Industrialized countries typically devote a substantial share of their public resources to social programs in order to redistribute income and reduce poverty. To assess the poverty impact of social programs, it is common to estimate the change in a poverty index they induce. For this, a benchmark scenario that captures pre-transfer income is first defined, along which poverty indices are then calculated. Next, the distribution of income resulting from a social programme is simulated. The poverty indices are then calculated again on that distribution, and the differences in them are interpreted as the poverty impact of the social programme.

The estimated poverty impact of the program then depends upon the poverty reduction it enables per dollar spent. A problem arises, however, when evaluating a set of co-existing redistributive programs. The order in which the impact of the various programs is assessed can indeed influence the poverty reduction attributed to each of them. To illustrate this, consider a country with two identical universal programs. Each of these awards everyone a transfer equal to the poverty line (i.e. regardless of the person's pre-transfer income), so that no person is poor after the implementation of either programme. The poverty impact of each programme is assessed by comparing poverty with and without it. If the baseline income used to infer the poverty impact of a programme includes the value of the other, none of them will show any impact on poverty, albeit both necessarily eliminate poverty
totally if the other program is not included in the benchmark income. As it is usually arbitrary to prefer a given order rather than another, it would seem natural to use a sharing rule that assigns to each program a share of the total poverty impact that does not depend on the order of the different income sources.
The aim of this paper is then to estimate and compare the poverty impact of a comparable set of tax and transfer programs that are in force in some developed countries. Comparing national experiences in taxes and transfers and in poverty alleviation programs may inform the understanding and the design of alternative welfare programs. We
do this by importing from cooperative game theory the Shapley value -- introduced in 1953-- and by applying it to poverty measurement. We also take into account the size of the
different income sources in assessing their impact on poverty.

In assessing the poverty impact of tax and transfer programmes, concerns regarding the identification of the poor and the aggregation of individual poverty are as important as in simply comparing poverty across distributions. Since the assessed poverty impact will usually depend on the choice of a poverty line and of a poverty index, we estimate that impact over wide ranges of poverty lines and over broad classes of poverty indices.

We use data from the Luxembourg Income Study (LIS) on Canada, United States, United Kingdom, Germany, France, and Sweden, all with a recent 2000-2004 LIS database and with relatively similar tax and transfer systems.