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Unformatted text preview: NBER WORKING PAPER SERIES ROBUST INFERENCE FOR MISSPECIFIED MODELS CONDITIONAL ON COVARIATES Alberto Abadie Guido W. Imbens Fanyin Zheng Working Paper 17442 http://www.nber.org/papers/w17442 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 September 2011 Financial support for this research was generously provided through NSF grant 0820361. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. 2011 by Alberto Abadie, Guido W. Imbens, and Fanyin Zheng. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including notice, is given to the source. Robust Inference for Misspecified Models Conditional on Covariates Alberto Abadie, Guido W. Imbens, and Fanyin Zheng NBER Working Paper No. 17442 September 2011 JEL No. C01 ABSTRACT Following the work by White (1980ab; 1982) it is common in empirical work in economics to report standard errors that are robust against general misspecification. In a regression setting these standard errors are valid for the parameter that in the population minimizes the squared difference between the conditional expectation and the linear approximation, averaged over the population distribution of the covariates. In nonlinear settings a similar interpretation applies. In this note we discuss an alternative parameter that corresponds to the approximation to the conditional expectation based on minimization of the squared difference averaged over the sample, rather than the population, distribution of a subset of the variables. We argue that in some cases this may be a more interesting parameter. We derive the asymptotic variance for this parameter, generally smaller than the White robust variance, and we propose a consistent estimator for the asymptotic variance. Alberto Abadie John F. Kennedy School of Government Harvard University 79 JFK Street Cambridge, MA 02138 and NBER alberto_abadie@harvard.edu Guido W. Imbens Department of Economics Littauer Center Harvard University 1805 Cambridge Street Cambridge, MA 02138 and NBER imbens@fas.harvard.edu Fanyin Zheng Harvard University fzheng@fas.harvard.edu 1 Introduction Following the seminal work by White (1980ab, 1982), researchers in economics routinely report standard errors that are robust to misspecification of the models that are being estimated. Muller (2011) gives the corresponding confidence intervals a Bayesian inter pretation. A key feature of the approach developed by White (see also Eicker (1967) and Huber (1967)) is that in regression settings it focusses on the best linear predictor (blp) that minimizes the distance between the linear predictor and the true conditional expec...
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