We simulate atmospheric composition changes in response to increased methane and tropospheric ozone precursor emissions from the preindustrial to present-day in a coupled chemistry-aerosol-climate model. The global annual average composition response to all emission changes is within 10% of the sum of the responses to individual emissions types, a more policy-relevant quantity. This small non-linearity between emission types permits attribution of past global mean methane and ozone radiative forcings to specific emissions despite the well-known non-linear response to emissions of a single type. The emissions-based view indicates that methane emissions have contributed a forcing of ~0.8--0.9 W m-2, nearly double the abundance-based value, while the forcing from other ozone precursors has been quite small (~-0.1 for NOx, ~0.2 for CO + VOCs).