Arbitraging Narrow Bracketers

Many important economic outcomes result from the combined effects of several choices, so the best option is not determined from each choice in isolation, but depends on how each choice alters total outcomes. We formally show that narrow bracketing -- treating choices in isolation -- can be distinguished from broad bracketing -- combining the choices -- if and only if there exist price variation across context: there is some bundle for which a person is willing to pay more in one choice than in another. In this case, a narrow bracketer can be arbitraged, buying the bundle when it is expensive and selling when it is cheap in simultaneous choices. We design and run two experiments to identify bracketing from price variation. In a between-subjects design where we vary the amount of work to generate price variation, we reject broad bracketing and fail to reject narrow bracketing. In a within-subject design we directly test bracketing by attempting to arbitrage our participants. For price variation coming from varying amounts of money, 50.3% of subjects are classified as narrow bracketers, and only 14.6% as broad bracketers, the remainder being inconsistent with both. This changes for price variation coming from violations of expected utility -- 13.6% narrow vs 46.3% broad -- and of the weak axiom of revealed preference -- 26.3% narrow vs 38.1% broad.