We combine H \alpha and H \beta spectroscopic measurements and UV photometry for a sample of 673 galaxies from the MOSDEF survey to constrain hydrogen-ionizing photon production efficiencies ( \xi _ { \mathrm { ion } } ) at z = 1.4 - 2.6 . We find \langle \log ( \xi _ { ion } / [ { { s ^ { -1 } / erg s ^ { -1 } Hz ^ { -1 } } } ] ) \rangle = 25.06 ~% { } ( 25.34 ) , assuming the Calzetti ( SMC ) curve for the UV dust correction and a scatter of 0.28 dex in \xi _ { \mathrm { ion } } distribution . After accounting for observational uncertainties and variations in dust attenuation , we conclude that the remaining scatter in \xi _ { \mathrm { ion } } is likely dominated by galaxy-to-galaxy variations in stellar populations , including the slope and upper-mass cutoff of the initial mass function , stellar metallicity , star-formation burstiness , and stellar evolution ( e.g. , single/binary star evolution ) . Moreover , \xi _ { \mathrm { ion } } is elevated in galaxies with high ionization states ( high [ O iii ] / [ O ii ] ) and low oxygen abundances ( low [ N ii ] /H \alpha and high [ O iii ] /H \beta ) in the ionized ISM . However , \xi _ { \mathrm { ion } } does not correlate with the offset from the z \sim 0 star-forming locus in the BPT diagram , suggesting no change in the hardness of ionizing radiation accompanying the offset from the z \sim 0 sequence . We also find that galaxies with blue UV spectral slopes ( \langle \beta \rangle = -2.1 ) have elevated \xi _ { \mathrm { ion } } by a factor of \sim 2 relative to the average \xi _ { \mathrm { ion } } of the sample ( \langle \beta \rangle = -1.4 ) . If these blue galaxies are similar to those at z > 6 , our results suggest that a lower Lyman continuum escape fraction is required for galaxies to maintain reionization , compared to the canonical \xi _ { \mathrm { ion } } predictions from stellar population models . Furthermore , we demonstrate that even with robustly dust-corrected H \alpha , the UV dust attenuation can cause on average a \sim 0.3 dex systematic uncertainty in \xi _ { \mathrm { ion } } calculations .