It is time to stop quivering in our boots in pointless fear of the future and just roll up our sleeves and build it.
- Ray Pierrehumbert

Wednesday, June 20, 2007

Economics and Global Change: The Bathub Analogy

I posted this to the globalchange list some time ago, but now that I have the attention of a couple of market conservatives, let me post it here. Apologies to those for whom it is a rerun. Note that the apparently rational strategy actually guarantees an eventual flood.

Imagine that you are an economist who enjoys playing Tetris on your computer, so while your bathtub is filling you decide to play a round in the TV room upstairs.

The round of Tetris is going fabulously well. You are in the zone. You are placing piece after piece where it goes; you have long since passed your all time high score; you are having a whale of a time. Your bathtub is meanwhile filling up.

A tiny corner of your mind suggests that you ought to go downstairs and check your bathtub, even though it would interrupt your excellent Tetris game.

Fortunately, you are an economist. The tiny corner of your mind that is concerned with the structural integrity of your house and not the joy of Tetris is sufficient to reason as follows.

Probably the tub is not full yet, so the utility to me to keep playing this next piece exceeds the utility of running downstairs to turn off the water.

Maybe the tub is already flooding. Well, then, that is too bad, but the additional flood cost of playing this next piece will be small compared to the total flood cost, while the pleasure I am getting from this game going so well would be terminated.

Perhaps the tub is right at the point of starting a flood; a "tipping point". Well in that case you certainly would run right downstairs and turn it off, but what are the odds of that? There is no way to prove this highly unlikely ands speculative circumstance to you. There really isn't enough information to know exactly when that moment might be, so this almost certainly isn't it. Surely you can just dispense with that sort of wild speculation.

You have just proven that the matter does not deserve much attention for the duration of placing this next Tetris block. You will revisit this problem later when you are placing another block, with the same small shred of your attention. Tetris is such fun!

So you keep playing, secure in the knowledge that you have maximized utility.


Mark Powell said...

Hey, can I borrow your excelleng bathtub analogy in describing overfishing? Surely it's ok to take just one more fish?

Do you need royalties each time I use it?

Michael Tobis said...

It's as of now in the creative commons.

I welcome a link if it's online or a reference if it's in print, but I won't enforce it anyway.

Glad you like it.

James Annan said...


I think as soon as you try to put sensible numbers on it, your analogy will fall flat. That is, the pleasure of playing tetris is unlikely to outweigh even a small risk of damage. I'd like to see a worked example (perhaps with a more realistic context) if you disagree.

As for fishing, well that depends on a lot of things, such as the time scale of fish decline, and what will happen when the fisheries collapse (eg the govt aid gravy-train). There's also a tragedy of the commons angle, which may well turn out to be the biggest part. That's not a defence of overfishing, just an explanation of it.

Tony said...

I love thinking about things in analogies, because they seem to cut to the chase, and they're great as educational "framing" tools. I also think that the indifference and plain dishonesty of many sceptics to the creeping danger of climate change is a scandal -- and a challenge -- of our times. The trick is in choosing the right analogy (something that many sceptics suck at, to be honest).

OK, so much for the throat-clearing. I think you're onto something here, but I want to play devil's advocate.

(For the purposes of the analogy, I'm assuming there's no "pause" key on the game.)

Firstly, you posit the filling of the bathtub and the enjoyment of tetris as independent. But insofar as the free market is based on production and industry, you can't even begin to play the game without filling up the bathtub -- because the flow of water from the tap powers the computer. Stop the flow of water and you head off a flooding -- but you also stop the game. Which, by the way, is not just a game, but the modern lifestyle. Therefore, to the free market devotee, the analogy falls down.

A better form of the bathtub analogy (which I've seen elsewhere), is one with the plug pulled (i.e., the retirement of CO2 from the atmosphere). The bathtub is still filling and if it fills too fast it will flood. However, the tap is running, and can still power industry.

The trick therefore becomes adjusting the relative levels of the three processes, keeping in mind that the only control we really have is over the rate of water flow out of the tap.

Actually, I'm not really sure if even this analogy will satisfy the free market types. I sense that their opposition to anything with even a taint of environmentalism clouds their judgement, and also that their belief in the good of greed is psychologically fundamental to the way they construct their self. But that's a whole other story.

Mark Powell said...

Thanks. It's here on blogfish, attributed and linked.

"Why keep overfishing? The best analogy I've ever seen..."

Like your comments on the bird decline news too, gave me something to think about. All the other coverage I've seen just repeated the conclusion.

Michael Tobis said...

Thanks for commenting, James.

I think the Tetris situation is untenable if the player actually pauses to work out the risks and thinks like a homeowner. However, that is different than thinking like a tetris player.

From the point of view of the Tetris player, turning off the bathtub IS WORTH ZERO POINTS.

If we judge everything on economic grounds, we place a great deal of weight on economic timescales on which five years is a very long time. However, from the point of view of stewards of the only planet which can keep us alive, five years is a very short time.

The point is not whether a real Tetris player would consciously make this mistake. That's crazy. The point is that we are making a similar mistake. That's crazy too.

Michael Tobis said...

Well, shucks Mark, I'm blushin'.


James Annan said...

From the point of view of the Tetris player, turning off the bathtub IS WORTH ZERO POINTS.

In that case I think I've missed the whole point of your analogy, which was (AIUI) that the short-term gain of playing outweighed the risk of long-term (but temporally uncertain) damage, not that the player simply didn't regard the damage as damage, or just didn't think about it at all.

In your revised version, what does tetris have to do with anything? You are just asserting (correctly) that someone who does not place any negative value on a particular future outcome, will not take any action to prevent it. Whereas the AGW question is mainly concerned with how different approaches stack up in terms of costs and benefits.

Michael Tobis said...

Hmm. The fact that the intent wasn't clear is interesting. I am not revising. This represents my initial intent as I clearly recollect.

The Tetris player is concentrating on Tetris points and doesn't want to be distracted by threats to the structural integrity of his house.

The focus on Tetris points is taken much too seriously. The Tetris player demands certainty of a non-Tetris risk on the time constant of an individual tile play; else he will not interrupt the game.

That the Tetris player absurdly overvalues Tetris points is not a valid criticism of the analogy because it is the point of the analogy.

Tetris points are like GDP.

The question I raise is whether the risks are appropriately measured in Tetris points.

Stern says yes, arguing in somewhat tortured way that the bathtub flood may short out the electricity and cause a loss of Tetris points. I think that's silly.

I am sure we need to think quantitatively, yet I think our measures are fundamentally inappropriate for our circumstances. This is why economics is getting in the way rather than helping us think this through.

I don't know what the right metric is in detail, but I am coming to think that sustainability can be defined as an objective quantity.

Anwyay I'm pretty sure GDP is no better than Tetris points in our present quandary.

Phil said...

Ah, but our Tetris player is a cunning fellow. Knowing that an overflowing bath can diminish his enjoyment of the game, he uses his best technological skills and attaches a collar to the bath to increase its height so it will overflow later and give him more time to play the game.

But because this collar is not an integral part of the bathtub, it's going to be prone to catastrophic failure as the level rises...

Aren't analogies fun?

mz said...

"Measuring water damage in tetris points" - that's a nice way of putting it!

James Annan said...

If you are making the analogy that tetris points are like GDP then you cannot simply assert that the player assign no points to the flood damage - at least, without making your "analogy" basically invalid.

Moreover, if the player really is going to assert that the flood is worth nothing, then all the "probably...maybe...perhaps" stuff in your later 3 paragraphs is completely moot.

Michael Tobis said...

I'll try to defend the Tetris thing one last time for James.

If disturbances of the planet are believed appropriate only and exactly to the extent that they interfere with GDP growth, it requires an argument that GDP growth is the right thing to optimize for. I find such argument to be absent; it is commonly taken as an assumption.

It is not inconceivable to me that GDP will continue to grow while sea level rises 6 meters, but I don't think we will necessarily have maximized utility in the process compared with a world with static GDP and no comparable sea level rise.

To those who find this inconceivable, I offer the Tetris analogy.

If disruptions to the structure of my house are treated as of concern only to the extent they interfere with accumulation of Tetris points that makes the presumption that winning at Tetris is what we are trying to do.

If I keep playing and take the small risk that the flood will interfere with my Tetris playing, I am successfully maximizing Tetris points. There is no doubt that Tetris points do correlate with happiness, but I will find in the end that I would have been happier with some more complex scoring system.

In short I am asking what the right metric is for our objective. I hope this clarifies matters.

Michael Tobis said...

in the first paragraph above "appropriate" should read "inappropriate". Oops.

James Annan said...


I have some sympathy with your dislike of GDP optimisation, but there is a clear disconnect between your mention of optimising GDP growth and discussion of whether GDP may grow despite sea level rise. Growth, and optimal growth, are fundamentally orthogonal concepts.

Are you actually prepared to claim that a strategy which results in 6m of sea level rise (presumably, over some short time scale) will optimise GDP growth?

Michael Tobis said...

James, we have to leave the bathtub behind at this point, which I think is what you want to do anyway.

The short answer is yes; I think we can optimize ourselves into a terrible state, and I think in North America we can prove it because we already have.

Whether we can trick ourselves into 6 m of sea level is exactly the question that has Hansen pushing the limits of scientific propriety.

If we do, the extent to which that ends up being because of misplaced optimism versus misplaced optimization will be hard to sort out.

Your question leads deeper into economics than I am comfortable with at present, but I am trying to think about it. A problem I have in thinking about it is that I am very skeptical of both the conventional wisdom and the more obvious challenges to it. I don't have much to work with in terms of studying the matter.

Of course, one crucial factor in how misguided our optimization can get has to do with discount rates, and I don't have to say anything very original to make that case.

It's commonly observed that discount rates applied to public policy institutionalize generational inequities, like flooding our great grandchildren, for instance.

James Annan said...

The biggest institutionalised generational inequality I can see is that our great grandchildren will be much better off than us in many ways, as we are compared to our great grandparents. More possessions, more technogadgets, more food, more knowledge, more healthcare.

It is, however, probably true that they will be no happier than us, and they may not be able to see (insert your favourite threatened species here). I do agree that these are significant issues to deal with (really!), especially for us pampered rich westerners for whom further GDP growth is fairly meaningless. I think it was the PM of Tibet (or someone similar) who said that increasing happiness was one of his Govt's goals, along with wealth.

Michael Tobis said...

I believe that the relatively benign outcome you describe is technically feasible but I don't it's socially likely. I think a severe global population collapse within the next two centuries is more likely than not.

I think we can agree that we should minimize the possibility of such a thing, but it seems consequential in designing the strategy whether one thinks the crash is likely or unlikely.

James Annan said...

A severe population crash in Japan has already started, although it's hardly got teeth yet.

What sort of policies do you think are necessary (and/or desirable) to address it?

IMO fewer people is a good thing, although getting there may pose some challenges (not by any means insurmountable).

Michael Tobis said...

That's an interesting question, but I think you are talking about a voluntary fertility-based population decline rather than an involuntary mortality-driven one. It is the latter that I hope we can avoid.

A gradual voluntary decline in population is probably a good thing, though growth-driven economics would argue against it.

Heiko said...

I think the point of your analogy is that economics doesn't value the right things. But it goes way overboard. You can argue that some economic analysis doesn't value the rights of the poor, species loss, or future generations properly, but the Tetris analogy implies that these choices should be damn obvious to any right thinking person, which they aren't.

And I think you are quite aware of this.

I also think you agree that some attempt at quantification of benefits/costs is useful in aiding decision making.

For me, the use of money in analysis implies, not short sightedness or neo-liberal ideology, it's a particular measuring tool for value, namely revealed preference.

You can ask people what they value, or you can impose standards on them paternalistically, and these are often necessary tools to deal with the deficiencies of the revealed preference approach.

I do think that revealed preference as measured through market transactions gives a lot of useful information, and it's an easy to measure and difficult to manipulate metric.

The main concerns I see that need correcting are the weighting of need by wealth implied by this methodology, and the reasons why paternalism makes sense, ie people may not do what is truely best for them, which is why even the most market ideology minded won't put much stored in what revealed preference says about the value of illegal, addictive drugs.

It's also not enough to agree on a way of measuring value. If we had two futures to choose from, and we knew everything about them with certainty, we'd just have to sit down and agree which one is more desirable, ie how to quantify value and how to weight relative needs.

But we don't have such a straight choice, because the future is clouded with uncertainty.

Going back to your Tetris analogy, some people may like Tetris, some don't, some people may be more concerned than others about their bathroom flooding, but, actually, you'll find very few who would actually value finishing a game of Tetris above rescuing their home,

and so, a more apt way of interpreting the analogy would be that the Tetris player wrongly perceives the likelihood of problems.

Coming back to climate and what we should do about it,

I think both dimensions matter. Firstly, there is disagreement of what is important and what isn't. Particular examples I can think of is the welfare of people in other countries (revealed preference in many ways says that's valued quite low, not just by comparing GDP based cost impacts, even more so when considering social security spending / military spending, compared to aid, or willingness to allow foreigners into the country to receive social spending), or lifestyle choices relating to car use.

But equally importantly, there is fundamental uncertainty about the future, and I've noticed that "environmentalists" generally are much more concerned that economic growth simply can't be sustained (as in conventionally measured GDP reaching $70,000 per capita for the world in 2100) than techno optimists, or the majority of economists. And at the bottom, that's not about valuing things, it's actually a disagreement about the facts.

As I've mentioned before, it's funny how these two different dimensions seem to correlate in practise, ie people who think that we don't value the needs of the poor in developing countries enough and who think we ought to live simple lives and that the car does often do more harm than good, with much related behaviour being worthy of seen in the same light as addictive drugs, also tend to regard it as much more likely that their preferred behaviour is actually a necessity to continue a workable development of society.

Michael Tobis said...

the Tetris analogy implies that these choices should be damn obvious to any right thinking person, which they aren't

I have learned my lesson. I will never again publish an analogy without very explicitly saying what I mean by it.

In this case, I agree that the correct metric is not obvious. I only mean to say that there is no guarantee that the existing metric achieves the purposes for which it is intended.

That said I think we agree on much of what you have said. I agree that your two concluding paragraphs disentangle a strong de facto correlation between expectations and preferences. Fot his I thank you.

I don't think behavior reveals preferences as much as is generally expected by people who take conventional macroeconomics as valuable.

There was a book on the market called "hypercompetition" that describes how large companies even short of monopoly can control the marketplace to reduce consumer choice and enhance their advantages. This was not a left-wing jeremiad; it was a how-to book.

Microsoft and McDonalds come to mind immediately.

McDonalds used to advertise "America's favorite fries", and by the doctrine of revealed preference they might have a point, but in fact most people prefer the french fries as prepared by a local provider. However, the local provider does not have the scale of McDonalds, who in fact produce AMerica's most tolerated fries.

Is Microsoft the manufacturer of the world's favorite software? According to the idea that behavior reveals preferences, it is. However, I have yet to hear many examples of enthusiasm for their products coming from anyone who is not currently in Microsoft's employ.

By my beahvior, you will see that I "prefer" to drive to work than to bicycle or take a train. This revealed preference can be used to argue against public expenditures on bicycles and trains, but the preference revealed is wrong.

My mundane daily decisions are affected by my environment and meanwhile my environment is affected by the decisions I and others make. My decisions only reflect the choices I make in the market as it currently exists and do not at all reflect the way I wouldlike the amrket itself to be structured.

It's a very poor design for a control system, and it is why so many features of modern life are out of control.

James Annan said...

It's a very poor design for a control system...but still better than all the alternatives that have been tried (or even proposed?) :-)

Heiko said...

Maybe I am more of an environmentalist on some issues than I'd like to believe myself ;-),

but quite a few of your thoughts here sound very similar to my own:

In particular, this section:
"there are network effects. Part of the reason for individuals to price exurbanism is that other people do. Large cars have much more safety value when they are competing against other large cars. Having an exurban lifestyle is much more attractive when there are friends who encourage it and praise you for your achievement, or conversely who look down upon you, because you are still stuck in a flat. And the attractiveness of public transport partially depends on the number of people using it."

Heiko said...

Following up on James, I think the general approach taken in Western economies is the right one, and that is to accept market based approaches, and to tweak them where there are (perceived) failings, such as putting taxes on alcohol/tobacco, outlawing certain drugs, redistributing income via taxes and social spending, or by putting government money into public transport or cycle infrastructure.

Particularly the micro level is where revealed preference and market based transactions for economic control absolutely excel when compared to central planning based on a combination of paternalism / asking people questions about what they'd like to have. Whether people want red or blue bikes and how much extra resources should be expended for blue compared to red bikes, that kind of stuff I think really shouldn't be decided by surveys, but by the marketplace.

ariafritta said...

Nice and clever analogy.

May I ask for the permission to translate it into Italian, and post it in my blog?

Naturally, author and source will be clearly showed.

Thanks in advance.

Michael Tobis said...

Thank you so much!

Certainly you may translate it! (I would probably never have known anyway...) I cannot speak Italian but I love the sound of it. It would be a delight to see my own ideas in Italian.

If you find this interesting I would also recommend to you the wonderful essay by my new friend Paul Baer called "The Worth of an Ice Sheet".

Please paraphrase as you will.

However, I recommend that you explain the point of the analogy, as it apparently was not obvious to the readership. I would append some paragraphs from the commentary, perhaps:

It is not inconceivable to me that GDP will continue to grow while sea level rises 6 meters, but I don't think we will necessarily have maximized utility in the process compared with a world with static GDP and no comparable sea level rise.

To those who find the suggestion confusing, that maximizing wealth and maximizing utility could be very different, I offer the Tetris analogy.

The Tetris player is concentrating on Tetris points and doesn't want to be distracted by threats to the structural integrity of his house.

The Tetris player demands certainty of a non-Tetris risk on the time constant of an individual tile play; else he will not interrupt the game.

If disruptions to the structure of my house are treated as of concern only to the extent they interfere with accumulation of Tetris points that makes the presumption that winning at Tetris is what we are trying to do. As such, the Tetris player is behaving rationally, pursuing the goal that makes perfect sense in the Tetris context.

If I keep playing and take the small risk that the flood will interfere with my Tetris playing, I am successfully maximizing Tetris points. There is no doubt that in typical circumstances Tetris points do correlate with happiness, but the player will find in the end that he would have been happier with some more complex scoring system.

King of the Road said...

How about this for an analogy? I wake up at night feeling warm. I notice someone has thrown a blanket on me. I think, well, I know there's a lag between the heat of the day and the peak temperature in my house, maybe I'm just now reaching that peak. Or it could be that someone broke in and started a fire in my fireplace. My wife was baking earlier, perhaps she left the oven on. It could be that a statistical anomaly has caused the internal energy in the air in my house to be temporarily concentrated over my bed.

Nobody can prove to me that it's this extra blanket, and anyway, just because I'm sweating like crazy, I'm probably not hot anyway.

Brian said...

After this fall, I believe you can extend the original analogy to include at least one "game over". Does Mister Economist head downstairs now, thanks to the forced interruption of his game, or does he press "Play Again" in an effort to try to recapture that Tetris feeling with minimal downtime?

See also The Way Things Break.