Calculate Equity Weights — calc_equity

Derives equity weights from the Atkinson social welfare function. Equity weights represent the relative social value of a one-unit health gain in each socioeconomic group given inequality aversion \(\eta\).

Usage

calc_equity_weights(baseline_health, pop_weights, eta = 1, normalise = TRUE)

Arguments

baseline_health: Numeric vector of baseline health (HALE) by group (ordered from most to least deprived).
pop_weights: Numeric vector of population weights.
eta: Inequality aversion parameter (default = 1).
normalise: Logical. If TRUE (default), weights are normalised so their population-weighted mean equals 1. If FALSE, returns raw marginal welfare derivatives.

Value

Named numeric vector of equity weights, one per group.

Details

For the Atkinson SWF, the equity weight for group \(i\) is proportional to \(h_i^{-\eta}\): groups with lower baseline health receive higher weights when \(\eta > 0\).

References

Cookson R, Griffin S, Norheim OF, Culyer AJ (2020). Distributional Cost-Effectiveness Analysis. Oxford University Press. Oxford University Press (ISBN:9780198838197).

Robson M, Asaria M, Cookson R, Tsuchiya A, Ali S (2017). Eliciting the Level of Health Inequality Aversion in England. Health Economics 26(10): 1328-1334. doi:10.1002/hec.3386

Examples

baseline <- c(60, 63, 66, 69, 72)
weights  <- rep(0.2, 5)
calc_equity_weights(baseline, weights, eta = 1)
#> [1] 1.0954413 1.0432775 0.9958558 0.9525577 0.9128678