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We present a new analysis of the rest-frame UV and optical spectra of asample of three $z>8$ galaxies discovered behind the gravitational lensingcluster RX\,J2129.4+0009. We combine these observations with $z>7.5$ galaxiesfrom the literature, for which similar measurements are available. As alreadypointed out in other studies, the high [\oiii]$\lambda$5007/[\oii]$\lambda$3727ratios ($O_{32}$) and steep UV continuum slopes ($\beta$) are consistent withthe values observed for low redshift Lyman continuum emitters, suggesting thatsuch galaxies contribute to the ionizing budget of the intergalactic medium. Weconstruct a logistic regression model to estimate the probability of a galaxybeing a Lyman continuum emitter based on the measured \MUV, $\beta$, and$O_{32}$. Using this probability and the UV luminosity function, we constructan empirical model that estimates the contribution of high redshift galaxies toreionization. The preferred scenario in our analysis shows that at $z\sim8$,the average escape fraction of the galaxy population (i.e., including both LyCemitters and non-emitters) varies with \MUV, with intermediate UV luminosity($-19<M_{UV}<-16$) galaxies having larger escape fraction. Galaxies with faintUV luminosity ($-16<M_{UV}<-13.5$) contribute most of the ionizing photons. Therelative contribution of faint versus bright galaxies depends on redshift, withthe intermediate UV galaxies becoming more important over time. UV brightgalaxies, although more likely to be LCEs at a given log($O_{32}$) and $\beta$,contribute the least of the total ionizing photon budget.

An Empirical reionization history model inferred from the low-redshift Lyman continuum survey and the star-forming galaxies at $z>8$