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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.

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Experimental Estimation of Heterogeneous Treatment Effects for Treatments Prone to Self-Selection

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  1. 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

  2. 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

  3. Figure 1: The Self-Selection Experiment and Heterogeneity Distributions and Expected Means for Response Variable Y:

  4. 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

  5. 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

  6. Figure 2: Simulated Treatment-Effect Estimates

  7. Figure 3: Misclassification and Estimation

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