# Lorenz dominance and the variance of logarithms

Article Abstract:

Possible disagreements between the variance of logarithms (V(sub L)) and the Lorenz criterion have been studied. V(sub L) is widely used in measuring dispersion but is suspected of not being a proper measure of inequality because it violates the principle of transfers. Disagreements may center onbroad-based changes in incomes up and down the distribution. Results indicate that it is possible that the V(sub L) may indicate that a distribution whose Lorenz curve approximates the L-shaped curve of complete inequality is more equal than a distribution whose Lorenz curve approximates the 45 degree line of equality.

Publication Name: Econometrica

Subject: Mathematics

ISSN: 0012-9682

Year: 1999

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# Conventional confidence intervals for points on spectrum have confidence level zero

Article Abstract:

A confidence level zero can be obtained from textbook confidence intervals. Under the standard assumptions, such level can be attained also at any finite-length confidence intervals with probability one. Under mild conditions, the occurrence of finite-length confidence intervals for points on the spectrum occurs when the maintained model is limited to a finite-dimensional space of Wold representations. Results obtained are closely associated to near observational equivalence of unit root and stationary processes.

Publication Name: Econometrica

Subject: Mathematics

ISSN: 0012-9682

Year: 1999

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# When are variance ratio tests for serial dependence optimal?

Article Abstract:

A study was done to evaluate statistics which can be expressed as the ratio of a filtered time series' sample variance to the original series' sample variance. Under normal conditions, these statistics exhibit optimal behavior for testing a null of white noise against serially dependent options. These statistics require a filter for alternative model application. Results show that the variance ratio test is optimal for mean reversion.

Publication Name: Econometrica

Subject: Mathematics

ISSN: 0012-9682

Year: 1992

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