JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 128.235.251.160 on Tue,In this article we study the small sample properties of the so called general k-class estimators of simultaneous equations. Two members of the family of k-class estimators are found, one of whiclh is unbiased to the degree of our approximation and the other possesses a minimum second moment around the true parameter value, again to the order of ouir approximation. GENERAL ASSUMPTIONS, THEOREMS I AND IILet the equation to be estimated be written as (2.1) y -Yy + X1f: + U, where y is the column vector of T observations on the jointly dependent variable "to be explained," Y is a T x m matrix of values taken by the m 1 I am indebted to Professor H. Theil for the suggestion of the problem and for valuable discussions from time to time.

Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals associated with these estimators. This paper reviews the different underlying models, reaffirms their appropriateness in this context, examines the statistical properties of resulting indices, gives analytical expressions of their variances and establishes certain exact relationships among them.

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