Revealed Bounded Rationality: testing Present Bias in a Rational Addiction Equation

This paper deals with one of the main theoretical and empirical problems associated with the rational addiction model, namely that the demand equation derived from the rational addiction theory is not empirically distinguishable from models with forward-looking behavior, but with time-inconsistent preferences. The implication is that, even when forward-looking behavior can be convincingly supported, this equation cannot provide evidence in favor of time-consistent preferences against a model with dynamic inconsistency. In fact, we show that the possibility of testing for exponential versus non-exponential time discounting is nested within the rational addiction model. We propose a test of time consistency that uses only the information obtained from the general rational addiction demand equation and the price effects. A pseudo panel of Italian households is used to test for rational addiction in tobacco consumption. GMM estimators are used to deal with errors in variables and unobserved heterogeneity. The results conform to the theoretical predictions. We find evidence that tobacco consumers are forward-looking, but time-inconsistent. The values of the derived present bias and long run discount parameters are statistically significant and in line with the literature.