  Recent surveys have identified a seemingly ubiquitous population of galaxies with elevated [OIII]/H$\beta$ emission line ratios at $z > 1$, though the nature of this phenomenon continues to be debated. The [OIII]/H$\beta$ line ratio is of interest because it is a main component of the standard diagnostic tools used to differentiate between active galactic nuclei (AGN) and star-forming galaxies, as well as the gas-phase metallicity indicators $O_{23}$ and $R_{23}$. Here, we investigate the primary driver of increased [OIII]/H$\beta$ ratios by median-stacking rest-frame optical spectra for a sample of star-forming galaxies in the 3D-HST survey in the redshift range $z\sim1.4-2.2$. Using $N = 4220$ star-forming galaxies, we stack the data in bins of mass and specific star formation rates (sSFR) respectively. After accounting for stellar Balmer absorption, we measure [OIII]$\lambda5007$\AA/H$\beta$ down to $\mathrm{M} \sim 10^{9.2} \ \mathrm{M_\odot}$ and sSFR $\sim 10^{-9.6} \ \mathrm{yr}^{-1}$, more than an order of magnitude lower than previous work at similar redshifts. We find an offset of $0.59\pm0.05$ dex between the median ratios at $z\sim2$ and $z\sim0$ at fixed stellar mass, in agreement with existing studies. However, with respect to sSFR, the $z \sim 2$ stacks all lie within 1$\sigma$ of the median SDSS ratios, with an average offset of only $-0.06\pm 0.05$. We find that the excitation properties of galaxies are tightly correlated with their sSFR at both $z\sim2$ and $z\sim0$, with a relation that appears to be roughly constant over the last 10 Gyr of cosmic time. 
The Relation Between [OIII]/H$\beta$ and Specific Star Formation Rate in   Galaxies at $z \sim 2$