The Hicksian definition of complementarity and substitutability may not apply in contexts in which agents are not utility maximisers or where price or income variations, whether implicit or explicit, are not available. We look for tools to identify complementarity and substitutability satisfying the following criteria: they are behavioural (based only on observable choice data); model-free (valid whether the agent is rational or not) and they do not rely on price or income variation. We uncover a conflict between properties that it is arguably reasonable for a complementarity notion to possess. We discuss three different possible resolutions of the conflict.
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We thank the Editor Martin Cripps, four anonymous referees, Miguel Angel Ballester, Jean-Pierre Dubé, Matthew Gentzkow, Faruk Gül, Patrick Harless, Rich McLean, Luigi Pistaferri, John Quah, Tomas Sjöström and seminar audiences at Birkbeck College, ECARES, LSE, the University of Manchester, Queen Mary University of London, Rutgers University, Université de Paris and the University of St Andrews for very useful comments. Levent Ülkü acknowledges financial support from the Asociación Mexicana de Cultura. The usual disclaimers apply.
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