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Calculate Equally Distributed Equivalent Health (EDE)

Source: R/06_social_welfare.R
calc_ede.Rd

Uses the Atkinson social welfare function to calculate EDE health — the level of health that, if equally distributed, would generate the same social welfare as the actual distribution given inequality aversion parameter \(\eta\).

Usage

calc_ede(health_dist, pop_weights, eta = 1)

Arguments

health_dist

Numeric vector of health values by group (must be strictly positive).

pop_weights

Numeric vector of population weights (will be normalised to sum to 1).

eta

Inequality aversion parameter (numeric scalar, default = 1).

  • \(\eta = 0\): returns arithmetic mean (no inequality aversion).

  • \(\eta = 1\): returns geometric mean (moderate aversion).

  • \(\eta > 1\): increasing inequality aversion.

  • NICE relevant range: 0 to 10.

Value

EDE health value (numeric scalar). Returns NA with a warning if any health values are non-positive.

Details

$$ \text{EDE}(\eta) = \left(\sum_i w_i h_i^{1-\eta} \big/ \sum_i w_i\right)^{1/(1-\eta)} \quad \text{for } \eta \neq 1 $$ $$ \text{EDE}(1) = \exp\!\left(\sum_i w_i \ln(h_i)\right) \quad \text{(geometric mean, } \eta = 1\text{)} $$

References

Atkinson AB (1970). On the Measurement of Inequality. Journal of Economic Theory 2(3): 244-263. doi:10.1016/0022-0531(70)90039-6

Examples

health  <- c(60, 63, 66, 69, 72)
weights <- rep(0.2, 5)

# eta = 0: arithmetic mean
calc_ede(health, weights, eta = 0)
#> [1] 66

# eta = 1: geometric mean
calc_ede(health, weights, eta = 1)
#> [1] 65.8633

# eta = 5: high inequality aversion
calc_ede(health, weights, eta = 5)
#> [1] 65.31903