We have observed a sample of 22 luminous quasars, in the range 2.0 less tha
n or similar to z less than or similar to 2.5, at 1.6 mu m with the near-in
frared (NIR) spectrograph FSPEC on the Multiple Mirror Telescope. Our sampl
e contains 13 radio-loud and nine radio-quiet objects. We have measured the
systemic redshifts z,,, directly from the strong [O III] lambda 5007 line
emitted from the narrow-line region. From the same spectra, we have found t
hat the nonresonance broad HP lines have a systematic mean redward shift of
520 +/- 80 km s(-1) with respect to systemic. Such a shift was not found i
n our identical analysis of the low-redshift sample of Boroson & Green. The
amplitude of this redshift is comparable to half the expected gravitationa
l redshift and transverse Doppler effects and is consistent with a correlat
ion between redshift differences and quasar luminosity. From data in the li
terature, we confirm that the high-ionization rest-frame ultraviolet broad
lines are blueshifted similar to 550-1050 km s(-1) from systemic and that t
hese velocity shifts systematically increase with ionization potential. Our
results allow us to quantify the known bias in estimating the ionizing flu
x from the intergalactic medium J(nu)(IGM) via the proximity effect. Using
redshift measurements commonly determined from strong broad-line species, l
ike Ly alpha or C IV lambda 1549, results in an overestimation of J(nu)(IGM
) by factors of similar to 1.9-2.3. Similarly, corresponding lower limits o
n the density of baryons O, will be overestimated by factors of similar to
1.4-1.5. However, the low-ionization Mg II lambda 2798 broad line is within
similar to 50 km s(-1) of systemic and thus would be the line of choice fo
r determining the true redshift of 1.0 < z < 2.2 quasars without NIR spectr
oscopy and z > 3.1 objects using NIR spectroscopy.