Data Collectionhard
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In a study of vocational training effects on earnings, researchers use propensity score matching combined with outcome regression (doubly-robust estimation). For a participant:

  • Propensity score: P(Training=1|X) = 0.70
  • Observed earnings (trained): Y = $36,000
  • From outcome regression, predicted earnings if not trained: Y^0=$30,000\hat{Y}_0 = \$30,000
  • Matched non-participant's earnings: $31,500

Which estimates of the treatment effect are reasonable?