Inference for Misallocation Statistics Using Influence Functions

I provide formulas for the influence function of two common misallocation statistics: TFP loss from misallocation and potential TFP gain from reallocation. I also show how to use a finite-difference approximation to Gateaux derivatives to obtain sample analogs to influence functions for calculating the asymptotic variance and standard errors of statistics. This approach applies to a wide range of statistics and is useful for conducting inference in a minimum-distance estimation procedure. This approximate approach is simpler to execute than analytical influence functions and is faster than the bootstrap when the estimation procedure is computationally challenging