Precautionary saving increases when second-period utility has a positive third derivative in a two-period model.
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Retrieved economic literature establishes that foundational models by Leland and Sandmo demonstrate that a positive third derivative of the utility function is required for positive precautionary saving.
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## Economics Letters
Volume 150, January 2017, Pages 18-20
# Precautionary saving: A taxonomy of prudence
Marcos Vergara
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https://doi.org/10.1016/j.econlet.2016.10.029 Get rights and content
## Highlights
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We provide necessary and sufficient conditions on preferences to guarantee a precautionary effect.
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We derive a general prudence index.
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For the special cases of labor income risk and wealth risk, the general index is reduced to prudence and relative prudence.
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For the cases of asset risk and capital risk the general index is reduced to partial prudence.
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The precautionary effect arises if the utility premium is decreasing in saving.
## Introduction
Precautionary saving is described as the extra saving generated by uncertainty regarding future income. This idea was first studied by Leland (1968) and Sandmo (1970), who showed that a positive third derivative of the utility function is required for positive precautionary saving. This condition is referred to as “pr