Guest Post by Willis Eschenbach
It’s morning here in Reno, and I thought I’d write a bit more about the Kaya Identity and the Beer Identity. My last post about the Kaya Identity was controversial, and I wanted to see if I could clarify my point. On the last thread, a commenter did a good job of laying out the objections to my work:
Sorry but I think you’ve all entirely misunderstood the point of the identity. The Kaya identity is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions.
These are analogous to mathematical factors, for e.g. 6 = 3 x 2. This illustrates that 2 and 3 are factors of 6. This doesn’t prove anything mathematically – it’s just an identity. But it is informative nonetheless. It tells you that 6 can be broken down into factors of 2 and 3. In the same way, CO2 emissions can be broken down into factors of population, GDP per population, energy per population, and CO2 emissions per energy.
That is a very clear and succinct description of what the Kaya Identity is supposed to do. The only problem is … it doesn’t do that.
Let me take another shot at explaining why. To start with, the Kaya Identity states:
where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.
The Beer Identity, on the other hand, states the following:
Where all of the other variables have the same value as in the Kaya Identity, and “GBP” is gross beer production by the country.
I think that everyone would agree with those two definitions. They would also agree that both of them are clearly true.
Now, as the commenter said above, when we write
6 = 3 x 2
it tells us that six can be broken into factors of three and two. Not only that, but we can say that for example
(6 * 0.9) = 3 x (2 * 0.9)
That is to say, if we change one of the factors by e.g. multiplying it times 0.9, the total also changes by multiplying it by 0.9.
But is that true of the Beer Identity? Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer. Will this decrease our CO2 production by 10%, such that
Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%. In other words, despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions. And the reason why it is not true is that it doesn’t include all of the factors that go into the emission of the CO2, it only includes the beer.
Now, I can hear you thinking that, well, it doesn’t work for gross beer production, but it does work for gross domestic production.
And up until yesterday, I was convinced that the Kaya Identity doesn’t work for GDP any more than it works for GBP … but I couldn’t figure out why. Then yesterday, as I was driving along the Lincoln Highway on my holiday with the gorgeous ex-fiancee, I realized the factor that is missing from the Kaya Identity is … me, driving along the Lincoln Highway on my holiday with my gorgeous ex-fiancee.
The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.
So in fact, the Kaya Identity does NOT tell us the “factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions” as the commenter said.
And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t. And because it looks like mathematical truth, we have folks who take it as gospel, and object strongly when it is questioned or laughed at. Steven Mosher thinks I was wrong to laugh at the Kaya Identity, and I do respect his and the other opinions on the matter, his science-fu is strong … but in fact, the Kaya Identity is no more complete than the Beer Identity, which is why I laughed at it.
So that’s my objection. It’s not that the Kaya Identity is false. It can’t be, by definition its true.
It is that it gives the false impression of mathematical certitude, the impression that it represents the real world, the idea that it identifies the “factors of which CO2 emissions are comprised” … but it doesn’t. This false certainty, because people think it’s “mathematically demonstrable”, leads people to not question whether it applies to the real world.
Finally, in closing let me repeat something I said in the comments on the first thread, which likely didn’t get seen because it was somewhere down around the five hundredth comment.
l hear rumblings that people think that Anthony shouldn’t have published this piece of mine, or should disavow it in some fashion. This totally misunderstands both what Watts Up With That (WUWT) does, and Anthony’s position in the game. The strength of WUWT is not that it is always right or that it publishes only the best stuff that’s guaranteed to be valid.
The beauty and value of WUWT that it is the world’s premier location for public peer review of climate science. On a personal level, the public peer review afforded by WUWT is of immense use to me, because my work either gets falsified or not very quickly … or else, as in this case, there’s an interesting ongoing debate. For me, being shown to be wrong is more valuable than being shown to be right. If I’m right, well, I thought so to begin with or I wouldn’t have published it, and it doesn’t change my direction.
But if someone can point out my mistakes, it saves me endless time following blind alleys and wrong paths. And my opinions on the Kaya Identity may indeed be wrong.
There is much value in this public defenestration of some hapless piece of bad science, whether it is mine or someone else’s. It is important to know not only which ideas are wrong, but exactly why they are wrong. When Anthony publishes scientific claims from the edges of the field, generally they are quickly either confirmed or falsified. This is hugely educational for scientists of all kinds, to know how to counter some of the incorrect arguments, as well as giving room for those unusual ideas which tomorrow may be mainstream ideas.
So it is not Anthony’s job to determine whether or not the work of the guest authors will stand the harsh light of public exposure. That’s the job of the peer reviewers, who are you and I and everyone making defensible supported scientific comments. Even if Anthony had a year to analyze and dissect each piece, he couldn’t do that job. There’s no way that one man’s wisdom can substitute for that of the crowd in the free marketplace of scientific ideas. Bear in mind that even with peer review, something like two-thirds of peer-reviewed science is falsified within a year, and Anthony is making judgements, publish or don’t publish, on dozens of papers every week.
So please, dear friends, cut Anthony some slack. He’s just providing the arena wherein in 2014 we practice the blood sport of science, the same sport we’ve had for a few hundred years now, ripping the other guys ideas to bits, also known as trying to scientifically falsify another person’s claims that you think don’t hold water. It is where we can get a good reading on whether the ideas will stand up to detailed hostile examination.
It is not Anthony’s job to decide if mine or any other ideas and expositions and claims will withstand that test of time … and indeed, it is often of value for him to publish things that will not stand the test of time, so that we can understand exactly where they are lacking.
So please don’t fill up the poor man’s email box with outrage simply because you think a post is not scientifically valid enough to be published. Send your emails to the guest author instead, or simply post your objections in a comment on the thread. Anthony is just providing the boxing ring. It is not his job to predict in advance who is going to win the fight. His job is to fill the fight cards with interesting bouts … and given the number of comments on my previous post about the Beer Identity, and the huge popularity of his website, he is doing it very well.
Regards to each and all of you, my best to Mosher and all the folks who have commented, and my great thanks to Anthony for the huge amount of work he does behind the scenes to keep this all going. I’m on the road again, and my highway CO2 emissions are still not included in the Kaya Identity …
w.
As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.
Well, that is indeed the case if the ratios stay more or less constant.
Of course, one could posit that such increase would change the other ratios, but that must be evaluated on a case-by-case basis.
It seems climatereflections and JK are both correct. Cf using the (implied?) equation and JK the identity. Is the difference between “=” and “≡”?
Daniel G:
Thanks for your comments.
“co2(Total) = pop * (gdp/pop) * (energy/gdp) * (co2(for a unit of energy)/energy)”
That is somewhat better, yes. But we can still drop the pop and GDP completely from the above equation and get the same result.
The following would be a different story:
co2(Total) = # of persons * (GDP(individual)/person) * (# energy units/GDP(individual) * (co2/energy unit)
If the latter is the way it is actually done, and if we know the three ratios individually: (i) individual GDP per person, (ii) # energy units per individual GDP, and (iii) amount of co2 per energy unit, then, yes, I agree the Kaya Identity would be a useful calculation. However, I have sometimes seen it described the way Willis described it, including on Wikipedia. So maybe all this disconnect is simply an issue of properly laying out the equation so that people can see the actual units? I am personally rather new to this issue, so if the equation in practice is calculated the way I laid it out in the second example above (and not as Willis and Wikipedia have described it), I’d be grateful to know.
—–
Incidentally, my comments thus far have been separate from the question of whether the Kaya Identity gives the right answer. Probably most people would agree that the amount of co2 per energy unit is readily calculable (within some reasonable margin of error). The other two factors: GDP per person, and energy units per individual GDP, are presumably subject to quite a bit more subjectivity. But that is a separate matter.
Reply to JJ ==> Exactly so, sir.
Man, what a lot of verbage.
It is really simple:
When you’re in Kaya during the dry season, you drink beer.
Flag is good and brewed in Ouagadougou..
If you just reduce GDP by itself – What happens to CO2 emissions – Nothing.
If you just reduce Population by itself – What happens to CO2 emissions – Nothing.
If you just reduce Energy by itself – What happens to CO2 emissions – Nothing.
If you reduce GDP, Population and Energy ALL at the same time – what happens to CO2 emissions – Nothing
————————————————–
That is what is wrong with the equation.
You cannot reduce CO2 emissions without reducing CO2 emissions.
Let me rephrase my question, Daniel. How would you calculate the Kayla equation the very first time?
Willis! You’re obviously a brilliant guy but you were wrong about this in the first post and you’re wrong about it again. The car you’re driving in, the road you’re driving on, the fuel the car burns, etc. are all components of GDP.
The equation is valid but the only thing it does is approximate how much plant food we emit. It says nothing about whether that plant food will cause dangerous warming or how long it will remain in the atmosphere or anything else that might inform the debate.
Hard to comprehend why there are hundreds of comments on such a simple thing. It must be this burning desire to see Willis fail, no matter how trivial the point. I haven’t read all the comments – who has? – so there is a slight possibility that the following is duplicated.
This kind of expansion is similar to a chain rule expansion in calculus. For example we might write Newton’s second law in the following form (rectilinear motion).
F(x)/m = dv/dt = (dv/dx)(dx/dt) = vdv/dx
This simplifies the equation that can now be solved for “v” as a function of “x” if you know F(x). The important thing to note is that you can only do this if there is only one independent variable, here time “t”. On the other hand if there is more than one independent variable, application of the chain rule involves partial derivatives and more than one term. It might look like this:
du/dt = (du/dx)(dx/dt) + (du/dy)(dy/dt)
where the derivatives on the right hand side are partial. My point in all this math is that the Kaya identity assumes that there is only one independent variable (path) and that Willis is pointing out that there are many paths or variables.
Bill I,
GDP includes consumption. It even includes government handouts, even if they’re financed by debt. The only American’s who don’t emit CO2 are Luddites who live on self-sufficient farms and don’t use fossil fuel, even for kerosene lights.
If you add up all the energy consumed in America and divide by all the number people, you get something like the equivalent of a 7.5 horsepower engine, per person, running 24 hours per day. I think we should be proud of that fact.
American’s emissions went down significantly in the last recession because fewer products were being made and consumed.
America emits more CO2 than Canada mostly because we have more people.
Kaya Identity. Useless equation. You can always put an infinite number of terms into an equation that all cancel out. F= ((((Ma +C-C)/142)*142)/e**2)* e**2. The CO2 emissions per unit energy consumption of the country times the energy consumption of the country gives you the CO2 emissions. Population and GDP have nothing to do with it. If three people lived in the country and they had the same energy consumption as the United States (with the same energy mix) they would have the same CO2 emissions as the United States.
CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}
So your saying I can do my share to fight Global Waming and stop being a vile Denier by simply drinking less beer and more mead, I can do that!
Scott Scarborough says:
What those three people are doing with all that energy? How do they manage to produce, distribute, consume that energy? Yeah, you have only proved that Kaya identity breaks down in a fantasy scenario.
Willis’ request cuts both ways. Quote the exact words of him saying that.
[obs: I don’t get what you are saying.]
Population would be a factor if you wanted to count breathing as CO2 pollution.
JFD, the equation is used to calculate HUMAN emissions add to the environment by HUMAN activity. Since virtually all human activity that produces GDP requires burring fossil fuels the equation gives a close approximation.
Looks like a bit of semantic legerdemain.One is taking a semantic construct and mistaking it for a mathematical construct. Let’s take the M&M example. It is taking the phrase “Boxes per Crate” and rewriting it in a mathematical formula as B/C as though we are literally dividing the number of boxes by the number of crates. If the Ms on both sides of the equation are identical then this is patently useless. If the Ms are not identical then it is patently wrong. Let’s do the math. Let C=2, B=3, P=4. Lets use Mp to represent the number of M&Ms per package and Let Mp=5. We can all agree (hopefully there’s no debate 🙂 that the total number of M&Ms in all packages is:
Mt = C*B*P*Mp = 2*3*4*5 = 120. So far so good. Now let’s apply the M&M formula as written and as the authors apparently intended it to be applied, that is: Mt = C * B/C * P/B * Mp/P where the Ms on either side represent different quantities. So then we have Mt = 2 * 3/2 * 4/3 * 5/4 = 5. Patently wrong. On the other hand if both Ms are the same value then we have
Mt = 2 * 3/2 * 4/3 * 120/4 = 120. Which is patently useless as we need to know a priori the value of Mt.
The Mark Twain quote above says it all.
The Kaya Identity reminds me of a joke my college mathematics professor played on us back in the 1960s. He announced in class one day that someone had recently discovered a function f(n) whose value was a prime number for all positive integers, n:
f(n) = 10 + [sqrt(2)*exp(2*pi*n)+sin(2*pi*n) + etc. + etc.]^0
There are many ways. You could go and see how each energy source emits co2, take some samples, make the proper weighted average. There you have: carbon intensity of energy.
Measure gdp, energy consumption, and population. Calculate the ratios. Put on the Kaya Identity.
But the most simple way of using the identity is estimating energy-related co2 emissions some other way. And then start hypothesizing on what happens when rhs variables change. The relation between a rhs variable and energy-related co2 emissions might not be linear, but that is due to relationships between the rhs variables. The correct math is always to multiply the factors.
climatereflections says:
It is a technical convention, they are representing a [ratio variable] by a ratio of [variables], if you read the english on the paper, you may become less confused.
thallstd says:
July 12, 2014 at 9:37 am – re adding 10% to pop not necessarily reducing GDP/capita by 10%.
There is more to this. Indeed a history of GDP PER CAPITA GROWTH shows that GDP by the nature of its economic mechanics is not independent of population growth. In productive economies growing population causes excess GDP growth over and above the rate of population growth. This is a huge error in the Kaiya formula and demonstrates the level of economics understanding of sinistras. Indeed, one can see that their formula only works for despotic political economies by the fact that many of these have negative per capita growth.
Moreover, the CO2/energy also has an effect on GDP – the “alternative energies” reduce GDP growth and in the extreme even reduce population through destruction of economic activity, fuel poverty, etc. Ya know, when you are an elite who knows best for the great unwashed, these aspects are undescoverable to them.
Good call Willis, but its worth than you thought.
We can and do measure how much fossil fuels we burn. We can and do measure how much GDP we produce (which includes consumption). We can and do measure how many people there are. All these factors are knowable so the equation can and does allow one to approximate HUMAN emissions of CO2. Which is all it was trying to do.
The equation allows us to quickly compute approximately how much plant food we made in a given time period. That might be all it’s good for but it is good for that.
@Daniel G.
Here it is “And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.” I paraphrased. Of course I am assuming that you are speaking to me. You didn’t say. 🙂
“I don’t get what you are saying.” To channel Dirac, this is not a question.
Willis and friends,
First, I take it that the discussion has progressed to the point that you (Willis) and most readers now see that a mathematical identity can be useful if it serves to account for real-world causal relationships that affect the magnitude we’re interested in — in this case, CO2 emissions. The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified. The fact that the equation reduces algebraically to 1=1 is a red herring, because the ratios are measured directly as separate causal effects; the ratios are NOT measured simply as one empirical grand total divided by another empirical grand total. The Kaya Identity serves simply to account for the hypothesized causal effects and shows how they fit together into a bigger picture. It has no empirical content in itself, and it proves nothing itself — or as you say, “despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions.” The real-world conditions need to be tested. Still, the Kaya Identity is useful in providing an analytical framework that clarifies what conditions are to be tested. Agreed?
What you (Willis) appear to remain unconvinced about is that GDP is sufficiently correlated with energy usage (or that it addresses enough CO2 sources) to make for useful analysis. I believe you are mistaken.
Let me first join you and others here in acknowledging that GDP is an imperfect measure, especially when it comes to the value of non-marketed ‘household production’ and, for that matter, the enjoyment (or blessing or utility — all loaded words) derived from consumption activities. We economists know this, and we tell it to our students. If your gorgeous ex-fiancee had paid you for your drive (and this were reported to the IRS as self-employment income), or if you had taken the bus, then the trip as such would have counted directly toward GDP. Even so, as several commenters have pointed out, consumption expenses are accounted for anyway within GDP. GDP is (by definition) not only the total value of production, but also (roughly) the total value of income. Greater GDP means greater income, meaning greater household consumption, including consumption of energy.
Already on this basis, it doesn’t matter whether (quoting Willis), “I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.” Our GDP includes your income that you spend in part on energy consumption, whether from domestic or foreign sources.
Beyond that, it turns out that, given the ways that international payments have to add up, the value of oil imports still affects the total value of U.S. production. Greater imports lead, via depreciating exchange rates, to greater exports and thus greater U.S. goods production, at least to a first approximation. (A decent macroeconomics textbook will explain why. It’s analogous, by the way, to why we don’t care whether your drive affected the GDP of California or of Nevada. It truly doesn’t matter.)
Your counterexample does not stand.
(Willis, 11:02 a.m.): “consider things like the flaring of gas from oil wells, or the CO2 coming from underground coal fires in Pennsylvania, India, and China. None of them are in the Kaya identity, but all of them emit copious quantities of CO2.”
The Kaya Identity does not purport to account for all CO2, in particular what comes from natural sources (volcanos) or unintended human sources (underground fires, or forest fires for that matter). Those are not the object of proposed “levers”. Gas flaring is a normal part of energy production, so it’s accounted for in the CO2 intensity of energy usage. Furthermore, the reduction of flaring is indeed a potential lever.
These counterexamples do not stand either.
Do you have another?
Greg Smith says:
July 12, 2014 at 1:44 pm
Here is another “identity” along the lines of what dp and John West were explaining
G = M / MPG
where G is gallons of gasoline consumed
M miles in trip
MPG vehicle mileage in miles per gallon of gas consumed
Which when you look at the terms
(Gasoline consumed) = (miles traveled) / (miles traveled per gallon consumed)
Whoopie, we now have
(Gasoline Consumed) = (Gasoline Consumed)
So, the “identity” tells us that the gasoline used for a given trip is the gasoline used for a given trip. Big whoop.
I put “identity” in quotes since this is really a DIMENSIONAL EQUATION that lets me determine how much gasoline I will need for the 230 mile trip from my place in Southern California to Las Vegas. (I know what kind of MPG my car gets.) You can argue all you want about how useful the equation might be if you have no clue as to how you get MPG for your car. I know what MY car gets in fuel economy.
It’s not as simple as that. A car’s MPG varies with highway or city driving, traffic conditions, engine maintenance—and driving style. Two cars in identical condition driven through the same area in identical traffic conditions can have different MPG depending on how they’re driven.
As for anthropogenic CO2 emissions, doesn’t the Kaya Identity apply to countries? If a country imports and consumes a lot of soft drinks, beer, champagne, and other bubbly (carbonated) drinks, wouldn’t the release of all that CO2 count in the consuming country’s emissions, but the sales would be reflected mainly in the manufacturing country’s GDP?
But personally, I agree with BioBob when he said, “this discussion is pretty much like arguing about how many angels dance on the head of a pin.” Anthropogenic CO2 is a minuscule percentage of total CO2. And the threat of catastrophic warming from CO2 is only in the models—models that haven’t been validated. In reality, the increase in CO2 has been beneficial in greening the planet. Even if total CO2 were to reach 10 times—or even 20 times—the current level, it would still be within the safe range for human life, so why are we bothering with accounting for it?
http://wattsupwiththat.com/2012/10/17/claim-co2-makes-you-stupid-as-a-submariner-that-question/
All valid equations have the units cancel out. The question remains whether there is validity to the equation and if it captures most of the important variables related to emissions. It has some validity. After all, humans do emit CO2 in a variety of ways. But this equation leaves out natural emissions.
I like it because it will be obvious to most people that the goal of the extremists is to lower the number of people and to lower standards of living. I hope Hilary uses it in a commercial or a debate.