Author: Tom

The Temperature-System Dynamics feedback

The recurrent heat waves coincident with system dynamics conferences have led me to some new insights about the co-evolution of systems thinking and climate. I’m hoping that I can get a last minute plenary slot for this blockbuster finding.

A priori, it should be obvious that temperature and system dynamics are linked. Here’s my dynamic hypothesis:

This hardly requires proof, but nevertheless data fully confirm the relationships.

Most obviously, the SD conference always occurs in July, the hottest month. The 2011 conference in Washington DC was the hottest July ever in that locale.

In addition, the timing of major works in SD coincides with warm years near Boston, the birthplace of the field.

I think we can consider this hypothesis definitively proven. All that remains is to put policies in place to ensure the continued health of SD, in order to prevent a global climatic catastrophe.

 

Population Growth Up

According to Worldwatch, there’s been an upward revision in UN population projections. As things now stand, the end-of-century tally settles out just short of 11 billion (medium forecast of 10.9 billion, with a range of 6.8 to 16.6).

The change is due to higher than expected fertility:

Compared to the UN’s previous assessment of world p opulation trends, the new projected total population is higher, particularly after 2075. Part of the reason is that current fertility levels have been adjusted upward in a number of countries as new information has become available. In 15 high-fertil ity countries of sub-Saharan Africa, the estimated average number of children pe r woman has been adjusted upwards by more than 5 per cent.

The projections are essentially open loop with respect to major environmental or other driving forces, so the scenario range doesn’t reflect full uncertainty. Interestingly, the UN varies fertility but not mortality in projections. Small differences in fertility make big differences in population:

The “high-variant” projection, for example, which assumes an extra half of a child per woman (on average) than the medium variant, implies a world population of 10.9 billion in 2050. The “low-variant” projection, where women, on average, have half a child less than under the medium variant, would produce a population of 8.3 billion in 2050. Thus, a constant difference of only half a child above or below the medium variant would result in a global population of around 1.3 billion more or less in 2050 compared to the medium-variant forecast.

There’s a nice backgrounder on population projections, by Brian O’Neil et al., in Demographic Research. See Fig. 6 for a comparison of projections.

Defense of the 1%?

Digitopoly has an interesting take on Greg Mankiw’s Defending the 1%.

You should go read the sources, but Mankiw’s basic scenario is,

Imagine a society with perfect economic equality. … Then, one day, this egalitarian utopia is disturbed by an entrepreneur with an idea for a new product. Think of the entrepreneur as Steve Jobs as he develops the iPod, …. When the entrepreneur’s product is introduced, everyone in society wants to buy it. They each part with, say, $100. The transaction is a voluntary exchange, so it must make both the buyer and the seller better off. But because there are many buyers and only one seller, the distribution of economic well-being is now vastly unequal.

Mankiw goes on to mention but dismiss other drivers, like rent seeking and monopoly. Krugman rejoins with a strong critique, and Digitopoly raises some interesting complications to the innovation policy arguments.

I think the thought experiment, framing the problem as a matter of innovation policy, oversimplifies and misses major drivers of what’s happening. As I wrote in Fortress USA,

The drivers of rising inequity in the US seem fairly simple. With globalization, capital has become mobile while labor remains tied to geography. So, capital investment flees high wage countries (US) and jobs follow. Asset income goes up, because capital is leveraged by cheaper labor and has good bargaining power among hungry host countries. There’s downward pressure on rich world wages, because with less capital per capita employed, the marginal productivity of labor is lower.

It’s not all bad for the rich world working class, because cheaper goods (WalMart) offset wage losses to some degree. If asset and wage income were uniformly distributed, there might even be a net benefit.

However, asset income and wages aren’t uniformly distributed, so income disparity goes up. Pre-globalization, this wasn’t so noticeable, because there was an implicit deal, in which wage earners knew that, even if they didn’t own all the capital in their country, at least they’d be the beneficiaries of it in some sense through employment and trickle down. Free trade and mobile capital turns the deal into a divorce, which puts a sharp point on questions of property rights allocations that were never quite fair, and sows the seeds of future discontent among the losers.

In addition to disparities in the fate of labor vs. capital, it’s hard not to see abundant rent seeking in the consolidation of firms and the pervasive role of money in government.

The simple, pure economic thought experiment often brings great insight. But I think this illustrates why models often have to get big before they can get small. Total analytic knowledge of a small model is fairly useless, unless that model encompasses the right structure. It’s hard, a priori, to decide what’s the right structure to include, without distilling that insight from a more complex model.

Do social negative feedbacks achieve smooth adjustment?

I’m rereading some of the history of global modeling, in preparation for the SD conference.

From Models of Doom, the Sussex critique of Limits to Growth:

Marie Jahoda, Chapter 14, Postscript on Social Change

The point is … to highlight a conception of man in world dynamics which seems to have led in all areas considered to an underestimation of negative feedback loops that bend the imaginary exponential growth curves to gentler slopes than “overshoot and collapse”. … Man’s fate is shaped not only by what happens to him but also by what he does, and he acts not just when faced with catastrophe but daily and continuously.

Meadows, Meadows, Randers & Behrens, A Response to Sussex:

The Sussex group confuses the numerical properties of our preliminary World models with the basic dynamic attributes of the world system described in the Limits to Growth. We suggest that exponential growth, physical limits, long adaptive delays, and inherent instability are obvious, general attributes of the present global system.

Who’s right?

I think we could all agree that the US housing market is vastly simpler than the world. It lies within a single political jurisdiction. Most of its value is private rather than a public good. It is fairly well observed, dense with negative feedbacks like price and supply/demand balance, and unfolds on a time scale that is meaningful to individuals. Delays like the pipeline of houses under construction are fairly salient. Do these benign properties “bend the imaginary exponential growth curves to gentler slopes than ‘overshoot and collapse'”?

Emissions trading goes live in China

Shenzhen kicks off China’s pilot emissions trading scheme today, with 635 companies trading, covering about 40% of emissions. It’ll be interesting to see how much the market really benefits from learning from the European experience.

Interestingly, China’s emissions trading plans are proceeding in spite of immaturity and stability concerns, but a national carbon tax is on hold, even though it’s small and economically benign.

Flow down, stock up

A simple example of bathtub dynamics:

Source: NYT

The flow of plastic bags into landfills is dramatically down from the 2005 rate. But the accumulation is up. This should be no surprise, because the structure of this system is:

The accumulation of bags in the landfill can only go up, because it has no outflow (though in reality there’s presumably some very slow rate of degradation). The integration in the stock renders intuitive pattern matching (flow down->stock down) incorrect.

Placing the flow and the stock on the same vertical scale, is also a bit misleading, because they’re apples and oranges – the flow of disposal has units of tons/year, while the accumulation has units of tons.

Also, initializing the stock to its 2005 value is a bit weird. If you integrate the disposal flow from 1980 (interpolating as needed), the accumulation is much more dramatic: about 36 million tons, by my eyeball.

Timing Vensim models

Need to time model runs? One way to do it is with Vensim’s log commands, in a cmd script or Venapp:

LOG>CREATE|timing.txt
LOG>MESSAGE|timing.txt|"About to run."
LOG>TIMESTAMP|timing.txt
MENU>RUN|o
LOG>TIMESTAMP|timing.txt
LOG>MESSAGE|timing.txt|"Ran."

These commands were designed for logging user interaction, so they don’t offer millisecond resolution needed for small models. For that, another option is to use the .dll.

Generally, model execution time is close to proportional with equation count x time step count, with exceptions for iterative functions (FIND ZERO) and RK auto integration. You can use the .dll’s vensim_get_varattrib to count equations (expanding subscripts) if it’s helpful for planning to maximize simulation speed.

Depleting fossil water

The NYT has an interesting article on the decline of the High Plains aquifer, which includes the famous Ogallala aquifer. Water tables are dramatically down (red) in many areas, making irrigation impractical.

Vast stretches of Texas farmland lying over the aquifer no longer support irrigation. In west-central Kansas, up to a fifth of the irrigated farmland along a 100-mile swath of the aquifer has already gone dry. In many other places, there no longer is enough water to supply farmers’ peak needs during Kansas’ scorching summers.

And when the groundwater runs out, it is gone for good. Refilling the aquifer would require hundreds, if not thousands, of years of rains.

This is a widespread, generic problem, and instance of the tragedy of the commons archetype:

Alternately, as an economist might put it, depletion of groundwater is typically an externality, with zero rent paid from users to owners (us).

There are three facets to management of the problem: the commons problem, detail complexity from the complex geology of aquifers, and dynamic complexity. Allocation of property rights solves the commons problem, but not the others (see Erling Moxnes’ interesting work on this).

Sniffing around for material for this post, I found it easy to get lots of complicated information about aquifers, but hard to find any simple stock-flow pictures that revealed their state or dynamics, like this:

Source: USGS

This suggests that there’s some low-hanging fruit to be harvested through provision of simple feedback, as in the Climate Scoreboard.