Influence functions for distributional statistics

Social evaluation functions used in policy impact analysis can be viewed as real-valued functionals of the underlying outcome distributions. Influence functions may be used to identify the sources of variation in social outcomes in terms of individual or household characteristics. This paper sets forth in clear terms the definition of the influence function and recentered influence function, and catalogs these functions for a wide range of distributional statistics, including measures of central tendency, inequality and poverty and also measures of the degree of pro-poorness of a shock- or policy-induced change in income levels.