Parental transfers under ambiguity

ABSTRACT

This note introduces parental uncertainty into parent–child monetary transfers. A parent questions the probability distribution of a child’s future economic success. As a result, the parent endogenously tilts his/her subjective probability model away from an approximating probability model. In this case, parental transfers increase with model uncertainty, thereby reducing the child’s effort and probability of economic success. This theoretical result raises several empirical questions, of which two are as follows. For one thing, informed parents (e.g. those who hold the same job as their child) transfer less money, and their child exerts more effort. Another is that economic uncertainty (e.g. recessions or pandemics) prompts higher parental transfer payments and reduces the child’s effort.

KEYWORDS:

• Bequest
• ambiguity
• knightian uncertainty
• robust control
• inheritance

JEL CLASSIFICATION:

• D13
• D81
• E20

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Another large branch of the literature studies the consequences of accidental bequest (See Yaari (1965) and Davies (1981)).

² See Hansen and Sargent (2008) for more examples of applications.

³ Note that our model coincides with the standard altruistic parent model if $\bar{\in }=\underset{\_}{\in }=0$.

⁴ The Online Appendix contains the detailed derivation of each equation.

⁵ Note that relative entropy is convex and grounded.

⁶ Note that the optimal distortion converges to 1 as $\theta \to \mathrm{\infty }$ for all $\in$.

⁷ For more details about the construction of the Historical Economic Uncertainty Indexes, see https://www.policyuncertainty.com/us_historical.html and https://www.policyuncertainty.com/uk_historical.html.

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science [Grant-in-Aid for Research Activity Start-Up (No. 19K23239)].