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A novel theory of time discounting is proposed in which future consumption is less valuable than present consumption because of waiting costs. Waiting is intermittent as consumer's attention is periodically distracted away from future gratifications. A new axiom is introduced, called weak impatience, according to which consumers are impatient only if they pay attention to the good in the present, or when all options are in the future, a strictly positive probability exists they will pay attention to it. The model unifies and reinterprets three empirically relevant properties of intertemporal preference: decreasing impatience, present bias and sub-additive discounting. In addition, the model predicts new testable behavioral patterns, not predicted by other discounting models.

A focused definition of present bias is proposed which takes preferences as primitives. A present biased individual over-weights immediate costs and benefits relative to those occurring at any point in the future. The definition allows to sort out previous confounds, such as decreasing impatience, choice reversal or short-term impatience. It intuitively connects to usual utility representations of present bias like the quasi-hyperbolic model of Laibson (1997) or the fixed cost model of Benhabib, Bisin and Schotter (2010). J.E.L. codes: D8, E21

A novel theory of time discounting is proposed in which future consumption is less valuable than present consumption due to waiting costs. Waiting is intermittent as consumer's attention can be distracted away from future gratifications. The model unifies several properties of intertemporal preference like present bias, decreasing impatience or sub-additive discounting. A quantitative puzzle is presented, supported by preliminary experimental evidence, which shows how impatience over short delays may translate into excessive impatience over long delays. The wait-based model offers a solution to the puzzle, contrary to usual models of discounting. J.E.L. codes: D8, E21

Two-Stage Exponential (TSE) discounting, the model developed here, generalises exponential discounting in a parsimonious way. It can be seen as an extension of Quasi-Hyperbolic discounting to continuous time. A TSE discounter has a constant rate of time preference before and after some threshold time; the switch point. If the switch point is expressed in calendar time, TSE discounting captures time consistent behaviour. If it is expressed in waiting time, TSE discounting captures time invariant behaviour. We provide preference foundations for all cases, showing how the switch point is derived endogenously from behaviour. We apply each case to Rubinstein's infinite-horizon, alternating-offers bargaining model.