Of Bathtubs, Bombshells and Boilerplate

The bathtub in question is the analogy Linda Booth Sweeney and John Sterman use to illustrate a dynamic stock-flow system, such as the relationship between greenhouse gas emissions (a flow) and the accumulation of greenhouse gases in the atmosphere (a stock). Gernot Wagner and Martin Weitzman stress the importance of the bathtub analogy in their new book, Climate Shock.

What's fascinating about the bathtub analogy is how consistently people get the dynamics of accumulation wrong. Or at least how often business school graduate students with backgrounds in science, technology, math and economics get it wrong. Sterman has pioneered a cottage industry publishing articles about the inability of large numbers of students to correctly identify the effects of flow variations on stock levels. A frequent source of error is something Booth Sweeney and Sterman call "correlation heuristic": students often expect that changes in stock will have the same shape as changes in flow. 

This common error has implications for people's attitudes about the action and policy needed to mitigate climate change, Booth Sweeney and Sterman point out. According to the correlation heuristic logic, many people would assume that a reduction in greenhouse gas emissions would directly translate into less greenhouse gases in the atmosphere. It doesn't.

A bombshell dud

A few weeks ago, Scientific American called the International Energy Agency's announcement a week earlier that global GHG emissions for the generation of energy were unchanged in 2014 from 2013 a "bombshell" that "flew in the face of established economic wisdom." The article went on to point out that scientists had "mixed opinions" about the long term significance of this momentary and sector-limited decoupling of emissions from GDP growth. Some thought it was a hopeful sign that decoupling is already happening. Others warned that emissions were likely to resume their upward trend in 2015.

The article neglected to mention that even if total global emissions were to remain flat for years to come, the concentration of GHGs in the atmosphere would continue to increase relentlessly. Annual emissions would need to be cut to around half their current levels just to stabilize atmospheric concentrations at current levels. That's the difference between stocks and flows.

Happy talk about decoupling GDP growth from resource consumption and waste generation to achieve "green growth" ignores this crucial distinction. Even the more sober "prosperity without growth" critique that highlights the huge disparity between relative decoupling and absolute decoupling ignores this distinction. Accumulation is the bottom line. No mitigation without disaccumulation.

From shocks to stocks and flows... to lumps

The boilerplate is not Paul Guinan's imaginary steampunk contraption -- shown at left -- but the proverbial "fixed amount of work to be done" which has performed oh-so-much work for lazy journalists and economists assuaging those unfounded fears about unemployment that emanate from the economic illiterati. Come to think of it, though, a make-believe robot makes a good mascot for an oft-told tale about a make-believe fallacy. 

Do the erring graduate students in Sterman's and Booth Sweeney's experiments assume there is a fixed amount of water in the bathtub? No, they don't. They realize that the change in flow of water into the tub affects the accumulation of stock in some way. But they systematically mis-specify the timing and magnitude of the effects.

What happens if we dial back the preposterous "fixed amount of work" assertion of the lump-of-labor fallacy claim to a more plausible "correlation heuristic"? Instead of assuming that there is only so much work to go 'round, the benighted Luddites, trade unionists and other economic populists might be suspected merely of committing the more common error of assuming that job losses in the economy as a whole are homologous to losses in a particular trade as the result of labor-saving technology. From a distance the two fallacies may appear indistinguishable. But there is a difference -- several differences, actually.

For starters, the correlation heuristic has been experimentally documented, not just asserted. Evidence trumps mere allegation. Secondly, the heuristic is not as obviously preposterous as the belief in a fixed amount of work. It seems more likely that people -- even Luddites -- would make a plausible error than an implausible one. But perhaps most importantly, the correlation heuristic error may pertain equally to those who allege the fallacy as to those who are alleged to commit it.

How so? Economists making the lump-of-labor fallacy claim insist that the price mechanism automatically adjusts the demand for labor to accommodate changes in the supply of labor. In terms of the bathtub analogy, this is the same as saying that the outflow of the drain self-adjusts to correlate with the inflow from the faucet. One can indeed imagine a device that could accomplish this feat -- a bulb, floating on the surface of the water, attached by a chain of a given length to a plug in an auxiliary drain, such that when the water rises above a certain level, the floating bulb pulls the plug out of the auxiliary drain.

It could work...

Unfortunately, as Mr. Keynes explained long ago, the propensity to consume doesn't float like a bulb on the surface of income. The economists' cherished notion of equilibrium remains a heuristic and nothing more. The pot has been calling the kettle black.

Out of the bathtub and into the frying pan

Why does the Sandwichman keep harping on this arcane specimen of journalistic and economic boilerplate? Because heuristics aside, there are statistical series that seriously, relentlessly correlate: energy consumption and hours of paid employment. Energy intensity per dollar of industrial production has declined for nearly a century. That's relative decoupling. Energy intensity per hour of paid employment does not decline. Greenhouse gas emissions per hour of paid employment does not decline. There is no relative decoupling, let alone absolute decoupling or -- sustainable pie in the sky -- disaccumulation of GHGs in the atmosphere.

To cut greenhouse gas emissions in half, we must cut hours of paid employment at least in half. What would John Sterman say to that?

With a few important exceptions (the work of Herman Daly and colleagues, e.g., Daly and Townsend 1993 ; see also Princen et al. 2002 ; Meadows et al. 2004 ; DeGraaf et al. 2005 ; Whybrow 2005 ; Victor 2008 ; Schor 2010 ), most of the research, teaching, and popular discourse on sustainability continues to focus on technological solutions—more energy, more resources, more efficient eco-friendly growth—while the actual leverage point—voluntarily limiting our consumption—remains largely undiscussable, particularly among our business and political leaders.

DeGraaf 2005, Victor 2008 and Schor 2010, by the way, all prescribe reductions of working time as key to reducing emissions. Wagner and Weitzman on Sterman's bathtub analogy: "climate scientists -- and the rest of us -- would be well advised to remind ourselves daily of its significance." Paul Krugman on Martin Weitzman's fat tail analysis: "So what I end up with is basically Martin Weitzman’s argument: it’s the non-negligible probability of utter disaster that should dominate our policy analysis. And that argues for aggressive moves to curb emissions, soon "

1. the possibility of disaster...
2. the significance of the bathtub analogy...
3. the actual leverage point... 
4. measured rather than heuristic correlations