In order to examine charitable giving, we must start with a model for charity. The model will have to be simple to start with. James Andreoni in "Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence," Journal of Political Economy, Vol. 97, No. 6 (Dec., 1989), pp. 1447-1458, develops such a model.
Charity is considered a public good in this model. Under a model of pure altruism, every dollar taxed to fund the private good results in a dollar decrease in private charity. This is known as crowding out. However, empirical results seem to conclude that there is very little crowding out of private giving due to the government funding of charity.
Andreoni's model of impure altruism can help to account for that. Under pure altruism, we gain utility from just the presence of charity not from the act of giving itself. This is because altruism is giving for givings sake. With impure altruism, we actually get satisfaction just for giving.
Under impure altruism, even if taxes were raised to fully fund charity to its socially optimal level, since people get satisfaction from the act of giving, charitable contributions will continue.
There are problems with this model. I people believe that government funding of charity will not be done in the best manner people may, for purely altruistic reasons, give to charities that they feel will be more efficient.