The Beer Identity

The Kaya identity is even more useless than the Drake equation. With the Kaya identity, anything can be put on the right-hand side, because they are not factors when they are on both the numerator and denominator. They are all 1.

Willis,
I am sure that *you* may not be contributing to the GDP by driving down the road, but your car and everything that supports the operation of that car are providing a service to you. And that service can be part of the GDP, can it not?
I read somewhere that GDP is actually not a good indicator of useful economic activity because it includes all of the goods and services produced, whether useful or not. Cleanup after a natural disaster is part of the GDP. So is war.
-BillR

You most certainly are a part of the GDP. You bought the gas and that was registered as part of the GDP when it was manufactured and sold to you. It is a decent assumption that most gas sold will be consumed in internal combustion engines and CO2 thereby released into the atmosphere, so your emissions are lumped in with mine and everyone elses.
Dave

The same problem of not representing the real world can be seen with climate models and the passionate belief some have in them. In fact many models in many fields.

So, I see you’ve quietly backed away from your original mathematical objections and resorted to even more specious objections.. Could you please comment on Pielke’s usage of the Kaya equation, and his findings that it matches real world numbers well? http://rogerpielkejr.blogspot.com/2014/06/clueless-krugman.html

I wasn’t very good at math but I think that if you write X= Y*z/y*w/z*x/w
The ys,zs,and ws all cancel each other, and all you are left with is x=x . You can substitute any terms you want and it doesn’t make any difference. So you have CO2 emissions= CO2 emissions. So what we know that.

My complaint is the evil simplicity inherit in such nonsense. Writing up some silly little line of mathematics, with values attributed to less than a handful of things… this is a reflection? Bollocks. The problem with science and all other analyticals are that they are still much too simple and pedestrian. How do I feel today? Feelings=S (stuff) multiplied by T (things) aggregated by O (others) trumped by W (weather). It’s bright and sunshiny. I feel like crap. But the lake is nearby and I’m gonna have an awesome day! Predict that. I dare you. Come up with an “Al Gore Rhythm” that predicts what sort of day I’m going to have. YOU CAN’T! I’m too complex. The world I live in is too complex. Am I to believe that my own little body, my own little brain is more complex than the entire world’s climate? Before your answer, know this: I’ve already got a big enough ego. No need to feed.

Gary says “Come up with an ‘Al Gore Rhythm’ that predicts what sort of day I’m going to have.”
Well, you did cause me to think about Willie Nelson’s “Sunny Side of the Street!”

Willis,
You REALLY should preface this entire topic by pointing out that:
1) human CO2 emissions comprise approximately 2% of TOTAL global CO2 production,
2) therefore this discussion is pretty much like arguing about how many angels dance on the head of a pin.
Humans always like to think of themselves as important. However, in this case, humans are pretty much as significant as the rounding error. But I agree with you that attempting to model complex systems with a simple equation is bound to fail to predict aspects of that system’s behavior.

About that Pielke piece. http://rogerpielkejr.blogspot.com/2014/06/clueless-krugman.html
“As an identity, it is expressed –> CO2 = P * GDP/P * E/GDP * CO2/E (where P is population and E is energy consumption). The math here is simple. Increases in GDP, all else equal, mean that CO2 emissions go up.”
Yes, the math is simple, and if you increase GDP it STILL CANCELS.
I think my PhD buddy calls this “Harvard Stupid”.
Pielke did what nearly everyone does — Transforms the text into a formula that does not capture the text.
“population * GDP per capita * energy intensity of the economy * carbon intensity of energy”
The problem is expressing each term as a ratio of the other terms. That makes it inherently reflexive or self-dependent (circular) and it DOES matter how you actually do this. The carbon intensity of energy is PER UNIT of each.

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.

That isn’t what the paper said it was doing:

The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO2 emissions.
CO2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO2 emissions per unit of energy:
CO2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy)
If we take as given the population trajectory and assume a rising trajectory of GDP per capita in line with a successful economic development program, then CO2 emissions are driven mainly by two factors: Energy/GDP and CO2/Energy. The first term is the energy intensity, meaning the amount of energy per unit of final output. The second term is the carbon intensity of energy.

Since GDP is defined as the sum total of all economic activity and every unit of economic activity requires some amount of energy to produce there is nothing wrong with the identity.
There is plenty of room to quibble with how those two values are comprised, and how they should be calculated. Saying the identity was a “basic math error” is simply an error on your part and a misrepresentation of what they were trying to do.

I don’t understand what the argument is about. The “Kaya equation” is mathematically meaningless. Standard mathematical reduction removes “Population”, “Energy” and “GDP” from the equation, leaving “CO2 = CO2”.
While this is obviously true, it is meaningless.
(Anyone not understanding “mathematical reduction” it means any expression “A / A” can be removed from an equation without changing the truth of the equation. This also includes such expressions as “(A / B) * (B / A)” – that also equates to “1”.)

Willis Eschenbach: 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.
If you could come up with some examples of such false sense of security, you might have a case.
Note that with the more complex applications of the general circulation models, there have been examples of a false sense that the model outputs are accurate. Much more complicated models, but it could be the case that the models themselves are complete and accurate, but the parameter values (analogous to the ratios in the RHS of the equation under discussion) might be wrong, either a few of them or many of them, by small or large amounts.
In lots of places it has been shown that correct applications of reasonable rules sometimes produce unreasonable results. By the usual rules of English, “grue” and “bleen” could be words, it just happens that they are not.
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.
Where you are wrong is in your inference that, because the Kaya identity may be used ridiculously, it must necessarily be ridiculous. But where you choose ridicule, others may choose utility.
I think that point doesn’t make sense to you (a guess!) because from the start you see no utility in reducing anthropogenic CO2 (another guess! or perhaps a reasonable inference?). On that I agree with you (or with my guess about you), but the flaw is not in the equation.

Clearly both identities need a additional factor, (1 + epsilon). And some way of estimating the size of epsilon. And in the case of the Beer identity, lots and lots of field work.

I agree with Arthur it is a meaningless formula as it is a beancounters approach to complex issues.

Thanks Willis, GDP is an interesting parameter, mass destruction, i.e. riots, wild fire, so on, will cause GDP to rise, if the effected society rebuilds.
So vandalism is arguably good for GDP.
The reaction to your earlier post is very interesting, almost an “Ah Ha” moment.
We see a major communication breakdown.
Why?
From my perspective, algebra requires agreed definitions and internal consistency, therefore I too LOL at the self cancelling Identity.
From others POV apparently the defined terms are flexible, CO2=Not CO2, but some other definition, yet they insist the equation as expressed is valid.
Either my reasoning processes are completely askew or we are not using the same language.
Now as a cynic with experience as a govt employee, I lean toward the belief this corruption of language(Algebra in this case) is deliberate.
Policy meetings are a revelation that should be compulsory viewing for all taxpayers.
This “Identity” has all the earmarks of bureau speak, as it says nothing of value, while appearing to contain information.

http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1684364
How about auto insurance, motor vehicle fees and property taxes? How do they count towards Kaya

Well, as the EU has included blow and hookers in its GDP, we can clearly now fix the Global Warming thing by using less blow and hookers because that way we would reduce our GDP. BTW we would get the added advantage of less addiction and STD’s.

What happens if we divide both sides with CO2?

I don’t know anything about Kaya’s Identity but shouldn’t it be:
CO2 emissions = Population * GDP * Energy use
_______________________
Energy efficiency
Where efficiency is based on CO2 generated per unit of energy?
cn

You can rearrange the equation in a multitude of ways, since terms cancel out. One way would be to say, ultimately, that co2 emissions = GDP * (dollar-of-GDP-specific co2 emissions).
Of course, the problem is that the last term, the dollar-of-GDP-specific co2 emissions*, can only be calculated by dividing the total amount of co2 emissions by the GDP. Consequently the rewritten identity predicts nothing.
The value of an “identity”, at least in accounting, is that you can have a basis to reconcile independently-determined terms in the identity. When you can’t get terms in the identity other than by “begging the question” (i.e. only as a function of other terms in the identity), then the identity is as useful as any other tautology.
*Why call them “carbon” emissions, when the molecule is represented as CO2, with twice as many oxygen atoms as carbon? Logically, we should call them “oxygen” emissions, in preference to “carbon” emissions, if we want not to call them carbon-dioxide emissions.

Steven Mosher says:
“If no one bought gas what would happen to gdp”
I do believe it would go down and the equation in question would suggest CO2 emissions would also go down. How about that, an equation that reduces to X=X revealing useful information.
Kinda like:
Seconds = Seconds
Seconds = Minutes X Seconds/Minute
Seconds = Hours X Minutes/Hour X Seconds/Minute
Seconds = Days X Hours/Day X Minutes/Hour X Seconds/Minute
Seconds = Years x Days/Year X Hours/Day X Minutes/Hour X Seconds/Minute
etc. etc.
So how many seconds in 3 years? Use the equation above that reduces to X=X without even knowing the answer to begin with but knowing how many seconds are in a minute, minutes in an hour, hours in a day, and days in a year you can calculate it. Amazing!
BUT: How many hours are in a day? 24 you say? Well, is that exactly 24? What difference does it make? For 3 years not much, but what if you were calculating for a few hundred million years? Hmmm. The accuracy of my equation is dependant upon the accuracy of the factors within it. Surprise surprise.

What about the methane from drinking beer and sending the used grains to the feedlots?

Willis,
Thankfully, you have dropped the mathematically ignorant look ma, everything cancels so it must be wrong and I must laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.
Unfortunately, that means that you’re doubling down on the remainder of your argument. That has two main components. The first is your “Beer Identity”. The second is used to enable the first, and is your use of equivocation, playing on the ambiguity of the vernacular descriptions of the KI terms. Both are fallacious.
Addressing the second first, we have this assertion from you:

“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.

That is not exactly correct. It is certainly good enough for people who read the whole paper and understand the KI and who are using it and discussing it in good faith. Unfortunately, that doesn’t describe how you are approaching it.
In the KI, “CO2 emissions” are not “the CO2 emissions of say a given country”. They are more specifically the energy-related CO2 emissions of a given country’s economic production.
Similarly, in the KI “Energy” is not “energy consumed by the country”. It is more specifically the energy consumed by the country for economic production.
You equivocate on these terms, switching back and forth between specifics of your choosing. You then think you have proved something when you point out the bust that you have fabricated by playing with the definition of terms. This is how you hide the fact that your “Beer Identity” is mal formed, when the KI is not. Uncovering your ruse is as simple as putting descriptive subscripts on the terms. The KI thus becomes:

And your “Beer Identity” kludged from the KI becomes:

With the equivocation removed, the reader now easily sees that some things in your “Beer Identity” look a little odd. A couple of your terms express a ratio of one item defined relative to GBP vs another item defined relative to GDP. Those terms don’t seem particularly useful, as (unlike all of the terms in the Kaya Identity) they don’t have any meaning WRT things we commonly talk about in the real world.
More importantly, the reader now easily sees that there are some things in your “Beer Identity” that are very different than you describe them. This is shown in you supposition:

Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer.

And in your subsequent restatement of the “Beer Identity” with the figure 0.9 thrown in, which allegedly represents an increase in the energy efficiency of beer production.
The problem is, there is no term for the efficiency of producing beer in your “Beer Identity”. That term would look like this:

And that term is not to be found anywhere in your “Beer Identity”. So, your claim that your application of the 0.9 factor to your “Beer Identity” represents a 10% increase in beer production energy efficiency is simply false. You did not do the math correctly.
I trust that the website owner will now add to this post the entirely accurate sub heading:
“Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.

Arthur says:
July 12, 2014 at 12:03 pm
=================
As I mentioned above, it is useful if you have determined the quantities that you plug into the identity independently of each other, otherwise it is not.
Consider the identity:
Balance in my bank account = (statement balance) + (deposits made since statement) – (withdrawals made since statement).
Ultimately, this says “balance in my bank account = balance in my bank account”.
However, since you can determine each quantity independent of the others, when you go through the motions and find out that it does NOT balance, you look for an error.
Millions of accountants do this every day, and have done so for a good number of years. They don’t seek to derive new insight from the identity itself, they use the identity as a way of validating independent observations of the factors in the identity.

Willis is completely missing the point of this identity. The Kaya Identity has 4 terms and shows that an UP or DOWN change in any of those 4 terms will result in a corresponding change, in the same direction, in the CO2 output. It doesn’t include coefficients or non-linearities. It doesn’t communicate the _magnitude_ of change, only its _direction_.
Willis says:
“Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%.”
You are correct, Willis, It will not reduce CO2 emissions by exactly 10%. But that’s where you are getting lost, You are looking for this identity to predict precisely how large the change will be and it simply doesn’t attempt to do that. The identity only shows you the _direction_ off the affect, not its magnitude.

kabend says:
July 12, 2014 at 10:53 am

V = R * ( I / R ) * ( V / I )

To rephrase it and expose the subtlety:
The equation:
V = I / R
Expressed simply as an identity:
V = R * ( I / R ) * ( V / I )
Then verbosely expressed as a dimensionless identity,
units of voltage = units of resistance * (units of current / units of resistance ) * (units of voltage / units of current )
defines a dimensionless unit (of voltage) on the LHS and nothing else. It does not resolve to a value expressed in this form.
V = I/R produces a quantity expressed in volts where variable I is a quantity of current, and the variable R is a quantity of resistance

Sheesh. Mr. Kaya must be laughing his ^%$* off at how seriously everyone is taking his equation. The thing is nothing more than a political statement masquerading as a scientific formula. It deserves ridicule, not serious thought.

I may be missing the higher point about the Kaya identity equation, but I agree with Willis it is practically useless. In order determine a value, we must already know so much about energy consumption, GDP, and CO2 emissions and their relationships it would be more direct to just use total fossil fueled power consumption and the rate of CO2 per unit of power consumed (gas, oil, coal)? Also, Kaya implies that for any society or country the rate of non-GDP power consumption will be the same. Comparing for example China and in the U.S., the Kaya calculation of CO2 would skew the numbers favorably to the U.S., because although not included in the GDP, power consumed (and thereby CO2 emitted) for personal auto use, home heating, recreational uses, etc.) per GDP would be much higher in the U.S. than in China. Of course, the power used in producing the energy is included in GDP, but the potential energy in the fuels burned is not. I think that with the huge amount of data already available about the hot-potato issue of CO2, concepts such as the Kaya identity have no practical or scientific value.

In order to consume a car, insurance, gas, sandwiches, beer, sunglasses, and the road you’re driving on those goods must first be produced. The total value of goods produced must equal total expenditures. You can calculate GDP by adding up either one (or incomes for that matter).

Wouldn’t one need to know all of the inclusions that go into calculating GDP before they could exempt their activity from the equation? Likewise, the Kaya equation places value on economies that can create higher GDP with lower CO2 emissions which both presently and unfortunately incentivizes paying more than we should for energy. The US political risk on coal should cause its price to plummet so keep building those coal plants China your ROI can only get better.

Arthur says:
July 12, 2014 at 10:10 am
I don’t understand what the argument is about. The “Kaya equation” is mathematically meaningless. Standard mathematical reduction removes “Population”, “Energy” and “GDP” from the equation, leaving “CO2 = CO2″.

Your misunderstanding comes from misreading. It is “Kaya Identity”, not “Kaya equation”. There have been multiple examples given of what identities are and now they differ from a mathematical formula, but this is not being understood by the identity deniers. (I say, that’s a joke, son)
The Kaya identity if perfectly valid as a mathematical tool when used correctly. Whether it is useful for analyzing the import of CO2 to GDP growth, population growth, and rate of energy consumption is certainly debatable. The difficulty thus far has been the lack of scope of the variables, GDP, population, and energy. Even if scoped there is still the disagreement of the validity of the scope. In the PNAS and Roger Pielke Jr. analyses the scopes have been identified but with no consensus, but that does not prevent discussing the results. As a visualization tool it is perfectly suited to what-if’ing a problem where ranges of reasonable data are tested.
The calculator here is buggy but does give you a sense of impact the variables impose on the results.
http://forecast.uchicago.edu/kaya.html
For example, set the end population to the current population, 6 billion (population does not change over time) the result is just what you expect – a flat line. That is an unrealistic value, though, unless there is a pandemic or catastrophic world war. Reasonable best, and worst case values can be plugged in to see what happens over the period of analysis.
It may not be obvious, but the analysis is done over the time period 1900 – 2100, and observed is shown by red dots ending at Y2K, and the errors are obvious though the trends are close.

Kabend 10:53 says
“V is proportional to (I/R),” which is NOT true.
Being a New Yorker, I felt it incumbent on me to write something obnoxious like, “The proportionality constant is R*R, which is a constant, as those little lines someone drew around the circumference of my resistors tell me.” But then, a light bulb went off in my head: I doubled my thinking intensity, but the flow of ideas increased by only 25%! Sincerely, thanks for a great idea for helping my students understand that V = IR is not a complete statement of Ohm’s Law.
Now, this brings us to use of Kaya-Beer and the use of GDP as a surrogate for carbon dioxide emissions, or, for that matter, tree rings for temperatures. As noted above, the nonlinearities and excluded variables kill you. I never did like the Chain Rule anyhow. Fortunately (?), the UN realizes that a “carbon” tax based on GDP is a non-starter, as the PRC is still a developing nation, and would never go for it. Unless Kerry was a better diplomat around the time of his Jakarta speech than he was a Climate Scientist.

Kate Forney says:
July 12, 2014 at 1:22 pm
I certainly don’t *believe* per-capita GDP can be determined without separately determining GDP and population, neither do I *believe* energy used per dollar of GDP can be determined without determining total energy used and total GDP.

For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.

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.
Anyway, the “Kaya Identity” is NOT an identity but a DIMENSIONAL EQUATION. And the REAL question is: How do you measure CO2 emissions per GDP? (And is that even a worthwhile measurement?)

dp says:
July 12, 2014 at 1:38 pm
For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.
===============
Why yes, thank you for that, although that is of only tangential bearing on my argument, except to illustrate that there is no way of ascertaining the ratios without first ascertaining the principal quantities and dividing, unlike, say density, mass and volume: It is possible to estimate density without first measuring mass and volume and then dividing. If you do so, then the tautology/identity/definition of density=mass/volume becomes a useful tool for you to check on the correctness of your three estimated quantities.

Well MY problem, with granting the “Kaya Identity”, with any credibility at all, is that ANYBODY can simply write his own product of factors; each of which is some ratio, that all conveniently, cancel via the Willis math; and simply concoct an illusion that some factor is a significant issue in climate.
Take “Energy / GDP ” for example. What evidence is there that this is an important climate phenomenon. ??
For starters, The USA is a big energy user; but we also have a big GDP; well we used to pre-Obama. We also don’t have that large a population, in World terms. So why is the USA the whipping boy in the pollution sweepstakes. and the USA is a net carbon sink, because of our agriculture and forestry. In fact we are the only large (land) one on the planet. Also, the USA spends vast amounts of its resources, which are energy intensive, on defence. much of that is to provide defence of others, who spend little of their own resources for their own defence; relying on the USA to bail them out.
How do you compare the GDP and population, and petroleum based US economy, with the GDP. population, and cow dung fuelled economy of some other country.
If energy consumption per GDP is an important factor to minimize, then PV and wind solar should be abandoned immediately. Natural gas and petroleum, are much more efficient at GDP production.
No I put the Kaya Identity at about the same place as the Drake Equation (identity), as something to sit up and take notice of; pretty much idle nonsense.
And that is a personal opinion. No great climate significance should be assigned to my opinion.
g

I wasn’t very good at math but I think that if you write X= Y*z/y*w/z*x/w
The ys,zs,and ws all cancel each other, and all you are left with is x=x . You can substitute any terms you want and it doesn’t make any difference. So you have CO2 emissions= CO2 emissions. So what we know that.
The z/y and w/z and x/w are just representing ratio variables.
Again, I will invoke the M&M’s example:
You have crates (C crates), inside those crates there are boxes (B boxes). Inside those boxes, there are M&M’s packages (P packages), and of course, there are M&M’s (M M&M’s) inside of those.
The number of M&M’s can be found by multiplying the number of crates by three rations: boxes per crate, packages per box, M&M’s per package. Those ratios can be represented by B/C, P/B, M/P
Then:
M = C * (B / C) * (P / B) * (M / P)
Is this identity too trivial? Useless?

The Kaya identity is even more useless than the Drake equation. With the Kaya identity, anything can be put on the right-hand side, because they are not factors when they are on both the numerator and denominator. They are all 1.

The factors are population, gdp per capita, energy intensity of the economy and co2 intensity of energy. They are not all 1.
Willis Eschenbach wrote:

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.

Fuel is included in the gdp, duh.

“””””……dp says:
July 12, 2014 at 12:21 pm
kabend says:
July 12, 2014 at 10:53 am
V = R * ( I / R ) * ( V / I )
To rephrase it and expose the subtlety:
The equation:
V = I / R ……””””””
Well I don’t know at what school you studied Electricity, but a simple dimensional check would show you that V most certainly does not, nor cannot, be equal to I/R.
For that to be true, I would have to have units of volt, instead of amp, and R would have to be a dimensionless number, instead of ohm; or at least R^2 would, since you have, in effect:-
volt = (volt / ohm) /ohm = volt / ohm^2
I have no idea what ohm^2 represents in electricity.

george e. smith says:
July 12, 2014 at 2:14 pm
You’re correct – I miss managed a cut/paste from the OP’s post.

How would one go about actually *applying* the Kaya Identity?
I’m struggling to see how it would work in practice.

climatereflections says:

How would one go about actually *applying* the Kaya Identity?
I’m struggling to see how it would work in practice.

See J.K.’s example in the previous post by Willis.

The Kayla equation leaves out valuable input information. Carbon dioxide emissions come from nature as well as GDP generation activities. Carbon dioxide from burning fossil fuels is 10 billion tonnes per year. Loss of wetlands in just Brazil and Indonesia total 2.5 billion tonnes per year of carbon dioxide emissions. GDP implicitly implies human activities. The Kayla equation would have to be rearranged to a fixed (natural) + variable (human) term to be of any use for climate predictions involving GDP. GDP is not uniformly generated either. The 80-20 rule basically applies to GDP. Twenty percent of the population generate 80% of the GDP while 80% of the population generates 20% of the GDP. Thus, there is no direct 1 to 1 relationship as suggested by the Kayla equation between GDP and population increase. It would take more factors to come up with the proper coefficients to use for the GDPs in the 20% group and in the 80% group relative to energy use.
I think that Willis wins this one while Mosh loses big time.

Daniel G. says:
July 12, 2014 at 2:06 pm
Then:
M = C * (B / C) * (P / B) * (M / P)
*********************************************
Why so many terms to prove your case? Why not just M = P * M/P ?
Lets say M = the grand total final number of M&Ms we are trying to find without knowing ahead of time how many.
Lets say P = number of packages = 100. (I like M&Ms)
Lets say M/P = the grand total final number of M&Ms we are trying to find without knowing ahead of time how many DIVIDED BY number of packages = 100. Your know, just to be clear so no one thinks we have a 3 card monty going on here.
Ah but it is a shell game, the M on the left is not the same M we have on the right is it?

Does it respect the efficiency of car engines?

Hey, take a look at one of your ratios: (CO2 / (number of cars))

Anthony or Mods – The LaTex encoded formulas in my post above got stripped, leaving a long post that is more or less pointless as the referenced formulas cannot be seen. Could you
a) replace the post above with the post appended below, which is identical except in that it replaces the stripped LaTeX references with hyperlinks that I have run thru the WWUT test page to ensure function
b) point toward a couple tips on the best method for posting LaTex to WUWT?
Thx
********
Willis,
Thankfully, you have dropped the mathematically ignorant look ma, everything cancels so it must be wrong and I must laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.
Unfortunately, that means that you’re doubling down on the remainder of your argument. That has two main components. The first is your “Beer Identity”. The second is used to enable the first, and is your use of equivocation, playing on the ambiguity of the vernacular descriptions of the KI terms. Both are fallacious.
Addressing the second first, we have this assertion from you:

“To start with, the Kaya Identity states:
Kaya Identity EQN
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.

That is not exactly correct. It is certainly good enough for people who read the whole paper and understand the KI and who are using it and discussing it in good faith. Unfortunately, that doesn’t describe how you are approaching it.
In the KI, “CO2 emissions” are not “the CO2 emissions of say a given country”. They are more specifically the energy-related CO2 emissions of a given country’s economic production.
Similarly, in the KI “Energy” is not “energy consumed by the country”. It is more specifically the energy consumed by the country for economic production.
You equivocate on these terms, switching back and forth between specifics of your choosing. You then think you have proved something when you point out the bust that you have fabricated by playing with the definition of terms. This is how you hide the fact that your “Beer Identity” is mal formed, when the KI is not. Uncovering your ruse is as simple as putting descriptive subscripts on the terms. The KI thus becomes:
Kaya Identity EQN w/expanded descriptions
And your “Beer Identity” kludged from the KI becomes:
Beer Identity w/expanded descriptions
With the equivocation removed, the reader now easily sees that some things in your “Beer Identity” look a little odd. A couple of your terms express a ratio of one item defined relative to GBP vs another item defined relative to GDP. Those terms don’t seem particularly useful, as (unlike all of the terms in the Kaya Identity) they don’t have any meaning WRT things we commonly talk about in the real world.
More importantly, the reader now easily sees that there are some things in your “Beer Identity” that are very different than you describe them. This is shown in you supposition:

Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer.

And in your subsequent restatement of the “Beer Identity” with the figure 0.9 thrown in, which allegedly represents an increase in the energy efficiency of beer production.
The problem is, there is no term for the efficiency of producing beer in your “Beer Identity”. That term would look like this:
Energy Efficiency of Beer Production Term
And that term is not to be found anywhere in your “Beer Identity”. So, your claim that your application of the 0.9 factor to your “Beer Identity” represents a 10% increase in beer production energy efficiency is simply false. You did not do the math correctly.
I trust that the website owner will now add to this post the entirely accurate sub heading:
“Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.

The fact the IPCC uses this ‘equation’ to determine the impact humans have on the climate, invalidates everything done by the IPCC.

Well, is that true? I didn’t read the AR5 WGII report, but can you find the chapter for me?

Ah but it is a shell game, the M on the left is not the same M we have on the right is it?

Kaya Identity is analogous, because we have been using symbolic a/b to represent a ratio variable.

How would you use the Kayla equation to predict the relationship between population and CO2 emissions? It certainly is not 10% growth in population = 10% more CO2 emitted.

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.

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.

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..

Let me rephrase my question, Daniel. How would you calculate the Kayla equation the very first time?

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.

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.

Scott Scarborough says:

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.

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.

Population would be a factor if you wanted to count breathing as CO2 pollution.

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.

Let me rephrase my question, Daniel. How would you calculate the Kayla equation the very first time?

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:

So maybe all this disconnect is simply an issue of properly laying out the equation so that people can see the actual units?

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.

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?

Dr. Doug @ July 12, 2014 at 4:42 pm
Thanks for your clear, lucid, and compelling argument. . . truly a welcome voice of reason. Yet after two or three day of WUWT folks decrying that the Kaya Identify is nonsense because the identity balances dimensionally . . . and regrettably this group includes Mr. Eschenbach. To me, identities and equations, such at the Kaya Identity are common in What-If analyses as well as in macroeconomics. But to Mr. Eschenbach and his acolytes this means nothing and they reject any such thoughts on trivial dimensional grounds.
Thanks again for your clarity of thought. Maybe you’ve made inroads in providing a useful perspective to Willis and company. But I fear that Willis has entrenched and doesn’t seem to want to listen or attempt to understand alternative perspectives. Sad.
Best
Dan

Don’t you see that how many people produce the CO2 has absolutely nothing to do with how much CO2 is produced? If 10 people produce 1 lb of CO2 or 1000 people produce 1 Lb of CO2 it makes no difference at all to the amount of CO2 produced. No “scenarios” involved.

Charles the moderator –
I don’t know whether you’re recent response to noaaprogrammer was the comment at July 12, 2014 at 4:33 pm
But his/her equation: f(n) = 10 + [sqrt(2)*exp(2*pi*n)+sin(2*pi*n) + etc. + etc.]^0 evaluates to 11 for all n (presuming the etc. etc. don’t exhibit singular lies). You’re correct, it’s simply “cute” and not very informative but 11 is a valid prime number. Correct me if I’m wrong.
Dan

Lots of folks are still not getting it.
The Kaya Identity is an identity, not an equation. The identity contains only units. The units better cancel out in an identity, or the identity is false. There are no variables in an identity. It’s purpose, useful or not, valid or not, is not about calculating a value. It can’t; it has no placeholders for values.
An equation has variables in it, and can be used to calculate something.
If the Kaya identity was altered to be an equation, is would look something like:
.
(T Co2 Emissions) = (X Population) * (Y GDP / Z Population) … * (A Co2 Emissions / B energy)
And X and Z would have different values. X might be something lke 100,000,000, and Z would probably be something like 1. Similarly, A and T would have different values.
Other people’s discussions about the functional validity of the identity can’t be understood without recognizing the difference between an identity and an equation.

10 July: Bloomberg: Eric Roston: Fix the Climate Problem? Easy. Cut U.S.
Emissions to 1901 Levels
A draft report prepared for the United Nations suggests, out loud, what the
U.S. needs to do about climate change: Cut emissions to one-tenth of current
levels, per person, in less than 40 years…
The report, Pathways to Deep Decarbonization, describes how nations might be
able mitigate against dangerous climate change.
***Two organizations wrote it to provide national leaders and UN agencies with a specific vision of how 15
leading economies can slash climate pollution.
The study contains detailed sections on each of a dozen large national
emitters, including the U.S., China, Russia and the U.K. It suggests to
national leaders that cutting carbon may be possible, without economic
compromise and without fear that they’ll have to go it alone. Such analysis
might help them generate the political support they’ll need to make the UN
climate negotiations in Paris at the end of 2015 successful…
http://www.bloomberg.com/news/2014-07-09/fix-the-climate-problem-easy-cut-u-s-emissions-to-1901-levels.html
***Bloomberg’s Roston may have provided a link to the following, but it was clear he wasn’t eager to name his “two organizations”!
UN Sustainable Development Solutions Network: Deep Decarbonization Pathways
The Sustainable Development Solutions Network (SDSN) and the Institute for
Sustainable Development and International Relations (IDDRI) co-founded and
lead the DDPP.
Currently, the DDPP comprises 15 Country Research Teams composed of leading
researchers and research institutions from countries representing 70% of
global GHG emissions and different stages of development: Australia, Brazil,
Canada, China, France, Germany, India, Indonesia, Japan, Mexico, Russia,
South Africa, South Korea, the UK, and the USA…
Several Partner Organizations contribute to the analysis and outreach of the
DDPP, including the German Development Institute (GDI), the International
Energy Agency (IEA), the International Institute for Applied Systems
Analysis (IIASA), and the World Business Council on Sustainable Development
(WBCSD). We invite other organizations to become DDPP partners and
contribute to practical problem solving for deep decarbonization.
Australia:
Centre of Policy Studies, Victoria University
ClimateWorks Australia, Monash University
Commonwealth Scientific and Industrial Research Organisation (CSIRO)
Crawford School of Public Policy, Australian National University
United States
Energy and Environment Economics (E3)
http://unsdsn.org/what-we-do/deep-decarbonization-pathways/

It’s worth noting the name, ‘Kaya Identity’. From a branding perspective, it’s an ideal choice of name. It evokes colour, rainforests, peaceful tribes, femininity, compassion and magical force.
If it had been called the Schmidt* Identity, people would dismiss it more readily as something that comes from a paper-pusher.
* A Hogan’s Heroes reference.

Here’s something to ponder based on Willis’ gasonline / GDP example. The oil used in the gas Willis purchased was from Saudi Arabia. They sold it, it became a part of their GDP, but no carbon was released from that oil to add to the CO2 emissions in Saudia Arabia. The oil was then sold in the us as gasoline and burned, adding to the US GDP and CO2 emissions. You could almost argue that two GDPs combined to create the subsquent CO2 emitted. When I looked at what I think was the original definition of the Kaya Identity, it was global GDP, population, energy and CO2 emissions being described. As such, is the Kaya Identity useful at all when used to analyze individual countries or should it be confined to analysis global in scope?

Rdcii @5:35 p.m.
Just to be clear, are you saying that the Kaya Identity does not in fact calculate anything, contra to what Daniel G has been arguing, and contra to what Daniel G says the UN paper does?

Consumption Production – even though putting gas in one’s car contributes to commerce, driving down the road for pleasure is not a productive activity – nothing of value results from it. Contrary to Krugman’s fantasy, a country’s wealth lies in its productivity, not its spending. Since war is destruction, it cannot contribute to our productivity, once the bomb has been used, nothing of value remains, and much of value has been destroyed, just as the hundreds of billions of dollars wasted by the federal government on useless programs and fraud are actually decreasing our national product rather than increasing it, yet both of these examples are included in the current GDP calculation. So I concur with Willis, driving down the road using gasoline is contributing to the CO2 in the atmosphere but not the true GDP.

I have a NEW Equation / Identity! Klimut Science = CO2 = GDP / CO2 = Bullshit produced * $ / CO2 THEREFORE: CO2 * Klimut Science = Bullshit produced * $ AND: Klimut Science / $ = Bullshit Produced

Yes unfortunately GDP is not linked to energy use in any formal sense, though there might be a loose association, such the GC02-e rises at the same time as GDP. The question is one of causality, which is unproven. I think you are making a case for the green argument such that they claim to believe that economies can be uncoupled from carbon energy. Though I don’t think they really know how.

Andrew N @6:15 pm:
Whether it is “fundamentally correct” depends on whether the variables do what they are claimed to do. Which is another topic. (See #2 of my comment @5:03 pm.)
That said, I suspect you are right that we are dealing with confusion due to how the Kaya Identity was presented (by Willis, Wikipedia, and who knows who else). The way you have outlined it @6:15 makes sense and is a bona-fide, legitimate calculation.
Ironically, some here who seem intent on arguing that the “identity” is useful and meaningful are arguing over the wrong thing. The way Willis (and Wikipedia) present the Kaya Identity, it *cannot possibly* be meaningful. Thus, those who want to support the Kaya Identity should be arguing over what the Kaya Identity really is — the proper way to write the equation — not digging in their heels with the indefensible position that if we put an (X/X) on one side of the equation then we have done something meaningful.
So, on the generous assumption that all the smart and clever people who have been using the Kaya Identity in actual practice for years aren’t clueless, I’m tempted to assume for the time being that you are correct and that what we are dealing with here is an initial failure to properly state what the Kaya Identity actually is.

Willis, have you looked at the talk tab on the Kaya Identity page?
http://en.wikipedia.org/wiki/Talk:Kaya_identity

Given: CO2(POP,GDP,E,CO2)=POP*(GDP/POP)*(E/GDP)*(CO2/E), an equation of CO2 that is a function of POP, GDP, E and CO2.
I was taught in Physics that one thing that must be true if an equation is correct: the units must match on both sides of the equal sign. That is true in this case, so we have one thing correct.
The next thing that I was taught is that to predict things you use calculus. So what happens when we increase population or other factors without changing anything else?
dCO2/dPOP=0 or CO2 doesn’t increase if POP does and everything else stays the same.
dCO2/dGDP=0 or CO2 doesn’t increase if GDP does and everything else stays the same.
dCO2/dE=0 or CO2 doesn’t increase if E does and everything else stays the same.
dCO2/dCO2=1 or CO2 increases linearly if CO2 does and everything else stays the same.
Well, that doesn’t tell us much!

Dear Willis, I usually am in agreement with your rants and discussions and presentations.
Once again, it is a badly symbolized equation, true, but it holds as an algebraic equation if one does not confuse units/dimensions with constant values.
The last in a row for example is a constant measured in a chemistry lab which tells us how much CO2 is emitted in producing a gram of , in units of grams/joule.
energy/GBP is a constant . a number, measurement of the total energy spent in producing beer , somebody has to measure it in units of joules per gram.
GBP/population is also a measured constant in grams/(number of people)
and finally somebody has to measure the population.
These are a series of measurable constants and will give different results for different inputs.
And finally this is a CO2 constant/contribution in grms from beer production in a specific country. This will be reduced by 10% if beer production per unit emits less CO2 by 10%. It will ofcourse become insignificant in the total CO2 sum.
So it is true that it is a badly expressed algebraic equation where units and constants are mixed up but there is some sense in it, and that is why you are getting all these comments.

Continued:
It is also true that the equation does not count all of the CO2 emitted on earth by biological organisms , as we all are, we are not adding to the GDP by existing ( except in some countries where there is a head tax) . But it is also true that the GDP is strongly connected to energy consumption and it must be true as an algebraic relationship to first order. How much GDP has a poor nation in Africa? Isn’t our argument that CO2 reduction hits the poor much more as it does not allow them to expand in energy usages which is important for the enrichment of an economy?
If we did not burn fuels other than wood we would still be in the stone age. What is the GDP of a stone age economy.
So the algebraic equation is a first order equation of the multitude of variables that enter such estimates.

pwl – will these help?
http://therefusers.com/refusers-newsroom/90-of-peer-reviewed-clinical-research-is-completely-false-greenmedinfo/#.U8IG27FCx8E
http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fjournal.pmed.0020124

Those are excellent Robert in Calgary. Any for climate science?

Willis Eschenbach: 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.
In common with most mathematical expressions in science, the Kaya equation does not have everything relevant in it. The first mathematical expression for conservation of energy, for example, was way off because entropy had not yet been discovered and included. Later Einstein added in a constant times mass, though the correction is not needed in most analyses of electrical generation from fuel. In pharmacokinetic equations (used for computing dosing regimens) most important factors are omitted and “blended” (aka “confounded”) in just a few rate equations among non-physical concepts such as “apparent volume”. In fact, “apparent volume” is a ratio: total dose in the body divided by concentration in the plasma; for drugs that concentrate in the fat, or bones, etc, the “apparent volume” may greatly exceed the actual volume of the animal, hence the abstract name “apparent volume”. Science is full of incomplete equations of this nature, that are nevertheless useful in planning or other ways.
GDP is a limited measure of the rate of growth of wealth, but urinary melatonin metabolite is a limited measure of the rate of secretion of melatonin and melatonin metabolism. To a greater or lesser degree, every measurement type has limitations of accuracy; the existence of known limitations of GDP hardly disqualifies every particular use for it.

anna v has it right, and I am astounded at the large number of commenters who don’t apparantly understand the first thing about math, and proceed to display their ignorance in spades.
In the Kaya Identity, the UNITS cancel, but not the VALUES.
For instance, the population term is in units of people, so the first term is the total population VALUE, but the second term expressing per-capita GDP the population term is in UNITS of 1 person – that’s the definition of per-capita.
The same goes for the other terms – the denominator is expressed as single units (People, dollars, joules, kegs, whatever) which don’t vary, and the numerator is what’s possible to vary to determine the effect on the output.
The appropriateness of the selected variables can be argued for certain, as can the unexpressed interdependencies of the variabiles (e.g., if population is halved what really happens to GDP/population? If practical nuclear fusion is achieved, what happens to energy/GDP and co2/energy?) – but as presented the Kaya identity seems to be a reasonable first-order estimation tool.
The one thing that’s interesting to me about the Kaya Identity is that the way it’s composed, the only way to reduce the output is to reduce one or more of the inputs – a handy policy tool indeed.

pwl @8:43pm:
Yes, I do recall seeing several of those kinds of studies a few years ago. Unfortunately, they have now been falsified. 🙂

[snip off topic – not going there again -mod]

“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.”

Just get pulled over and fined for one of the many imaginary “victimless crimes” and you’ll be part of the GDP – if you pay of course.. 😉

My first article in Communications of the ACM had some major issues. Unlike the academic journals in my field of information systems, CACM publishes letters to the editor and I really got hammered. It was a very painful experience for me, but the problems did get adequately exposed.
In contrast, there was a seriously flawed publication by a prominent figure in a top academic journal in my field. A colleague saw it, recognized the problems and submitted a rebuttal paper. Although the reviewers acknowledged the problems, it went through a stalling process of multiple review cycles and then was rejected.
I suspect things work like that in other fields also.

Rdcii says:
July 12, 2014 at 5:35 pm
(T Co2 Emissions) = (X Population) * (Y GDP / Z Population) … * (A Co2 Emissions / B energy)
*************************************************
The population can’t be different values in the same equation, X = Z. Goes for the CO2 also, CO2 emissions has to be the same on both sides of the equation (T = A).