Table 2.

Bequest motives used to calculate the aggregate demand for annuities. Utility from consumption is constant relative risk aversion, $u\left(c\right)=\frac{c^{1-\sigma }}{1-\sigma }$, in all cases. Unlike the previous sections, preferences are defined over real bequests rather than the present value of bequests because all of the estimated bequest motives come from models in which preferences are defined over real bequests.

Paper	Bequest motive	Parameters
Ameriks et al. (2009)	$v\left(b\right)=\frac{\omega }{1-\sigma }{\left(\varphi +\frac{b}{\omega }\right)}^{1-\sigma }$	w = 16, φ = 5.05
De Nardi (2004)	$v\left(b\right)={\varphi }_1{\left(1+\frac{b}{{\varphi }_2}\right)}^{1-\sigma }$	φ1 = −9.5 φ2 = 11.6
De Nardi et al. (2010)	$v\left(b\right)=\theta \frac{{(k+b)}^{1-\sigma }}{1-\sigma }$	θ = 2,360 k = 273
Hurd and Smith (2002) *	v(b) = θb	θ = 25.5−σ
Kopczuk and Lupton (2007)	v(b) = θb	θ = 23.8−σ
Lockwood (2010)	$v\left(b\right)={\left(\frac{m}{1-m}\right)}^{\sigma }\frac{{\left(\frac{m}{1-m}{c}_0+b\right)}^{1-\sigma }}{1-\sigma }$	m = 0.96, c0 = 18

^*The “Hurd and Smith (2002)” bequest motive is one I estimate to match Hurd and Smith’s estimates of average anticipated bequests.