  We have used a combined sample of JADES and CEERS objects in order to
constrain ionizing photon production efficiency ($\xi_{\rm ion}$) from
JWST/NIRSpec and JWST/NIRCam data. We examine 163 objects at 1.06 < z < 6.71
with significant (3$\sigma$) spectroscopic detections of H$\alpha$ and H$\beta$
in order to constrain intrinsic H$\alpha$ luminosities corrected from nebular
dust attenuation via Balmer decrements. We constrain dust-corrected UV
luminosities from best-fit spectral-energy distribution modeling. We find a
sample median log$_{10}$($\xi{\rm ion,0}$/erg Hz$^{-1}$) =
$25.29^{+0.29}_{-0.37}$, assuming f$_{\rm esc}$=0 for the escape fraction of
Lyman continuum emission. We find significant correlation between $\xi_{\rm
ion,0}$ and z, with 17 objects at z > 4.64 having median log$_{10}$($\xi_{\rm
ion,0}$/erg Hz$^{-1}$) = $25.38^{+0.38}){-0.38}$, with those below having
log$_{10}$($\xi_{\rm ion,0}$/erg Hz$^{-1}$) = $25.24^{+0.30}_{-0.33}$. We also
find significant, positive correlations between $\xi_{\rm ion,0}$ and LUV;
W{\lambda}([O iii]); [O iii]{\lambda}5007/[O ii]{\lambda}{\lambda}3726, 3729;
and inverse correlations with metallicity. In contrast with some previous
results, we find no trends between $\xi_{\rm ion,0}$ and stellar mass, stellar
dust attenuation, or UV slope. Applying a multivariate fit to $\xi_{\rm
ion,0}$, z, and MUV to an empirically-motivated model of reionization, and
folding in f$_{\rm esc}$ estimates from direct observations of the Lyman
continuum at z ~ 3 from the Keck Lyman Continuum Spectroscopic survey, we find
that the number of ionizing photons entering the IGM causes reionization to end
at z ~ 5 - 7.
