Introduction

The Coronavirus Disease 2019 (COVID-19) has exacted a considerable toll, with impacts measurable in lives lost, freedoms curtailed, and reductions in economic welfare (Baker et al., 2020; Guerrieri et al., 2020; Gormsen & Koijen, 2020; Reis, 2020).Footnote 1 Even in the presence of effective vaccines, governmental efforts continue to rely on behavioral restrictions and recommendations, such as mask mandates, hygiene requirements and social distancing rules. These measures are likely to remain common in the immediate future.

The mortality benefits of abiding by behavioral restrictions are estimated to be worth around $60000 per US household (Greenstone & Nigam, 2020). Improving compliance with such restrictions could, thus, have large social payoffs. We do not yet know, however, the determinants of individual compliance and how they might change over time (Anderson et al., 2020; Avery et al., 2020; Briscese et al., 2020; Hsiang et al., 2020; Lewnard & Lo, 2020). In particular, we do not understand the role of individual beliefs, and whether these beliefs can be revised in ways that generate greater compliance.

To shed light on these questions, we conducted an online experiment in the US and UK with 3,610 participants. Participants are randomly assigned to a control condition or one of two treatment groups. Those in the first group (referred to as the ‘lower-bound’ condition) are told that those who contract the virus are likely to infect two other people.Footnote 2 Those in the second group (referred to as the ‘upper-bound’ condition) are told that those who contract the virus are likely to infect five other people. These estimates are from epidemiological studies and reflect uncertainties regarding the characteristics of the virus and people’s behavior (Liu et al., 2020).

Our analysis yields three main empirical findings. First, we find that participants over-estimate the infectiousness and deadliness of COVID-19. For example, participants believe, on average, that one person will infect 28 others; whereas experts estimate that the figure is between one and six (Liu et al., 2020). This result is consistent with previous studies which suggest that individuals are likely to overestimate risks that are unfamiliar, outside of their control, inspire feelings of dread, and receive extensive media coverage (see, e.g., Slovic (2000)).

Second, we show that people update their posterior beliefs about COVID-19 in response to expert information––at least in the short-run. The modal belief is that one person will infect two others in the lower-bound group, while the modal belief is that one person will infect five others in the upper-bound group. However, not all participants fully believe or understand the information conveyed in the treatments, with 46% and 61% of participants believing that one person will infect more than six others in the upper- and lower-bound groups respectively.

Third, we examine how beliefs causally affect behavior. In general, this is a difficult task. Randomly providing certain individuals with information can both influence their beliefs and ‘prime’ them to consider these beliefs when making decisions (Haaland et al., 2020). We are able to overcome this issue by exploiting variability in expert estimates. By providing information about infectiousness to both treatment groups, we make this issue salient for all of our experimental participants (ignoring our control group, which we drop in most analyses). As a result, our findings cannot be attributed to differential priming of our participants; and we are able to estimate the causal impact of beliefs on behavior by using the random assignment of individuals to the upper- or lower-bound groups as an instrument for their beliefs.

This approach yields our third central finding: exaggerated posterior beliefs about the infectiousness of COVID-19 make individuals less willing to comply with best practice behaviors, a phenomenon we call the “fatalism effect”. On average, for every additional person that participants believe someone with COVID-19 will typically infect, they become 0.5 percentage points less likely to say that they would avoid meeting people in high-risk groups. They also become 0.26 percentage points less likely to say that they would wash their hands frequently.

While others have observed the existence of a fatalism effect (see, e.g., Ferrer and Klein (2015) or Shapiro and Wu (2011)), we are among the first to demonstrate the existence of such effects using experimental methods (for another example, see Kerwin (2018)).Footnote 3 We also develop a basic model that is capable of explaining the fatalism effect. The model applies not just to this pandemic, but also to more general situations where people must choose whether to change their behavior to reduce personal or societal risks.

The intuition of our model is straightforward. Increasing individual estimates of the infectiousness of COVID-19 raises their perception of the probability that they will contract the disease even if they comply with best practice behaviors. This, in turn, reduces the perceived benefit of complying with such behaviors.Footnote 4 Consistent with this explanation, we also find that increasing individual assessments of the infectiousness of the virus leads people to be less optimistic about their future prospects, suggesting that they interpret information about infectiousness in the way assumed by our model.

The fatalism that we document could cause substantial reductions in individual and societal welfare. For example, by making individuals less likely to regularly wash their hands, it makes them more vulnerable to respiratory illnesses like COVID-19 (Rabie & Curtis, 2006). A conservative back-of-the-envelope calculation suggests that if average beliefs about the infectiousness of COVID-19 increase by eight units (e.g., someone with the virus is likely to infect 18 rather than 10 people), then we expect to see a mortality loss of $3.7 billion in the US alone, solely as a result of reduced handwashing (not counting morbidity losses, spillovers, or further waves of infection).Footnote 5 Our findings thus suggest that there may be dramatic gains from providing the public with accurate information insofar as this information revises exaggerated beliefs downwards.

This paper contributes to a number of areas in economics and psychology. First, we contribute to the literature on the perception and misperception of risk (see, e.g., Viscusi (1990), Slovic (2000), Cawley and Ruhm (2011) or indeed Fetzer et al. (2020) for a contemporaneous examination of risk perceptions during the COVID-19 pandemic). Second, while we examine individuals’ risk perceptions, we also go on to study the causal effect of these perceptions on their willingness to comply with best practice behaviors.Footnote 6 Third, we contribute to a small literature on rational fatalism; both by studying this in a novel context (compare Kerwin (2018)’s findings from Malawi) and by providing a model to explain the observed fatalism in the tradition of Kremer (1996). Fourth, we contribute to the growing literature on how policymakers can best respond to the COVID-19 pandemic by showing that it is both possible, and important, to correct people’s beliefs about the virus.Footnote 7Footnote 8

The remainder of the article is structured as follows. Section 2 reviews our experimental design. Section 3 presents the main empirical results. Section 4 develops a formal model of the fatalism effect. Finally, Sect. 5 concludes.

Experimental design

We conducted the experiment between March 26 and March 29, 2020.Footnote 9 Our sample consists of 3,610 participants (1,859 from the US and 1,751 from the UK). Participants were recruited via the panel provider Prolific Academic.Footnote 10Footnote 11 All participants were paid for their participation.Footnote 12

Participants are randomly assigned to a control group that receives no intervention or one of two treatment groups. Those in the first group (the lower-bound treatment) are shown a message explaining that studies show that those who contract COVID-19 will, on average, infect two other people––see Fig. 1. Those in the second group (the upper-bound treatment) are instead told that studies show that those who contract COVID-19 will, on average, infect five other people. Otherwise, the message they receive is the same.Footnote 13 The treatment messages are coupled with graphics illustrating how COVID-19 might spread if the virus is passed on three times at the respective levels of infectiousness.Footnote 14 The statistic that we show participants in the treatments is known as \(R_0\) in the epidemiological literature and indicates how many people one infected person is likely to infect.

Both before and after exposing subjects to the treatments, we measure our key object of interest: participants’ beliefs about the infectiousness of COVID-19.Footnote 15 More specifically, we ask: “On average, how many people do you think will catch the Coronavirus from one contagious person? Please only consider cases transmitted by coughing, sneezing, touch or other direct contact with the contagious person.” Participants are free to enter any integer between 0 and 100.

Next, we ask participants about two other COVID-19-related beliefs: (1) the probability of being hospitalized conditional on contracting the virus; and (2) the probability of dying conditional on being hospitalized for the virus.Footnote 16Footnote 17 We do not reward correct estimates with financial incentives when assessing ‘pre-beliefs’ since we do not want to induce the participants to look up numbers online. We also do not incentivize correct estimates when eliciting post-beliefs since we do not want to encourage individuals to report the number conveyed in their treatment regardless of whether it fits their beliefs. In other words, we suspect that incentivization would simply lead subjects to automatically report the expert estimate with which they were presented in a bid to earn the financial pay-off.Footnote 18

Fig. 1
figure 1

Treatment messages. Notes. The first image displays the treatment message showed to the lower-bound group. The second image displays the treatment message showed to the upper-bound group

Further, we ask people about their willingness to comply with three COVID-19-related best practices for 1 week and 2 months. These best practices are: (1) frequent handwashing; (2) working from home; and (3) not meeting people in high-risk groups. We choose these outcomes because they represent behaviors that are common components of governments’ COVID-19 mitigation strategies (see, for example, CDC (2020), Office (2020) and WHO (2020)).Footnote 19 We only measure stated intentions for future behavior and recognize the limitations of such measures; however, we see no reason to think that these limitations will have more of an effect on one treatment group than another.Footnote 20

Finally, we ask people whether they are optimistic about their future prospects. Optimism and expectations about the future are key drivers of macroeconomic activity.Footnote 21 Measuring optimism also allows us to verify that our subjects interpret the information provided about infectiousness in the expected manner.

When analyzing the experimental data, we begin by conducting linear first-stage regressions, estimating the effects of random \(R_0\) information assignment on beliefs:

$$\begin{aligned} R_i = \gamma _0 + \gamma _1 upperbound_i + \gamma _2 \mathbf {controls}_i + \epsilon _i \end{aligned}$$
(1)

where \(R_i\) represents beliefs about \(R_0\); \(upperbound_i\) is a dummy variable indicating whether the participant is randomly assigned to the upper-bound \(R_0\) information condition; and \(\mathbf {controls}_i\) represents a vector of socioeconomic and demographic variables (e.g., age and years of education). Thus, \(\gamma _1\) represents the average treatment effect on beliefs. We do not use participants in the control group when conducting this analysis (i.e., those in the lower-bound group are the “reference group”).Footnote 22

We then conduct Two-Stage Least Squares (2SLS) regressions to estimate the Local Average Treatment Effect (LATE) of beliefs about \(R_0\) on people’s optimism and their willingness to socially distance:

$$\begin{aligned} y_i = \beta _0 + \beta _1 \hat{R_i} + \beta _2 \mathbf {controls}_i + v_i \end{aligned}$$
(2)

where \(y_i\) represents people’s willingness to socially distance or whether they are optimistic about their future (binary variables); \(\hat{R_i}\) represents the fitted values obtained using Eq. (1); and \(\mathbf {controls}_i\) is a vector representing the same set of demographic and socioeconomic variables. Again, we exclude those in the control group when conducting this analysis to ensure that the exclusion restriction is met. Our estimate of \(\beta _1\) is the LATE of changing beliefs about \(R_0\) people’s stated behavior and optimism.Footnote 23

Results

Participant characteristics

We begin by providing an overview of participant characteristics. Approximately 59% of respondents are female and 75% of respondents are between the ages of 18 and 44. The monthly average pre-tax household income was $4461 in 2019.Footnote 24 Sixteen percent of participants claim to know someone that has contracted COVID-19; 4% claim to have been in contact with someone that has been diagnosed with COVID-19; 38% of participants claim to display one or more of the known symptoms of COVID-19; and 48% of respondents believe that restrictions will remain in place for more than three months.Footnote 25

People have exaggerated prior beliefs about the infectiousness and dangerousness of COVID-19

We now study the accuracy of subject beliefs concerning the infectiousness (\(R_0\)) and Case Fatality Rate (CFR) of COVID-19. As shown in Fig. 2, we find that the overwhelming majority of subject estimates are outside of the bounds of expert consensus.Footnote 26 On average, participants believe that the typical person with COVID-19 gives it to 28 others; in contrast, expert estimates of \(R_0\) at the time of the experiment put it in the 1 to 6 range (Liu et al., 2020). Similarly, participants, on average, believe that the CFR (the share of people who contract COVID-19 that die) is 10.79%; according to the CDC estimates, the case fatality rate in the US is between 1.8 and 3.4% (CDC, 2020).

The fact that participants have incorrect prior beliefs about COVID-19 is consistent with many of the findings from the literature on risk perception. According to this literature, the public is likely to overestimate risks when they are new or unfamiliar, seen as outside of their control, inspire feelings of dread, and receive extensive media coverage (see Slovic (2000) for a review). Clearly, all of these apply to COVID-19; so it is perhaps not surprising that subjects overestimate the risk of, and danger posed by, COVID-19. We also note that our finding is consistent with contemporaneous work by Fetzer et al. (2020) who find similar biases in subject beliefs.

We estimate two linear probability models to investigate heterogeneity in subjects’ beliefs (complementing the analysis in de Bruin et al. (2020)). As detailed in Appendix D, we find that men, those who are not in a risk group, and the more educated are significantly less likely to overestimate \(R_0\) and the CFR. People in both the UK and the US are likely to overestimate \(R_0\), but those in the US are 12 and 9.5 percentage points more likely than those in the UK to overestimate CFR and \(R_0\) respectively (ceteris paribus). Further, those that consume right-wing news are more likely to overestimate \(R_0\). These results are consistent with the general finding that different demographic groups can perceive risks in different ways. It is also consistent with more specific findings from the literature on risk perception: for example, a large number of papers find, as we do in our particular context, that men tend to rate risks as smaller than women do.Footnote 27

Fig. 2
figure 2

Baseline prior beliefs about \(R_0\) and the CFR. Notes. The first diagram displays the distribution of beliefs regarding the infectiousness of COVID-19 (\(R_0\)) at baseline. The second displays the distribution of beliefs regarding case fatality rate (CFR) at baseline. Participants’ perceived CFR is calculated by multiplying their belief regarding the risk of being hospitalized conditional on contracting COVID-19 by the risk of dying conditional on being hospitalized for COVID-19. See Appendix F for the exact questions that were used to construct these variables

Providing information about the infectiousness of COVID-19 corrects beliefs

Table 1 presents the effects of being assigned to the lower- and upper-bound conditions on beliefs regarding: (1) \(R_0\) and (2) the CFR. In other words, Table 1 reports the difference in mean beliefs between the treatment and control groups (controlling for demographic variables).Footnote 28

Table 1 Effects of randomly assigned \(R_0\) information on beliefs

The table reveals that being shown lower- or upper-bound estimates of \(R_0\) decreases average estimates of \(R_0\) from 29 to 21 and 26, respectively (see column 1). We also find that, on average, being told that \(R_0\) is one percent greater prompts respondents to revise their beliefs upward by 0.16 percent (i.e., the elasticity is 0.16). Further, we obtain an F-statistic of 16.71 when regressing treatment assignment on beliefs about \(R_0\) (excluding the control group), suggesting that we have an informative instrument (i.e., a strong ‘first stage’) and can proceed to use treatment assignment as an instrumental variable for beliefs about \(R_0\).Footnote 29

Figure 3 reveals the effect of the treatments on the entire distribution of beliefs about \(R_0\). The treatments shift the modal belief in the expected way: these are 5 and 2 in the upper- and lower-bound groups respectively (i.e., the estimates that the respective groups were presented with). However, not all individuals change their beliefs in line with the information that they are given, with 46% and 61% of participants still believing that \(R_0\) is above 6 in the upper- and lower-bound groups respectively.Footnote 30Footnote 31

Since baseline beliefs are measured prior to information provision (for a randomly selected subset of participants), it is also possible to run a before and after comparison. We find that there are substantial differences in pre- and post-treatment beliefs. Post-treatment beliefs are, for example, more centered around the \(R_0\) values that the treatment messages convey, and a greater portion of participants hold beliefs within the expert estimates (i.e., between 1 and 6).

Our analysis suggests that expert information about the infectiousness of \(R_0\) can update (and correct) people’s beliefs––at least in the short-term. It also demonstrates that our instrument is informative; we thus proceed with the instrumental variable analysis in the next section.

Fig. 3
figure 3

Effect of treatments on posterior beliefs of \(R_0\). Notes. The first diagram displays the distribution of beliefs about \(R_0\) in the lower-bound group pre- (prior) and post-treatment (posterior). The second diagram displays the distribution of beliefs about \(R_0\) in the upper-bound group pre- and post-treatment. Participants can enter any number between 0 and 100 when stating their beliefs about \(R_0\)

Increasing people’s posterior beliefs of the infectiousness of COVID-19 makes them less willing to engage in best practices

We now examine whether changing beliefs regarding \(R_0\) changes participants’ stated willingness to comply with best practice behaviors. We ask participants how willing they would be to frequently wash their hands, avoid seeing people in high-risk groups, and work from home assuming that “the Coronavirus outbreak is still ongoing 7 days/2 months from today.” Participants provide answers on a five-point scale, with one representing ‘extremely unlikely’ and five representing ‘extremely likely’. We transform this variable into a binary outcome, defined as one if participants state that they would be ‘extremely likely’ or ‘likely’ to adopt a given behavior and otherwise as zero.Footnote 32

Table 2 The effect of posterior beliefs about \(R_0\) on willingness to engage in best practices

Table 2 reveals that the Local Average Treatment Effect (LATE) point estimates are consistently negative, and statistically significant for the willingness to wash hands frequently (2 months) and visiting risk groups (7 days and 2 months). In other words, we find that increasing the perceived infectiousness rate actually makes individuals less willing to engage in best practice behaviors, a phenomenon we dub the ‘fatalism effect’.Footnote 33 We view our point estimates as surprisingly large. For example, we estimate that decreasing individual estimates of \(R_0\) by one unit makes individuals around 0.5 percentage points more likely to avoid meeting people in high-risk groups (see columns two and four in Table 2). Since the individuals in our sample, on average, overestimate the infectiousness rate by over 20 units, this suggests that there may be substantial gains from correcting public misconceptions on these and related issues.Footnote 34

Since these results may seem surprising, we conduct a series of robustness checks. We begin by dropping participants who guessed that \(R_0 = 100\) at baseline since such participants may not have understood the question. As Table 16 makes clear, removing these outliers does not make any discernible difference to our results.

Second, we re-estimate the ITT and LATE using a probit model. As can be seen from Table 11, this again makes little difference to our results. As before, we find significant negative effects of \(R_0\) beliefs on willingness to avoid high-risk groups; and negative (but still only marginally significant) estimates for willingness to wash hands frequently.

Third, we re-run the regressions displayed in Table 2 in order to see whether the point estimates differ when including two instruments, rather than one. To do this, we introduce the control group into the analysis. We find that the point estimates remain qualitatively similar (see Table 9 for the full results). However, it is possible that the exclusion restriction is not met here since those in the control group were not primed in the same way as those in the treatment groups (Haaland et al., 2020). As a result, this is not our preferred specification.

Fourth, we conduct a simple OLS analysis (while controlling for a range of demographic and other characteristics) to measure the association between beliefs about \(R_0\) and individuals’ willingness to engage in best practices – see Tables 12, 13 and 14. For what it is worth, our OLS estimates again suggest a significant fatalism effect on willingness to avoid seeing people in high-risk groups (but not for the other two outcomes). While this may lend further plausibility to our main findings, these results should be treated with caution in light of possible omitted variable bias.Footnote 35

Fifth, we conduct a heterogeneity analysis that examines whether the effect of \(R_0\) beliefs depends on individuals’ prior beliefs about \(R_0\). To do this, we drop individuals for whom we did not elicit baseline beliefs (half the sample) and then split the remaining sample into three subgroups, corresponding to perceived \(R_0\) below 33, perceived \(R_0\) above 67 and an ‘intermediate’ group. Our estimated coefficients are negative for all outcomes and all groups with the exception of washing hands for those with a baseline belief greater than 67 (see Tables 17 and 18). However, the dramatic reduction in sample size means that our results lose significance.

Finally, we consider whether our result might somehow be due to subject inattention. In principle, it is not obvious why inattention should be expected to generate a fatalism effect – both because attention should be roughly balanced in both treatment groups (due to the randomization) and because it is unclear how inattention should affect subject responses. Nonetheless, we now investigate this issue more fully by dropping those who proceeded very quickly through the survey (less than ten, eight and six minutes), dropping those who only spent the mandatory amount of time (twenty seconds) on the treatment screen, and dropping those who gave the same response to all the questions about COVID-19 (which were all elicited on the same 0-100 scale). As shown in Tables 19, 20 and 21, none of these exercises appreciably alters the estimated coefficients or standard errors – providing further evidence that our results are not driven by inattention.

In summary, the ‘fatalism effect’ that we find would appear to be a robust feature of our data. It persists regardless of whether we drop outliers or apparently less attentive subjects, whether we estimate a linear probability model or use probit, and if we introduce a second instrument (through use of the control group). Moreover, we find suggestive evidence of a fatalism effect within almost all of the subgroups we consider. Hence, while such a novel finding inevitably stands in need of replication, the data in our experiment do provide strong evidence that at least some individuals exhibit fatalism in the context of the COVID-19 pandemic.

Believing that COVID-19 is more infectious makes individuals less optimistic

Finally, we study the impact of changing people’s beliefs about COVID-19 on their optimism about the future. We expect people to become less optimistic about the future if they are told that experts estimate that \(R_0\) is greater, as this may imply that the virus is likely to have a greater impact on the economy (and society in general). This is exactly what we find. Table 15 shows that when participants are told that \(R_0\) is five, as opposed to two, they become significantly less optimistic. Quantitatively, a one-unit increase in beliefs about \(R_0\) leads to a one percentage point drop in the share of participants that are optimistic about the future.Footnote 36 These results are of interest insofar as optimism affects the evolution of key macroeconomic variables. Further, the result suggests that subjects understand that a higher rate of infectiousness translates into a more severe impact from the virus, confirming that they process the information provided in the experiment in the expected way.

Towards a theory of fatalism

In this section, we propose a model that can explain the fatalism effect that we find in our experiment. The intuition behind the model is straightforward. If individuals come to believe that the virus is more infectious, then they revise upwards their assessment of the probability that they will get the virus even if they socially distance (or follow other best practices such as washing their hands frequently). But if individuals come to believe that they are likely to get the virus no matter what they do, then they may decide to ignore social distancing measures: in other words, we get a rational “fatalism effect”.

More formally, we consider an individual who must choose between two actions: socially distancing (denoted \(A = 0\)) or instead socializing as usual (denoted \(A = 1\)). If they socially distance, then there is a probability \(p \in [0, 1]\) that they will contract the virus nonetheless (e.g. while doing essential shopping). If they socialize as usual, there is a further probability \(q \in [0, 1]\) that their friends will give them the virus. Assuming independence of risks for simplicity, their overall probability of contracting the disease is thus \(p + q - pq\) in the \(A = 1\) scenario.Footnote 37

If the individual socializes, they receive a psychic benefit \(B > 0\) and their expected utility is given by \(U(A = 1) = B - \alpha (p + q - pq)\) where \(\alpha > 0\) measures the rate at which they are willing to trade the benefit of socializing off against the risk.Footnote 38 If they instead socially distance, then their expected utility is \(U(A = 0) = -\alpha p\). They therefore choose to socialize if and only if

$$\begin{aligned} \text {U}(A = 1) \ge \text {U}(A = 0) \iff q(1 - p) \le B' \end{aligned}$$
(3)

where we have defined \(B' \equiv B/\alpha\). To capture variation in the cost of socially distancing within the population, we will assume that \(B'\) is drawn from some strictly increasing probability distribution \(F:[0, 1] \rightarrow \mathbb {R}\). Thus,

$$\begin{aligned} \text {P}(A = 1) = \text {P}(q(1 - p) \le B') = 1 - \text {F}(q(1-p)) \end{aligned}$$
(4)

and so the probability that the individual socializes is strictly decreasing in \(q(1-p)\). In other words, the greater the additional risk from socializing, the less likely the individual is to socialize.

Finally, note that the subjective probabilities p and q depend on the individual’s estimate of the infectiousness of the disease, denoted \(e \in \mathbb {R}\). Accordingly, we will write \(p = p(e)\) and \(q = q(e)\); and we will further assume that p and q are strictly increasing and differentiable functions.

We now examine how the individual’s willingness to socialize depends on their estimate of the infectiousness rate. To this end, it will be convenient to define \(\beta (e) \equiv p'(e)/q'(e)\), i.e. \(\beta\) is the ratio of derivatives of the risk functions. It is also helpful to define fatalism more formally. We will say that there is a fatalism effect if and only if

$$\begin{aligned} \frac{\text {d} \text {P}(A = 1)}{\text {d} e} > 0 \end{aligned}$$
(5)

that is, a small increase in the perceived infectiousness rate makes the individual more likely to socialize. We can then observe the following:Footnote 39

Proposition 1

There is a fatalism effect if and only if \(p(e) + \beta (e) q(e) > 1\).

Proposition 1 sheds some light on when fatalism is likely to arise. First, fatalism is more likely to arise when the background risk p is high. This is not a surprise: if p is large, then the individual is likely to contract the disease anyway so loses little from going outdoors. Second, fatalism is more likely to arise when the relative sensitivity of the background risk to the perceived infection rate is large. This is also not surprising: if increasing e dramatically increases the risk from staying at home, but only slightly increases the risk from socializing, then it may induce individuals to socialize. Finally, a fatalism effect becomes more likely when the socializing risk q becomes larger. While this effect is more subtle, the intuition can be readily grasped by considering the extreme case of \(q = 0\): in that case, the individual will socialize with probability 1 (there is no risk in doing so), so increasing e cannot make them more likely to socialize (i.e. there can be no fatalism effect).

While useful, it may be hard to check whether the inequality in Proposition 1 holds in practice. As a result, we now study the relationship between the possibility of a fatalism effect and the overall probability that an individual contracts the disease if they socialize \(p + q - pq\). To this end, let \(p^S \equiv p + q - pq\) (suppressing the dependence of the probabilities on e for ease of notation) and define the function \(g :\mathbb {R}^+ \rightarrow [0, 1]\) as follows:

$$\begin{aligned} g(\beta ) = {\left\{ \begin{array}{ll} (4 - \beta )/4 \text { if } \beta \in (0, 2]\\ 1/\beta \text { if } \beta > 2 \end{array}\right. } \end{aligned}$$
(6)

We then have the following result:

Proposition 2

If there is a fatalism effect, then \(p^S \ge g(\beta )\). Conversely, if \(p^S > g(\beta )\), then there must exist probabilities \(p \in [0, 1]\) and \(q \in [0, 1]\) that are consistent with \(p^S\) and generate a fatalism effect.

Proposition 2 provides an easily checked inequality that determines the possibility of a fatalism effect. For example, suppose that \(\beta = 1\) (i.e. both probabilities are equally sensitive to the estimated infectiousness rate e). Then \(g(\beta ) = 3/4\), so fatalism is possible only if the individual thinks that they have at least a 75% chance of getting the disease if they socialize. Conversely, if the individual thinks that they have at least a 75% chance of getting the disease if they socialize, then we can always find probabilities p and q that generate a fatalism effect (e.g., if \(p^H = 0.75\), then \(p = q = 0.5\) will work). Note that, in general, the probability \(p^S\) need not be as high as 75% to generate fatalism. Indeed, given that \(g(\infty ) = 0\), fatalism is consistent with an arbitrarily low probability \(p^S\) provided that the ratio of derivatives \(\beta\) is sufficiently large.

In summary, our model demonstrates that fatalism is possible under a range of conditions; and that a fatalism effect is more likely to arise if the probabilities p, q and the ratio of derivatives \(\beta\) is large. Importantly, our model can also be reinterpreted in various ways. For example, while we described the action \(A = 1\) as ‘socializing as usual’, it could also be interpreted as ‘not regularly washing one’s hands frequently’ or ‘refusing to work from home’, allowing the model to explain the fatalism effect we also observe for these outcome variables. Similarly, the risks could be re-interpreted as not risks to oneself but rather as risks to others, allowing the model to explain why one might become fatalistic when (for example) deciding whether to visit an elderly relative.

As shown in the appendix, it is possible to extend the basic model in various ways. For example, it is possible to relax the assumption that the risks are independent; and it is also possible to allow for the conjunction of selfish and altruistic motives for social distancing behavior. These extensions slightly complicate the formulae above but do not change the main insights of the model. A more interesting extension is to recognize that the probabilities of contracting the disease p and q actually depend on the fraction who socially distance, which in turn depends on the probabilities p and q. It is thus possible to find ‘equilibrium’ probabilities and levels of social distancing: i.e., probabilities p and q that induce a level of social distancing that is then consistent with p and q.

Finally, we recognize that, while the model provides one explanation for the observed effect, it is not the only plausible explanation. For example, it might be that increasing individual assessments of the infectiousness of disease makes them think that many others will likely get the virus anyway, thereby diminishing the perceived social value of efforts to depress \(R_0\).Footnote 40 While this explanation is logically distinct from ours, it is similar in spirit insofar as both explanations stress the damaging effect of high \(R_0\) assessments on individuals’ motivation to combat the virus.

Conclusion

This paper describes three key results of an online experiment that studies individual beliefs and behaviors during the COVID-19 pandemic. First, individuals overestimate both the infectiousness and dangerousness of COVID-19 relative to expert opinion, a result that is in line with findings from the risk perception literature. Second, messages conveying expert estimates of \(R_0\) partially correct people’s beliefs about the infectiousness of COVID-19. Third, individuals who believe that COVID-19 is more infectious are less willing to comply with social distancing measures, a finding we dub the “fatalism effect”.

We are not the first to uncover a fatalism effect in the context of decision-making under uncertainty. Earlier observational studies suggest that higher risk perceptions make anxious individuals less likely to engage in exercise, less likely to meet fruit and vegetable consumption guidelines and less willing to quit smoking (Ferrer and Klein (2015)). We contribute to this literature by demonstrating the existence of a fatalism effect using experimental methods and by providing evidence of such an effect in the context of a pandemic. We also develop a model that is capable of explaining the fatalism effect.

Our study has several limitations. For example, we consider the impact on stated behaviors; we do not measure the long-run impact of beliefs on behavior; and there is a possibility that our results may not generalize to those who do not complete online experiments. These limitations could, perhaps, be overcome by conducting long-term and large-scale natural field experiments.

These limitations notwithstanding, our findings may have important implications for policy in the face of the COVID-19 pandemic. In particular, they suggest substantial gains from providing the public with accurate information, insofar as this information revises public assessments of the virus’ infectiousness downwards. To get a sense of the magnitude of this effect, we perform a conservative benefit calculation, and find that revising individual assessments of \(R_0\) downwards by just 8 units could create at least $3.7 billion in mortality benefits in the US simply by getting people to wash their hands more frequently.Footnote 41 It might also be worthwhile for governments to track how people’s beliefs and sentiments change over the course of the pandemic, as this would inform the need for––and help target––policy interventions.

More generally, our study has implications for how policymakers can best mobilize populations in the face of a crisis. In particular, our findings suggest that policymakers need to tread a fine line, communicating in ways that convey the seriousness of the crisis, but without triggering a fatalism effect. Understanding how exactly to tread that line is an important task for future research.