In economics, the exponential discounting has been used as a standard model for intertemporal choice. However, experimental and empirical studies report numerous anomalies for the exponential discounting model. This study overviews how the intertemporal choice model has been developed to accommodate those anomalies such as the common difference effect, the magnitude effect, separation of attitudes between risk and intertemporal substitution, the equity premium puzzle and the risk-free rate puzzle, additive separability across time, and attitudes toward time lotteries. In particular, we will explain in detail the author's research (Noor and Takeoka (2020)), called the costly empathy model, which is motivated to accommodate the magnitude effect.
