4.13 ITE: Exercise

  • Estimation requires filling in counterfactual (Missing data problem)
  • RQ: Does Aspirin (0/1) cure a headache (0/1)? What would have happened if Paul had not taken the Aspirin?
  • Yellow: Measurement of Paul (t = 40)
  • Green: Measures of Paul, Simone and Kathrin
  • Q: Which green measurements would you take as comparison observation (as “counterfactual”) for the yellow measurement? What assumptions are we making? Discuss! (hint: unit homogeneity, temporal stability, causal transience)17
  • Will see later that we pursue similar reasoning (about ‘good’ counterfactual) when comparing averages

  1. We could compare Paul to another unit and make the assumption of “unit homogeneity” (Holland 1986, 948) (probably measured at the same moment in time to make our assumption more realistic). We could also compare Paul to himself at an earlier moment in time and make the assumptions of “temporal stability” and “causal transience” (Holland 1986, 948). The former states that the outcome value for unit u under control, does not depend on when the sequence “apply c to u then measure Y on u” occurs, i.e., Paul’s value under control would be the same regardless of when Paul is assigned to the control condition (a). The latter (b) states the outcome value of unit u under treatment is not affected by the prior exposure of u to the sequence in (a). For Holland (1986, 947) these assumptions belong to the scientific solution of the fundamental problem of causal inference (linked to their individual-level nature). Later we’ll talk about the statistical solution (comparing averages in the long run).↩