Foundations of Econometrics

1st Edition, Volume 7 - January 1, 1976
Author: Albert Madansky
Editors: C. J. Bliss, M. D. Intriligator
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 5 2 5 - 3

Advanced Textbooks in Economics, Volume 7: Foundations of Econometrics focuses on the principles, processes, methodologies, and approaches involved in the study of econometrics.… Read more

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Advanced Textbooks in Economics, Volume 7: Foundations of Econometrics focuses on the principles, processes, methodologies, and approaches involved in the study of econometrics. The publication examines matrix theory and multivariate statistical analysis. Discussions focus on the maximum likelihood estimation of multivariate normal distribution parameters, point estimation theory, multivariate normal distribution, multivariate probability distributions, Euclidean spaces and linear transformations, orthogonal transformations and symmetric matrices, and determinants. The manuscript then ponders on linear expected value models and simultaneous equation estimation. Topics include random exogenous variables, maximum likelihood estimation of a single equation, identification of a single equation, linear stochastic difference equations, and errors-in-variables models. The book takes a look at a prolegomenon to econometric model building, tests of hypotheses in econometric models, multivariate statistical analysis, and simultaneous equation estimation. Concerns include maximum likelihood estimation of a single equation, tests of linear hypotheses, testing for independence, and causality in economic models. The publication is a valuable source of data for economists and researchers interested in the foundations of econometrics.

PrefaceI. Matrix Theory 1. Matrix Operations 2. Euclidean Space and Linear Transformations 3. Matricial Representations of Linear Transformations 4. Projection Transformations 5. Determinants 6. Orthogonal Transformations and Symmetric Matrices 7. Generalized Inverse 8. Derivatives of Functions of Matrices 9. ReferencesII. Multivariate Statistical Analysis: Distribution and Point Estimation Theory 1. Multivariate Probability Distributions 2. Multivariate Normal Distribution 3. Point Estimation Theory 4. Maximum Likelihood Method of Point Estimation 5. Maximum Likelihood Estimation of Multivariate Normal Distribution Parameters 6. ReferencesIII. Linear Expected Value Models 1. Independent Samples 1.1. Maximum Likelihood Estimation in Normal Models 1.2. Least Squares Estimation in Linear Expected Value Models 2. Correlated Samples 2.1. Maximum Likelihood Estimation in Normal Models 2.2. Least Squares Estimation 2.3. Autoregressive Errors 3. Linear Stochastic Difference Equations 4. Errors-in-Variables Models 4.1. Models 4.2. Estimation in Non-Normal Structural Relations 4.3. Instrumental Variables 4.4. Maximum Likelihood Estimation in Restricted Models 5. ReferencesIV. Simultaneous Equation Estimation 1. Identification of a Single Equation 2. Maximum Likelihood Estimation of a Single Equation 3. Maximum Likelihood Estimation of a System of Simultaneous Equations 4. Simultaneous Least Squares Estimation 5. Simultaneous Equation Estimation via Instrumental Variables 5.1. Two-Stage Least Squares Estimate 5.2. k-Class Estimate 5.3. Estimates Based on Characteristic Vectors of Functions of Exogenous Variables 5.4. Comparison 5.5. Iterative Instrumental Variable Estimate 5.6. Three-Stage Least Squares Estimate 6. Iterative Least Squares Estimate 7. Random Exogenous Variables 8. ReferencesV. Multivariate Statistical Analysis: Hypothesis Testing Theory 1. Hypothesis Testing Theory 2. Sampling Distributions 2.1. Chi-Square Distribution 2.2. F-Distribution 2.3. t-Distribution 2.4. Asymptotic Distribution of Likelihood Ratio 2.5. Pearson Family Approximation 3. Tests of Linear Hypotheses 4. ReferencesVI. Tests of Hypotheses in Econometric Models 1. One-Way Analysis of Variance 2. Tests of Linear Hypotheses in Regression Models 3. Test of Equality of Regressions 4. Testing that Multiple Regression Coefficient is Zero 5. Testing for Independence 6. Testing for Identifiability 7. ReferencesVII. A Prolegomenon to Econometric Model Building 1. The Error Term in Economic Modeling 2. Causality in Economic Models 3. Simultaneous Equation Model Types 4. ReferencesIndex