Between 2005 and 2012, U.S. emissions of nitrogen oxides (NO_x) and sulfur dioxide (SO₂) decreased by 42% and 62%, respectively. These species, as well as ammonia (NH₃), are precursors of inorganic fine aerosols, which scatter incoming shortwave radiation and thus affect climate. Scaling aerosol concentrations to emissions, as might be done for near-term climate projections, neglects nonlinear chemical interactions. To estimate the magnitude of these nonlinearities, we conduct a suite of simulations with a chemical transport model and an off-line radiative transfer model. We find that the direct radiative effect (DRE) over the North American domain decreases by 59 and 160 mW m⁻² in winter and summer, respectively, between 2005 and 2012. The sensitivities of DRE to NO_x and SO₂ emissions increase, by 11% and 21% in summer, while sensitivity to NH₃ emissions decreases. The wintertime sensitivity of DRE to NO_x emissions is small in 2005 but is 5 times as large in 2012. Scaling radiative effects from 2005 to 2012 based on 2005 sensitivities overestimates the magnitude of the DRE of 7% and 6% of the U.S. attributable DRE in January and July, respectively. The difference between the changes in DRE and the changes in sensitivity suggests that scaling to SO₂ emissions alone has so far been an accurate approximation, but it may not be in the near future. These values represent the level of accuracy that can be expected in adjusting aerosol radiative effects in climate models without chemistry.