Table 5. Sensitivity analysis for redistribution and efficiency cost calculations (γ = 3).

Same calculations as in Table 3 with varying parameters. Table 3’s baseline results appear in bold. Panel 1 considers the effects of varying the fraction of females in the annuitant pool, holding all other parameters constant at the Table 3 baseline levels. Panel 2 considers the effects of varying the mortality hazards for high and low-risk types at age 65. These hazards are varied so as to keep the aggregate mortality rate at age 65 constant. All other parameters are held at the Table 3 baseline levels. The redistribution and efficiency cost metrics are described in Eqs. (15) and (14), respectively. ‘MWS’ refers to the Miyazaki (1977), Wilson (1977), Spence (1978) equilibrium. This is the constrained efficient market outcome with the least redistribution. ‘SS’ refers to the constrained efficient outcome with pooling of risk types. This is the outcome that we consider with the most redistribution; it loosely corresponds to banning gender-based pricing in a compulsory Social Security setting.

Parameter(s) being varied and new value(s)	Redistribution to women (R̃W), per woman as % of endowment		Efficiency cost as % of endowment		Efficiency cost per dollar of distribution
	MWS	SS	MWS	SS	MWS	SS
Panel 1: Varying θ (fraction female)
θ = 0.1	6.37%	13.63%	0.00%	0%	0.32%	0%
0.3	4.84	10.30	0.01	0	0.89	0
0.5	3.39	7.14	0.02	0	1.45	0
0.7	2.00	4.17	0.03	0	1.97	0
0.9	0.66	1.35	0.01	0	2.40	0
Panel 2: Varying αH, αL = mortality hazards at age 65 for high-risk and low-risk types
αH, αL =.001, .046	4.72%	8.63%	0.02%	0%	0.91%	0%
.002, .043	3.98	7.85	0.02	0	1.18	0
.0031, .041	3.39	7.14	0.02	0	1.45	0
.005, .036	2.62	6.01	0.03	0	1.97	0
.008, .028	1.65	4.16	0.03	0	3.27	0