Intertemporal Discrete Choice

The discounted logit is widely used to estimate time preferences using data from field and laboratory experiments. Despite its popularity, it exhibits the "problem of the scale": choice probabilities depend on the scale of the value function. When applied to intertemporal choice, the problem the scale implies that logit probabilities are sensitive to the temporal distance between the choice and the outcomes. This is a failure of an intuitive requirement of stationarity although future values are discounted geometrically. As a consequence, patterns of choice following from the structure of the logit may be attributed to non-stationary discounting. We solve this problem introducing the discounted Luce rule. It retains the flexibility and simplicity of the logit while it satisfies stationarity. We characterize the model in two settings: dated outcomes and consumption streams. Relaxations of stationarity give observable restrictions characterizing hyperbolic and quasi-hyperbolic discounting. Lastly, we discuss an extension of the model to recursive stochastic choices with the present bias