Is It the Message or the Messenger? Examining Movement in Immigration Beliefs

Is It the Message or the Messenger? Examining Movement in Immigration Beliefs was written by Hassan Afrouzi, Carolina Arteaga, and Emily Weisburst. It was published in the Journal of Political Economy Microeconomics volume 2 (2024).

The authors design an experiment to isolate the effects of political messages and the effects of who gave the political message. Pro- and anti-immigration speeches, as well as non-ideological (turkey pardoning) speeches, are selected from Obama and Trump. The same speeches are reproduced with a voice actor. The non-ideological speeches enable control for effects of political messages. The reproduction enables control for the effects of who gave the political message.

Probability Theory

A sample space Ω represents an individual's opinion about immigration (binary; favorable or unfavorable). Subjective opinions--as in given S sources of political messages and M expected messages from each source--are given in Ω‾ = Ω * M * S.

The unconditional probability of belief ω is given by P(ω) = Σ P(ω,s',m') for all s' ∈ S and m' ∈ M.

For a 'treatment' s' ∈ S and m' ∈ M, the conditional probability of belief ω is given by P(ω|s',m').

It is more realistic to measure relative probabilities of beliefs in an experiment, however. Therefore the treatment belief relative to the unconditional belief is given by:

This can be decomposed (with Bayes rule and log probabilities) into separate anonymous message effects and source persuasion effects:

More generally, note that P(ω|m) = P(ω)P(m|ω) / P(m), or using an odds ratio (Θ) formulation, P(ω|m) = P(ω)Θ(m|ω). Measuring from a treatment of a message m' ∈ M, the anonymous message effect (β_m) is present if the odds ratio is not 1.

Similarly, note that P(ω|m,s) = P(ω|m)P(s|ω,m) / P(s|m) = P(ω|m)Θ(s|ω,m).

TODO: actually the derivation of remark 2 is completely beyond me, come back to this another day

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