Modelling reference dependence for repeated choices: A horse race between models of normalisation

In the logit model, a choice between options is driven by payoff differences. Existing evidence on repeated choices suggests that the way payoff differences are evaluated depends on historically observed differences. We capture such reference dependence using the value normalisation approach developed in neuroscience. We use experimental data and run a horse race between various models with normalisation, including widely used divisive and range normalisation. We show that a parsimonious logit model with maximum difference normalisation has both the best goodness of fit and a strong quasi-out-of-sample predictive power. In this structural parameter-free logit model, an agent makes a choice based on the difference in payoffs in the previous period, normalised by the maximum difference in payoffs in two previous periods. The model has a wide range of applications, from studying learning dynamics in repeated games to predicting retirement plans choices.