Econometrica: Mar, 2022, Volume 90, Issue 2
Jawwad Noor, Norio Takeoka
The agent is modeled as a current self that optimally incurs a cognitive cost of empathizing with future selves. The model unifies well‐known experimental and empirical findings in intertemporal choice and enriches the multiple selves model with a notion of self‐control. The defining feature of the model is magnitude‐decreasing impatience: greater patience toward larger rewards. Two behavioral definitions of magnitude‐decreasing impatience are provided and the model is characterized under each of them.
Supplement to "Optimal Discounting"
Noor, Jawwad, and Norio Takeoka
This supplementary appendix for Noor and Takeoka  provides (i) a characterization for the General Discounted Utility (GDU) model both on the deterministic streams and on the streams of lotteries, (ii) a weaker definition of present equivalents in the off-diagonal approach, (iii) omitted proofs for results in Noor and Takeoka , and (iv) a new axiomatization result about a variant of homogeneous CE representation, called the smooth homogeneous CE model.