Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Horizontal equity measurement function for health care delivery and finance

f(y_i, x_ji, z_ki, f_t, V, H, R) = (yX_i, yIS_i, HI, S, RE)

Maps data on the use of health care, proxies of need and compulsory health payments, for people ranked by income or another measure of living standards, to measures of horizontal equity: need-expected use from a need regression, need-standardised use, the horizontal inequity index for the delivery of care, its rule-of-75 reading, and the horizontal inequity term in the decomposition of the redistributive effect of health finance. Equal treatment for equal need is judged against the average relationship between need and use in the sample, so the vertical norm is assumed rather than tested. The grouped-data concentration index (HE-FM-HINQ-005 on the Health Inequality page and HE-FM-VEQ-002 on the Vertical Equity page) and the Kakwani index (HE-FM-VEQ-001) have their own records and are not repeated here.

  • Need-expected use of health care by indirect standardisation

    yX_i = alpha_hat + sum_(j=1)^J [beta_hat_j * x_ji] + sum_(k=1)^K [gamma_hat_k * z_bar_k]

    Predicts the use of care each person would be expected to have given their need, from a linear regression of use on need variables and non-need control variables. Each person's own need values enter the prediction, while every control is set to its sample mean, so the controls protect the need coefficients from omitted-variable bias without being standardised for. This is the first step of indirect standardisation; the second is HE-FM-HEQ-002.

  • Need-standardised use of health care in a horizontal equity analysis

    yIS_i = y_i - yX_i + y_bar

    Gives the use of care a person would have irrespective of differences in need across income, as actual use minus need-expected use plus the sample mean of actual use. Its distribution across income groups shows the inequality in use that remains after differences in need are allowed for. Because the formula is linear, it applies equally to the group means of a quintile table.

  • Horizontal inequity index as a difference of concentration indices

    HI = C_M - C_N

    Measures horizontal inequity in the delivery of care as the concentration index of actual use minus the concentration index of need-expected use, with people ranked by income or another living standards measure from poorest to richest. It equals the concentration index of need-standardised use and is sometimes labelled HI_WV after Wagstaff and van Doorslaer. Zero is consistent with horizontal equity, a positive value indicates pro-rich inequity and a negative value pro-poor inequity. Each concentration index is computed as in HE-FM-HINQ-005 on the Health Inequality page.

  • Rule of 75 reading of a horizontal inequity index

    S = 75 * HI

    Turns a concentration index into the percentage of the variable that would have to be redistributed linearly from the richer half of the population to the poorer half to bring the index to zero, by multiplying the index by 75. Applied to the horizontal inequity index, the variable is need-standardised use. A negative index gives a negative percentage, a redistribution from the poorer half to the richer half.

  • Decomposition of the redistributive effect of health payments with horizontal inequity

    RE = V - H - R

    Splits the redistributive effect of a compulsory health payment, the fall in the Gini coefficient from income before payment to income after it, into vertical redistribution minus horizontal inequity minus reranking, as shown by Aronson, Johnson and Lambert. H measures unequal payments among households with the same pre-payment income and R the change in the order of households. V is computed as in HE-FM-VEQ-004 on the Vertical Equity page.