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.
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Supplement to "Optimal Discounting"
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.