In response to testing shortages, the CDC—under direction from the White House—now recommends testing only the symptomatic. The fewer tested, the fewer bottlenecks. This means the virus will continue to spread unchecked through the asymptomatic, taking more lives and shuttering schools and businesses along the way. Luckily, there is an innovative financing system called quadratic funding that can spur the investments in testing capacity we need.
Proposed two years ago, quadratic funding has already been used to align incentives to build public goods like decentralized, open source software projects. Despite the geeky name, it has a simple fundamental logic: It rewards cooperation.
Puja Ohlhaver is a chief executive of ClearPath Surgical and member of the Harvard Edmond J. Safra Center for Ethics Rapid Response Task Force on Covid-19. Zoë Hitzig is a PhD candidate in economics at Harvard. She is the author of Mezzanine: Poems (Ecco/HarperCollins 2020).
Cooperation between states is key. With collapsing tax revenues, many states are cautiously buying only the tests they need today. This has led to volatile demand and expensive zero-sum bidding wars during outbreaks, where big states crowd out small states. States would be better off if they coordinated massive purchase guarantees to test suppliers, who would in turn rapidly build capacity at lower costs. The problem is states would rather conserve cash—pinning their hopes on a vaccine or breakthrough therapeutic—than contribute scarce funds for a demand shock.
The $50 billion bipartisan Suppress Covid-19 Act attempts to solve this collective action dilemma by carving out a $5 billion incentive for states that form interstate compacts to buy tests. This is a step in the right direction, but the incentive is flawed. States are rewarded in proportion to their population, so big states have incentive to form compacts with other big states, but not with small states. Quadratic funding could change this.
To illustrate how quadratic funding works, take a simple example. Say there are four compacts, each funded a total of $100 million, comprised of two, four, six, and eight states respectively. In quadratic funding, the $5B bonus pie would be divided among them in a 1:3:5:7 ratio. The smallest compact with two states would be rewarded the least ($313 million), the largest compact with seven states the most ($2.2 billion), seven times as much.
In quadratic funding, the more states that participate in supplying $100 million, the more federal bonus funds their compact receives. In other words, there are diminishing returns to one state’s potential for bonus funds, but increasing returns to more states participating. As more states contribute to a compact, the impact of each previous contribution increases.
The trick in quadratic funding is to make sure that larger contributions don’t dwarf the effect of smaller contributions. Mathematically, this is accomplished by taking the square root of each state contribution as a first step. Consider two contributions of $16 and $4, whose square roots are $4 and $2, respectively. Even though the $16 contribution is four times the $4 contribution, its square root is only twice as much. As a second step, the square roots of each state contribution are summed, and then squared to get back to the scale of millions of dollars. This gives the total funds a compact should receive, including both state contributions and federal bonus funds.
Compact’s Total Funds = (√New York + √Massachusetts + √Vermont)2
The bonus funds are these total funds minus the state contributions.
Compact’s Bonus Funds = (√NY + √MA + √VT)2 – (NY + MA + VT)
In quadratic funding, the incentive is proportional to the square of the sum of the square roots of individual state contributions. This proportionality ensures that both the number of states contributing to a compact and the sizes of the states’ contributions determine the bonus. Smaller contributions by many states are rewarded more than a few large contributions by bigger states.
The government has flexibility: It can strengthen or weaken the incentive for cooperation with multipliers, or scale the quadratic bonus so that it stays within a federal budget. A compact’s share of a fixed budget is simply the fixed budget multiplied by the ratio of a compact’s bonus funds to the sum of all compacts’ bonus funds.
Quadratic funding is superior to other popular incentive schemes, including linear matching. Consider the example where New York and Massachusetts each contribute $16 million and Vermont contributes $4 million to a compact. Under 1:1 federal matching, Vermont brings just 11 percent of the compact’s value. This doesn’t solve the free-rider problem that big states face from smaller states.
Quadratic funding changes incentives by rewarding big states more federal money for collaborating with smaller states. When Vermont joins the compact, the federal reward doubles, so Vermont brings 36 percent of the compact’s total value. If another state, say Connecticut, joins with $9 million, the bonus nearly doubles again. Smaller states, in turn, get a stronger voice at the table.
This holds true even if the bonus were scaled back 75 percent to meet a budget constraint. Vermont and Connecticut would still double the federal bonus to the compact and deliver roughly 23 percent and 30 percent of the value, respectively.
Linear matching might seem simpler on the front-end, but this is largely cosmetic. Budgets force backend caps based on population, income, or a mix of arbitrary factors. Many states spend just up to the cap, as evidenced by the Interstate Highway System. Sometimes this leads to overspending, where states pursue projects that fail cost-benefit tests to get as many federal dollars as possible. Other times, states underspend because of artificially low caps, and they end up with ailing infrastructure.
Quadratic funding has more front-end complexity than matching, but the “square of the sum of the square roots” principle can scale within budgets without distortions by caps. Funds are balanced across states based on their relative level of cooperation and contributions to compacts. Rich infrastructure states don’t hit a ceiling cap, but can always get more funding by cooperating with poorer states, who in turn get more funding than linear matching. Quadratic funding spurs states to both have skin in the game and compete in positive-sum cooperation, rather than gaming an arbitrary formula for a fixed slice of a fixed pie.
We’ve already seen quadratic inroads in digital infrastructure. Since January 2019, GitCoin—a nonprofit that provides grants to open source developers—has run six quadratic funding campaigns to allocate $2.5 million for open-source digital infrastructure projects. Each campaign has averaged 1,200 donors. Projects with the most popular support were matched at higher ratios such as 1:4, while projects with few contributors achieved matching ratios closer 1:1.
Philanthropists are also experimenting with quadratic funding. In downtown Boulder, Colorado, local philanthropists set up a $25,000 Covid-19 relief fund for half a dozen businesses. The innovative funding rule, despite its mathy name, didn’t stymie participation, but raised an additional $38,000 with 325 contributions from Boulderites. Within three days, the total philanthropic budget was exhausted.
Quadratic funding’s novel way of combining centralized and decentralized funding should have bipartisan appeal. In the context of testing, Democrats should appreciate that the incentive coordinates big and small states to co-create a larger economic testing pie. Republicans should appreciate that the incentive has more fidelity to federalism, encouraging states to form compacts with more flexibility than a federal agency to invest in innovations and rapidly respond to local needs.
Quadratic funding could spur states to build the testing infrastructure we need to stop this pandemic. Millions of tests a day would empower states to suppress the virus to near-zero incidence through testing, tracing, and supported isolation––a strategy that has proven to work in other advanced market economies like Taiwan, South Korea, and Germany. But without cheap and abundant tests, states can’t move beyond the false choice of lockdowns or letting the disease rampage, both of which destroy lives and the economy. If Congress offers a $5 billion incentive to states, it should be quadratic. This innovative funding design could be key to saving lives and livelihoods.
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