Long Division Is the Most Important Tool for Policy Analysis

LONG DIVISION IS THE MOST IMPORTANT TOOL FOR POLICY ANALYSIS

To assess a policy, first estimate what it achieves and what resources it requires. Divide the output by the input to compare it with other options. Suppose you were in charge of determining vaccination sites for a state and giving them resources. To operate a site for a day costs $50,000, and on average it delivers 1,000 vaccinations a day. Thus, the cost of operation is $50 per vaccination. Would you pay $50 per vaccination? Alternatively, you can think in terms of output per unit of input, such as benefit per $1,000 spent. In this case, 20 vaccinations per $1,000 spent.

Cost-benefit and cost-effectiveness analyses develop this comparison further, including how to define and value the outcomes. Coming back to the vaccination example, suppose you oversee many possible sites and have a fixed budget. How should you decide which sites to operate? If all vaccinations are equally valuable and costs per vaccination remain constant, start with the site that yields the most vaccinations per $1,000. Then move to the next site with the most vaccinations per $1,000, allowing for each site’s capacity and any fixed costs.

Choose the output to match what you are trying to achieve. In the case of vaccinations, the goal is not to deliver as many vaccines as possible, but to prevent death and severe illness due to the infectious disease. Since the disease differentially affects some groups, say nursing home patients and Hispanic communities, who often have more crowded housing conditions and are often “essential workers” who must report to job sites, prioritizing vaccinations for groups at greater risk can prevent more severe or fatal cases.

Richard explains how the comparison changes when inputs are scarce or returns diminish.

Long division in more complicated scenarios Richard Zeckhauser Often the input will be something other than dollars, or dollars are a secondary consideration. Let’s say that we decided to turn a five-acre area into a park. We could have shuffleboard courts, a soccer field, tennis courts, etc. If your goal is to maximize total participant recreation hours, you could ask an expert to estimate how many hours of participant time per day you would get per 1,000 square feet from each of these activities. We would then start with the greatest number of hours per 1,000 square feet and work our way down.[63] Of course, output per dollar spent may not be constant. For most activities, we would expect diminishing returns as we spend more. (This is called diminishing marginal returns – the “margin” in this case is the last dollar spent.) For example, the third nurse hired in a health clinic is likely to generate greater health benefits than the eleventh nurse. Suppose you run a health clinic that can run a variety of activities, such as immunizations, well baby care, annual checkups, etc., and that your output measure is quality-adjusted life years (QALYs).[64] What should you do if you spend $100,000 on the first activity, $200,000 on the second, and $150,000 on the third, and the benefit at the margin is 10 QALYs/$10,000 expenditure from the first, 8 QALYs from the second, and 11 QALYs from the third? You should boost your QALY output by trimming the second, expanding the third, and adjusting the first. Eventually, we would reach the optimum, where each activity yielded say 9.7 QALYs/$10,000 expenditure. To get there, we would always be using long division to determine how many QALYs we got from the last $10,000 spent on the activity. Often, we have to evaluate an indivisible project, such as building a bridge or an addition to a rapid transit system. Too often we just say that it is important to extend rapid transit. This maxim would say instead that you should use long division to see what you are getting for what you are spending. Suppose the extension might cost $1 billion/year to operate. (That includes interest on the bonds, plus salaries, maintenance, etc.) It would save passengers 500 million minutes a year. It is useful to know that it cost $2/minute saved. Given this statistic, we might decide that the rapid transit extension was not worth it, because people do not value their time at $120/hour.[65] Frequently, long division of output divided by dollar or by some other input (such as one’s time) is just a way to enable clear thinking about an issue. Even if the numbers are hard to calculate, guesstimating the value of the ratio of outputs to inputs tells us if we are in the ballpark of reasonability. Moreover, if the value is high, we might do more of the activity, perhaps in some other locale. If it is low, we should consider cutting the activity. As an extreme example, the value of a life saved is far higher than an hour of aesthetic pleasure. Thus, placing a defibrillator in a company office should get priority over putting an equally expensive picture in its lobby, even though the former is only expected to be used once on average in a decade, whereas the latter might receive 2,000 admiring views over that period.

A measure of “bang per buck” can also expose spending priorities that deserve another look. Erin St. Peter, a former student of Richard’s described here as a research analyst at Wharton’s Risk Center and Real Estate Department, used this approach during a summer fellowship in graduate school. She had the opportunity to observe and work with a state government and department of transportation to evaluate different strategies to reduce traffic fatalities. The list of projects under consideration or in various stages of completion included road sign changes, speed traps, increased police presence, impaired driving interventions, and the one that struck her as most peculiar – a multi–million dollar wrong-way driving detection system that the state had fully implemented on a highway segment.

“Wrong-way driving traffic fatalities represent about 1 percent of traffic-related deaths nationwide, but it was a top priority for the state at the time. Furthermore, most wrong-way driving fatalities involve impaired individuals, so more general impaired driving interventions might also help reduce these fatalities. Long division, the essence of cost-benefit analysis, was the most important framework I used to evaluate the different interventions. I compared different interventions according to their associated reduction in traffic fatalities per dollar spent.”

Taran Raghuram, described here as a student and teaching assistant of Richard’s at the Harvard Kennedy School, saw how this maxim applied in his work as a consultant for public school districts in the United States.

Long Division in Public Education Taran Raghuram Looking back at my work in public education, long division was certainly the most useful tool we had at our disposal. In my conversations with school district leaders, simple ratios conveyed more meaning and led to better conversations than sophisticated statistical methods ever did. Whether comparing the extent of resources (staffing ratios/class sizes) or the effectiveness of certain strategies over others (return-on-investment), thoughtful long division provided metrics that were both simple and comparable. One metric we used was how many principals every managing administrator was responsible for. That simple number carried so much weight because we could compare districts to one another and communicate a clear story – if you have forty principals reporting to each administrator and in another district, they have ten, then they probably have a better idea of what’s happening in their schools than you do. The smartest people I’ve met in public organizations took this maxim to heart. They may have never taken convex optimization or studied algebraic topology, but they were masters at finding a simple but powerful metric for any situation. I think this is possibly Richard’s most underrated maxim for aspiring policy wonks.

David Slusky, Taran and Richard also examined deaths during the COVID-19 pandemic, dividing 2020 deaths by 2019 deaths in three age categories. The account reports a 21 percent overall increase in deaths. “Long division revealed very different stories for the three groups. About 79% percent of increased deaths in March to December 2020 for those over 75 were due to COVID. For those aged 45 to 75, COVID accounted for 67% of increased deaths. For those under 45, COVID only accounted for 25% of the increase, while nonnatural deaths (auto accidents, overdoses, homicides, suicides) accounted for 50%.”[66]