Collaborative Research: Honest Inference and Efficiency Bounds for Nonparametric Regression and Approximate Moment Condition Models

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In analyzing economic data, researchers use models and assumptions that are typically best thought of as approximations of reality. This project will develop statistical methods that are valid when these models are only approximately correct, rather than exactly correct. The methods developed in this project can also be used to provide simple ways of assessing the sensitivity of the conclusions of an empirical study to its underlying assumptions. These methods can be applied to numerous commonly studied problems that are relevant for policy and for understanding the economy.This project will develop confidence intervals in approximate moment condition models with convex parameter spaces, as well as sharp efficiency bounds showing that they are as tight as possible in a certain precise sense. The setup covers inference on a linear functional of a nonparametric regression function, such as its value at a point, the regression discontinuity parameter, or an average treatment effect under unconfoundedness. The setup also covers parameter constraints in the linear regression model as well as moment condition models such as generalized method of moments (GMM) or minimum distance models in which the moment condition is locally misspecified. The confidence intervals are simple to construct, and valid in an "honest" or uniform sense. As special cases of the results, the project obtains optimal kernels for inference in nonparametric regression models, and optimal weights for GMM under misspecification.