## The Annals of Applied Statistics

### Agnostic notes on regression adjustments to experimental data: Reexamining Freedman’s critique

Winston Lin

#### Abstract

Freedman [Adv. in Appl. Math. 40 (2008) 180–193; Ann. Appl. Stat. 2 (2008) 176–196] critiqued ordinary least squares regression adjustment of estimated treatment effects in randomized experiments, using Neyman’s model for randomization inference. Contrary to conventional wisdom, he argued that adjustment can lead to worsened asymptotic precision, invalid measures of precision, and small-sample bias. This paper shows that in sufficiently large samples, those problems are either minor or easily fixed. OLS adjustment cannot hurt asymptotic precision when a full set of treatment–covariate interactions is included. Asymptotically valid confidence intervals can be constructed with the Huber–White sandwich standard error estimator. Checks on the asymptotic approximations are illustrated with data from Angrist, Lang, and Oreopoulos’s [Am. Econ. J.: Appl. Econ. 1:1 (2009) 136–163] evaluation of strategies to improve college students’ achievement. The strongest reasons to support Freedman’s preference for unadjusted estimates are transparency and the dangers of specification search.

#### Article information

Source
Ann. Appl. Stat. Volume 7, Number 1 (2013), 295-318.

Dates
First available in Project Euclid: 9 April 2013

https://projecteuclid.org/euclid.aoas/1365527200

Digital Object Identifier
doi:10.1214/12-AOAS583

Mathematical Reviews number (MathSciNet)
MR3086420

Zentralblatt MATH identifier
06171273

#### Citation

Lin, Winston. Agnostic notes on regression adjustments to experimental data: Reexamining Freedman’s critique. Ann. Appl. Stat. 7 (2013), no. 1, 295--318. doi:10.1214/12-AOAS583. https://projecteuclid.org/euclid.aoas/1365527200.

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