  We present the results of a quantum Monte Carlo study of the extended $s$ and
the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard
model, computed with the constrained-path method. For small lattice sizes and
weak interactions, we find that the $d_{x^2-y^2}$ pairing correlations are
stronger than the extended $s$ pairing correlations and are positive when the
pair separation exceeds several lattice constants. As the system size or the
interaction strength increases, the magnitude of the long-range part of both
correlation functions vanishes.
