In countries where local governments are heavily involved in financing health care for the indigent, regional disparities in local revenues may adversely affect the access of the poor to medical care. It is thus important to examine how central governments provide funds for such local medical needs. In Japan, local governments finance all medical costs for the poor through their Public Assistance (PA) programs. Using the unique mechanism of the Japanese system of central grants, I construct a measure of "transfer deficit" which shows the portion of the PA expenditures that fails to be secured by the central grants. The distribution of such a measure provides important information to assess the regional equity in financing local programs. The results suggest a compromise on the regional equity in financing medical care for the indigent. Then, I explore the determinants of the deficit measure by performing a quantile regression analysis. Since no effects of potential determinants imply that the central grants well accommodate changes in local needs, finding such effects helps evaluate the performance of the transfer system. The results shows that, among others, the number of PA households and the factors related to mental illness of PA recipients have positive impacts that attenuate toward the top of the conditional quantile of the transfer deficit. I will elaborate on plausible causes of such attenuating responses.