Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions

Victor Chernozhukov and Vira Semenova
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Vira Semenova: Institute for Fiscal Studies and Harvard

No CWP40/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper provides estimation and inference methods for a structural function, such as Conditional Average Treatment Effect (CATE), based on modern machine learning (ML) tools. We assume that such function can be represented as a conditional expectation = of a signal , where is the unknown nuisance function. In addition to CATE, examples of such functions include regression function with Partially Missing Outcome and Conditional Average Partial Derivative. We approximate by a linear form , where is a vector of the approximating functions and is the Best Linear Predictor. Plugging in the fi rst-stage estimate into the signal , we estimate via ordinary least squares of on . We deliver a high-quality estimate of the pseudo-target function , that features (a) a pointwise Gaussian approximation of at a point , (b) a simultaneous Gaussian approximation of uniformly over x, and (c) optimal rate of convergence of to uniformly over x. In the case the misspeci cation error of the linear form decays sufficiently fast, these approximations automatically hold for the target function instead of a pseudo-target . The fi rst stage nuisance parameter is allowed to be high-dimensional and is estimated by modern ML tools, such as neural networks, -shrinkage estimators, and random forest. Using our method, we estimate the average price elasticity conditional on income using Yatchew and No (2001) data and provide uniform con fidence bands for the target regression function.

Date: 2018-07-04
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
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Citations: View citations in EconPapers (5)

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