We propose and implement a new approach that allows us to estimate income-specific changes in household welfare in contexts where well-measured prices are not available for important subsets of consumption. Using rich but widely available expenditure survey microdata, we show that we can recover income-specific equivalent and compensating variations from horizontal shifts in what we term “relative Engel curves”—as long as preferences fall within the broad quasi-separable class (Gorman 1970; 1976). Our approach is flexible enough to allow for nonparametric estimation at each point of the income distribution. We apply the methodology to estimate inflation and welfare changes in rural India between 1987 and 2000. Our estimates reveal that lower rates of inflation for the rich erased the real income convergence found in the existing literature that uses the subset of consumption with well-measured prices to calculate inflation.

中文翻译：

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用不完整的价格信息衡量福利和不平等

我们提出并实施了一种新方法，使我们能够在重要消费子集无法获得精确衡量的价格的情况下估计家庭福利的收入特定变化。使用丰富但广泛可用的支出调查微观数据，我们表明，只要偏好属于广泛的准可分离类别，我们就可以从我们所说的“相对恩格尔曲线”的水平变化中恢复特定收入的等值和补偿变化（Gorman 1970） ；1976）。我们的方法足够灵活，可以在收入分布的每个点进行非参数估计。我们应用该方法来估计 1987 年至 2000 年间印度农村地区的通货膨胀和福利变化。