Intertemporal Discrete Choice

Random utility models are widely used to estimate preference parameters. In the case of intertemporal choice, the two most common models are the discounted logit and one we call the discounted Luce. Due to their apparent similarity, the choice to use one model or the other seems irrelevant. In this paper, we argue that the discounted Luce is superior to the discounted logit in two significant aspects. First, in relevant applications, the discounted Luce is monotone in the sense of Apesteguia and Ballester (2018), while the discounted logit is not. Second, we show that the discounted logit is incompatible with a property of choice probabilities we call “weak stationarity”. The latter is compatible with common assumptions on the random nature of choices and is often not falsifiable with commonly available data. Fitting a logit model to weakly stationary choice probabilities biases the time-preference estimates. On the contrary, the discounted Luce can be safely used when choice probabilities are weakly stationary. An application to an existing dataset supports the theoretical results.