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Brian J. Gaines James H. Kuklinski University of Illinois at Urbana-Champaign Department of Political Science Institute of Government and Public Affairs. Experimental Estimation of Heterogeneous Treatment Effects for Treatments Prone to Self-Selection. Table 1: Assumptions.

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experimental estimation of heterogeneous treatment effects for treatments prone to self selection

Brian J. Gaines

James H. Kuklinski

University of Illinois at Urbana-Champaign

Department of Political Science

Institute of Government and Public Affairs

Experimental Estimation of Heterogeneous Treatment Effects for Treatments Prone to Self-Selection
table 1 assumptions
Table 1: Assumptions
  • Y is a dichotomous variable that measures a behavior of interest
  • α is the proportion of the population that self-selects into treatment when given the choice
  • In the absence of treatment, self-selectors have probability ys, and non-self-selectors have probability yn, of exhibiting the behavior of interest
  • The treatment effects, which alter the probabilities and are not assumed to be equal, are ts for self-selectors and tn for non-self-selectors
  • (for now) the process of selecting treatment can be perfectly simulated within the experiment
figure 1 the self selection experiment and heterogeneity
Figure 1: The Self-Selection Experiment and Heterogeneity

Distributions and Expected Means for Response Variable Y:

table 2 hypothetical population conditions

Type

Proportion in

population

Marginal effects of seeing negative ads on pr(vote)‏

Baseline

pr(vote)‏

pr(exposed to real negative ads)‏

conflict-averse

0.60

-0.10

0.50

0

conflict loving

0.40

+0.05

0.58

1

Table 2: Hypothetical Population Conditions
slide5
Table 3: Predictions of Three Types of Study: Naïve Observational, Random Assignment Experimental, and Self-Selection Experimental
  • Naïve Observational: +.13, based on 50% turnout among non-selectors and 63% turnout among selectors
  • Note: The +.13 conflates the true teatment effect among selectors (+.05) and the difference in baseline rates (+.08) between selectors and non-selectors
  • Random Assignment Experimental: Expected Average Treatment Effect = E(V|T)-E(V|C) = ((.40)(.58+.05)+(.60)(.50-.10))-((.40)(.58) + (.60) (.50)) = -.04
  • Note: This is the correct estimate only when everyone watches the ads
  • Self Selection Experimental:
    • Selectors: (E(V|S)-E(V|C))/E(α)=(.552-.532)/.40=.05
    • Non-Selectors: (E(V|T)- E(V|S))/(1-E(α))=(.49-.55)/(.60)= -.10
  • Note: These are the correct estimates, as shown in Table 2