On the equivalence between internal and external habits in a growth model with subtractive preferences

In the context of a representative agent growth model, it is shown that, under a 'subtractive' specification of preferences, the difference between the competitive equilibria in the 'external habits' and 'internal habits' cases widely investigated in the literature disappers. It is also proved that the subtractive specification is the only functional form of individuals' preferences for which this equivalence holds. The results highlight the fact that subctrative preferences are a rather special case, useful when the interest lies in assessing in a simple way the role played by habit formation.