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Composite Index: Methods and Properties
Keywords
Composite index, Geometric mean, Monotonicity, Time-reversal test, Chain indices
Abstract
Composite Index (CI) depends on method of combining several variables or indicators to reflect overall assessment. Each method of combining the component indicators results in different values of CI and different rankings from a given dataset. The paper describes problems for construction of CI at various stages and proposes a number of methods for obtaining CI along with desired properties which a good CI will satisfy. Existing and proposed methods to construct CI can be compared with respect to those desired properties. The Geometric Mean approach satisfies all the desired properties and avoids calculation of weights or variance-covariance matrix or correlation matrix. The Geometric Mean approach is applicable for situation even where only the two vectors X and T are given for the current year and the previous year. Thus, the Geometric Mean approach is well applicable for assessment of impact. The approach also helps to identify relative importance of the component indicators in terms of values of the ratios and also identify the critical areas and facilitate initiation of corrective measures. Such identification is important from a policy point of view. The GM method reduces the level of substitutability between component indicators and facilitates statistical test of significance of equality of two geometric means. Thus, the Geometric Mean approach and may be taken as best among the methods discussed.