Primary Outcomes (explanation)
> We are particularly interested in how consent designs affect website competition. To this end, we plan to focus on the following website characteristics to examine site-level heterogeneity in the treatment effects:
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> - Website popularity.
> - Website category.
> - Familiarity with the website.
> We have 6 treatment conditions, described in more detail in the ``Experiment Design'' Section.
> Our Baseline specification is as follows, where we index treatments 1 through 6, with the omitted category being treatment 1 (Accept all, Reject all, Cookie settings):
$$ y_{id} = \sum_{k \in \{2, 3, 4, 5, 6\}} \tau_{k} 1(Treat_{id} = k) + \gamma_{i} + \mu (X_{d} - \bar{X}) + \epsilon_{id} $$
> In this specification, $i$ denotes a participant and $d$ denotes a website, or domain. We care about several outcomes $y$, which are dummy variables for each of the various consent choices: accepting all cookies; clicking on “Cookie settings” and making granular choices; rejecting all cookies; closing the banner without making a choice. Note that when users click on "Cookie Settings" and then make a choice consistent with either rejecting or accepting all cookies, we classify such choice as either accepting or rejecting all cookies. We include fixed effects for individuals $\gamma_{i}$ and domain characteristics $\mu (X_{d})$ (such as website category).
> Our tests of theoretical mechanisms will consist of hypothesis tests about differences among treatment arms, which correspond to differing mechanisms. The three mechanisms we are interested in evaluating are the following: removing options from the available choices; re-ordering options; emphasizing particular options through colors. The treatment arms described in the ``Experiment Design'' Section help us separate the effects of these strategies on consumer choice.
> We will conduct this analysis separately for the websites visited during the initial survey and for the websites organically browsed by the participant. For the analysis of the cookie choices for the websites visited during the initial survey, we will replace $\mu (X_{d})$ with website fixed effects.
> Our heterogeneity specifications will interact the treatment indicators in the above specification with proxies for website popularity, website category, and participant's familiarity with the website, as in the specification below. Each dimension of heterogeneity will be explored separately (i.e., in different regressions).
> We will conduct this analysis separately for the survey websites and for the organic websites that individuals browse after the survey.
$$ y_{id} = \sum_{k \in \{2, 3, 4, 5, 6\}} \tau_{k} 1(Treat_{id} = k) + \rho_{k} 1(Treat_{id} = k)(X_{d} - \bar{X}) + \gamma_{i} + \mu (X_{d} - \bar{X}) + \epsilon_{id} $$
> The specification $(X_{d} - \bar{X})$ will be simply $X_{d}$ where the dimension of heterogeneity is identified by a dummy variable.
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where the dimension of heterogeneity is identified by a dummy variable.