As part of the “$5k challenge to quantify the impact of 80,000 hours' top career paths,” we aim to estimate the average impact of a grantmaker focused on pressing world problems. To ground our inputs, we chose to focus specifically on one grantmaking organization -- ARPA-E. We chose ARPA-E because other ARPA agencies are explicitly called out by 80,000 Hours profile of grantmaking (i.e., DARPA, IARPA) and because ARPA-E has usable cost and benefit data.
The calculations below -- which can be plugged into Squiggle -- estimate the average impact of an ARPA-E grantmaker. Our inputs were primarily pulled from ARPA-E’s website. We then make a series of intermediate calculations to estimate the net present costs and benefits. Finally, we combine the cost and benefit estimates to make a benefit-to-cost ratio.
Our model has significant limitations, some of which are discussed in the “comments” below.
Our average impact estimate for ARPA-E grantmakers is a ~6 to 1 average benefit-to-cost ratio and ~$82 million average net benefit. These figures can be compared to other careers' estimated BCRs and net benefits to understand which career choice has higher estimated average impact. Benefits and costs are expressed in net present value of US dollars. Our calculations assume a 7% discount rate, but, if desired, users can adjust the discount rate in the code below.
//INPUTS
//Most inputs are expressed as point estimates instead of distributions since we pulled this data directly from ARPA-E’s website and other DOE resources.
arpae_budget_total = 3270000000 // from ARPA-E website
arpae_managers_annual = 17 // from ARPA-E website
projects_total = 1415 // from ARPA-E website
years_of_arpae = 13 // ARPA-E started in 2009
valuations = 21800000000 // value from ARPA-E website
discount_rate = 0.07 // Department of Energy discount rate
avg_proj_length = 1 to 3 // from ARPA-E FAQs
//PROJECT NUMBER CALCS
projects = projects_total/years_of_arpae // assumes equal number of projects per year
projects_per_manager = projects/arpae_managers_annual//= 6.4
projects_per_manager_dist = truncateLeft(normal(projects_per_manager,pow(6.4,1/2)), 1)
//COST CALCS
budget_per_project = arpae_budget_total/projects_total //= 2,310,954
budget_per_project_dist = .5M to 6M // Log normal with 2.3 mean + wikipedia estimates https://en.wikipedia.org/wiki/ARPA-E
npv_budget_per_project = (1+discount_rate)^avg_proj_length*budget_per_project //= 2,547,827
npv_budget_per_manager = projects_per_manager * npv_budget_per_project //= 6.4 * 2,547,827 = 16,306,091
//BENEFITS CALCS
benefit_per_project = valuations/projects_total //= 15,406,360
benefit_per_manager = benefit_per_project * projects_per_manager
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We make two key assumptions here.
- First, we assume all benefits are counterfactual since ARPA-E is meant to fund “white space” -- i.e., disruptive technology that is not mature enough and/or on too long of a time-horizon for VC. The implication of ARPA-E funding "white space," is that ARPA-E funds projects that counterfactually would not have been funded. Support for this claim can be found here and here. However, in reality, we think many of these technologies would be developed at some point -- ARPA-E simply speeds up the development. Thus, we believe that, all else equal, this first assumption leads to an overestimation of benefits. Future work could take advantage of other DOE BCR calculations that accounted for this consideration (links here, here, here, and here).
- Secondly, we assume that all benefits -- including health benefits, reduction of monetary costs associated with climate change, reduction of existential risk associated with climate change, and spillover benefits into other industries -- are incorporated into the market valuation. We believe that markets likely price in the aforementioned externalities (e.g., health and enviro benefits) (support for this claim here). Furthermore, the valuations listed on ARPA-E’s site are from after the Inflation Reduction Act passed, which, itself, internalized a significant chunk of emission reductions associated with US tech. For these reasons, we believe it’s reasonable to assume a significant amount of external benefits have been internalized into markets, but, perhaps, not all benefits. Thus, we believe that, all else equal, this assumption leads to an underestimation of benefits.
//BENEFIT-COST CALCS
bcr_per_project = benefit_per_project/npv_budget_per_project = 98,600,704/16,306,091 = 6.04
net_benefits = benefit_per_project - npv_budget_per_project = 98,600,704 - 16,306,091 = 82,294,613
Appreciate the feedback. We definitely agree that not all benefits are captured in market valuation and that this leads to an underestimate. While working on this, we initially tried creating an "external benefits multiplier,” but ultimately couldn’t come up with a particularly sound way of estimating this multiplier prior to the submission deadline. Regardless, I think we were not focused enough on the fact that the US plays this significant role in the global energy innovation system, so thanks for bringing that up too. In retrospect, we should’ve just added something as a placeholder and then made updates later.
The general framework we could use to create this multiplier is to calculate the ratio of a standard carbon price recommended by environmental economists (e.g., ~$51 - 125 per ton) over an estimate of the “implicit US carbon price” (i.e., standard carbon price/implicit US carbon price). The implicit US carbon price could be derived by calculating an emissions-weighted carbon price associated with RGGI and the California cap-and-trade market, as well as the implied dollar paid per emission abated through current US subsidies for carbon reduction technologies. We could rely on work from UChicago’s EPIC to help guess the implied dollar paid per emission abated through US subsidies. However, as you can see in the aforementioned UChicago paper, US policies likely pay way more than $125/ton in some instances (e.g., with the weatherization assistance program) and miss cheap emissions reduction opportunities in other instances (e.g., nature-based solutions). This could make the “implicit US carbon price” look artificially high. Regardless, the implied emissions price may still be relatively low (e.g., <$30/ton). Thus, the external benefits multiplier might be something like 2 or 3.
If we further account for the US’ role in the global innovation system, potential existential risks associated with climate change, etc., we could increase the numerator.
Would love either of your thoughts on this approach!