Esfandiar Maasoumi

The Measurement and Decomposition of Multi-dimensional Inequality

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Entropy and predictability of stock market returns

Abstract We examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties. We compare our results with a number of traditional measures. The metric entropy is capable of detecting nonlinear dependence within the returns series, and is also capable of detecting nonlinear “affinity” between the returns and their predictions obtained from various models thereby serving as a measure of out-of-sample goodness-of-fit or model adequacy. Several models are investigated, including the linear and neural-network models as well as nonparametric and recursive unconditional mean models. We find significant evidence of small nonlinear unconditional serial dependence within the returns series, but fragile evidence of superior conditional predictability (profit opportunity) when using market-switching versus buy-and-hold strategies.

A compendium to information theory in economics and econometrics

An extensive synthesis is provided of the concepts, measures and techniques of Information Theory (IT). After an axiomatic description of the basic definitions of “information functions”, “entropy” or uncertainty and the maximum entropy principle, the paper demonstrates the power of IT as both an interpretive and techinically productive tool. It is argued that this power and universality is promarily due to the common need for (i) measures of distance and discrimination and, (ii) appropriate partitioning- aggregation properties. IT offers a very suggestive unification for a bewildering and arbitrary set of approaches that have evolved in different disciplines. Applications are discussed or indicated. These applications have relevance to economics, finance, industrial organization, marketing, statistical ingerence and model selection, political science and communication. A main focus of the discussion is the generative power of IT measures in statistical examinations of unknown distributions and random phe...

Ordering univariate distributions by entropy and variance

This paper examines the role of variance and entropy in ordering distributions and random prospects. There is no universal relation between entropy and variance orderings of distributions. But we place their relationship in the context of a stronger ordering relation known as dispersion ordering. Further, some conditions are identified under which variance and entropy order similarly when continuous variables are transformed. We also analyze parametric changes which do not disturb the agreement between these rankings. The results are conveniently tabulated in terms of distribution parameters.

Multivariate Measures of Well-Being and an Analysis of Inequality in the Michigan Data

We demonstrate a multidimensional approach for combining several indicators of well-being, including the traditional money-income indicators. This methodology avoids the difficult and much criticized task of computing imputed incomes for such indicators as net worth and schooling. Inequality in the proposed composite measures is computed using relative inequality indexes that permit simple analysis of both the contribution of each welfare indicator (and its factor components) and within and between components of total inequality when the population is grouped by income levels, age, gender, or any other criteria. The analysis is performed on U.S. data using the Michigan Survey of Income Dynamics.

Cluster analysis for measuring welfare and quality of life across countries

Abstract The dream of a multiattribute approach to empirical welfare analysis is coming closer to reality because of significant advances in both theoretical and measurement areas. In this paper we propose statistical cluster analysis methods to explore different ways and levels for clustering of 23 diverse attributes such as political rights, civil liberties, life expectancy, literacy, real domestic product, etc. Several key attribute categories are identified which should be very helpful in dealing with the problem of ‘double counting’ in multidimensional analyses. Aggregate measures of welfare are computed for many countries, and the sensitivity of several key inequality measures with respect to clustering and degrees of aggregation is studied.

A class of generalized measures of mobility with applications

Abstract A class of anonymous measures of mobility is defined that considers the relationship between the long-run and short-run distributions of income. Several measures of long-run income and inequalityare explored. Michigan panel data are analyzed.

Multidimensioned Approaches to Welfare Analysis

A general survey of multidimensional approaches to the measurement and comparisons of welfare situations is provided. The survey covers some aspects of welfare representation, data availability and experience, axiomatic characterization of inequality measures, existing multidimensional indices, the stochastic dominance alternative for comparing welfare situations, and mobility. Applications to national and international data are described. The paper emphasizes implementability issues and statistical methods in the context of a comparative analysis of the philosophical and theoretical desirability of alternative approaches.

Generalized entropy measures of mobility for different sexes and income levels

Abstract A family of mobility measures is investigated using the Michigan panel data on income dynamics, These measures are decomposed in order to learn about components that are due to differences in gender and income groups, on the one hand, and within-group components which are free of such group characteristics. These measures compute the degree of equalization over time of the distribution of ‘permanent incomes’. Permanent or average income of an individual is computed over an increasing number of points within a time interval of interest. This degree of equality is compared (as a ratio) to the equality of incomes at any reference point of interest in order to give us a measure of stability in the size distribution of incomes. We take an average of inequality values over the time interval as our reference value for ‘short-run’ inequality. Mobility is greater the greater this degree of relative equalization. Several aggregator functions have been used to compute the ‘permanent income’ variable. Their justification and role in robustifying our inferences is briefly discussed. The mobility profiles here suggest that there has not been much equalization between different sexes, but there is not a lot of inequality between these groups in our sample. Most of the inequality is within groups where the annual distributional changes belie the relative stability of the permanent income distribution.

On the behavior of inconsistent instrumental variable estimators

Results published recently by Hendry (1979) for the limiting distribution of inconsistent instrumental variable estimators in misspecified dynamic systems are incorrect. In particular, Hendrys derivations involve the use of an appropriate control variate and lead to an expression for the covariance matrix of the limiting distribution which, in general, omits many additional terms. Correct formulae are given in the present paper and the accuracy of the asymptotic distribution in finite samples is investigated in a simple case using the know exact small sample distribution. On the basis of our exact results, we argue for caution in the use of response surface regressions of the type recommended by Hendry in Monte Carlo experiments; and we emphasize the need for qualifying statements concerning the parameter environments in which the adequacy of these regressions has been substantiated.