  We present a dedicated analysis of the influence of excited states on the
calculation of nucleon matrix elements. This calculation is performed at a
fixed value of the lattice spacing, volume and pion mass that are typical of
contemporary lattice computations. We focus on the nucleon axial charge, g_A,
for which we use about 7,500 measurements, and on the average momentum of the
unpolarized isovector parton distribution, <x>_{u-d}, for which we use about
23,000 measurements. All computations are done employing N_f=2+1+1
maximally-twisted-mass Wilson fermions and using non-perturbatively calculated
renormalization factors. Excited state effects are shown to be negligible for
g_A whereas they lead to an O(10%) downward shift for <x>_{u-d}.
