Knowledge that Transforms

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.

Nobel Prize winner Amartya Sen's first great book, now reissued in a fully revised and expanded second edition 'Can the values which individual members of society attach to different alternatives be aggregated into values for society as a whole, in a way that is both fair and theoretically sound? Is the majority principle a workable rule for making decisions? How should income inequality be measured? When and how can we compare the distribution of welfare in different societies?' These questions, from the citation by the Swedish Academy of Sciences when Amartya Sen was awarded the Nobel Memorial Prize in Economics, refer to his work in Collective Choice and Social Welfare, the most important of all his early books. Originally published in 1970, this classic work in welfare economics has been recognized for its ground-breaking role in integrating economics and ethics, and for its influence in opening up new areas of research in social choice, including aggregative assessment. It has also had a large influence on international organizations, including the United Nations, particularly in its work on human development. In its original version, the book showed that the 'impossibility theorems' in social choice theory-led by the pioneering work of Kenneth Arrow-need not be seen as destructive of the possibility of reasoned and democratic social choice. Sen's ideas about social choice, welfare economics, inequality, poverty and human rights have continued to evolve since the book's first appearance. This expanded edition, which begins by reproducing the 1970 edition in its entirety, goes on to present eleven new chapters of new arguments and results. As in the original version, the new chapters alternate between non-mathematical chapters completely accessible to all, and those which present mathematical arguments and proofs. The reader who prefers to shun mathematics can follow all the non-mathematical chapters on their own, to receive a full, informal understanding. There is also a substantial new introduction which gives a superb overview of the whole subject of social choice.