Sometimes even economists get mixed up about the sunk cost fallacy

In an interesting article in The Conversation this week, Aaron Nicholas (Deakin University) wrote:

Have you ever encountered a subpar hotel breakfast while on holiday? You don’t really like the food choices on offer, but since you already paid for the meal as part of your booking, you force yourself to eat something anyway rather than go down the road to a cafe.

Economists and social scientists argue that such behaviour can happen due to the “sunk cost fallacy” – an inability to ignore costs that have already been spent and can’t be recovered. In the hotel breakfast example, the sunk cost is the price you paid for the hotel package: at the time of deciding where to eat breakfast, such costs are unrecoverable and should therefore be ignored.

The problem is, the example of the subpar hotel breakfast doesn't necessarily illustrate the sunk cost fallacy at all. At least, just because some people choose the subpar hotel breakfast, it doesn't mean that those people have fallen victim to the sunk cost fallacy.

To see why, let's first consider what a purely rational decision-maker might do. A purely rational decision-maker considers only the costs and benefits of each of the alternatives available to them. As Nicholas notes, sunk costs are unrecoverable and therefore ignored. In the case of the subpar hotel breakfast, the benefits of the hotel breakfast are low, but the costs are effectively zero (since it has already been paid for). The benefits are greater than the costs. However, going down the road to a cafe has greater benefits (better food), but also comes with greater costs (the time and effort to get to the cafe, plus the monetary cost of the breakfast). It's not certain that the net benefit (benefits minus costs) would be greater for the cafe breakfast than for the hotel breakfast, even for a purely rational decision-maker. So, just because someone chooses the subpar hotel breakfast, it doesn't mean that they have fallen victim to the sunk cost fallacy.

Now consider a quasi-rational decision-maker. Quasi-rational decision-makers are loss averse (they value losses greater than monetarily-equivalent gains), and engage in mental accounting. Mental accounting suggests that we keep 'mental accounts' associated with different activities. Quasi-rational decision-makers put all of the costs and benefits associated with the activity into that mental account, and when they stop that activity, they close the mental account associated with it. And since they are loss averse, they are reluctant to close an account where the costs are greater than the benefits. In the case of the hotel breakfast, the mental account for breakfast has the cost of the breakfast in it (even though it is a sunk cost), so a quasi-rational decision-maker is more likely to stay for the subpar hotel breakfast than a purely rational decision-maker, because the quasi-rational decision-maker wants benefits (however modest) to offset the cost of the breakfast before they close the breakfast mental account. It is mental accounting (and loss aversion) that makes quasi-rational decision-makers susceptible to the sunk cost fallacy.

Taken altogether, this suggests that quasi-rational decision-makers are more likely to stay for the subpar hotel breakfast. It does not mean that staying for the subpar hotel breakfast means that a decision-maker is quasi-rational (and falling victim to the sunk cost fallacy), since a purely rational decision-maker could decide on the subpar hotel breakfast as their better option, even ignoring the sunk cost.

The other examples that Nicholas uses are better. The best examples of the sunk cost fallacy involve decision-makers continuing an activity they have started, even though the remaining costs will outweigh the remaining benefits. The sunk cost fallacy (arising from mental accounting and loss aversion) keeps us in unpromising projects for too long, as well as unhappy relationships, and bad jobs. 

Most real-world decision-makers are susceptible to the sunk cost fallacy. That's why it's sometimes more notable when we see decision-makers not falling victim to it (see here and here, for example). However, when economists explain sunk costs and the sunk cost fallacy, we need to make sure that we are using examples that unambiguously illustrate the problem.

Drip pricing and quasi-rational behaviour

In an interesting article in The Conversation last month, Ralf Steinhauser (Australian National University) explains the idea of drip pricing:

You see a fantastic offer, like a hotel room. You decide to book. Then it turns out there is a service fee. Then a cleaning fee. Then a few other extra costs. By the time you pay the final price, it is no longer the fantastic offer you thought.

Welcome to the world of drip pricing – the practice of advertising something at an attractive headline price and then, once you’ve committed to the purchase process, hitting you with unavoidable extra fees that are incrementally disclosed, or “dripped”.

Drip pricing – a type of “junk fee” – is notorious in event and travel ticketing, and is creeping into other areas, such as movie tickets. My daughter, for example, was surprised to find her ticket to the Barbie movie had a “booking fee”, increasing the cost of her ticket by 13%.

Steinhauser then goes on to explain why consumers are susceptible to drip pricing, blaming present bias and loss aversion:

In the case of booking that hotel room, you could abandon the transaction and look for something cheaper once the extra charges become apparent. But there’s a good chance you won’t, due to the effort and time involved.

This is where the trap lies.

Resistance to the idea of starting the search all over again is not simply a matter of laziness or indecision. There’s a profound psychological mechanism at play here, called a present-bias preference – that we value things immediately in front of us more than things more distant in the future...

Beyond the challenge of starting over, there’s another subtle force at work when it comes to our spending decisions. Drip pricing doesn’t just capitalise on our desire for immediate rewards; it also plays on our innate fear of losing out.

This second psychological phenomenon that drip pricing exploits is known as loss aversion – that we feel more pain from losing something than pleasure from gaining the same thing...

Imagine you’re booking tickets for a show. Initially attracted by the observed headline price, you are now presented with different seating categories. Seeing the “VIP” are within your budget, you decide to splurge.

But then, during the checkout process, the drip of extra costs begins. You realise you could have opted for lower-category seats and stayed within your budget. But by this stage you’ve already changed your expectation and imagined yourself enjoying the show from those nice seats.

Going back and booking cheaper seats will feel like a loss.

In my view, Steinhauser is absolutely correct that drip pricing exploits consumers' quasi-rationality (that is, that consumers are subject to biases in their decision-making). However, he is not fully correct about the sources of the quasi-rational behaviour.

First, present bias would tend to work against drip pricing, because (using Steinhauser's example) consumers are weighing up the cost of the tickets (which they face now) against the benefit of the concert they will attend (which is in the future). If consumers weigh the present more heavily than the future, then the costs weigh more heavily than the benefits, which would work against the consumers paying the junk fees.

Second, Steinhauser is correct about loss aversion, but for the wrong reason. Nobel Prize winner Richard Thaler noted that people engage in mental accounting related to particular decisions. People like to keep their mental accounts in positive balances, and are reluctant to give up on something if the mental account has a negative balance, because that would result in 'booking a loss'. Since people are loss averse, they will only want to close mental accounts that have a positive balance.

What does that mean for a consumer buying a concert ticket? They have spent some time and effort selecting their seats and completing most of the booking process. That puts their mental account for the concert into a negative balance. So, facing a small additional fee seems like a good deal, when compared to closing the mental account with a loss. The consumer pays the fee. They don't necessarily feel happy about it, but it is better than the alternative. The only way to get their mental account for the concert into a positive balance is to attend the concert.

A related way of thinking about the process of buying concert tickets with junk fees is the concept of switching costs. Switching costs are the costs of switching from one seller to another, or from one good or service to another. In this case, for a quasi-rational consumer who is running a mental account for the concert, giving up on buying the ticket when they are faced with the junk fees creates a switching cost - the loss in their mental account. When consumers face high switching costs, they can become locked in to buying a product. The seller can then take advantage of their locked in consumers by increasing the price (which is what the junk fees effectively do).

If you are a strong believer in the tenets of neoclassical economics, then the consumer response to drip pricing seems somewhat at odds with rational behaviour. For a purely rational consumer, the time and effort spent on the booking process up to the time that they face the additional of the junk fees is a sunk cost. It shouldn't affect the decision about whether to proceed with buying the ticket or not, because that decision should depend only on the costs and benefits of attending the concert. If the junk fees increase the costs of attending the concert to such an extent that they are higher than the benefits of attending the concert, a purely rational consumer would stop the ticket-buying process at that point. However, a quasi-rational consumer, who is running a mental account for the concert, would be more likely to proceed with the purchase even when presented with the junk fees.

So, overall, drip pricing leads to more sales if consumers are quasi-rational than if consumers are purely rational. It's lucky (and very profitable) for the ticket sellers that so many of us are not purely rational consumers.

The Victorian government shows they can avoid the sunk cost fallacy

You may have seen the news last week. The Victorian state government in Australia has cancelled the 2026 Commonwealth Games. As Jack Anderson (University of Melbourne) wrote in The Conversation:

The cancellation of the 2026 Commonwealth Games by Victorian Premier Daniel Andrews took all stakeholders – Commonwealth Games officials, athletes, sports bodies and local government officials – by surprise.

The Andrews administration will likely deal with the political fallout from not honouring its contract to host the games, but there may be legal and reputational damage ahead.

The decision was a surprise, but not for the reason many people think. Once a government has decided to hold a big event, they will usually be loath to change their mind. Behavioural economics suggests that quasi-rational decision-makers are susceptible to the sunk cost fallacy. Sunk costs are costs that have already occurred and that cannot be recovered, like the millions the Victorian government has already spent on the Commonwealth Games. Sunk costs should not affect decisions because, regardless of what the decision-maker chooses to do, those sunk costs have already been incurred. Any money that the government has already spent on the Games has already been spent, and will have been spent regardless of whether or not the Commonwealth Games goes ahead. So, at this point, the government should make the decision about whether to go ahead with the Games should be made on the basis of costs and benefits that are to come. Essentially, the Victorian government weighed up the billions of dollars they would face in the future against the benefits from hosting the Games. The costs must have outweighed the benefits.

The sunk cost fallacy typically occurs because of mental accounting, which suggests that we keep 'mental accounts' associated with different activities. We put all of the costs and benefits associated with the activity into that mental account, and when we stop that activity, we close the mental account associated with it. At that point, if the mental account has more costs in it than benefits, it counts as a loss. And because we are loss averse, we try to avoid closing the account. If the Victorian government were affected by mental accounting, they may have still gone ahead with the Games, trying their hardest to avoid banking a loss on the Games. Mental accounting is responsible for keeping us in unpromising projects for too long, as well as unhappy relationships, and bad jobs.

So, the Victorian government were not affected by mental accounting (just like Warner Bros, when they cancelled the release of the Batgirl movie). Even the prospect of bad publicity (of which there has been plenty, and which must have been anticipated) was not enough to dissuade them from the cancellation.

The cancellation of Batgirl shows Warner Bros are not fooled by mental accounting

The Guardian reported earlier this week:

The previously announced Batgirl film starring In the Heights actor Leslie Grace, Michael Keaton and Brendan Fraser will not be released at all, Warner Bros Discovery has unexpectedly announced, despite shooting already being completed and the film being in post-production.

Directed by Ms Marvel directors Adil El Arbi and Bilall Fallah, the film was initially greenlit in 2021 as part of a wider move at Warner Bros to create feature films specifically for the streaming service HBO Max. But the studio confirmed on Tuesday that the film would never get any release, either theatrically or on HBO Max...

The Hollywood Reporter said Batgirl’s budget was a factor in the decision, having risen to nearly $90m (£74.1m, A$130m) due to costs relating to it being shot during the Covid-19 pandemic. While the budget is lower than the average DC superhero film, it was reportedly decided that it did not have the “spectacle that audiences have come to expect from DC fare” and would not recoup its losses from being released.

However, the New York Post, which broke the story on Tuesday, cited an unnamed source who said the budget had actually exceeded $100m and that the film had performed so poorly during early test screenings that Warner Bros decided to cut its losses.

“They think an unspeakable Batgirl is going to be irredeemable,” the source told the New York Post.

Behavioural economics suggests that quasi-rational people are susceptible to the sunk cost fallacy. Sunk costs are costs that have already occurred and that cannot be recovered, like the US$90 million or more already spent on the Batgirl movie. Sunk costs should not affect decisions because, regardless of what the decision-maker chooses to do, those sunk costs have already been incurred. Since the US$90 million has already been spent, it has been spent if the movie is released, and it has been spent if the movie is not released. So, at the point of post-production the decision about whether to go ahead and release the movie should be made on the basis of costs and benefits that are to come. Essentially, Warner Bros was weighing up the further costs they would face (on additional post-production, marketing, etc.) against the benefits they would receive (box office receipts, and other revenue). The costs must have outweighed the benefits.

The sunk cost fallacy typically occurs because of mental accounting, which suggests that we keep 'mental accounts' associated with different activities. We put all of the costs and benefits associated with the activity into that mental account, and when we stop that activity, we close the mental account associated with it. At that point, if the mental account has more costs in it than benefits, it counts as a loss. And because we are loss averse, we try to avoid closing the account. If Warner Bros were affected by mental accounting, they may have released the movie anyway, trying their hardest to avoid banking a loss on the movie. Mental accounting is responsible for keeping us in unpromising projects for too long, as well as unhappy relationships, and bad jobs.

So, Warner Bros were not affected by mental accounting, and it appears that the viewing public will be saved from a terrible Batgirl movie. It's a pity that didn't happen to the truly horrible Moonfall (my movie ticket was a sunk cost on that one), or everyone's favourite superhero move to hate, Green Lantern.

[HT: Mark from my ECONS102 class]

Autism vs. the sunk cost fallacy

One of the many ways in which 'real world' decision-makers fall short of the purely rational ideal is that decision-makers in the real world are subject to the sunk cost fallacy. Sunk costs are costs that have already occurred and that cannot be recovered. In his book Misbehaving: The Making of Behavioral Economics (which I reviewed here), the 2017 Nobel Prize winner Richard Thaler argues that the sunk cost fallacy arises because of a combination of loss aversion and mental accounting.

In general, people are loss averse because we value losses more than we value equivalent gains. Gaining $10 makes us happier, but losing $10 makes us unhappier to a greater extent than gaining $10 makes us happier. So, we generally try to avoid losses.

Mental accounting suggests that we keep 'mental accounts' associated with different activities. We put all of the costs and benefits associated with the activity into that mental account, and when we stop that activity, we close the mental account associated with it. At that point, if the mental account has more costs in it than benefits, it counts as a loss. And because we are loss averse, we try to avoid closing the account.

Part of the issue with susceptibility to the sunk cost fallacy is that real world decision-makers are thinking emotionally. If they were dispassionate logical-thinking robots, they wouldn't take sunk costs into account in their decisions. But although decision-makers are not all equally susceptible to the sunk cost fallacy, the costs in terms of sub-optimal decision-making may be substantial. So, studies of the sunk cost fallacy in different population groups are important.

One interesting new study by Nicky Rogge (KU Leuven), published in the Journal of Economic Psychology (sorry I don't see an ungated version online), looks at the difference between people with autism spectrum disorder (ASD) and neurotypical people. Rogge first reminds us of 'Dual Process Theory', which posits that:

...reasoning and decision making can be described as a function of two processing or reasoning systems: the intuitive reasoning system and the deliberative analytic-logical reasoning system. The intuitive reasoning system involves an implicit, unconscious reasoning process that is independent of cognitive ability and working memory, and that is rapid and automatic. The deliberative analytic-logical reasoning system involves an explicit (controlled), conscious reasoning process that depends strongly on cognitive ability and working memory, and is slower and more effortful.

Some of you may recognise this as the 'System 1' and 'System 2' thinking processes that 2002 Nobel Prize winner Daniel Kahneman outlined in his book Thinking, Fast and Slow. Rogge then outlines some of the literature on thinking processes among people with ASD, and notes that:

Brosnan et al. (2016, 2017) and Lewton et al. (2019) argued that the pattern of reasoning and decision-making styles adopted by individuals with ASD is more biased away from intuitive reasoning and more towards deliberative reasoning styles, as compared to what is observed in neurotypicals.

That suggests that, to the extent that the sunk cost fallacy arises from decision processes occurring within the intuitive 'System 1', that people with ASD may be less susceptible to the sunk cost fallacy (as well as potentially other heuristics and biases that together define 'quasi-rational' behaviour).

Rogge then tests a number of hypotheses related to this, using data collected from an online survey of 332 people from Belgium, 187 of whom self-reported as having been diagnosed with ASD, while 34 reported a strong suspicion of ASD but no diagnosis, and 111 'neurotypicals', who reported no ASD. Rogge doesn't just take the research participants' word for it - he administers to AQ-Short test to derive a quantitative measure of where each research participant (self-reported ASD or neurotypical) fits on a scale (the AQ-10 scale). The survey asked participants about six problems, where:

Each of the six sunk-cost decision tasks presents a hypothetical decision scenario which involves a sunk cost...

For each decision task, research participants rated how relatively likely they were to choose between two options, one of which involved accepting a sunk cost. Rogge then uses the responses from the six decision tasks to derive a score for susceptibility to the sunk cost fallacy. He also knows how long each research participant spent on each decision task, which he uses to proxy for how thoughtfully they considered the options (i.e. how much 'System 2' thinking was involved). Then, he uses propensity score matching to create a matched sample of research participants with ASD and neurotypicals, and analyses the differences in sunk cost score between the groups. He finds that:

...(a) the sunk cost did impact the decision made by the average participant across the six sunk-cost decision tasks... (b) participants with ASD were generally less subject to the sunk-cost bias as compared to neurotypical participants... (c) participants with ASD and more autistic traits (as measured by the AQ10-score) were generally less subject to the sunk-cost bias as compared to individuals with ASD and less autistic traits (and neurotypical individuals)... (d) the time to complete a sunk-cost decision task related negatively to the sunk-cost bias for participants with ASD... and (e) this negative relation between time spent in the decision task and the sunk-cost bias was more pronounced for individuals with more autistic traits as compared to their counterparts with less autistic traits (both ASD and neurotypical)...

So, score a win for people with ASD. They are less susceptible to the sunk cost fallacy, and consistent with that, they spend more time on the decision tasks than neurotypicals do. That doesn't answer the bigger question of 'why', but it does demonstrate that people with ASD have more rational decision-making processes in this context.

Of course, there are some problems with this study, and it needs replication in other samples. The biggest issue is the nature of the hypothetical scenarios. It would be interesting to see if similar results would be found in an experimental setting, rather than in an online survey. Also, this type of study could easily be extended, as Rogge notes in his conclusion:

It would be interesting for future studies to measure and compare the sunk-cost bias of individuals with ASD and neurotypical individuals in real-world decision scenarios involving sunk costs and explore the role of, for instance, social and communication skills in sunk-cost bias. Another research question consists in exploring whether individuals with ASD take hypothetical and experimental tasks more seriously and, if so, whether this explains for why they make more consistent and less biased decisions than neurotypical individuals.

Both of those options would be worthwhile additions to the growing research literature on decision-making among people with ASD.

Of mice and men

When considering a decision about whether to do something or not, we are thinking about the future. For example, say that we are managing a firm that has an ongoing project and we are considering whether to persist with the project or to stop the project and divert the resources to an alternative project. In this case, we should only be considering the future. Costs (and benefits) that have already occurred and that cannot be recovered are sunk costs. They should not affect our decision-making. And yet, so often they do.

Richard Thaler, the 2017 Nobel Prize winner whose work is neatly summarised in his book Misbehaving: The Making of Behavioral Economics (which I reviewed here), says that the sunk cost fallacy arises because of a combination of loss aversion and mental accounting.

In general, people are loss averse because we value losses more than we value equivalent gains. Gaining $10 makes us happier, but losing $10 makes us unhappier to a greater extent than gaining $10 makes us happier. So, we generally try to avoid losses.

Mental accounting suggests that we keep 'mental accounts' associated with different activities. We put all of the costs and benefits associated with the activity into that mental account, and when we stop that activity, we close the mental account associated with it. But if the mental account has more costs in it than benefits, it is a loss. And because we are loss averse, we try to avoid closing the account.

So, you can see why a manager might be reluctant to stop a project that is incomplete, even if (and maybe especially if) it has cost a lot so far. Sunk costs may not affect the decision-making of a purely rational decision-maker, but for someone who is quasi-rational (and therefore affected by loss aversion and mental accounting), the sunk costs are relevant to their decision.

Now, it seems that humans are not the only creatures subject to the sunk cost fallacy. New research, reported in the New York Times last week, suggests that mice have the same problem:

This “sunk cost fallacy,” as economists call it, is one of many ways that humans allow emotions to affect their choices, sometimes to their own detriment. But the tendency to factor past investments into decision-making is apparently not limited to Homo sapiens.

In a study published on Thursday in the journal Science, investigators at the University of Minnesota reported that mice and rats were just as likely as humans to be influenced by sunk costs.

The more time they invested in waiting for a reward — in the case of the rodents, flavored pellets; in the case of the humans, entertaining videos — the less likely they were to quit the pursuit before the delay ended.

“Whatever is going on in the humans is also going on in the nonhuman animals,” said A. David Redish, a professor of neuroscience at the University of Minnesota and an author of the study. 

So take heart. You may not be purely rational but, in the animal kingdom, you're not alone.

[HT: Marginal Revolution]

Big data, student dropouts, and failing fast

Amy Wang at Quartz reports:

At the University of Arizona, school officials know when students are going to drop out before they do.

The public college in Tucson has been quietly collecting data on its first-year students’ ID card swipes around campus for the last few years. The ID cards are given to every enrolled student and can be used at nearly 700 campus locations including vending machines, libraries, labs, residence halls, the student union center, and movie theaters.

They also have an embedded sensor that can be used to track geographic history whenever the card is swiped. These data are fed into an analytics system that finds “highly accurate indicators” of potential dropouts, according to a press release last week from the university. “By getting [student’s] digital traces, you can explore their patterns of movement, behavior and interactions, and that tells you a great deal about them,” Sudha Ram, a professor of management systems, and director of the program, said in the release. “It’s really not designed to track their social interactions, but you can, because you have a timestamp and location information,” Ram added...

The University of Arizona currently generates lists of likely dropouts from 800 data points, which do not yet include Ram’s research but include details like demographic information and financial aid activity. Those lists, made several times a year, are shared with college advisers so they can intervene before it’s too late. The schools says the lists are 73% accurate and Ram’s research yields 85% to 90% accuracy, though it did not give details on how those rates are measured.

This sort of story isn't anything new. I blogged on a story about the University of Maryland doing something quite similar back in 2016. Student retention is a big issue, and its often presented as such because losing students results in lost custom for universities. However, there is another aspect of students dropping out that is more than a little problematic for me as an economist.

On the one hand, as a teacher I don't like to see students' efforts go to waste. And signing up for a degree programme that you don't complete really is a waste (and you'll be paying off those student loans for a while, for little to no benefit). On the other hand, as an economist I recognise that past costs that cannot be recovered are sunk costs, and shouldn't be relevant to a student's decision today about whether they complete their degree (those past study costs have already happened - you won't get them back if you drop out, but you also won't get them back if you continue to study either). The decision about whether to continue to study should come down to a dispassionate analysis of the future costs and benefits of continuing to study, and not be affected by things that have already happened and can't be changed.

How do I reconcile those two views? If we can identify at-risk students, perhaps we can help to find ways to ensure they succeed. Or, maybe we can counsel them on alternative options that would avoid wasting future study costs. In the latter case, I'm sure there are at least some students (hopefully few) for whom university study is probably not the best option, or at least not the best option for them at this time. For instance, I have a current research project that is looking into the reasons why students (specifically management students) drop out of university, and in many cases it is non-student life intervening that makes study difficult (more on that in a future post).

In the case of these students, I would expect that the Silicon Valley mantra failing fast and failing cheap applies, even though it has come under a lot of fire of late (see here or here, for example). If a student is going to fail anyway, wouldn't it be better to fail at low cost after one or two semesters than to fail at much higher cost after many semesters of low performance? Or, in the case of university students, perhaps the mantra should be failing fast and coming back later when life is no longer getting in the way? (that was my road through university study, after all).

[HT: Marginal Revolution]

Read more:

• Predicting student success, and failure

The behavioural economics of Lotto

Lotto (and similar lotteries in other countries) presents a problem for economists' assumption of rational behaviour. A rational, risk-averse person should never choose to play Lotto - it has a negative expected value (playing Lotto hundreds of times will lose you money, on average). This point has been made many times (see here for one example from Stats Chat - a simple search on Stats Chat will find you dozens more posts relating to Lotto).

So, if a rational person would never play Lotto, there must be some other explanation for that behaviour. So, I was happy to read this article in The Conversation by Ryan Anderson and David Mitchell (both James Cook University), which used some behavioural economics (among other reasons) to explain why people play Lotto. One reason related to availability bias:

The availability bias/heuristic relates to the idea that people judge the likelihood of something based roughly on how readily examples of it come to mind.

For example, you can probably think of news stories about when a shark has bitten a swimmer. One reason is this kind of a story is sensational, and will likely be highly reported. How often have you seen the headline: “No sharks at the beach today”?

Because you can easily bring to mind examples of shark attacks, you might be tempted to conclude shark attacks are far more common than they actually are. In fact, the chances of being attacked by a shark are somewhere in the neighbourhood of one in 12 million.

You hear and read stories about lottery winners all the time. Jackpot winners always make the news, but the battlers who have been playing for 20 years without winning are relegated to obscurity.

Based on this, it’s at least reasonable to think “jackpotting” can’t be that rare. The net effect is that winning seems possible.

Another related to the sunk cost fallacy:

In economics, a sunk cost is any previous expense that can’t be recovered – like a previous business expenditure on software, education, or advertising. Because this cost has already occurred and can’t be recovered, it should no longer be factored into future decisions. But this is seldom the case.

The sunk-cost fallacy occurs when you make a decision based on the time and resources you have already committed. Research suggests adults are more likely to fall victim to the sunk-cost fallacy than either children or lower-order animals.

In lotto, people will often persevere with what they sometimes know is economically irrational – like buying more lotto tickets – simply because they have already invested so much.

People are susceptible to the sunk cost fallacy because of loss aversion and mental accounting. Loss aversion simply means that we value losses more than we value equivalent gains - we prefer to avoid losses more than we seek to capture gains. This would seem to suggest we should avoid the losses that are inherent in Lotto. However, mental accounting (as the name implies) suggests that we keep 'mental accounts', such as an account for Lotto, and we like to keep those accounts in positive balances. Once we've played Lotto once, we will continue to play because if we stopped when we are behind, then we have to accept the loss from that mental account. As long as we keep playing, there is the chance that we win and the mental account turns positive. Note that this is also an explanation for much gambling behaviour, but also why we stay in jobs we hate, relationships we don't enjoy, investments that are not paying off, and so on. We don't want to acknowledge the loss.

Another behavioural economics explanation that Anderson and Mitchell referenced was our misunderstanding of small probabilities:

Gambling studies professor Robert Williams suggests that although humans have evolved some appreciation for numbers, we don’t really understand big numbers.

We deal with amounts like six, 24 and 120 all the time, but throughout history it’s never really been important to measure out 18 million of something, or count 50 million of something else.

Odds of one in 200 million don’t seem that different to odds of, say, one in 3 million. In both cases success is really unlikely.

Give someone a choice between odds of one in three and one in 200, however, and the difference is really obvious. It’s certainly not that people can’t grasp really big numbers, but that they don’t have much meaning until we stop and think about them.

It's actually worse than Anderson and Mitchell infer. Not only do people not understand probabilities, we have a tendency to overestimate the likelihood of very unlikely events. This is one of the cornerstones of prospect theory, the theory developed by Nobel Prize-winner Daniel Kahneman, along with Amos Tversky. So, if we overestimate small probabilities, we overestimate our chances of winning Lotto, and this makes us more likely to play (compared with if we understood the real probability of winning).

Finally, Anderson and Mitchell also made a point that I have made before, that people facing hard times have less to lose and are more willing to take a punt on Lotto. This isn't behavioural economics at work though - it is people becoming less risk averse. Either way, Lotto is more proof (if any were needed) that our behavioural biases are actively working against us making rational decisions, and the assumption of rationality is dead.

Try this: Broadway economics

The latest issue of the Journal of Economic Education has a short paper about the website Broadway Economics, by Matthew Rousu (Susquehanna University). From the paper:

Songs from musicals tell stories, and many of the concepts we strive to teach our principles of economics students are illustrated in songs such as “Stars” from Les Misérables (inelastic preferences) and “If I Were a Rich Man” from Fiddler on the Roof (inequality, economic growth). While titled Broadway Economics, the site also includes songs from non-Broadway musicals, such as “Let it Go” from Frozen (which illustrates sunk costs). Topics covered more often in upper-level courses such as signaling and screening and consumer time preferences are also well represented by Broadway musical songs.

I'm not much into show tunes, but perhaps you are or you know some economics students who are. The site has videos of the songs, with associated discussion questions that link the song lyrics or theme to economic concepts. For instance, for "Let It Go" from the Disney movie Frozen, the discussion questions are:

1.) What is a sunk cost?

2.) Why should sunk costs be ignored when considering future decisions?

3.) Provide one example where you’ve earned a sunk cost (Hint – the cost need not be a monetary one – it could be time you’ve invested).

 Enjoy!

Why your anti-drug policies just might annoy your neighbours

A few weeks ago, Michael Clemens on the CGD Views from the Center blog alerted me to this recent CGD Working Paper by Juan Camilo Castillo and Daniel Meija (both of Universidad de los Andes) and Pascual Restrepo of MIT. In the paper, the authors attempt to evaluate the effect of cocaine scarcity on violence in Mexico. The authors begin with the Hobbesian argument that in situations where there is a lack of third party enforcement (of contracts, property rights, etc.) through the rule of law, then individuals (or groups) would have to use their own means of protecting their interests, such as through violence. This seems likely for illegal drugs, as the government isn't going to enforce contracts or protect property rights with regards to the actions of cartels. The authors argue that:

Our basic intuition is that scarcity increases violence if the demand for certain goods whose market is illegal is inelastic. In this case, a decrease in supply causes a larger increase in prices, therefore increasing total revenues and the stakes. This leads to more predation and violence.

Now, it's not a simple matter to evaluate the link between drug supply shortages and violence in a single country as there are two mechanisms at work simultaneously. The authors note above one mechanism that links the ongoing 'war on drugs' to violence in Mexico: an increase in attacks on cartels reduces the supply of drugs, raising prices, and increasing the returns to having control over market supply, which can be gained through violence. The second mechanism is more direct - if you fight a 'war on drugs' against the cartels, they fight back, which increases the levels of violence. They may also fight each other, especially if you are moderately successful in reducing the power of one of the rival cartels. So, in order to disentangle the two effects the authors instead look at the effects of anti-narcotic policy in Colombia (the main drug supplier to the Mexican cartels) on the degree of violence in Mexico. I like the authors' approach here, mainly because it doesn't rely on instrumental variables to isolate the effect of the supply shocks.

The authors argument relies on demand for cocaine in the U.S. market being inelastic - thus when prices rise, the quantity demanded decreases but by a smaller percentage than the increase in price, such that total revenue increases (if instead demand were elastic, the decrease in supply would still raise prices, but would reduce total revenue). This argument assumes that suppliers make their decisions about effort (including violence) based on revenues, rather than profits - quite a strong assumption, given that we would usually expect firms (including Mexican drug traffickers) to make decisions based on profits, not revenues. However, once the drugs have crossed the border from Colombia into Mexico, and been paid for by the Mexican cartels (no self-respecting Colombian drug lord is going to extend credit to the Mexican cartels), the cost of their purchase becomes a sunk cost - there is no way for the cartel to recover the amount they paid for the drugs if they are captured by a rival (or by Mexican authorities), and thus the cost of the drugs is not relevant to the decision about how much violence is optimal to pursue in order to translate the drugs into cartel profits. Thus, the decision about the optimal level of violence is likely to be based on drug revenues and the costs of violence, rather than the profits (revenues minus the cost of the drugs). Of course, this assumes that the cartels aren't subject to the sunk-cost fallacy.

If the Mexican traffickers instead made their decisions based on profits rather than revenues, then we would have to recognise that profits must fall for the Mexican traffickers. The cost of obtaining cocaine from Colombia has increased (analogous to a decrease in supply), so even though prices have gone up, producer surplus must have decreased. This happens irrespective of whether demand for cocaine in the U.S. is elastic or inelastic. So, why would violence increase if profits are falling? In this case you could argue that the traffickers would still have to meet their fixed costs (paying your network of large-scale logistics, drug mules, not to mention armed guards, etc. doesn't come cheap). If the cartels were rational, they might downscale their operations, but we know that decision-makers are subject to the sunk-cost fallacy and are willing to increase investment in order to avoid a loss. Cartels are unlikely to be any more rational that anyone else, so they increase their level of violence as they try to capture a bigger share of the cocaine trafficking market into the U.S.

The difference between increased revenue driving increased drug violence, and decreased profits driving increased violence isn't just a minor quibble. The policy implications of the two possibilities are the exact opposite of each other. If you believed that increased revenue was to blame, then in order to reduce violence you find some way of reducing drug revenues, but that would actually increase violence if it turns out that decreased profits were to blame.

Anyway, regardless of how you argue that the decrease in Colombian supply would affect the incentives for Mexican cartels to engage in violence and the appropriate policy remedies to that violence, the authors find that:

...violence increases in Mexico during months with supply shortages caused by seizures in Colombia. Moreover, violence increases especially in the north, and within the north specifically in places close to entry points to the U.S., as predicted by our model. Violence also increases more in northern municipalities that have historically voted for PAN, President Felipe Calderon's party, in which local authorities are more likely to support federal government efforts against cartels in their area, thus increasing the turnover of cartel leaders. Finally, violence increases more in places with cartel presence, especially in places with two cartels or with two rival cartels operating at the time of the supply shock...

Our estimates suggest that, for the period 2006-2010, scarcity created by more efficient cocaine interdiction policies in Colombia may account for 21.2% and 46% of the increase in homicides and drug related homicides, respectively, experienced in the north of the country. Thus, at least in the short run, scarcity created by Colombian supply reduction efforts has had negative spillovers in the form of more violence in Mexico during its so-called War on Drugs.

So, Colombia's anti-drug efforts may be responsible for over 20 percent of homicides in northern Mexico over 2006-2010. Of the 28,000 homicides to occur in the 5 percent most northern municipalities over those five years, Colombia's anti-drug efforts may be responsible for nearly 6,000 of them. Now that's a bad neighbour policy - Colombia's anti-drug efforts have created a pretty large externality for Mexico.