A consistent decomposition of the redistributive, vertical, and horizontal effects of health care finance by factor components.

In studies on the redistributive, vertical, and horizontal effects of health care financing, the sum of the contributions calculated for each financial instrument does not equal the total effects. As a consequence, the final calculations tend to be overestimated or underestimated. The solution proposed here involves the adaptation of the Shapley value to achieve additive results for all the effects and reveals the relative contributions of different instruments to the change of whole-system equity. An understanding of this change would help policy makers attain equitable health care financing. We test the method with the public finance and private payments of health care systems in Denmark and the Netherlands.