Joint Econometrics and Statistics Seminar Series

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Title: Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders

Abstract: We consider estimation of average treatment effects given observational data with high-dimensional pre-treatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers n^{1/2}-consistent estimates of the average treatment effect when the propensity score follows a sparse logistic regression model; the regression functions are permitted to be arbitrarily complex. Our theoretical results quantify the price to pay for permitting the regression functions to be inestimable, which shows up as an inflation of the variance of the estimator compared to the semiparametric efficient variance by at most O(1) under mild conditions. Given the lack of assumptions on the regression functions, averages of transformed responses under each treatment may also be estimated at the n^{1/2} rate, and so for example, the variances of the potential outcomes may be estimated. We show how confidence intervals centred on our estimates may be constructed, and also discuss an extension of the method to estimating projections of the heterogeneous treatment effect function. This is joint work with Rajen Shah (University of Cambridge). 

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Title: Matching for causal effects via multimarginal optimal transport

Abstract: Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge in these settings stems from the often high-dimensional structure of the problem. Many methods have been introduced to deal with this challenge, with different advantages and drawbacks in computational and statistical performance and interpretability. Moreover, the methodological focus has been on matching two samples in binary treatment scenarios, but a dedicated method that can optimally balance samples across multiple treatments has so far been unavailable. We introduce a natural optimal matching method based on entropy-regularized multimarginal optimal transport that possesses many useful properties to address these challenges. Our method provides interpretable weights of matched individuals that converge at the parametric rate to the optimal weights in the population, can be efficiently implemented via the classical iterative proportional fitting procedure, and can even match several treatment arms simultaneously. It also possesses demonstrably excellent finite sample properties.

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Title: Flexible Covariate Adjustments in Regression Discontinuity Designs

Abstract: Empirical regression discontinuity (RD) studies often use covariates to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than the linear adjustment estimators that are currently used widely in practice. Our approach can accommodate a possibly large number of either discrete or continuous covariates. It involves running a standard RD analysis with an appropriately modified outcome variable, which takes the form of the difference between the original outcome and a function of the covariates. We characterize the function that leads to the estimator with the smallest asymptotic variance, and show how it can be estimated via modern machine learning, nonparametric regression, or classical parametric methods. The resulting estimator is easy to implement because tuning parameters can be chosen as in a conventional RD analysis. An extensive simulation study illustrates the performance of our approach. This is joint work with Tomasz Olma and Christoph Rothe.

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Title: Quadratic Prediction Methodology and Calibration of Prediction Intervals Based on Subsampling.

Abstract: We consider nonlinear prediction of a stationary time series using quadratic functions of the past data. We derive explicit formulae for the best quadratic predictor and its MSPE. We also give conditions under which the quadratic approach improves over the standard linear case and provide a complete characterization for such processes. We next consider the problem of constructing asymptotically valid prediction intervals based on a general point predictor. While much of the existing literature either assumes a parametric time series model or makes specific distributional assumptions (e.g., Gaussian), this work relaxes both and develops a nonparametric method that is applicable to a general stationary sequence. Specifically, we propose a Subsampling method for constructing distribution free prediction intervals for linear and nonlinear prediction methods and establish its validity. For the case of best linear predictor, we also derive the optimal rate of the subsample block size. The results in the prediction context are very nonstandard when compared with the known results on optimal block sizes for the Block Bootstrap/Subsampling in standard variance estimation problems. Finite sample properties of the proposed method are illustrated with simulation.

This event is hybrid and will take place in the Leverhulme Library COL 6.15.

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