Estimation and Inference for Moments of Ratios with Robustness against Large Trimming Bias

Empirical researchers often trim observations with small denominator A when they estimate moments of the form E[B/A]. Large trimming is a common practice to mitigate variance, but it incurs large trimming bias. This paper provides a novel method of correcting large trimming bias. If a researcher is willing to assume that the joint distribution between A and B is smooth, then a large trimming bias may be estimated well. With the bias correction, we also develop a valid and robust inference result for E[B/A].