Chapter 7 · Section 3 practice

Double Machine Learning

0 of 2 answered

These questions review the examples in the companion slides. Choose an answer, then check the explanation.

Question 1

The choices refer to treating the linear nuisance fits as correctly specified conditional means.

OLS with \(X\) as controls assumes…

  • \(X\) is uncorrelated with \(D\)
  • \(X\) has no effect on \(Y\)
  • \(\mathbb E[Y \mid X]\) and \(\mathbb E[D \mid X]\) are linear in \(X\) — a curved confounder leaks through
  • Nothing — controls always close the backdoor path

Question 2

Scope: the fitted same-row learner in this chapter’s seeded example. The direction of bias is not a universal property of same-row residuals.

Fit \(\hat m\) and \(\hat\ell\) on all \(n\) rows with a learner flexible enough to memorise, then compute \(\hat\theta\) on the same rows. The estimate will be…

  • Unbiased — more data for the nuisance models can only help
  • Biased toward zero — the in-sample residuals of \(D\) have absorbed the noise that identifies \(\theta\)
  • Biased away from zero — overfitting inflates every coefficient
  • Undefined — the residuals are exactly zero