Journal of Official Statistics, Vol.16, No.1, 2000. pp. 39–52
Optimal Weighting of Index Components: An Application to the Employment Cost Index
Michael K. Lettau and Mark A. Loewenstein
Abstract:This article considers the problem of how best to estimate an index whose components are themselves estimated with varying degrees of precision. We first characterize the weights that minimize the expected mean squared error in the index. These weights depend upon unobserved cell means and variances, but in practice one can substitute estimated cell means and variances for the unknown true parameters. We show that this is a more conservative reweighting scheme than one that minimizes a statistic that is an unbiased estimate of the mean squared error. We apply our procedure to the wage component of the Employment Cost Index (ECI) making use of the historical data that are used in the actual calculation of the ECI. While we apply our procedure to the ECI, our approach is equally valid for other indices.
Keywords:Index number; composite estimation.
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