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ALTERNATIVE ASYMPTOTICS AND THE PARTIALLY LINEAR MODEL WITH MANY REGRESSORS

Published online by Cambridge University Press:  19 October 2016

Matias D. Cattaneo ,
Michael Jansson  and
Whitney K. Newey
Matias D. Cattaneo
Affiliation:
University of Michigan
Michael Jansson
Affiliation:
University of California Berkeley and CREATES
Whitney K. Newey*
Affiliation:
Massachusetts Institute of Technology
*
*Address correspondence to Whitney K. Newey, Department of Economics, MIT, E52-424, Cambridge, MA 02139, USA; e-mail: wnewey@mit.edu.
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Abstract

Many empirical studies estimate the structural effect of some variable on an outcome of interest while allowing for many covariates. We present inference methods that account for many covariates. The methods are based on asymptotics where the number of covariates grows as fast as the sample size. We find a limiting normal distribution with variance that is larger than the standard one. We also find that with homoskedasticity this larger variance can be accounted for by using degrees-of-freedom-adjusted standard errors. We link this asymptotic theory to previous results for many instruments and for small bandwidth(s) distributional approximations.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 2 , April 2018 , pp. 277 - 301
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

The authors are grateful for comments from Xiaohong Chen, Victor Chernozhukov, Alfonso Flores–Lagunes, Lutz Kilian, seminar participants at Bristol, Brown, Cambridge, Exeter, Indiana, LSE, Michigan, MSU, NYU, Princeton, Rutgers, Stanford, UCL, UCLA, UCSD, UC-Irvine, USC, Warwick and Yale, and conference participants at the 2010 Joint Statistical Meetings and the 2010 LACEA Impact Evaluation Network Conference. We also thank the editor, Peter Phillips, the co-editor and two reviewers for their comments. The first author gratefully acknowledges financial support from the National Science Foundation (SES 1122994 and SES 1459931). The second author gratefully acknowledges financial support from the National Science Foundation (SES 1124174 and SES 1459967) and the research support of CREATES (funded by the Danish National Research Foundation under Grant No. DNRF78). The third author gratefully acknowledges financial support from the National Science Foundation (SES 1132399).

References

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