Redistributive Effects for Discretely-Valued Inputs

Abstract

In this paper we study the effect of reallocating an indivisible input across a population of production units on average output. We define the Average Redistributive Effect (ARE) as the effect of such a reallocation on average output. We consider the case where inputs are discretely-valued, studying the case where they take two or three levels in detail. In these cases the set of feasible reallocations are respectively indexed by one and four parameters. With two input levels the ARE is a linear function with a slope coefficient equal to a measure of input complementarity. The average output maximizing allocation is completely determined by the production technology. With three input levels the optimal allocation depends on both the form of the production function and the availability of inputs at each level in potentially complicated ways. We provide conditions under which the ARE is identified and consider some non-standard aspects of inference. We relate the ARE to the average treatment effect (ATE) estimand and our constrained input allocation problem to the unconstrained treatment assignment problem considered by Manski (2004) and Dehejia (2005).