A Jab in the Right Direction: Lottery Tickets as Behavioral Incentives
The 7-day average for COVID-19 vaccination rates in the United States fell to its lowest level since January this past month (Keating et al.). Indeed, ever since reaching a peak in April, new immunizations have been steadily declining, with the country failing to meet the Biden administration’s goal of a 70% vaccination rate by the Fourth of July (LaFraniere).
While skepticism on patients’ part is the driving force behind the stagnation (Bebinger), some state and local governments have reacted by offering incentives to those who do get a shot. Washington State recently paid out a $1 million lottery ticket to a vaccinated man (Zhou), and California is offering a similar $1.5 million cash prize along with a multitude of other smaller rewards (Vax for the Win).
This is all in the name of herd immunity, a phenomenon through which an infectious disease will begin to lose its capacity to spread throughout a population if a high enough proportion of people are immune. Thus, while individuals may be motivated to get a vaccine for the safety of their family and friends, there lies a hidden benefit in that every additional shot increases the chance that the disease will lay dormant due to herd immunity. However, since these benefits may not be immediate to the person receiving the vaccine, they may not receive much consideration.
In economics, this is known as a positive externality--an additional benefit created by an activity that is not immediately felt by a consumer, and is often not included in the cost-benefit decision process. One of the core issues of goods that produce positive externalities is that they are often lower in demand than they should be. For instance, if someone was on the fence about receiving the vaccine, then relaying them the benefits of herd immunity may be enough to convince them to go through with it. On a larger scale, however, policymakers have to get crafty about incentivizing economic actors. The aforementioned lotteries, then, are an artificial boost to the marginal expected utility of receiving a coronavirus vaccine.
COVID-19, however, is just the most recent in a line of many pandemics, and vaccinations are just one action with a positive impact on society. This begs the question: how have governments historically employed games of chance to generate large positive externalities?
The operation of lotteries by governments has a rich history, but it is important to note that they most commonly served as a method of raising government revenue in times of need, as total winnings were often kept below the cost of all the tickets. In fact, in the early 1770s, lottery tickets made up more than 7% of the income of the British government, as the government raised over £70 million to help fund its war against the Thirteen Colonies (Raven). In this sense, lottery tickets functioned in a similar way to government bonds today, as it was relatively inexpensive to issue many of them and they did not necessarily have to pay interest (though some did). In the 1930s, the Chinese government sold lottery tickets to fund projects in communications and water control, as did regional authorities (Pan). Many governments still raise revenue through lotteries, but they were much more important financial instruments several centuries ago as government government projects were generally small enough to be financed with ticket sales, and direct administrative tax collection was more expensive than it would become in the 19th and 20th centuries (Aidt and Jensen).
However, though lotteries functioned as a crude form of raising state revenue, it did not preclude their use as a way of raising charitable donations. One of the earliest records of a lottery in post-Roman Europe, for instance, was organized by the citizens of the Belgian town of Bruges in the 15th century to raise money for the poor (Reith). Philanthropy is perhaps one of the starkest examples of positive externalities--altruism provides little economic utility to a donor in the short term, except for perhaps moral satisfaction, yet the marginal benefit to society has the potential to be quite large, as reducing poverty creates a multitude of healthy economic effects, such as improved educational opportunities and lower crime rates. Without any personal incentives, however, rates of charitable donations will be lower than optimal. Thus, in an era centuries before the emergence of the welfare state, policies that encouraged charitable donations would help increase general societal well-being. In this sense, lotteries served as a tool for redirecting economic surplus to the destitute. In certain cases, extra-governmental institutions organized the lotteries and were later recognized by the state once they were well-developed.
The Catholic Church, for instance, organized a lottery to benefit a nursery for abandoned children in Paris in the 17th century, and eventually did so with direct permission from the King of France (Kruckerberg). Spain’s national organization for the blind, ONCE, began as an independent institution that raised welfare funds for the blind during the Spanish civil war through lottery ticket sales, but eventually rose to handle all affairs regarding blind Spaniards during the fascist regime (Garvía). In fact, its lottery was one of the only ones that the country’s dictator, Franco, did not outlaw (Jiménez-Murcia). Thus, although charity lotteries in Europe emanated for a wide array of reasons, many gained significant recognition from the state.
Lotteries are well-suited to generate externalities through charitable donations as, by their nature, they will accumulate large sums of money. However, the lotteries that states are currently offering vaccinated patients are different--entry can only occur after a specific action rather than the purchase of a ticket. The study of incentives for carrying out healthy behaviors is one that has emerged relatively recently and incorporates a rich blend of public health, economics, and psychology, but it has generated a significant amount of experimental and observational data. For instance, direct payments upon taking prescribed antidepressants tend to boost a patient’s adherence to the medication (Marcus et al.), although reimbursing consumers for buying healthy foods seems to have no significant effects (Gopalan et al.). While both of these behaviors generate positive externalities, researchers wanted to see if they could continuously reinforce an action. As such, they did not hand out lottery tickets but instead compensated participants multiple times for maximum effect. The Austrian government has actually employed such a system for childhood vaccinations since the mid 1970s, whereby mothers receive cash payments of several hundred dollars if they frequently bring their children in for checkups over the first few years of the child’s life (Hemenway). Once again, since children must receive many vaccinations in their early years, governments may aim to give out direct payments. Lotteries work better for individual actions, such as receiving one or two shots against COVID-19, because people tend to overestimate their chance of winning large prizes, even if they only have one ticket (Milkman and Shapiro).
However, this does not mean that there are no historical examples of mass health lotteries either. The Scottish government, for instance, undertook a country-wide tuberculosis screening campaign in 1957 which involved a massive propaganda campaign as well as raffle tickets for Glasgow residents who were tested. This occurred several years before TB vaccines began circulating in the UK, and as such, individual tests contributed significantly by lowering the spread of the disease overall (Levitt).
Smaller scale experiments have also yielded promising results. One group attempted to immunize more than a thousand preschoolers who were behind on their shots, and found that the best incentive was to give the families of vaccinated children a lottery ticket. This proved to be even more effective than keeping clinics open for longer hours (Yokley and Glenwick). More recently, researchers with the World Bank entered thousands of villagers in Lesotho into a lottery with monetary prizes if they tested negative for treatable STIs (Björkman et al.). While 3.8% of the population tested positive, those receiving lottery tickets with the largest prizes only had a positivity rate of 0.2%--participants were more likely to engage in less risky behavior and also were more likely to be tested. This example, however, revealed a distinct psychological aspect to lottery incentives: risk-loving individuals, who are more likely to engage in unprotected sexual activity, were much more likely to follow through with the lottery scheme. In any case, as HIV is responsible for severely reducing Lesotho’s life expectancy (HIV), increasing medical testing and treatment will be a massive positive externality, as lower disease rates will decrease the amount of orphans and increase productivity as residents live longer lives.
While it is too early to generate any comprehensive literature on the efficacy of coronavirus vaccine lotteries throughout the United States, multiple working papers and drafts have emerged in the weeks following the conclusion of Ohio’s Vax-A-Million program, the earliest statewide lottery immunization effort, which ran from May 12 until June 20 (Barber and West). State officials claimed to news agencies that the program immediately led to a large spike in vaccinations, but it is important to note that the beginning of the effort coincided with the CDC’s approval of the Pfizer-BioNTech vaccine for teenagers and its relaxation on mask-wearing for the fully vaccinated (Brehm et al.). Indeed, several days after the final prize drawing, a group of doctors writing for the Journal of the American Medical Association came to a less exciting conclusion: there was no significant difference in vaccination rates between Ohio and the rest of the country while Vax-A-Million was running (Walkey et al).
However, other researchers have found the methodology of this study to be inappropriate. Rather than place Ohio against the other forty-nine states, three separate teams have aimed to compare the state against a hypothetical version of itself where it never undertook the lottery scheme through a process known as synthetic control. To accomplish this, they generated a “synthetic Ohio” by weighing various economic and COVID-19-related statistics across other states that did not employ a lottery system while Ohio’s program was ongoing to create an artificial control group. One paper closely matches 16 statistics ranging from daily case counts to 2020 presidential election results to try to emulate Ohio as accurately as possible (Barber and West). Researchers were then able to plot Ohio’s vaccination statistics against the weighted vaccination data from the states making up synthetic Ohio over the nearly month-long lottery period and beyond. By doing so, it became possible to potentially understand how the lottery program affected just the state of Ohio. This has proven to be important as prior to Vax-A-Million, Ohio’s rates of vaccine hesitancy and vaccinations were significantly higher and lower than the nationwide average, respectively. Thus, the synthetic control removed many potential confounding variables that may have led to the statistically insignificant results in the first paper.
Among the two exclusively synthetic control studies, one finding was common to both: Ohio’s vaccine lottery program had no significant effect on the number of fully vaccinated individuals in the state (Barber and West), (Lang et al.). However, this result may be implicit in the structure of the lottery itself, as participants would only enter into the drawing if they received one dose of a COVID-19 vaccine. Thus, there was no economic incentive to complete a full round of vaccinations. One of the two studies took this into consideration by also measuring the percentage of people who had received at least one dose and found that this value was significantly higher in Ohio than its synthetic counterpart by about 0.7 percentage points (Barber and West). This led to the conclusion that the state’s program successfully led to more vaccinations. Importantly, because the authors of this paper were the ones who tracked a variety of coronavirus statistics, they were also able to estimate the effects of the lottery on the number of COVID-19 cases and hospitalizations. It appears that more than 82,000 Ohioans were on the margin about being vaccinated before the program began, based on the study’s findings and levels of vaccine hesitancy in the state. The prospect of winning the lottery increased the marginal benefit of vaccination just enough to the point where they went through with their first shot, which led to an estimated drop in COVID-19 cases by 1.3%, and a fall in ICU usage by 2.6%. The authors note that these effects seem large based on the relatively small increase in vaccinations. This feels like the case especially when considering that one would not expect 1.3% out of the total extra 1.5% of vaccine recipients to contract COVID-19. However, the authors collected the infection data until July 20, almost a month after the last prize was drawn, and the reasons for this were three-fold. Firstly, because it can take up to 14 days until vaccines take effect, it is inappropriate to stop measuring the effects of the program as soon as the lottery finishes. Secondly, most people receiving two doses of the vaccine will receive their second shot several weeks after the first, meaning that those who participated in the lottery in late June might not receive the full health benefits until mid July. Finally, since virus cases grow exponentially, the magnitude of the effects of any increase in vaccinations will grow over time. This, indeed, is a major positive externality given that patients do not necessarily consider how many people they could eventually infect down the line if they remain unvaccinated.
Barber and West’s results are exciting, but they are definitely not conclusive. However, another study corroborated their findings through the use of both synthetic control methods and difference-in-differences analysis (DID) (Brehm et al.). DID involves comparing how a variable changes across different treatment groups. In this case, researchers compared first-dose vaccination rates in counties along Ohio’s borders: those within Ohio that were part of the lottery program, and those in other states that had none (Indiana, Pennsylvania, and Michigan). Even though these counties are in different states, since they are geographically close, many of them have no significant differences in many relevant demographic, political, and health statistics. Therefore, the researchers were able to isolate many confounding effects and instead focus on how the vaccine lottery alone affected immunization rates in otherwise similar regions. This has an advantage over synthetic control in that the bordering counties in other states are real and not aggregates of other statistics. However, the authors also did employ synthetic methods and found that the lottery led to 77,000 more vaccinations, quite close to Barber and West’s 82,000 figure. The DID county effects also proved to be statistically significant, and impressively, when scaled to the entire state population, they suggest that the lottery led to an extra 54,000 or 81,000 more vaccinations, depending on the model used, close to the effects observed in synthetic Ohio.
The results from these first few studies suggest that, when using synthetic and DID methods to isolate Vax-A-Million’s effects to Ohio, lottery incentives do create more vaccinations. By estimating the reduced number of hospitalizations, Barber and West found that the economic benefits of the state’s vaccine lottery are at least $66 million, without accounting for the value of saved lives or increases in patients’ quality of life. Considering that the program only cost the state government $5.6 million to implement, it would appear as if vaccine lotteries will prove to be a resounding success. However, Lang et al. caution that it is dangerous to extrapolate any findings about Ohio’s program to other states given differences in demographics and the structure of the lotteries themselves. The above studies attempted to account for these issues by focusing on only first-dose vaccination rates and by using synthetic control groups, and similar adjustments will be necessary for tracking results in other states. Indeed, Barber and West identify 20 different state vaccine lotteries as of July 2021, which differ across a range of factors such as total prize pools, eligibility, and the frequency of prize draws. These variables may very well affect the overall efficacy of vaccination lotteries, though researchers cannot be sure until they conduct more studies in different states.
Incentives to engage in positive behaviors are perhaps very well-known anecdotally. When it comes to implementing them on a large scale, however, lotteries have proven to be an effective mechanism for two reasons. On one hand, they can pool together large quantities of money when fundraising is below its economically optimal level, and on the other, they can simply encourage large swaths of the population to modify or begin a behavior which will have greater societal effects. It remains to be seen whether or not COVID-19 vaccine lotteries will create a significant boost in nationwide immunization rates, but promising results from Ohio suggest that under circumstances, they can. Doctors, economists, and policymakers will not know the full story until more studies are conducted in more states. Only then can they begin to compare results across different circumstances to hopefully identify the most effective strategies in using games of chance to encourage vaccinations before the next health crisis strikes.
Written by Zion Gassner, UCLA Undergraduate Economics Student
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