The aggregate cost of the living index requires averaging across household indices. But what if the aggregate index was constructed for the “representative” household as is usually done? The paper examines the resulting bias in the Tornqvist index, widely used for constructing superlative indices as well as for the Cobb–Douglas index, which has a similar functional form. We show that the difference between the two consists of a “plutocratic” bias and a “curvature” bias. The former is well known, but the latter has not been recognized earlier. In empirical applications, the curvature bias is small and orders of magnitude smaller than the plutocratic bias. This suggests much of the overall bias would be removed by constructing the representative agent by democratic averages of budget shares.

中文翻译：

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生活成本指数中的代表性代理人偏差

生活指数的总成本需要对家庭指数进行平均。但是，如果按照通常的做法为“有代表性的”家庭构建综合指数呢？本文研究了 Tornqvist 指数中由此产生的偏差，该指数广泛用于构建最高级指数以及具有类似功能形式的 Cobb-Douglas 指数。我们表明，两者之间的差异包括“财阀”偏见和“曲率”偏见。前者广为人知，而后者更早未被认识。在经验应用中，曲率偏差很小，并且比财阀偏差小几个数量级。这表明，通过预算份额的民主平均值构建代表代理人，可以消除大部分总体偏见。