Calculation of the Social Returns To Innovation

Benjamin Jones and Lawrence Summers, “A Calculation of the Social Returns To Innovation,” National Bureau of Economic Research, September 2020, https://www.nber.org/papers/w27863

On capital deepening, “…Finally, note that incorporating capital investment doesn’t diminish the society wide gains. Rather it acts to spread the gains over a broader set of investments, beyond R&D. The social returns to capital deepening thus appear much larger than the equilibrium private rate of return to capital investment would suggest. To the extent that embodiment is important, R&D investment and capital investment collectively unlock large social returns. From a policy point of view, supporting R&D and capital deepening together would may then be important to attain the high social returns from innovative investments….”

Key to their formula, “.. The cost, in the denominator, is the ratio of innovation investment expenditure (𝑥) to GDP (𝑦). The benefit, in the numerator, is the growth rate (𝑔) that results, discounted to the present at the discount rate (𝑟).We are suppressing time in this expression to emphasize that the ratio of innovation investment expenditure to GDP and the growth rate of income are approximately constant over time..Namely, we can think of the cost benefit ratio as the cost of one year’s innovation (𝑥/𝑦) producing a stream of output gains that are𝑔percent higher. The present value of this permanent output gain is𝑔/𝑟.”

Here they explain their core logic, “We present new calculations for the social returns to innovation investment, building on core features of the innovation and growth literatures. Our measures emphasize the advantages of examining the path of GDP, which acts to aggregate and net out complicated spillovers involved in the innovation process. The approach offers a seemingly quite general means of estimating the average social returns. Moreover, the simplicity of the method allows us to transparently examine the influence of other, potentially key features that are not typically addressed in studies of the social returns to R&D. These features include embodied vs. disembodied technological progress, diffusion rates, learning-by-doing, productivity mismeasurement, health benefits, cross-country spillovers, and other dimensions for assessing the social returns….Taking this approach seriously, the average returns to innovative investments are determined by linking the aggregate cost of innovation investments to the aggregate production increase that results. Intuitively, by looking at the net value-added gains in the GDP path, one can implicitly net out the spillover margins. By looking at total innovation investment, one includes both research successes and failures. A simple social returns calculation can proceed as follows. Let income per capita be y, innovation investment per capita be x, and the discount rate be r. If a year's worth of innovation investments creates a g percent increase in productivity, then the ratio of benefits to costs is: p=(g/r)/(x/y) The key idea here, as in endogenous growth theory, is that, by investing a GDP share𝑥/𝑦in innovation today (i.e., once), we permanently raise productivity in the economy by𝑔percent, the present value of which is𝑔/𝑟.* Notably, this approach suggests that the average social returns to innovation may be enormous. For example, if we take an R&D investment orientation, with the R&D share of GDP at its usual level in the U.S.,𝑥/𝑦 ≈ 2.7%, and let these investments drive productivity growth, then we have𝑔 ≈ 1.8%. 1 Standard discount rates then imply that 1$ of R&D investment today on average creates over $10 of economy-wide benefits in today’s dollars.2 This return is extremely large, but it follows from the basic mechanics of growth, as understood in advanced economies. That is, a permanent gain in living standards from a seemingly small investment in innovation will, by the above logic, tend to suggest enormous returns….”

“…Overall, we find that the average social returns to innovation investments appear very large. If formal R&D and new venture creation drive the bulk of productivity gains, then the social returns to these investments appear enormous. If a much broader set of investments, including capital embodiment, are needed to fulfill these productivity gains, then the social returns to these broader activities still appear large. Even under very conservative assumptions, it is difficult to find an average return below $4 per $1 spent. Accounting for health benefits, inflation bias, or international spillovers can bring the social returns to over $20 per $1 spent, with internal rates of return approaching 100%.We further consider how these average returns may relate to the marginal return of additional investment in innovation. Using various perspectives, motivated by the micro and macro literatures on innovation, there are good reasons to believe that the marginal returns are also high. The implication is that policies to support further innovation investment are broadly well motivated. Innovation investments can credibly raise economic growth rates and extend lives, paying for their costs many times over. And because the social returns exceed the private returns, public policy has a central role, and opportunity, in unleashing these gains….”

Looking at the US alone they calculate, “…Overall, it appears that a conservative estimate of theaverage social gains is about $5 in benefit per $1 invested. Considering reasonable amounts of inflation bias or health benefits can easily push the average benefit to $10 or even $20 per $1 invested. These gains are just in terms of the U.S. economy. Incorporating international spillovers extends the benefits further. In sum, analyzing the average returns form a wide variety of perspectives suggests that the social returns are remarkably high….”

New Summers tries to look at social return to innovation (including trying to account for research failures) and finds massive positive spillovers the internal rate approach 100%.