistics.- 4. Estimation of Simultaneous Equations Systems.- 4.1 Review of Classical Methods.- 4.2 Asymptotic Distribution of Aitken Estimators.- 4.3 Two-Stage Least Squares (2SLS).- 4.4 2SLS as Aitken and as OLS Estimator.- 4.5 Asymptotic Properties of 2SLS Estimators.- 4.6 The General k-Class Estimator.- 4.7 Three-Stage Least Squares (3SLS).- 5. Applications of Classical and Simultaneous Equations Techniques and Related Problems.- 5.1 Estimation of Production and Cost Functions and Specification Error Analysis.- 5.2 An Example of Efficient Estimation of a Set of General Linear (Regression) Models.- 5.3 An Example of 2SLS and 3SLS Estimation.- 5.4 Measures of Goodness of Fit in Multiple Equations Systems: Coeficient of (Vector) Alienation and Correlation.- 5.5 Canonical Correlations and Goodness of Fit in Econometric Systems.- 5.6 Applications of Principal Component Theory in Econometric Systems.- 5.7 Alternative Asymptotic Tests of Significance for 2SLS Estimated Parameters.- 6. Alternative Estimation Methods Recursive Systems.- 6.1 Introduction.- 6.2 Indirect Least Squares (ILS).- 6.3 The Identification Problem.- 6.4 Instrumental Variables Estimation.- 6.5 Recursive Systems.- 7. Maximum Likelihood Methods.- 7.1 Formulation of the Problem and Assumptions.- 7.2 Reduced Form (RF) and Full Information Maximum Likelihood (FIML) Estimation.- 7.3 Limited Information (LIML) Estimation.- 8. Relations Among Estimators . Monte Carlo Methods.- 8.1 Introduction.- 8.2 Relations Among Double k-Class Estimators.- 8.3 I.V., ILS, and Double Ar-Class Estimators.- 8.4 Limited Information Estimators and Just Identification.- 8.5 Relationships Among Full Information Estimators.- 8.6 Monte Carlo Methods.- 9. Spectral Analysis.- 9.1 Stochastic Processes.- 9.2 Spectral Representation of Covariance Stationary Series.- 9.3 Estimation of the Spectrum.- 10. Cross-Spectral Analysis.- 10.1 Introduction.- 10.2 Cross Spectrum: Cospectrum, Quadrature Spectrum, and Coherency.- 10.3 Estimation of the Cross Spectrum.- 10.4 An Empirical Application of Cross-Spectral Analysis.- 11. Approximate Sampling Distributions and Other Statistical Aspects of Spectral Analysis.- 11.1 Aliasing.- 11.2 Prewhitening, Recoloring, and Related Issues.- 11.3 Approximate Asymptotic Distributions Considerations of Design and Analysis.- 12 Applications of Spectral Analysis to Simultaneous Equations Systems.- 12.1 Generalities.- 12.2 Lag Operators.- 12.3 An Operator Representation of the Final Form.- 12.4 Dynamic Multipliers and the Final Form.- 12.5 Spectral Properties of the Final Form.- 12.6 An Empirical Application.- Mathematical Appendix.- A.1 Complex Numbers and Complex-Valued Functions.- A.2 The Riemann-Stieltjes Integral.- A.3 Monotonie Functions and Functions of Bounded Variation.- A.4 Fourier Series.- A.5 Systems of Difference Equations with Constant Coefficients.- A.6 Matrix Algebra.