We study the optimal nonlinear income tax problem with multidimensional individual characteristics on which taxes cannot be conditioned. We obtain an optimal tax formula that generalizes the standard one by averaging, with specific weights, the sufficient statistics of individuals who earn the same income. Our first main contribution consists in showing that multidimensional heterogeneity brings a new source of endogeneity to the sufficient statistics that we call composition effects. We highlight that composition effects may substantially affect optimal marginal tax rates. Our results put the stress on the need for empirical studies on sufficient statistics for different demographic groups e.g., according to gender, age, ethnicity. As a second main contribution, we show the equivalence between the tax perturbation and mechanism design approaches which bridges the gap between both methods that have, so far, been used separately in the literature.

中文翻译：

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具有组合效应的最优所得税

我们研究了不能以税收为条件的具有多维个人特征的最优非线性所得税问题。我们获得了一个最佳的税收公式，该公式可以通过对具有相同收入的个人的足够的统计数据进行平均，并使用特定的权重来对标准的一个公式进行推广。我们的第一个主要贡献在于，表明多维异质性为我们称为成分效应的充分统计数据带来了内生性的新来源。我们着重指出，构成效应可能会严重影响最佳边际税率。我们的结果强调需要对不同人口群体（例如，根据性别，年龄，种族）进行充分统计的经验研究。作为第二个主要贡献，