Statistical Properties of Equal-Weights Estimators of Composite Quality-of-Life Indices
Kenneth C. Land, Michael R. Hagerty
Department of Sociology, Duke University, Durham, NC, United States; Graduate School of Management, University of California-Davis, Davis, CA, United States

Methodological problems associated with the construction of summary quality-of-life (QOL) or well-being indices from many components are studied. Two types of QOL indexes are distinguished: (1) those rating multiple countries in the same time period (cross-sectional data), and (2) those rating a single country on multiple time periods (time-series). In the first case, we show that it is easy to create a QOL index on which most people in a society agree. In the second case, we show that it is more difficult, but define conditions under which it is possible. In particular we show that the equal-weighting strategy is privileged in that it is a minimax estimator–it minimizes maximal disagreement among all possible citizens' weights. As a minimax estimator, the equal-weighting strategy also has other statistical properties that are identifed. When the actual distribution of citizens' weights is known, then one can improve agreement further by using the mean weights applied by citizens. Finally, we examine nationally representative surveys of importance weights and show that they meet the conditions for successful construction of a QOL index that will be endorsed by a majority of citizens in a country. We conclude with recommendations for measuring weights and creating successful QOL indexes.

Keywords: Composite indicators; Quality of life; Minimax estimators

Biography: Kenneth Land is the John Franklin Crowell Professor of Sociology and Demography at Duke University in North Carolina. He is the author of over 200 books, journal articles, and book chapters. Ken is an applied statistician who has developed and exposited statistical methods for path analysis, multistate life tables, finite mixture models for developmental/life course trajectories, the construction of composite social indicators. He has been elected a Fellow of the American Statistical Association in recognition of his work.