Fermat's Library | Heads or Tails: The Impact of a Coin Toss on Major Life Decisions and Subsequent Happiness annotated/explained version.

Steven Levitt is an American economist, and the coauthor of Freakon...

Expected utility is one of the first theories of decision making an...

Prospect theory is a theory of behavioral economics/finance develop...

Here is the website, which is still up: https://www.freakonomicsexp...

This is an important, surprising discovery: "Those who were instruc...

Status quo bias: an emotional bias; a preference for the current st...

Really interesting finding: "there appears to be a causal impact of...

This is key to the study design and the validity of the results: "I...

"The coin-ﬂipper’s ex ante assessment of how likely he or she is to...

"In contrast, under the assumption that the only channel through wh...

This is indeed a large potential bias... this study will need to be...

"Summarizing the discussion above, it is likely that the ﬁrst-stage...

Review of Economic Studies (2020) 0, 1–28 doi:10.1093/restud/rdaa016

Heads or Tails: The Impact of a

Coin Toss on Major Life

Decisions and Subsequent

Happiness

STEVEN D. LEVITT

University of Chicago and NBER

First version received November 2017; Editorial decision October 2019; Accepted April 2020 (Eds.)

Little is known about whether people make good choices when facing important decisions. This

article reports on a large-scale randomized ﬁeld experiment in which research subjects having difﬁculty

making a decision ﬂipped a coin to help determine their choice. For important decisions (e.g. quitting a

job or ending a relationship), individuals who are told by the coin toss to make a change are more likely

to make a change, more satisﬁed with their decisions, and happier six months later than those whose coin

toss instructed maintaining the status quo. This ﬁnding suggests that people may be excessively cautious

when facing life-changing choices.

Key words: Quitting, Happiness, Decision biases

JEL Codes: D12, D8

1. INTRODUCTION

In every life, there arise difﬁcult decisions with potentially far-reaching consequences on lifetime

utility: whether to quit a job, seek more education, end a relationship, quit smoking, start a

diet, etc. Expected utility maximization is the workhorse economic model for thinking about

such choices. Behavioural economics offers a host of alternative descriptive models of decision-

making, e.g. prospect theory, hyperbolic discounting, and the sunk cost fallacy. Yet, from an

empirical perspective, economics has almost nothing to say about whether or not people are

actually making good choices when it comes to their most important decisions.

1. There is, of course, a rich experimental literature exploring individual decision making under uncertainty. For

surveysof this enormous literature, see Camerer (1995), Smith (1994), and Chaudhuri (2011).A notablerecent contribution

to decision-making under uncertainty is Gneezy et al. (2015). Most of this literature focuses on low-stakes decisions.

Slonim and Roth (1998) and Andersen et al. (2011) explore decision-making in a high-stakes dictator game. In recent

years, ﬁeld experiments exploring decision making in natural environments have become more common (Bowles et al.,

2001; Gneezy and List, 2006; Dellavigna, 2009; Levitt and List, 2009), but most of these have investigated relatively

The editor in charge of this paper was Nicola Gennaioli.

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2 REVIEW OF ECONOMIC STUDIES

One reason that so little is known about these important decisions is that researchers do not

generally have the power to randomize people into treatments that compel them to, say, quit

their jobs or leave their spouses. Even if it were possible to choose 1,000 married couples from

the general population and randomly force 500 of those couples to divorce, it would not be

particularly informative. Such a study would tell us about the average treatment effect of divorce.

What we really care about, however, is the impact on the marginal decision maker. It would not

be surprising if getting a divorce would have a devastating impact on the infra-marginal married

person. A much more interesting question is whether divorce, ex post, will be the right choice for

someone teetering on the edge of ending a relationship.

Even if one found such a group of individuals who are close to indifferent between remaining

married and getting divorced, an ex post comparison of the happiness of those who do and do not

make a change still would not have an easy causal interpretation, because the people who make

a change will systematically differ from those who do not on many dimensions. To convincingly

answer the question, a researcher would not only need to ﬁnd large numbers of these marginal

individuals, but also, through some sort of randomization, inﬂuence their important life choices.

That is what I do in this study. I created a website called FreakonomicsExperiments.com.

On the website, individuals who are having a difﬁcult time making a life decision are asked to

answer a series of questions concerning the decision they are struggling with. Users are presented

with a wide range of questions to choose from (see Supplementary Appendix A for the full set

of questions offered) or invited to create their own question. One choice (e.g. “go on a diet”) is

assigned to heads and the other choice (in this case “don’t go on a diet”) is assigned to tails. The

outcome of the coin toss is randomized and the user is shown the outcome of the coin toss. The

coin ﬂippers are then re-surveyed two and six months after the initial coin toss. Additionally, prior

to the randomization, coin ﬂippers are encouraged to identify a third party (a friend or family

member) to verify their outcomes. The third parties are also surveyed two and six months after

the coin toss.

While it might seem implausible that anyone would come to such a website and ﬂip a coin,

much less follow the dictate of the coin toss, the results obtained speak to the contrary. In the year

of data collection, over 20,000 coins were ﬂipped. A number of results emerge from the analysis.

First, two months into the study participants show a bias towards the status quo, in the sense

that people report making a change less frequently than they predicted they would before the coin

toss. Six months after the coin toss, however, this bias is gone.

Second, those who report making a change in follow-up surveys are substantially happier

than those who do not make a change, and they are more likely to say they would make the same

decision if they were to choose again. This is true for virtually every question asked both two

and six months later. This correlation does not, of course, necessarily imply causality. Those who

make a change differ from those who do not make a change on many dimensions.

Third, the outcome of the coin toss appears to inﬂuence the actions taken. Those who ﬂipped

heads were approximately 25% more likely to report making a change than those who got tails.

The coin toss had a roughly equal impact on decisions across the entire range of self-stated ex ante

likelihoods of making a change (i.e. the coin toss matters whether before the toss the coin-ﬂipper

says he/she has a 20%, 50%, or 90% likelihood of making the change). The coin toss was roughly

equally inﬂuential on men and women, the old and the young, and across income levels. The coin

minor decisions [e.g. what quality of baseball card to offer (List, 2002), whether to respond to a solicitation letter from a

charity (Falk, 2007), and when to make mail-order catalogue purchases (Anderson and Simester, 2003)].

2. To answer questions like that, previous research has typically had to rely on correlational studies (e.g.

Kalmijn et al., 2009; Pedersen and Schmidt, 2014) or natural experimental variation (e.g. Gruber and Mullainathan, 2005;

Meier and Stutzer, 2007), with the usual challenges to causal inference.

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LEVITT HEADS OR TAILS 3

toss, not surprisingly, had the biggest impact on relatively unimportant decisions like whether or

not to go on a diet, but also inﬂuenced much more important choices like job quitting and ending

relationships. The coin toss only inﬂuenced decisions made within the ﬁrst two months of the

coin toss; later changes were unrelated to the outcome of the toss.

Fourth, when it comes to “important” decisions (e.g. job quitting, separating from your

husband or wife), making a change appears to be not only correlated with increased self-reported

happiness, but also causally related, especially six months after the coin toss.

Those who were

instructed by the coin toss to make a change were both more likely to make the change (as

noted above) and, on average, report greater happiness on the follow-up surveys. This ﬁnding

is inconsistent with expected utility theory; those who are on the margin should, on average,

be equally well off regardless of the decision they make. This result provides strong empirical

support for the notion of a status quo bias (Samuelson and Zeckhauser, 1998; Kahneman et al.,

1991). There is suggestive evidence that the coin toss outcome on “less important” decisions (e.g.

going on a diet, dying one’s hair, quitting a bad habit) inﬂuences future happiness in a similar,

but more muted, fashion.

Fifth, for all decisions—not just the most important ones—there appears to be a causal impact

of making a change on how satisﬁed the subject is ex post with the decision. Those who were

instructed to make a change by the coin toss are substantially more likely to report that they made

the correct decision and that they would make the same decision again if given the chance.

All of these results are subject to the important caveats related to using self-reported happiness

as a proxy for utility, a research subject pool that is far from representative, potential sample

selection in which coin ﬂippers complete the surveys, and responses that might not be truthful.

I consider a wide range of possible sources of bias and where feasible explore these biases

empirically, concluding that it is likely that the ﬁrst-stage estimates (i.e. the effect of the coin toss

on decisions made) represent an upper bound. There is less reason to believe, however, that there

are strong biases in the 2SLS estimates (i.e. the causal impact of the decision on self-reported

happiness).

The structure of the remainder of the article is as follows. Section 2 describes in greater

detail the experiment and how it was carried out. Section 3 reports the results of the experiment.

Section 4 explores how a variety of potential biases might inﬂuence the inferences drawn from the

study and also considers how likely those biases are to be important. Because this study differs

in substantial ways from standard experimental interventions by economists, the issues of bias

that arise are not the typical ones economists are used to thinking about. Section 5 concludes.

2. EXPERIMENTAL DESIGN

The experiment was carried out online at the website www.FreakonomicsExperiments.com.

Users who arrived at the site were greeted with the home page shown in Figure 1, which offered

3. Richard Easterlin was one of the ﬁrst economists to be widely recognized for work with self-reported happiness

data, and since his contribution in 1974 on the link between income and subjective happiness many others have made use

of such data. Dolan et al. (2008) and Frey and Stutzer (2002) provide overviews of the use of self-reported happiness data

in the economics literature. Additional applications of happiness data in the ﬁeld are outlined by Di Tella and Macculloch

(2006) who conclude that, treated with caution, the data have the potential to add value to empirical work. Researchers

differ in their level of optimism regarding the validity of such data—Kahneman and Krueger (2006) note that the cleanest

use of self-reported happiness data would “avoid effects of judgment and of memory as much as possible” but acknowledge

that subject to these limitations such data can add important contributions to the ﬁeld, while Bertrand and Mullainathan

(2001) offer skepticism in noting that the use of a dependent variable that relies on self-reported happiness data can be

problematic because “the measurement error appears to correlate with a large set of characteristics and behaviours.”

4. For a further description of the experiment and preliminary results, written for a popular audience, see Dubner

and Levitt (2014).

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4 REVIEW OF ECONOMIC STUDIES

Figure 1

Website home page.

to help people make decisions through the use of a coin ﬂip. Those individuals who clicked “Learn

More” saw the screen-shot presented in Figure 2. If they proceeded further, they were shown a

menu of life decisions over which to ﬂip a coin from which they could choose; they were also

given the option of designing their own customized question. After selecting a question relevant

to their particular dilemma, subjects ﬁlled out a short survey that collected basic demographic

data, asked them to rate their current level of happiness, probed them about the decision they were

having trouble making, and gave them the opportunity to identify a third party, typically a friend

or family member, who could be surveyed in the future regarding their decision.

Approximately

30% of subjects provided the name and email address of a third party. This sub-sample of the data

is of particular interest for two reasons. First, naming a third party may signal greater commitment

to following the coin toss. Second, the existence of a third party provides an independent source

of information to verify later participant responses, as well as a source when the subject fails to

respond to follow-up surveys.

The participants were then led to a page where a simulated coin tied to a randomizing algorithm

was ﬂipped and came up either heads or tails.

Subjects were reminded of what action the coin

toss directed them to take, and if the coin toss said to make a change, they were encouraged to

5. Users were also shown, at random, a fact relevant to the decision they were about to make. For instance, those

pondering whether to quit their job were told either “The number of job openings is on the rise—up by nearly 70%

since 2009” or “Workers who dislike their jobs report lower levels of wellbeing than the unemployed. In fact, 81% of

the unemployed report that they are happy every day compared to only 69% of the unhappily employed.” There are no

statistically signiﬁcant differences in actions associated with having seen different facts.

6. Before the coin toss took place, subjects were asked how likely they were to make the change. If subjects

indicated that they were very likely or very unlikely to make a change, they were taken to a page telling them that it

seemed like they had already made up their mind. Those subjects then had the option of proceeding to the coin toss or

exiting. All users were given the choice of having their outcome determined by a single coin toss, or could opt for a “best

two out of three.” Approximately 56% of users chose the “two out of three” option. In terms of subsequent behavior,

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LEVITT HEADS OR TAILS 5

Figure 2

What potential study participants saw when they clicked “Learn More”.

make that change within the next two months. In those cases where the coin toss said don’t make

a change, the subjects were told to maintain the status quo for at least the next two months (e.g.

if the coin toss said not to quit one’s job, the subjects were asked to remain at the job for at least

two months). In most, but not all cases, heads was associated with making a change and tails was

associated with maintaining the status quo. For simplicity in exposition, I refer to heads in what

follows as meaning that the coin toss recommended a change.

Subjects were aware that they were part of an experiment and were required to explicitly give

their informed consent. Both the subjects and the third parties provided by the subjects were

then surveyed two and six months after the coin toss. Survey reminders were sent via email

and included a link to an online survey site where the follow-up surveys were done. In order to

encourage survey completion, those who ﬁlled out the surveys were provided with small gifts that

took the form of exclusive content from Freakonomics podcasts. It should be noted, however, that I

intentionally made it difﬁcult for subjects to determine the precise objective of the study. Subjects

were told that their participation would “help us gain important insights into decision-making.”

The initial survey, prior to the coin toss, asked many questions about motivations and feelings

surrounding the decision. The follow-up surveys also asked a number of questions unrelated to

the actual purpose of the study.

The website FreakonomicsExperiments.com was launched on 23 January 2013. Recruiting

was done through a variety of online and traditional media avenues including reddit.com, the

Freakonomics podcast, the Freakonomics blog, Marginal Revolution, and articles published in

The Financial Times and Forbes. Data collection at the site remained active for roughly a year,

after which a scaled down version of the site remained operational, but all survey activity ended.

there are no clear differences between those who went for the single coin versus best of three option. In what follows, I

use the shorthand of a coin toss to refer to both of these options.

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6 REVIEW OF ECONOMIC STUDIES

TABLE 1

Question attributes

Number Important? Choice between action

Question of tosses question? and Status Quo?

Should I quit my job 2,186 Yes Yes

Should I break up 1,686 Yes Yes

Should I go back to school 1,203 Yes Yes

Should I start my own business 893 Yes Yes

Should I move 762 Yes Yes

Should I quit smoking 499 Yes Yes

Should I have a child 415 Yes Yes

Should I propose 220 Yes Yes

Should I retire 120 Yes Yes

Should I adopt 42 Yes Yes

Create your own question 3,485 No No

Should I splurge 1,491 No Yes

Should I go on a diet 1,134 No Yes

Should I break my bad habit 984 No Yes

What should I major in 959 No No

Should I get a tattoo 876 No Yes

Should I try online dating 699 No Yes

What college should I go to 656 No No

Should I join a gym 630 No Yes

Should I dye my hair 514 No Yes

Should I sign up for a running event 431 No Yes

Where should I move to 425 No No

Should I grow facial hair 424 No Yes

Should I quit drinking 401 No Yes

Should I ask for a raise 385 No Yes

Should I start volunteering 364 No Yes

Should I rent or buy 295 No No

What school should I send my child to 130 No No

Should I get a roommate 106 No Yes

Which house should I buy 96 No No

Notes: This table presents summary information by question. The ﬁrst column displays the number of coins tossed for

each question. The second column indicates whether the question is considered an important question, where important

questions are displayed in the top panel of the table. The third column indicates whether a question represents a choice

between action or maintaining one’s status quo (Yes) as opposed to a choice between two possible actions (No).

During the time of the study, there were approximately 165,000 unique visitors. Roughly

23,500 coin tosses took place. Excluded from the analysis are coin tosses with technical problems

(primarily as a result of the user providing a faulty email address), leaving 22,511 usable coin

tosses.

The distribution of these coin tosses across questions is presented in Table 1. Questions

are divided into two categories corresponding to the importance of the decision for a person’s

life. This classiﬁcation is based on a survey of individuals who were not participants in the

original experiment.

I use this classiﬁcation to aggregate questions later in the article. “Important”

questions are listed ﬁrst in the table, followed by “less important” questions. Of the important

questions, the single most popular was “Should I quit my job?” which attracted 2,186 coin tosses.

The other “important” questions which yielded more than 1,000 coin ﬂips were “Should I break up

7. These raters were asked to rate the importance of each life decision on a scale from 1 to 5. The correlation in

rankings across individuals is quite high, with an average pairwise correlation of 0.707. The cutoff between “important”

and “less important” is by necessity somewhat arbitrary. There was a large gap in ratings between “Should I move?”

(average rating of 3.45) and “Should I go on a diet?” (average rating of 3.0), so I divided the sample there. The central

ﬁndings of the paper are reproduced if instead a continuous measure of importance is utilized.

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LEVITT HEADS OR TAILS 7

with my signiﬁcant other?” and “Should I go back to school?” Among “less important” questions,

over 3,000 individuals created their own questions. I mostly ignore these questions in the analysis

that follows. Other popular choices related to splurging and going on a diet.

Online surveys of both the participants and the third parties were conducted two and six months

after the coin toss. The surveys of coin ﬂippers reminded the recipient which question had led to

a coin being tossed (but did not remind them of the outcome of the coin toss), and then asked,

among other questions, (1) whether an action had been taken since the coin toss and (2) about

his/her overall happiness level and the degree of satisfaction with the speciﬁc decision on the coin

toss question. Third parties were asked a parallel set of questions, appropriately rephrased.

For

questions where a decision was essentially permanent (e.g. quitting a job), subjects were asked

whether they had taken the action. On topics for which a change was potentially temporary (e.g.

attempting to quit smoking which might succeed or fail), we asked subjects whether the attempt

had been made.

Figure 3 reports the degree of success in obtaining follow-up surveys. There is at least one

completed survey from roughly 58.34% of the coin ﬂippers who did not name a third party.

Those who named a third party before the coin toss were more likely (77.39%) to complete at

least one survey, consistent with the conjecture that naming a third party signals commitment to

the experiment. Adding in the surveys ﬁlled out by the third parties, I have at least one follow-up

survey for 83.57% of the coin ﬂippers who named a third party. Response rates were higher for

the two-month survey (a total of 13,935 completed surveys) than the six-month survey (8,159

completed surveys). Throughout the analysis, except where noted, I analyse the two-month and

six-month samples separately.

3. RESULTS

There are two questions of primary interest: (1) Did the coin toss inﬂuence behaviour? and (2)

What can be learned about the impact of choices on subsequent happiness? I begin with an

analysis of the ﬁrst question before turning to the second question. In this section, I simply

report the data generated by the experiment and the treatment effects that arise from those data.

There are many potential sources of bias that might arise as a result of survey non-response and

untruthful responses on the part of subjects. I defer careful consideration of these potential biases

to Section 4.

3.1. Did the outcome of the coin toss inﬂuence behaviour?

Figure 4 presents data on the rate of coin toss adherence among survey respondents. The green

bars correspond to two-month responses; blue represents data from the six-month survey. The

values reported in the columns are the percentage of coin ﬂippers whose actions correspond to the

dictate of the coin toss, i.e., making a change if heads came up and maintaining the status quo if

tails was the outcome.

If the coin toss has no impact on behaviour, then 50% of the actions taken

should match the coin’s dictate. The ﬁrst two bars in Figure 4 reﬂect data from all coin tosses.

After two months, roughly 63% of the respondents’ actions match the recommendation of the

coin toss. This implies that 13% of all actions were affected by the coin toss, i.e., that someone

8. Third parties were only asked about the general happiness level of the coin ﬂipper, not about the speciﬁc choice

(e.g. if the coin ﬂipper could go back in time and make the decision again, would they make the same choice). Ex post,

this is a research design decision that I regret.

9. For those cases where I have survey responses from both the coin ﬂipper and the third party, and they disagree

as to what action was taken, I use the stated action of the coin ﬂipper.

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8 REVIEW OF ECONOMIC STUDIES

coin tosses 22511

named third

party 6797

no third

party 15714

both completed

follow-up sur-

vey 2685

only participant

completed follow-

up survey 2588

only third party

completed follow-

up survey 427

neither com-

pleted follow-up

survey* 1097

completed follow-

up survey 9233

did not com-

plete follow-up

survey 6481

Figure 3

Follow-up survey response rates

Notes: This ﬁgure presents the number of total tosses and the number of completed surveys according to whether a third party was named. Note that the category consisting of participants who did not complete a

follow-up survey includes those who did not complete their ﬁrst follow-up survey and who never received a second follow-up survey because the experiment ended before the participant would receive this second

survey. 3,655 participants never received their second follow-up survey. 798 participants did not receive their ﬁrst follow-up survey due to the experiment’s end date and were thus excluded from our analysis.

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LEVITT HEADS OR TAILS 9

20 30 40 50 60 70 80

Percent Following the Coin Toss

All Important Less Important Coin Says

Change

Coin Says

Don't Change

2 Months 6 Months

Lower Bound/Upper Bound of 95% CI

Figure 4

Coin toss adherence among survey respondents

Notes: This ﬁgure presents coin toss adherence based on two- and six-month survey responses. The vertical axis reﬂects the percent

following the coin toss. The horizontal axis categorizes response rates by question type and survey.

who got heads was 26 percentage points more likely to have made a change than someone who

got tails. The corresponding numbers, here and in the remainder of the article, are slightly lower

at six months. This implies that some part of the impact of the coin toss is to accelerate changes

that would have happened anyway, but at a later date.

The next two sets of columns in Figure 4 divide the sample between “important” and “less

important” questions, as deﬁned above. On “important” questions, the rates of reported coin-toss

adherence are much lower than for the full sample (56.1% at two months; 55.8% at six months), but

still above 50%. For “less important” questions, more than 67% of the subjects report following

the coin toss at two months. The ﬁnal two sets of columns parse the data according to whether the

coin says to make a change or recommends maintaining the status quo. At two months, there is

a bias towards the status quo. Only half of the respondents told to make a change do so, whereas

75% of those told to maintain the status quo do so. At six months, roughly 60% of participants

follow the coin toss whether it comes up heads or tails.

Prior to the coin toss, participants were asked to report how likely they believed they were

ex ante to take the action associated with their coin toss, e.g., to propose to their signiﬁcant

other. They were given a menu of choices ranging from 0% to 100% at 10% intervals.

Figure 5

plots the impact of the coin toss as a function of these ex ante likelihoods. The horizontal axis

10. The fact that 13% of actions were affected by the coin toss has several implications. First, as hypothesized

earlier, it indicates that many people are on the margin when making a decision. More interestingly, it means some people

would prefer to give up control of their decision-making, even to something as arbitrary as a randomization device. One

potential mechanism could be regret aversion—regret is a product of decisions that one has control over, so by giving up

control, one minimizes regret.

11. The average predicted probability of taking the action across the research subjects was 41.94%. 8.38% predicted

that there was no chance of changing; 2.58% thought they would change for sure. The most popular response was 50%.

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10 REVIEW OF ECONOMIC STUDIES

0 20 40 60 80 100

% Participants Who Made a Change

0 20 40 60 80 100

Stated Probability of Taking Action (%)

coin toss says change coin toss says don’t change

Note: Excludes coin flips for questions that do not have clear yes/no actions.

Figure 5

Likelihood of taking action as a function of ex ante stated probabilities, two-month survey

Notes: This ﬁgure presents the percent of participants who make a change by the two-month survey mark according to their stated

probability of changing and the result of the coin ﬂip. The vertical axis reﬂects the percent of respondents who reported making a change.

The horizontal axis groups respondents according to to their stated ex ante likelihoods of making a change. Responses are categorized

according to whether the coin came up heads (make a change) or tails (no change).

corresponds to the participants’ stated likelihood of taking an action, prior to tossing the coin.

The vertical axis is the percentage of subjects who report taking the action on the two-month

survey. The two lines plotted in the ﬁgure correspond to those whose coin tosses came up heads

and tails respectively. A number of insights emerge from the ﬁgure. First, the outcome of the coin

toss exerted inﬂuence across the entire distribution of ex ante probabilities. This can be seen in

the fact that the line corresponding to heads is above the line for tails across the entire span of the

graph by an average of roughly 20 percentage points. The coin toss had the smallest impact (i.e.

the two lines are closest together) when the self-proclaimed likelihood of a change was small.

A second fact that emerges from the ﬁgure is that the lines in the graph slope upward, meaning

that the ex ante probabilities are correlated with actual actions. The predictions by the subjects

are not particularly accurate, however, as the slopes of the lines are well below the 45 degree

line. A non-trivial share of those who said that they would take a particular action (or non-action)

with certainty did the opposite. Finally, there is some evidence of a bias towards inaction in the

two-month survey data. Since roughly half the participants got heads and half tails, the overall

likelihood of taking the action falls halfway between the two lines in the ﬁgure. For ex ante

probabilities above 30%, the actual rate at which the action is taken is less than was predicted by

the individuals. The gap is most extreme among those who predicted they would make a change

with 100% certainty. In fact, only about 80% of those participants made a change in response to

heads, and less than half actually changed when the coin came up tails.

Figure 6 is identical to Figure 5, except that it shows results for the six-month survey rather

than the two-month survey. The general patterns observed are similar, with one notable difference.

Any evidence of a bias towards inaction has disappeared. Overall, after six months, the action is

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LEVITT HEADS OR TAILS 11

0 20 40 60 80 100

% Participants Who Made a Change

0 20 40 60 80 100

Stated Probability of Taking Action (%)

coin toss says change coin toss says don’t change

Note: Excludes coin flips for questions that do not have clear yes/no actions.

Figure 6

Likelihood of taking action as a function of ex ante stated probabilities, six-month survey

Notes: This ﬁgure presents the percent of participants who make a change by the six-month survey mark according to their stated probability

of changing and the result of the coin ﬂip. The vertical axis reﬂects the percent of respondents who reported making a change. The horizontal

axis groups respondents according to to their stated ex ante likelihoods of making a change. Responses are categorized according to whether

the coin came up heads (make a change) or tails (no change).

taken slightly more frequently than predicted ex ante by the participants.

It should be noted,

however, that the ex ante probabilities refer to the likelihood of making a change within two

months, not within six months.

Figure 7 shows the impact of the coin toss on actions across individual questions. Included

in the ﬁgure are the results for every question with at least 150 responses. The top portion of

the ﬁgure reports ﬁndings for the questions deemed “important;” the bottom part of the ﬁgure

corresponds to “less important” decisions. The values reported in the ﬁgure are the percentage

of all respondents to the two-month survey who report taking the action that corresponds to the

coin outcome. With the exception of “Should I move?” which shows no impact of the coin toss,

for all the other “important” choices between 55% and 60% of the subjects report following the

suggestion of the coin on the two-month survey. Decisions on “less important” questions, as might

be expected, are more affected by the coin toss, with the highest compliance rate on “Should I

break my bad habit” (over 80%), “Should I go on a diet,” “Should I quit drinking,” and “Should I

try online dating.” Supplementary Appendix Figure 1 is identical to Figure 7, except that it shows

results for the six-month survey rather than the two-month survey. The patterns are similar.

All of the numbers presented thus far are raw data. Table 2 demonstrates that the impact of

the coin toss is both robust to the inclusion of covariates and is highly statistically signiﬁcant.

Each column of Table 2 reports the results of a linear probability model in which the dependent

variable is a dichotomous variable corresponding to whether the survey respondent says a change

was made. Included as right-hand side variables are the result of the coin toss, how likely the

12. Supplementary Appendix Figures 2–5 mirror Figures 5 and 6, but divide the sample into “important” and “less

important” questions. The same patterns are present, except that the gap between the lines for “important” questions is

smaller throughout because of the reduced inﬂuence of the coin toss.

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12 REVIEW OF ECONOMIC STUDIES

Should I ask for a raise: 215

Should I start volunteering: 230

Should I quit drinking: 232

Should I grow facial hair: 264

What college should I go to: 267

Should I dye my hair: 327

Should I sign up for a running event: 345

Should I join a gym: 396

What should I major in: 397

Should I try online dating: 424

Should I get a tattoo: 533

Should I break my bad habit: 716

Should I go on a diet: 746

Should I splurge: 1054

Should I have a child: 268

Should I quit smoking: 292

Should I start my own business: 425

Should I move: 479

Should I go back to school: 751

Should I break up: 917

Should I quit my job: 1362

0 10 20 30 40 50 60 70 80 90 100

Percent Following the Coin Toss

Important Less important

Figure 7

Percentage following the coin toss, two-month survey

Notes: This ﬁgure presents the percentage of all respondents to the two-month survey who report taking the action that corresponds to

the result of the coin toss. The questions are listed on the vertical axis and are divided into “important” and “less important” groupings.

Questions with fewer than 150 responses were excluded from this ﬁgure.

subject said they were to change ex ante, a range of demographic variables, whether the subject

opted for the “best two out of three coin toss” option, and an indicator variable for the particular

question for which the coin was tossed. Columns 1 and 4 reﬂect the whole sample. Columns 2 and

5 are the subset of “important” questions, and columns 3 and 6 correspond to the “less important”

questions. The top row is the coefﬁcient on the coin toss coming up heads. For all questions on

the two-month survey, individuals who got heads report being 24.9 percentage points more likely

to have made a change than those who got tails. This result is highly statistically signiﬁcant.

The point estimate at six months is slightly smaller (0.211), implying that some of the impact

of getting heads operates through accelerating the timing of a change. Comparing important

questions (columns 2 and 5) to less important questions (columns 3 and 6), the impact of the

coin toss is only about one-third as large for important questions, but is still highly statistically

signiﬁcant. The coin-ﬂipper’s ex ante assessment of how likely he or she is to make a change is

also highly informative about whether a change is eventually made. If the subjects made unbiased

forecasts, the coefﬁcient on this variable would be one; in actuality it ranges between 0.279 and

0.597. Subjects are better predictors of their own behaviour on important questions than on less

important ones. The only other variable which has a strong and consistent relationship to making

a change is age. Older subjects are less likely to make changes, especially on important questions.

3.2. Is there a causal impact of making a change on happiness and satisfaction with the

decision?

The results above suggest that the outcome of the coin toss affected the behaviour of some

participants. Consequently, the coin toss has the potential to shed light on the question of whether

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LEVITT HEADS OR TAILS 13

TABLE 2

The impact of the coin toss on subsequent behavior

Two months after coin toss Six months after coin toss

All Important Less important All Important Less important

Heads 0.249

∗∗∗

0.111

∗∗∗

0.364

∗∗∗

0.211

∗∗∗

0.112

∗∗∗

0.295

∗∗∗

(0.009) (0.012) (0.012) (0.012) (0.017) (0.016)

Prob of change 0.445

∗∗∗

0.594

∗∗∗

0.279

∗∗∗

0.476

∗∗∗

0.597

∗∗∗

0.341

∗∗∗

(0.017) (0.023) (0.024) (0.023) (0.032) (0.033)

Male 0.012 0.005 0.018 −0.001 −0.001 −0.003

(0.009) (0.013) (0.012) (0.012) (0.018) (0.017)

Age −0.002

∗∗∗

−0.003

∗∗∗

−0.002

∗

−0.002

∗∗

−0.006

∗∗∗

−0.001

(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Married 0.002 −0.014 0.013 −0.014 −0.037 0.015

(0.011) (0.015) (0.016) (0.015) (0.021) (0.021)

US resident 0.033

∗∗∗

0.020 0.039

∗∗

0.008 0.002 0.007

(0.010) (0.014) (0.013) (0.014) (0.020) (0.018)

Black 0.006 −0.029 0.041 −0.046 −0.127

∗

0.042

(0.027) (0.035) (0.041) (0.039) (0.053) (0.055)

Asian 0.004 0.008 −0.012 −0.022 −0.041 −0.023

(0.013) (0.019) (0.018) (0.018) (0.027) (0.025)

Hispanic 0.019 0.007 0.027 −0.011 −0.013 −0.008

(0.017) (0.024) (0.023) (0.023) (0.034) (0.032)

Race-other 0.004 0.002 0.004 0.010 0.051 −0.038

(0.022) (0.

031) (0.030) (0.032) (0.046) (0.043)

4-year college −0.007 −0.013 −0.008 −0.003 0.008 −0.023

(0.010) (0.016) (0.014) (0.015) (0.023) (0.019)

Income > 50K 0.000 −0.015 0.016 −0.008 −0.011 0.003

(0.010) (0.014) (0.014) (0.014) (0.020) (0.019)

Live in a city 0.007 −0.003 0.013 −0.008 −0.003 −0.011

.009) (0.013) (0.012) (0.012) (0.018) (0.016)

Pre-toss happiness −0.002 0.002 −0.003 −0.006 −0.004 −0.006

(0.002) (0.003) (0.003) (0.003) (0.004) (0.005)

Best 2 of 3 ﬂip −0.009 −0.006 −0.010 −0.013 −0.006 −0.019

(0.011) (0.016) (0.014) (0.016) (0.024) (0.021)

Include question indicators Yes Yes Yes Yes Yes Yes

Observations 10,094 4,607 5,487 6,131 2,874 3,257

Notes: This table explores the impact of the coin toss on participants’ subsequent behavior. Each column reports the

results of a linear probability model in which the dependent variable is a dichotomous variable that corresponds to

whether the survey respondent says a change was made. Columns 1 and 4 reﬂect two- and six-month survey responses,

respectively, from the entire sample. Columns 2 and 5 present the same information for the subset of important questions,

and Columns 3 and 6 correspond to the less important questions. Standard errors are reported in parentheses. *, **, ***

denote signiﬁcance at the 5, 1, and 0.1% levels.

making a particular change (e.g. going on a diet) has a positive or negative impact on self-reported

happiness and other proxies for whether the right choice was made. Before the coin toss, those

who will get heads are, in expectation, identical in all respects to those who will get tails. If the

only channel through which the coin toss operates is to increase the likelihood that the particular

change in question is made, then the coin toss can serve as an instrumental variable.

More formally, let H represent happiness, which is inﬂuenced by the choice of whether or

not to take some binary action A. Additionally, let the set of all other factors that inﬂuence H

be captured by some vector of variables X. For instance, relevant X’s might include the salary

of one’s current job, what city one lives in, the level of education, how happily married one is,

etc. Some of these X’s might be observable, but many would not be. A simple comparison of

happiness amongst those who take the action (A=1) versus those who do not (A= 0), i.e.,

E[H|A =1]−E[H|A =0]

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14 REVIEW OF ECONOMIC STUDIES

is unlikely to have a causal interpretation because X is not held constant across those who do and

do not switch jobs. Empirically, those who make a change are statistically signiﬁcantly younger,

less likely to be married, less educated, and lower income than those who do not make a change.

While it is possible to control for these observable factors, it is likely that these two groups differ

substantially on unobservable dimensions as well. A priori, the sign of the bias in OLS is not

obvious.

OLS suffers from a second weakness: a simple comparison of everyone who quits their job

to everyone who does not quit their job does not answer the economically interesting question.

When considering the impact of making a change, it is the marginal actor who is of primary

interest. There are many happily married couples and a few that are so disastrously unhappy that

divorce is certain. A comparison of these two sets of couples tells us nothing about how getting

divorced will affect the happiness of the couples who are truly marginal.

The outcome of the coin toss, used as an instrumental variable, potentially solves both of those

problems. Let C represent an indicator variable corresponding to 1 if the coin comes up heads

and 0 otherwise. Under the assumptions that

E[A|C =1]−E[A|C = 0]=0 and

E[X|C = 1]−E[X|C =0]=0

then a simple Wald estimator provides an estimate of the causal impact of action A on happiness

Wald

E[H]|C = 1−E[H]|C =0

E[A]|C =1−E[A]|C = 0

As long as the only channel through which the coin toss operates is via inﬂuencing the likelihood

that the action in question is taken, then the Wald estimator represents a local average treatment

effect on H of taking the action A, for that group whose behaviour is inﬂuenced by the coin toss,

i.e., the people who are so marginal that they are willing to have their action swayed by a coin

toss.

Turning to the empirical ﬁndings, participants were asked ﬁve questions designed to ascertain

their satisfaction with life as a whole: (1) general level of happiness on a seven-point scale,

(2) how the subject believes friends would rate himself/herself on a seven-point happiness scale,

(3) whether the subject is better off, worse off, or the same relative to the point in time when the

coin was tossed. Two further questions focused more speciﬁcally on the decision for which they

ﬂipped a coin: (4) does the subject feel he/she made the correct decision on the choice for which

the coin was tossed, and (5) if the subject could go back in time, would he/she make the same

decision again. Questions 1 and 2 were asked on both the two-month and six-month surveys.

Question 3 was only asked on the six-month survey, and questions 4 and 5 were only asked at

two months.

Table 3 shows the degree of within-respondent correlation across these various outcomes.

The top and middle panels of Table 3 report results for the two-month and six-month surveys,

respectively. The bottom panel correlates responses across the two-month and six-month surveys.

On the two-month survey, the two questions addressing happiness (i.e. the standard measure of

self-reported happiness and how the subject thinks friends would rate his/her happiness) have a

correlation of 0.666. These two happiness measures are relatively weakly correlated with whether

someone reports having made the correct decision or whether they would have made the same

choice with perfect foresight. At six months, the happiness measures and reporting being better or

worse off now compared to the time of the coin toss are all relatively highly correlated. The bottom

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LEVITT HEADS OR TAILS 15

TABLE 3

Correlations across self-reported outcome measures within and across surveys

Panel A: Two-month survey

Happiness Appear happy Correct decision Perfect foresight

Happiness 1.000

Appear happy 0.666 1.000

Correct decision 0.177 0.117 1.000

Perfect foresight 0.104 0.054 0.278 1.000

Panel B: Six-Month survey

Happiness Appear happy Better/worse off

Happiness 1.000

Appear happy 0.701 1.000

Better/worse off 0.485 0.353 1.000

Panel C: Correlation across the two- and six-month survey

Two-month survey

Happiness Appear happy Correct decision Perfect foresight

Six Month

Happiness 0.465 0.360 0.102 0.031

Appear happy 0.390 0.466 0.066 0.014

Better/worse off 0.143 0.097 0.132 0.036

Notes: Panel A reports pairwise correlations in responses for study participants on the two-month survey. Panel B presents

parallel correlations, but for the six-month survey. Panel C reports correlations across time for participants who completed

both two-month (columns) and six-month surveys (rows). The results in this table include responses for both important

and less important questions.

panel reports correlations between the two-month outcomes (columns) and six-month outcomes

(rows). The direct happiness measures are much more strongly correlated than the others.

Table 4 presents the basic empirical ﬁndings regarding the link between choice and subsequent

life satisfaction outcomes. Columns 1–8 correspond to the two-month survey; columns 9–

14 reﬂect six-month survey responses. For each outcome question asked, we report both

OLS estimates (odd columns) and 2SLS estimates (even columns). The OLS estimates reﬂect

differences in outcomes across those who made a change and those who maintained the status

quo. The OLS estimates are explicitly correlational—to the extent that people who do and do

not make a change differ systematically, the OLS estimates will not have a causal interpretation.

In contrast, under the assumption that the only channel through which the outcome of the coin

toss affects happiness is through the choice made, the instrumental variable estimates in the even

columns capture the causal impact of the action on subsequent outcomes. The ﬁrst panel of the

table presents results aggregated across all the questions. The second and third panels also report

aggregated data, but classifying questions as either “important” or “less important.”

Each entry

in the table is from a different regression. Only the key coefﬁcient of interest is presented in the

13. Limiting Table 3 to the most important questions leads to somewhat higher correlations between the happiness

measures and the questions that more narrowly relate to the decision surrounding the coin toss. This would be expected,

since those decisions carry more signiﬁcant life implications.

14. I limit the sample of questions to those in which the coin ﬂippers are making a choice between a change and the

status quo. This eliminates questions like “Should I attend college A or college B?” Since colleges A and B are different

across people, it is difﬁcult to know how to evaluate such questions. The same is true with the widely varying “create

your own” questions, which are also excluded.

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16 REVIEW OF ECONOMIC STUDIES

TABLE 4

The link between choices and self-reported happiness (all outcomes)

Two months after coin toss Six months after coin toss

Happiness Appear happy Correct decision Perfect foresight Happiness Appear happy Better/worse off

Question OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS

All 0.449 0.041 0.309 0.236 0.173 0.325 0.079 0.235 0.584 0.476 0.442 0.149 0.109 0.167

(0.039) (0.139) (0.038) (0.134) (0.006) (0.024) (0.007) (0.027) (0.048) (0.214) (0.046) (0.207) (0.009) (0.038)

[μ =6.837] [μ =7.161] [μ =0.593] [μ =0.852] [μ =7.059] [μ =7.312] [μ =0.756]

Important 0.782 0.554 0.588 1.070 0.151 0.456 0.034 0.285 1.011 2.153 0

.717 1.418 0.146 0.412

(0.066) (0.495) (0.064) (0.491) (0.010) (0.085) (0.010) (0.082) (0.076) (0.652) (0.073) (0.619) (0.013) (0.112)

[μ =6.566] [μ =6.943] [μ =0.630] [μ =0.892] [μ =6.932] [μ =7.207] [μ =0.777]

Less important 0.213 −0.073 0.111 0.038 0.186 0.290 0.107 0.218 0.190 −0.077 0.168 −0.266 0.075 0.087

(0.047) (0.119) (0.045) (0

.115) (0.008) (0.022) (0.010) (0.027) (0.061) (0.194) (0.059) (0.189) (0.012) (0.038)

[μ =6.999] [μ =7.291] [μ =0.571] [μ =0.828] [μ =7.139] [μ =7.378] [μ =0.743]

Notes: This table presents regression results exploring the link between choices and various metrics of happiness. The ﬁrst column within each metric, “OLS”, shows the extent to which

those who make a change are more or less happy (as measured by that metric) than those who maintain the status quo. The second column is the mean value of the outcome variable. The

third column in each metric, “2SLS”, are the instrumental variable estimates. The left-hand side panels corresponds to the two-month survey; the right-hand side panel corresponds to the

six-month survey. “Happiness” refers to self-reported happiness. “Appear happy” refers to a participant’s guess of how happy their friend would say the participant is. “Correct decision”

equals 1 if the subject feels they made the correct decision two months ago, equals 0 if they feel they made the wrong decision, and .5 otherwise. “Perfect foresight” equals 1 if the subject,

given perfect foresight, would have made the same decision two months ago, equals 0 if they would have made a different decision, and .5 otherwise. “Better/worse off” equals 1 if

the subject thinks they are better off than they were six months ago, equals 0 if they think they are worse off than six months ago, and .5 otherwise. Standard errors are reported in parentheses.

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LEVITT HEADS OR TAILS 17

table. In all speciﬁcations, I include a basic set of control variables mirroring those included in the

ﬁrst-stage regressions reported earlier. Full results are available in an Supplementary Appendix.

For each question, the mean of the outcome variable is displayed in square brackets.

The OLS results carry a positive and statistically signiﬁcant coefﬁcient in all 21 possible cases.

This means that those who make a change report increased happiness/satisfaction with the choice

made relative to those who maintain the status quo. In ﬁve of the seven columns, the coefﬁcient is

larger for important decisions than for less important decisions. The magnitude of the coefﬁcients

is substantial. For instance, on happiness, those who make a change are roughly 0.5 points higher

on a 10 point scale, or nearly one-ﬁfth of a standard deviation. As argued above, however, these

OLS coefﬁcients need not imply causality.

Indeed, the instrumental variable estimates tell a more nuanced story than do the OLS

estimates. At two months, there is only weak evidence that making a change affects the happiness

measures (the only coefﬁcient that is borderline signiﬁcant at the 0.05 level is “appearing happy”

for the important questions), but there are large and highly statistically signiﬁcant impacts on

feeling that the correct decision was made and whether he/she would follow the same path

with perfect foresight. At six months, making a change is associated with large and statistically

signiﬁcant increases on the happiness measures for important questions, but not for less important

questions. On both categories of questions, but especially important ones, the 2SLS estimates

imply that those participants making a change are more likely to be better off relative to six

months ago. For important questions at six months, the 2SLS estimates are two to three times

larger than the OLS estimates.

Table 5 reports results for individual questions, only for the happiness measure. Parallel results

for the other outcome measures are presented in Supplementary Appendix Tables 2–5. The OLS

estimates on the individual questions classiﬁed as important are uniformly positive and often

statistically signiﬁcant. Most, but not all, of the less important questions carry a positive OLS

coefﬁcient. The 2SLS estimates are imprecise. Job quitting and breaking up both carry very large,

positive, and statistically signiﬁcant coefﬁcients at six months. Going on a diet is positive and

statistically signiﬁcant at two months, but has a small and insigniﬁcant impact by six months.

Online dating is positive and signiﬁcant at the 0.10 level at two months, but turns negative by

six months. Splurging is negative and signiﬁcant at the 0.10 level at two months, but has no

discernible impact by six months. Attempting to break a bad habit is negative with a t-stat of 1.5

at both points in time, perhaps because breaking bad habits is so hard. For those subjects who

reported trying to break a bad habit, third parties said the bad habit had actually been broken only

20.93% of the time at two months and only 24.49% at six months.

Table 6 explores the sensitivity of the estimates on the happiness outcome across subsamples

of the data. The columns in Table 6 match those of Table 4. The top row of Table 6 replicates the

full sample results as a baseline. Relatively few strong patterns emerge in Table 6. With respect

to the ﬁrst stage, the most pronounced result that emerges is that (as expected) those who report

being likely to follow the coin toss are, indeed, three to four times more likely to follow the coin

ﬂip. Those who name a friend (signalling greater commitment to the experiment) are also more

likely to follow the coin ﬂip. For the OLS estimates, older subjects have a greater increase in

15. As shown in the Supplementary Appendix, the results for the outcome of how happy one appears is broadly

similar to those for the happiness measure. Stronger results are obtained on the question of whether the correct decision

was made: the 2SLS coefﬁcient is positive and statistically signiﬁcant for breaking up, starting a new business, quitting

smoking, going on a diet, breaking a bad habit, joining a gym, signing up for a running event, quitting drinking, asking

for a raise, and starting to volunteer. On the perfect foresight question, quitting smoking, going on a diet, and breaking a

bad habit are all positive and signiﬁcant, while making a splurge is negative and signiﬁcant. With respect to being better

off relative to six months earlier, breaking up and joining a gym are both positive and signiﬁcant.

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18 REVIEW OF ECONOMIC STUDIES

TABLE 5

The link between choices and self-reported happiness

Two months after coin toss Six months after coin toss

Question 1st stage OLS 2SLS 1st stage OLS 2SLS

All 0.249 0.449 0.041 0.211 0.584 0.476

(0.009) (0.039) (0.139) (0.012) (0.048) (0.214)

Important 0.111 0.782 0.554 0.112 1.011 2.153

(0.012) (0.066) (0.495) (0.017) (0.076) (0.652)

Less important 0.364 0.213 −0.073 0.295 0.190 −0.077

(0.012) (0.047) (0.119) (0.016) (0.061) (0.194)

Should I quit my job 0.059 1.643 0.905 0.070 1.890 5.203

(0.022) (0.127) (1.

774) (0.031) (0.137) (2.313)

Should I break up 0.167 0.356 0.639 0.157 0.278 2.698

(0.030) (0.159) (0.818) (0.040) (0.192) (1.259)

Should I go back to school 0.119 0.595 −0.583 0.133 0.949 0.007

(0.030) (0.168) (1.162) (0.042) (0.190) (1.280)

Should I start my own business 0.168 0.399 0.000 0.077 0.520 5.256

(0.046) (0.185) (1.014) (0.074) (0.307) (5.707)

Should I move 0.004 0.795 56.326 0.087 0.823 3.176

.034) (0.233) (450.597) (0.053) (0.239) (2.775)

Should I quit smoking 0.129 0.160 1.417 0.147 0.313 −1.096

(0.051) (0.225) (1.498) (0.078) (0.304) (1.995)

Should I have a child 0.195 0.471 −1.598 0.193 0.395 −0.450

(0.046) (0.261) (1.083) (0.073) (0.270) (1.288)

Important

Should I propose 0.183 0.362 1.021 −0.041 1.529 −5.125

(0.075) (0.506) (1.862) (0.124) (0.640) (19.881)

Should I splurge 0.303 0.197 −0.555 0.204 0.458 0.163

(0.029) (0.096) (0.312) (0.035) (0.136) (0.594)

Should I go on a diet 0.488 0.413 0.754 0.471 0.146 0.154

(0.032) (0.126) (0.252) (0.044) (0.176) (0.361)

Should I break my bad habit 0.607 0.146 −0.325 0.384 −0.001 −0

.597

(0.030) (0.123) (0.199) (0.044) (0.168) (0.420)

Should I get a tattoo 0.111 0.524 −0.775 0.139 0.669 −1.123

(0.024) (0.255) (1.270) (0.044) (0.260) (1.478)

Should I try online dating 0.465 0.043 0.611 0.269 0.129 −0.429

(0.044) (0.180) (0.377) (0.060) (0.249) (0.846)

Should I join a gym 0.236 0.690 0.369 0.288 0.292 0.970

(0.045) (0.188) (0.686) (0.065) (0.209) (0.671)

Should I dye my hair 0.

315 0.327 0.266 0.148 0.664 1.863

(0.052) (0.188) (0.553) (0.068) (0.261) (1.623)

Should I sign up for a running event 0.265 0.437 −0.790 0.347 −0.234 −0.395

(0.049) (0.192) (0.675) (0.065) (0.216) (0.572)

Should I grow facial hair 0.390 −0.137 −0.275 0.234 −0.726 −0.624

(0.053) (0.209) (0.467) (0.079) (0.334) (1.149)

Should I quit drinking 0.446 −0.309 −0.427 0

.278 −0.083 1.150

(0.059) (0.246) (0.507) (0.087) (0.316) (1.068)

Should I ask for a raise 0.356 −0.037 −0.689 0.425 0.115 −1.116

(0.064) (0.276) (0.712) (0.087) (0.375) (0.833)

Less important

Should I start volunteering 0.303 0.037 −0.135 0.478 0.090 0.129

(0.054) (0.274) (0.714) (0.071) (0.303) (0.510)

Observations 10,094 10,094 10,094 6,131 6,131 6,131

Notes: This table presents regression results exploring the link between choices and self-reported happiness. Columns

1 to 3 correspond to the two-month survey; Columns 4 to 6 correspond to the six-month survey. Columns 1 and 4 are

ﬁrst-stage estimates and describe the degree to which the coin toss affected the action taken. Columns 2 and 5 are OLS

estimates, which show the extent to which those who make a change are more or less happy than those who maintain

the status quo. Columns 3 and 6 are the instrumental variable estimates. The row “Observations” reﬂects the number of

observations in the regression that includes all questions. Questions with fewer than 150 respondents were included in

the ﬁrst panel but are not presented as separate regressions. Standard errors are reported in parentheses.

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LEVITT HEADS OR TAILS 19

TABLE 6

Sensitivity analysis for all questions (dependent = happiness)

Two months after coin toss Six months after coin toss

Question 1st stage OLS 2SLS Observations 1st stage OLS 2SLS Observations

All 0.249 0.449 0.041 10,094 0.211 0.584 0.476 6,131

(0.009) (0.039) (0.139) (0.012) (0.048) (0.214)

Female 0.259 0.537 0.299 4,400 0.212 0.655 0.857 2,697

(0.013) (0.060) (0.207) (0.018) (0.071) (0.315)

Male 0.242 0.382 −0.149 5,694 0.211 0.522 0.230 3,434

(0.011) (0.051) (0.186) (0.016) (0.066) (0.290)

Younger than 30 0.265 0.335 −0.016 5

,777 0.214 0.452 0.547 3,469

(0.011) (0.050) (0.170) (0.016) (0.062) (0.270)

30 or Older 0.225 0.599 0.121 4,317 0.205 0.748 0.433 2,662

(0.013) (0.062) (0.239) (0.018) (0.077) (0.350)

No friend named 0.214 0.427 0.178 6,368 0.185 0.564 0.750 3,752

(0.011) (0.051) (0.208) (0.015) (0.062) (0.315)

Friend named 0.311 0.480 −0.116 3,726 0.251 0.624 0.178 2,

379

(0.014) (0.060) (0.175) (0.019) (0.076) (0.284)

Income below 50K 0.254 0.416 −0.173 5,504 0.201 0.451 0.237 3,289

(0.012) (0.053) (0.188) (0.016) (0.065) (0.304)

Income above 50K 0.242 0.482 0.287 4,590 0.219 0.735 0.729 2,842

(0.012) (0.057) (0.207) (0.017) (0.072) (0.305)

Report unlikely to follow toss 0.097 0.571 −0.220 3,947 0.064 0.786 1.871 2,420

(0.013) (0.070) (0.

598) (0.019) (0.081) (1.187)

Report likely to follow toss 0.344 0.374 0.060 6,125 0.306 0.458 0.295 3,698

(0.011) (0.047) (0.125) (0.015) (0.060) (0.187)

Below average pre-toss happiness 0.222 0.670 0.418 4,357 0.166 0.938 1.009 2,604

(0.013) (0.067) (0.268) (0.018) (0.083) (0.464)

Above average pre-toss happiness 0.271 0.273 −0.170 5, 737 0.246 0.315 0.262 3,527

(0.011) (0.045) (0.148) (0.015) (0.057) (0.216)

Notes: This table presents a sensitivity analysis for all questions. Columns 1 to 3 correspond to the two-month survey; Columns 4-6 correspond to the six-month survey. Columns 1 and

4 are ﬁrst-stage estimates and describe the degree to which the coin toss affected the action taken. Columns 2 and 5 are OLS estimates, which show the extent to which those who make

a change are more or less happy than those who maintain the status quo. Columns 3 and 6 are the instrumental variable estimates. The top row of this table replicates the second row of

Table 5, which serves as the baseline speciﬁcation against which the other results of this table can be compared. The remaining rows categorize the participants by gender, age, and the

like and evaluate the robustness of the results presented in Table 5. Standard errors are reported in parentheses.

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20 REVIEW OF ECONOMIC STUDIES

reported happiness from changes the younger subjects, as do people who reported being unlikely

to follow the coin toss, and whose baseline happiness is low. On the age dimension, this pattern

is interesting because older subjects are less likely to make changes than younger ones. There are

few discernible patterns in the 2SLS comparisons, in large part because of imprecision. There is

weak evidence of higher 2SLS of making a change for women, those with higher incomes, and

those with low pre-experiment happiness.

4. POTENTIAL BIASES

There are many potential biases in the results presented above. The sources of bias fall into three

broad categories: non-representativeness of the subject pool, selective response to the surveys,

and untruthful answers to the survey questions. I tackle these three sets of concerns in turn, in

each instance considering how the biases might affect the ﬁrst-stage estimates (i.e. the willingness

to follow the coin toss), the OLS estimates of the partial correlation between actually making a

change and future happiness, and the instrumental variable estimate of the causal impact of taking

an action on future happiness.

It is important to note, that with respect to the causal impact of

the decision, many stories that might at ﬁrst blush seem likely to bias the results (e.g. happy

respondents are more likely to complete surveys, people who change are more likely to respond)

in fact do not have a ﬁrst-order impact on any of the estimates because there is randomization. In

order for a factor to bias the 2SLS results, it must distort either the numerator or the denominator

in the equation characterizing the Wald estimator above. Factors that do not differentially impact

those who got heads versus tails wash out of that equation. I limit the discussion below to sources

of bias which, if present, will have a ﬁrst-order impact on the estimates. I focus the bias discussion

on the seven-point happiness outcome that is the mainstay in the literature. The underlying logic

extends to all the outcome measures.

Because there is no clear impact of less important decisions

on happiness empirically, I focus the bias analysis on the set of important questions; it is only for

these questions that the biases explored will affect the conclusions of the article.

4.1. Non-representative subject pool

There can be no doubt that the subject pool participating in this study is highly unusual. The

great majority of the recruitment for the study was done through social media associated with

Freakonomics, so participants are likely to both be aware of my prior research and favourably

inclined towards it. Participants tended to be young, male, and highly educated. Secondly, in the

recruiting for the study, I emphasized that I was only interested in people who were having a

difﬁcult time making a life decision. This was true both in the marketing to get subjects to the

website, and in the messaging once subjects arrived at the site. Consequently, individuals who

are on the margin are highly over-represented, intentionally, in the subject pool. Finally, this is a

group which is apparently attracted to the idea of using a coin toss to potentially resolve major

life dilemmas. It is unclear whether that is a trait that is widespread in the population. Finally,

because fans of Freakonomics are over-represented in this group, they might be especially likely

to be responsive to my requests that they should abide by the outcome of the coin toss.

16. While OLS is of less interest than either the ﬁrst stage or instrumental variable estimates, I also discuss the

impact of these biases on the OLS estimates.

17. The only happiness-related outcome asked of the third parties was the standard seven-point happiness question.

That is an important reason why I focus on that question in the bias analysis. I felt the third parties might not be well

situated to answer the other outcomes, although in retrospect I regret the decision not to ask the other questions.

18. For each bias analyzed, a parallel table for less important questions is presented in the appendix for completeness.

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LEVITT HEADS OR TAILS 21

All of these factors suggest that subjects in this sample are far more likely to have been

inﬂuenced by the coin toss than would a randomly drawn sample, i.e., the ﬁrst stage is much

stronger in this group than would be the case more generally.

It is less clear, however, precisely how or why this sample selection would bias the paper’s

estimates of causal effects of decisions. One possible channel would be that the people who

participated in this study are particularly bad at making decisions on their own. So, for instance,

they might tend to have difﬁculty making changes and wait far too long to make changes when it

is obvious that a change needs to be made, and thus accrue large improvements to happiness once

change occurs. However, if that were true I would have expected to see strong positive casual

effects on happiness of making a change in the two-month survey, but that does not occur.

4.2. Selective survey responses

The results presented throughout this article are based on the subset of study participants who

completed surveys. If survey respondents are not a random sample of the coin ﬂippers, a number

of different biases may be introduced, depending on the nature of the selection. The presence

of the third parties identiﬁed by the subjects potentially allow me to assess both the size and

direction of these possible biases.

Selective survey response can potentially affect each of the estimates presented in this article:

whether people follow the coin toss, the OLS estimates of changes on happiness, and the 2SLS

estimates that use the coin toss as an instrument. I deal with these three cases in turn.

4.2.1. Selective response biasing the ﬁrst stage: are those who follow the coin toss

more likely to report?. The measured impact of the coin toss on making a change will be

exaggerated if those who follow the coin toss are more likely to respond to the survey than those

who go against it. Given that the website made it clear to participants that following the coin toss

was important to me, it seems plausible that those who followed the coin toss would be more

likely to respond. Those who make a change might tend to ﬁll out the survey more often if they get

heads, and those who do not make a change might complete the survey with a higher probability

if they get tails.

To measure the actual degree of sample selection on this dimension requires some group of

research subjects for whom I know the action they took, even if they do not complete the survey.

The third parties are critical in this dimension. Conditional on a third party having completed a

questionnaire, I am able to compare the likelihood the subject completes a survey as a function

of whether or not they followed the coin toss (using as a proxy the third party’s assessment of

whether the coin toss was followed). Table 7 does precisely this. Entries in the ﬁrst two columns

of the table are the percentage of subjects who complete a survey, conditional on the third party’s

opinion as to whether the subject followed the coin toss (column 1) or did not follow the toss

19. The effect of this type of selection on estimates of the causal link between making a change and subsequent

happiness is more subtle. As long as the coin toss has some real impact on behavior, then the 2SLS estimates will be a

mixture of that causal, randomization-induced variation and variation induced by the sample selection. If, for instance, the

extra individuals who are induced to respond are (as good as) randomly drawn from the underlying subject distribution,

then the 2SLS will be a mix of the true causal impact and the OLS estimate of the correlation between change and

future happiness. But, it is also possible that the kind of people who are very sensitive to pleasing or disappointing the

experimenter are different, on average, than the other subjects. These subjects might feel guilty after making a change,

and be worse off after the change than other participants, leading the 2SLS estimate to be too small. One could tell equally

compelling stories as to how the bias could go the other direction as well.

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22 REVIEW OF ECONOMIC STUDIES

TABLE 7

Are coin ﬂippers who follow the toss more likely to report?

Third party says coin Third party says coin

ﬂipper followed toss ﬂipper did not follow toss Difference

Two-month survey 0.856 0.807 0.049

(0.017) (0.021) (0.027)

N = 443 N = 357

Six-month survey 0.752 0.681 0.071

(0.028) (0.032) (0.043)

N = 234 N =207

Notes: This table explores whether the survey response rate for important questions is affected by whether the coin ﬂipper

follows the result of the ﬂip. Questions which did not match up between the participant’s and the third-party’s survey

were excluded. Columns 1 and 2 present coin ﬂipper response rates according to whether the third party reported that the

coin ﬂipper did or did not follow the toss. Column 3 reports the resulting difference between the ﬁrst two columns. The

rows divide the results by two- and six-month survey responses. Standard errors are reported in parentheses.

(column 2).

The third column is the difference between the ﬁrst two columns. Standard errors

are in parentheses. The rows of the table correspond to the two-month and six-month surveys,

respectively. Starting in the upper left corner, when the third party completes a two-month survey

and says the action taken matches the coin toss, approximately 86% of the subjects also complete

the survey. The second entry in the top row shows that when the third party says the subject did

not follow the coin toss, reporting rates are roughly 81%, or 5 percentage points lower as shown

in column 3. All the reporting rates are lower at the six-month survey, but the relative patterns are

similar, with those who followed the coin toss 7 percentage points more likely to report. Thus,

there does appear to biased reporting along this dimension. To the extent that third parties have

imperfect knowledge of the actual actions taken by the coin ﬂippers,

the numbers above actually

understate the degree of selection due to attenuation bias.

A fair bit of algebra is required to ascertain the magnitude of the bias implied by the values in

Table 7. Assuming the same degree of sample selection observed among this set of subjects holds

across the whole population and factoring in measurement error as well, back-of-the-envelope

calculations suggest that, for important decisions, about one-ﬁfth of the estimated ﬁrst-stage

impact might be due to this bias on the two-month survey, and 25–30% of the six-month ﬁrst-stage

impact.

4.2.2. Selective response biasing OLS: are happy changers especially likely to report?.

It is possible that those who make a change feel particular pride if things turn out well and greater

shame if the change feels like a mistake ex post. If that is the case, and pride leads to reporting and

shame to non-reporting, then the OLS estimates of the beneﬁt of a change will be exaggerated.

20. Note that I did not ask the third parties whether the coin toss was followed, but rather, what action the subject

took, which I then compare to the recommendation of the coin.

21. One way of measuring whether third parties accurately observe the actions taken is to compare responses of

the coin ﬂippers and the third parties when both complete the survey. For important questions, the two sources agree on

the action taken roughly 90% of the time. For less important questions that number is roughly 83% of the time. Those

numbers represent a lower bound on accurate assessment by third parties because some of the discordance may come

from false reports on the part of the coin ﬂipper.

22. See the Supplementary Appendix for the algebra underlying these calculations.

23. Although it might seem like this type of selection would be very damaging to the interpretation of the 2SLS

results as well, in actuality, it is not likely to affect things much. It has no obvious impact on the ﬁrst-stage estimates,

because the selection is operating on the happiness dimension, not on whether a subject made a change or not. And

because this type of selection affects both those who got heads and those who got tails, the overall level of reported

happiness for those who ﬂipped heads and tails—which determines the numerator of 2SLS – is not obviously biased.

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LEVITT HEADS OR TAILS 23

TABLE 8

Are happy changers especially likely to report?

Third party says Third party says

coin ﬂipper coin ﬂipper did

made a change not make a change Difference

Two-month survey

Third party says coin ﬂipper 0.894 0.832 0.062

is happier than average (0.026) (0.028) (0.038)

N = 142 N = 185

Third party says coin ﬂipper 0.819 0.815 0.004

is less happy than average (0.036) (0.021) (0.041)

N = 116 N = 351

Six-month survey

Third party says coin ﬂipper 0.823 0.688 0.136

is happier than average (0.032) (0.044) (0.054)

N = 147 N = 112

Third party says coin ﬂipper 0.689 0.641 0.047

is less happy than average (0.060) (0.045) (0.075)

N = 61 N =117

Notes: This table explores whether the survey response rate for important questions is higher among happy coin ﬂippers

who make a change. Questions which did not match up between the participant’s and the third-party’s survey were

excluded. The percent of coin ﬂippers who completed a survey is presented in the cells. The ﬁrst two columns divide

responses according to whether the third party reported that the coin ﬂipper made a change. The third column takes the

difference between the ﬁrst two columns. Rows divide the sample by whether the third party reported that the coin ﬂipper’s

happiness was above- or below- average. The two panels reﬂect the two- and six-month survey responses, respectively.

Standard errors are reported in parentheses.

Table 8 explores this possible bias. The top panel of the table corresponds to the two-month

survey; the bottom panel reﬂects the six-month survey. In both cases, the sample is restricted

to those subjects for whom a third party survey is completed. I divide the sample of subjects

according to whether the third party says the subject is above or below the average level of

happiness at the time of the follow-up survey. The columns of the table reﬂect whether the third

party believes that the subject made a change. The entries in the table are the percent of subjects in

that category who complete a survey. The parameter of interest is the difference-in-difference: are

changers disproportionately likely to report when happy relative to non-changers. Focusing ﬁrst

on the top row of the top panel of the table, among subjects judged by their third party to be above

average on happiness, reporting rates are six percentage points higher (89.4% versus 83.2%)

when a change is made than when no change occurred. For subjects who are below average on

happiness in the eyes of the third party, the gap in reporting rates is only 0.4 percentage points.

This suggests that, indeed, there is potentially substantial bias at two months towards “happy

changers” reporting, although the estimates are imprecise so that the t-stat on the difference is

roughly equal to one. The same pattern, even stronger, appears in the bottom panel of the table

which reﬂects the six-month survey. The difference is nearly nine percentage points (although

again with a t-stat close to one because of imprecise estimates).

Back-of-the-envelope calculations imply that these differences in reporting will exaggerate

the OLS estimates of making a change by roughly 10% on the two-month survey and roughly

20% on the six-month survey.

4.2.3. Selective response biasing 2SLS: are happy heads and sad tails especially likely

to report?. It is not obvious why people who get heads would be disproportionately likely

to report if happy, whereas those who get tails would do the opposite. If they do, however, it

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24 REVIEW OF ECONOMIC STUDIES

TABLE 9

Are happy heads and sad tails especially likely to report?

Heads result Tails result Difference

Two-month survey

Third party says coin ﬂipper is happier than average 0.849 0.864 -0.015

(0.026) (0.025) (0.037)

N = 185 N = 184

Third party says coin ﬂipper is less happy than average 0.794 0.823 -0.029

(0.026) (0.023) (0.035)

N = 243 N = 283

Six-month survey

Third party says coin ﬂipper is happier than average 0.771 0.752 0.019

(0.037) (0.036) (0.051)

N = 131 N = 149

Third party says coin ﬂipper is less happy than average 0.663 0.630 0.033

(0.048) (0.049) (0.068)

N = 98 N = 100

Notes: This table explores whether the survey response rate for important questions is higher among happy coin ﬂippers

who ﬂip heads and sad coin ﬂippers who ﬂip tails. The percent of coin ﬂippers who completed a survey is presented in the

cells. The ﬁrst two columns divide responses according to whether the coin ﬂippers ﬂipped heads versus tails. The third

column takes the difference between the ﬁrst two. Rows divide the sample by whether the third party reported that the

coin ﬂipper’s happiness was above- or below- average. The two panels reﬂect the two- and six-month survey responses,

respectively. Standard errors are reported in parentheses.

will greatly bias the 2SLS estimates. Consequently, I explore whether this bias is present in

the data in Table 9.

This table has the same structure as Table 8. The only difference is that

the columns of this table correspond to whether the subject got heads or tails. Once again, the

difference-in-difference is the parameter of interest: if this bias is present, then happy heads should

disproportionately report.

The numbers in Table 9 show no evidence of this form of bias. On both the two-month and

six-month surveys, happy subjects are more likely to respond, but in neither case is there a notable

difference between those who got heads versus those who got tails.

4.3. Untruthful answers from the subjects

In the cases considered above, sample selection is induced by differences in survey response rates

across participants, but the maintained assumption is that the research subjects truthfully answer

the questions that are asked. If respondents lie, this will also affect the estimates. In what follows,

I consider three different types of lies that subjects might tell in follow-up surveys: (1) claiming

to have followed the coin toss when that is not true, (2) exaggerating the degree of happiness after

making a change, and (3) exaggerating how happy they are if they follow the coin toss. I address

these three concerns in turn.

In testing for untruthful answers on the part of subjects, my approach is always the same: I

compare the answers participants give to those of the third parties, under the assumption that the

third parties have no reason to lie, unlike the subjects, who may be embarrassed about their actions

24. One possible story is experimenter demand effects. If sophisticated subjects managed to (correctly) infer that

the purpose of this study was to use the coin toss as a randomizing device to estimate a causal impact of making a change

on future happiness, and additionally guessed (incorrectly) that I was hoping to ﬁnd that change is beneﬁcial, then in

order to please me, they might have differentially reported along these dimensions.

25. Interestingly, for less important questions at six months this bias is present, as shown in Supplementary Appendix

Table 18.

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LEVITT HEADS OR TAILS 25

TABLE 10

Do coin ﬂippers claim to have followed the toss when they have not actually done so? conditional on having a response

from both the coin ﬂipper and third party

Flipper Third party

Two-month survey 0.611 0.572

(0.019) (0.019)

N = 661 N = 661

Six-month survey 0.548 0.557

(0.028) (0.028)

N = 314 N = 314

Notes: This table explores whether coin ﬂippers overreport having followed the toss for important questions. Questions

which did not match up between the participant’s and the third-party’s survey were excluded. Column 1 presents the rate at

which coin ﬂippers report following the toss, while Column 2 presents the same information based on third party reports.

The rows show results from the two- and six-month surveys, respectively. Standard errors are reported in parentheses.

or the consequences of their actions. Not all disagreements imply lying—third parties might not

be fully informed—but to the extent that there are systematic patterns to the disagreements, this

may be a sign of lying.

4.3.1. Do subjects claim to have followed the toss when they have not actually done

so?. Subjects may feel pressure to say that they have followed the coin ﬂip, especially because

I so heavily emphasized the importance of doing so in advance of the coin being ﬂipped.

obvious impact of lying of this sort is that it will exaggerate the ﬁrst-stage estimates. The most

likely consequence for the 2SLS estimates will be to understate the true causal impact of a

change. This is because the 2SLS estimate is the ratio of the difference in happiness of those

ﬂipping heads versus tails over the difference in the probability of making a change across heads

and tails. The numerator is unaffected by this type of lying, but the denominator is exaggeratedly

large, shrinking the 2SLS point estimate. OLS estimates of the value of making a change will also

be biased towards zero because of attenuation bias associated with agents being misclassiﬁed.

Table 10 reports, for the set of subjects for whom I have survey responses from both the

participant and the third party, the rate of coin toss following. Starting in the upper left corner

of the table on the two-month survey, subjects report following the coin toss 61.1% of the time

compared to 57.2% for third parties. The gap is smaller and reverses sign at six months. The

data suggest some possibility that the two-month ﬁrst stage may be exaggerated slightly (with

the 2SLS estimates and OLS consequently understated), but do not support such a story for the

six-month survey.

4.3.2. Do subjects exaggerate how happy they are when they make a change?.

Although subjects do not have any particular reason to lie to the experimenter regarding how

happy they are after a change, it is possible that they lie to themselves for psychological reasons.

For instance, if making a change is costly (e.g. breaking up with a girlfriend), then it may be

difﬁcult for a person ex post to accept that the choice turned out poorly. A person may engage in

self-deception not to have to feel the regret associated with the action. This sort of deception will

have a ﬁrst-order impact of exaggerating the OLS estimates of the impact of making a change. It

will have no impact at all on the ﬁrst-stage estimates, but will somewhat inﬂate the 2SLS estimates

since a greater share of those who ﬂipped heads will have made a change and exaggerated how

happy they are.

26. Note, however, that both the two-month and six-month surveys emphasized that I only cared about the truth.

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26 REVIEW OF ECONOMIC STUDIES

TABLE 11

Do participants who make a change exaggerate how happy they are?

OLS 2M Observations OLS 6M Observations

Coin ﬂipper report of own happiness 0.828 4316 1.059 2708

(0.068) (0.079)

Coin ﬂipper report of own happiness 1.010 690 1.337 323

Conditional on having third party response (0.172) (0.233)

Third party report of coin ﬂipper happiness 1.006 690 1.407 323

Conditional on having coin ﬂipper response (0.180) (0.261)

Notes: This table explores whether coin ﬂippers who made a change are likely to exaggerate how happy they are for

important questions. Questions which did not match up between the participant’s and the third-party’s survey were

excluded. The ﬁrst row presents the coefﬁcent on whether the individual made a change from OLS regressions with the

ﬂipper’s self-reported happiness as the lefthand variable. The second row presents the same information but conditional

on having a response from the third party. The third row replaces the lefthand variable with the third party’s report of the

ﬂipper’s happiness. Columns report OLS results by two- and six-month survey results. Standard errors are reported in

parentheses.

To test for this source of bias, I estimate the basic OLS speciﬁcations of the table, but using the

third party estimate of how happy the subject is as the dependent variable, rather than the subject’s

own report. The assumption underlying this approach is that third parties have no obvious reason

to distort their responses.

I report the results of this exercise in Table 11. For purposes of comparison, the ﬁrst two

rows of the table report results using the subject’s own happiness report. The ﬁrst row replicates

the basic speciﬁcations reported in Table 3 for important questions. The second row is identical

to the ﬁrst row, except that it limits the sample to those subjects for whom there is also a third

party survey. This second row is relevant because that same sample restriction is present in

the third row, which uses third party assessments of happiness as the dependent variable. A

comparison between the three rows shows that restricting the sample somewhat increases the

measured impacts (i.e. making a change is associated with a greater increase in happiness in the

subset of the population where both the subject and the third party respond), but that the results are

not particularly sensitive to whether I use the subject’s own happiness as the outcome or the third

party’s assessment. Consequently, there is little evidence that this bias is present empirically.

4.4. Summary of potential biases

Summarizing the discussion above, it is likely that the ﬁrst-stage estimates in this paper are

exaggerated, both because of the selected sample participating in this study and reporting biases.

There is also evidence that differential reporting may bias upward the OLS estimates of making

a change on subsequent happiness by 10–20%. There is no obvious evidence for strong bias in

the 2SLS, nor does it seem to be the case that lying (as opposed to differential reporting rates) is

biasing the various estimates.

27. It is possible that the coin ﬂipper misrepresents his or her happiness not just to the experimenter, but also to

friends and family, in which case their assessment might also be biased. If that is the case, than using third party evaluations

may not fully address the bias due to misrepresentation.

28. In principle, I can carry out the same exercise using the third party happiness reports as the dependent variable

in the 2SLS estimates to test whether misreporting of happiness might bias the 2SLS estimates. In practice, however, the

estimates are so imprecise that they are uninformative. The 2SLS standard errors when I restrict the sample to cases where

both the subject and the third party report are roughly one in the two month survey and nearly three in the three-month

survey. Thus, no reasonable hypothesis can be rejected by the data.

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LEVITT HEADS OR TAILS 27

5. CONCLUSION

The results of this article suggest the presence of a substantial bias against making changes

when it comes to important life decisions, as evidenced by that fact that those who do make a

change report being no worse off after two months and much better off six months later. Stronger

results, with the same implication, are found using related outcome measures, such as whether the

participant is better off today than six months ago, whether he/she made the correct decision, and

whether he/she would stick to that decision in a perfect foresight world. The results of this article

are, of course, merely suggestive. If the results are correct, then admonitions such as “winners

never quit and quitters never win,” while well-meaning, may actually be extremely poor advice.

A reasonable question to ask is why so many study participants were willing to let major life

decisions be dictated by a coin toss. One simple explanation is that many participants were truly

on the margin. Consequently, very small beneﬁts (e.g. furthering scientiﬁc knowledge, a desire

to please the experimenter who made it clear that I hoped they would follow the coin toss) were

sufﬁcient to sway behaviour. Alternatively, more complex mechanisms such as regret aversion

(Fehr et al., 2013) may be responsible. If regret is a product of decisions that one has control over,

giving up control to a randomizing device may, lessen possible regret, thus enhancing expected

utility.

A large literature in psychology focuses on the “hedonic treadmill,” which posits that happiness

mean reverts to a relatively ﬁxed, individual-speciﬁc set point in the long run (see, for instance,

Lyubomirski, 2010). The results of my study suggest that this phenomenon does not appear to

operate strongly at a six-month time horizon, at least for the sample I observe. Unfortunately,

because the results and purpose of the coin ﬂipping experiment are now public, it would be

difﬁcult to obtain reliable happiness responses from my participants in the future.

Empirical economists are increasingly moving from a role of consumers of data to producers

of data. This article represents an extreme expression of that trend. It is difﬁcult to imagine how

one could hope to answer the questions addressed in this article without generating the data. As

the prominence of social media grows, opportunities to recruit subject pools for randomized ﬁeld

experiments from broad swaths of the population will only increase.

Acknowledgments. I would like to thank Gary Becker, Stephen Dubner, Henry Farber, Lawrence Katz, Alan Krueger,

John List, Susanne Neckermann, Chad Syverson, two anonymous referees, and the editor Nicola Gennaioli for valuable

comments. Erin Robertson did an amazing job spearheading the project. Anya Marchenko, Ellen Murphy, and Mattie

Toma provided outstanding research assistance.

Supplementary Data

Supplementary data are available at Review of Economic Studies online.

REFERENCES

ANDERSON, E. and SIMESTER, D. (2003), “Effects of $9 Price Endings on Retail Sales: Evidence from Field

Experiments”, Quantitative Marketing and Economics, 1, 93–110.

BECKER, S. and BROWNSON, O. (1964), “What Price Ambiguity? Or the Role of Ambiguity in Decision-Making”,

Journal of Political Economy, 72, 62–73.

BERTRAND, M. and MULLAINATHAN, S. (2001), “Do People Mean What They Say? Implications for Subjective

Survey Data”, American Economic Review, 91, 67–72.

BOWLES, S., BOYD, R. CAMERER, C., et al. (2001), “In Search of Homo Economicus: Behavioral Experiments in 15

Small-Scale Societies”, American Economic Review, 91, 73–78.

CAMERER, C. (1995), “Individual Decision Making”, in Kagel, J. and Roth, A. (eds) The Handbook of Experimental

Economics (Princeton, NJ: Princeton University Press).

CHAUDHURI, A (2011), “Sustaining Cooperation in Laboratory Public Goods Experiments: A Selective Survey of the

Literature”, Experimental Economics, 14, 47–83.

DELLAVIGNA, S. (2009), “Psychology and Economics: Evidence from the Field”, Journal of Economic Literature, 47,

315–372.

Downloaded from https://academic.oup.com/restud/advance-article-abstract/doi/10.1093/restud/rdaa016/5834495 by guest on 31 May 2020

28 REVIEW OF ECONOMIC STUDIES

DI TELLA, R. and MACCULLOCH, R. (2006), “Some Uses of Happiness Data in Economics”, Journal of Economic

Perspectives, 20, 25–46.

DOLAN, P., PEASGOOD, T. and WHITE, M. (2008), “Do We Really Know What Makes Us Happy? A Review of the

Economic Literature on the Factors Associated with Subjective Well-being”, Journal of Economic Psychology, 29,

94–122.

EASTERLIN, R. A. (1974), “Does Economic Growth Improve the Human Lot? Some Empirical Evidence”, in David, P.

and Rederm, M. (eds) Nations and Households in Economic Growth (New York and London: Academic Press).

FALK, A. (2007), “Gift Exchange in the Field”, Econometrica, 75, 1501–1511.

FOX, C. and TVERSKY, A. (1995), “Ambiguity Aversion and Comparative Ignorance”, The Quarterly Journal of

Economics, 110, 585–603.

FREY, B. and STUTZER, A. (2002), “The Economics of Happiness”, World Economics, 3, 1–17.

GNEEZY, U., IMAS, I. and LIST, J. (2015), “Estimating Individual Ambiguity Aversion: A Simple Approach” (NBER

Working Paper No. 20982).

GNEEZY, U. and LIST, J. (2006), “Putting Behavioral Economics to Work: Testing for Gift Exchange in Labor Markets

Using Field Experiments”, Econometrica, 74, 1365–1384.

GRUBER, J. and MULLAINATHAN, S. (2005), “Do Cigarette Taxes Make Smokers Happier”, The B.E. Journal of

Economic Analysis & Policy, 5, 1–45.

KAHNEMAN, D., KNETCH, J. L.and THALER, R. (1991), “Anomalies: The Endowment Effect, Loss Aversion, and

Status Quo Bias”, Journal of Economic Perspectives, 5, 193–206.

KAHNEMAN, D. and KRUEGER, A. (2006), “Developments in the Measurement of Subjective Well-being”, Journal

of Economic Perspectives, 20, 3–24.

KALMIJN, M., LIEFBROER, A., SOONS, J. (2009), “The Long-Term Consequences of Relationship Formation for

Subjective Well-Being”, Journal of Marriage and Family, 71, 1254–1270.

LEVITT, S. and DUBNER, S. (2014), Think Like a Freak. New York: William Morris.

LEVITT, S. and LIST, J. (2009), “Field Experiments in Economics: The Past, the Present, and the Future”, European

Economic Review, 53, 1–18.

LIST, J. (2002), “Preference Reversals of a Different Kind: The “More Is Less” Phenomenon”, American Economic

Review, 92, 1636–1643.

LYUBOMIRSKI, S. (2010), “Hedonic Adaptation to Positive and Negative Experiences”, in Folkman, S. (ed.) The Oxford

Handbook of Stress, Health, and Coping (Oxford: Oxford University Press).

MEIER, S. and STUTZER, A. (2007), “Is Volunteering Rewarding in Itself?”, Economica, 75, 39–59.

PEDERSEN, P. and SCHMIDT, T (2014), “Life Events and Subjective Well-Being: The Case of Having Children” (IZA

Discussion Paper No. 8207).

SAMUELSON, W. and ZECKHAUSER, R. (1998), “Status Quo Bias in Decisionmaking”, Journal of Risk and

Uncertainty, 1, 7–59.

SMITH, V. L. (1994), “Economics in the Laboratory”, Journal of Economic Perspectives, 8

, 113–131.

Downloaded from https://academic.oup.com/restud/advance-article-abstract/doi/10.1093/restud/rdaa016/5834495 by guest on 31 May 2020

Discussion

Here is the website, which is still up: https://www.freakonomicsexperiments.com/ ![Imgur](https://imgur.com/olFcjSa.png) "In contrast, under the assumption that the only channel through which the outcome of the coin toss affects happiness is through the choice made, the instrumental variable estimates in the even columns capture the causal impact of the action on subsequent outcomes." For more background on instrumental variables, which generally allow for this causal interpretation, and are widely employed in randomized control trials: https://en.wikipedia.org/wiki/Instrumental_variables_estimation This is key to the study design and the validity of the results: "It should be noted, however, that I intentionally made it difﬁcult for subjects to determine the precise objective of the study. Subjects were told that their participation would “help us gain important insights into decision-making.”The initial survey, prior to the coin toss, asked many questions about motivations and feelings surrounding the decision." "The coin-ﬂipper’s ex ante assessment of how likely he or she is to make a change is also highly informative about whether a change is eventually made. If the subjects made unbiased forecasts, the coefﬁcient on this variable would be one; in actuality it ranges between 0.279 and 0.597. Subjects are better predictors of their own behaviour on important questions than on less important ones. The only other variable which has a strong and consistent relationship to making a change is age. Older subjects are less likely to make changes, especially on important questions." "Summarizing the discussion above, it is likely that the ﬁrst-stage estimates in this paper are exaggerated, both because of the selected sample participating in this study and reporting biases.There is also evidence that differential reporting may bias upward the OLS estimates of making a change on subsequent happiness by 10–20%. There is no obvious evidence for strong bias in the 2SLS, nor does it seem to be the case that lying (as opposed to differential reporting rates) is biasing the various estimates." Status quo bias: an emotional bias; a preference for the current state of affairs. The current baseline (or status quo) is taken as a reference point, and any change from that baseline is perceived as a loss. Source: https://en.wikipedia.org/wiki/Status_quo_bias This is an important, surprising discovery: "Those who were instructed by the coin toss to make a change were both more likely to make the change (as noted above) and, on average, report greater happiness on the follow-up surveys. This ﬁnding is inconsistent with expected utility theory; those who are on the margin should, on average, be equally well off regardless of the decision they make." Prospect theory is a theory of behavioral economics/finance developed by Daniel Kahneman and Amos Tversky in 1979. Prospect theory shows how people decide between alternatives that involve risk and uncertainty, and it describes how individuals assess their loss and gain perspectives asymmetrically. Find an annotated version of Prospect theory here: https://fermatslibrary.com/s/prospect-theory-an-analysis-of-decision-under-risk Expected utility is one of the first theories of decision making and was first proposed by Daniel Bernoulli in 1738. In particular, Bernoulli proposed a modification on one of the oldest theories of decision making under risk: expected value. The expected value of an outcome is the sum of each individual outcomes payoff adjusted for its probability or risk, Bernoulli noticed a systematic bias in expected value. In particular, Bernoulli noticed that the value of payoffs is subjective and that the normative decision rule of expected value does not account for the value that individuals attach to payoffs. Bernoulli proposed the utility function and built a model where individuals attempt to maximize utility in their decision making. Steven Levitt is an American economist, and the coauthor of Freakonomics and its sequels. He won the 2003 John Bates Clark Medal for his work in the field of crime, and is currently a professor of economics at the University of Chicago. Source: https://en.wikipedia.org/wiki/Steven_Levitt This is indeed a large potential bias... this study will need to be replicated in different populations, and any generalizations should be made cautiously. Really interesting finding: "there appears to be a causal impact of making a change on how satisﬁed the subject is ex post with the decision. Those who were instructed to make a change by the coin toss are substantially more likely to report that they made the correct decision and that they would make the same decision again if given the chance."

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