David Joulfaian (Office of Tax Analysis, Treasury Department) has posted Estate Taxes And Charitable Bequests: Evidence From Two Tax Regimes on SSRN.  Here is the abstract:

Much of the literature on the effects of estate taxation on charitable bequests has relied on cross sectional data, reflecting the uniqueness of death. Few have explored longitudinal data to exploit exogenous variations in tax regimes. The latter, however, continue to be susceptible to omitted variable as well as measurement error biases attributable to changes in the treatment of spousal bequests and frequent changes in tax regimes. This paper explores the effects of the estate tax on charitable bequests using administrative data from two tax regimes where earlier biases are minimized. The deductibility of charitable bequests is found to have significant implications for giving. However, the effects of estate tax repeal are much smaller. These findings are sensitive to expectations of the tax regime in effect at time of death.