  Spectroscopic studies of elliptical galaxies show that their stellar
population ages, mean metallicity, and $\alpha$-enhancement traced by [Mg/Fe]
all increase with galaxy stellar mass or velocity dispersion. We use one-zone
galactic chemical evolution (GCE) models with a flexible star formation history
(SFH) to model the age, [Mg/H], and [Mg/Fe] inferred from simple stellar
population (SSP) fits to observed ellipticals at $z \sim 0$ and $z \sim 0.7$.
We show that an SSP fit to the spectrum computed from a full GCE model gives
ages and abundances close to the light-weighted, logarithmically averaged
values of the composite stellar population, <age>, <[Mg/H]>, and <[Mg/Fe]>.
With supernova Mg and Fe yields fixed to values motivated by Milky Way stellar
populations, we find that predicted <[Mg/H]>-<age> and <[Mg/Fe]>-<age>
relations are surprisingly insensitive to SFH parameters: older galaxies have
higher <[Mg/Fe]>, but the detailed form of the SFH has limited impact. The star
formation efficiency and outflow efficiency affect the early and late evolution
of <[Mg/H]>, respectively; explaining observed trends requires higher star
formation efficiency and lower outflows in more massive galaxies. With core
collapse supernova yields calibrated to the plateau [Mg/Fe]$_{\rm cc}
\approx0.45$ observed in many Milky Way studies, our models underpredict the
observed <[Mg/Fe]> ratios of ellipticals by 0.05-0.1 dex. Increasing the core
collapse yield ratio to [Mg/Fe]$_{\rm cc} = 0.55$ improves the agreement,
though the models still lie below the data. We discuss potential resolutions of
this discrepancy, including the possibility that many ellipticals terminate
their star formation with a self-enriching, terminating burst that reduces the
light-weighted age and boosts <[Mg/Fe]>.
