The rate at which the outgoing longwave radiation (OLR) responds to perturbations in temperature and moisture plays a fundamental role in determining climate sensitivity. This study examines the clear-sky OLR sensitivities to temperature and water vapor, as quantified by its partial derivatives (radiative Jacobians). The Jacobians, as computed by the Geophysical Fluid Dynamics Laboratory (GFDL)'s line-by-line (LBL) radiative transfer model are used to verify the results from the parameterized GFDL GCM (general circulation model) radiation code. The results show that the (1) Jacobians of OLR due to incremental changes in temperature and water vapor are insensitive to different formulations of water vapor continuum absorption and (2) Jacobians of OLR are properly captured by the GCM longwave band approximation. Simulations with the GCM demonstrate that uncertainties in the formulation of continuum absorption have little impact on the climate model simulation of clear-sky OLR changes in response to prescribed sea surface temperature (SST) perturbation. The numerically computed Jacobians of OLR are used to reconstruct the tropical annual mean OLR from the variations of temperature and water vapor over the period 1980--1999. The reconstructed OLR anomaly time series agrees well with that computed explicitly by the GCM. On the basis of this result, it becomes possible to separate out the temperature and water vapor contributions to the OLR variation. The results show that the temperature contribution dominates the water vapor contribution in the lower and middle troposphere, while in the upper troposphere the two contributions largely offset each other.