A reader asked about my take on the Kaya wars that are flaming at Anthony Watts’s place.
Here is the form of the Kaya Identity, which is to say, the Kaya non-equation:
The Ys and Xis are numbers and a free choice, given the limitations of algebra (no Xi equals 0). Try it and see: for fun, let . Works. A perfectly harmless manipulation.
There is no explicit word about causality in the Kaya. The Xis aren’t necessarily causing the Y or each other. If we wanted to know about what caused Y, and we believed that the Xis were in the causal path of Y, we wouldn’t set up an identity but an equation which looked like this:
Where X is a vector and where the vector of (known and unknown) parameters β may be larger or smaller than X. Notice that Y does not appear on the right hand side. We are solving for Y here. One possibility (and probably a too simple one for most Y)is a linear equation:
This is not regression. This is a causal model: it says Y will certainly change by when increases by 1 unit. Regression is a probability relationship where we first assume and then substitute μ for Y on the left hand side. Regressions says Y might, not that it certainly will, change.
Anyway, since the Kaya is an identity we can put anything we like in for the Xis and Y. Let’s try.
where each is a number existent or occurring over a year in some suitable units. Notice that I was careful to put things that we know change over time, but I needn’t have. Everything could be static (more or less), like this:
Some of these quantities are known for sure, and one, the amount of Gold, is not. But whether we know the value of any of these is immaterial to the Kaya. As long as none are null quantities, and Gold isn’t, we’re in business. Also note that the number of entries was up to me. I could have made the list shorter or longer as I pleased.
What do any of these things have to do with CO2? Who said the items had to have anything to do with CO2? Who said I had to use CO2? Insisting that the Xis are causative of Y and using the Kaya and not an equation is doing it, as they say, the hard way.
But we can certainly manufacture cause-like stories. Puppies eat, and their food both requires and releases CO2. Cats, too. Meteorites often have carbon in them, and boy do they disturb the atmosphere; lots of cloud nucleii strewn hither and thither during their journey. Same thing with cosmic rays. Plus, these energetic creatures effect life, and life is important for understanding carbon. This is just off the top of the head; spend some serious time and you can spin this tale out to saga length. Peer reviewed, of course.
The same thing can be done with the fixed Xs. Or with any items you care to put into the Kaya. As long as you stay away from 0, you’re in business.
Here’s what Kaya himself put (adapted to just the USA):
This is just as valid as the examples above, though this one seems more popular with economists. But then economists are prone to tying everything to GDP, which is a number, and economists love numbers (those without uncertainty, that is), often preferring them over reality. Never mind.
For an example of the Kaya in action, see the Pielke Jr video embedded at this link starting at around 21 minutes. Pielke appears to believe that the Kaya has something to do with causation and that he and fellow economists have captured all they need know about human beings and carbon.
The good news from an analytical standpoint is that there’s nothing else. There’s no other levers that you can use out there. This is comprehensive. You may wish there was some rabbit you can pull out of a hat because the good news is also the bad news: this is all you have.
That’s false, as we know from the Puppies example (recall we can add puppies or gold or whatever to the Kaya). And these items—GDP, etc.—are far from all we know about humans and carbon, though Pielke calls it an “extremely powerful tool for policy analysis.” For instance, he says (around 20 min. mark) that, as a lever governments can pull, “Less people, all else equal, equals less emissions” (I believe the guillotine had a similar lever). Another lever the government can yank, he says, is to purposely create poverty, i.e. “Limit generation of wealth” (does that include the wealth of government, one wonders?).
These claims are not quite false, but not quite true, either. More people mean more energy is used, but there’s also a greater chance for more innovation in, say, creating more efficient energy sources. And more people also means more food, and food is a terrific carbon sequestration vehicle, to say it in economic-speak. (Incidentally, one reason that there are more people is that there is more food.)
Now there’s nothing wrong with grappling with crude ratios like Energy/GDP to have some rough, first-blush idea of the amount of energy that is now required to generate such-and-such-a-sized economy, but as for the energy required to drive a future economy, who knows? Nobody in 1990 predicted Google. The Kaya is not a forecasting tool. And since it doesn’t carry any measure of uncertainty, and since every term is mixed up causally with every other term, nobody knows how much credence to give it.
And we can’t bypass the hard work of actually estimating the amount of carbon released and sequestered, both now and in the future. Yet the Kaya is mute on what causes CO2. GDP, after all, doesn’t cause CO2. That’s impossible.
The Kaya should be replaced with a probability model/equation, which can tell us how much change in GDP might be associated with a change in CO2.
That model ought to be under the same constraint as climate models. If it can’t make skillful predictions of future data, we shouldn’t believe it. Right? And how good are economists at forecasting the GDP or energy use one to two decades out?
Update I should have mentioned this above, but it might be in some problem that we know the last ratio Y/X_n (and each other ratio) but that we do not know Y. The Kaya can then be used to calculate Y. But in the case of CO_2, we do not know the last ratio.