We examine the quantitative impact of policy-induced changes in innovative investment by firms on growth in aggregate productivity and output in a model that nests several of the canonical models in the literature. We isolate two statistics, the impact elasticity of aggregate productivity growth with respect to an increase in aggregate innovative investment and the degree of intertemporal knowledge spillovers in research, that play a key role in shaping the model's predicted dynamic response of aggregate productivity, output, and welfare to a policy-induced change in the innovation intensity of the economy. Given estimates of these statistics, we find that there is only modest scope for increasing aggregate productivity and output over a 20-year horizon with uniform subsidies to firms' investments in innovation of a reasonable magnitude, but the welfare gains from such a subsidy may be substantial.