(Yet another) probably incredibly unreadable modelling thread

by Carrie Fri Nov 17th, 2006 at 08:28:55 PM EST

Following on the footsteps of Colman's highly successful Probably incredibly unreadable modelling thread (June 12th, 2006)

In Thursday's open thread, starvid commented

Lately, I have been thinking about the economic impacts of Peak Oil, and tried to understand what industries will profit the most from it who'll lose the most.

and in the subsequent thread I demanded "a Leontieff matrix". When pressed, I explained what I wanted like this:

So Peak Oil is a phenomenon involving the Oil and Gas Extraction sector, namely its predicted inability to grow its output (in energy, not monetary units) or even maintain it, no matter what.
So, what are the inputs into Oil and Gas Extraction, and why is it that increasing any of the inputs won't increase the output?
Also, what sectors does the output from Oil and Gas Extraction feed into?

and managed to extract this

Inputs. Capital obviously. Plenty of that around. Skilled labor. We're seeing a shortage of that. Equipment. Most of it's old and rusty. New fields to exploit. This is the most important. Production can not grow without new fields. New technology only minimize decline rates and prolong high production and increase reserves (if they even do that, some people mean new technology only means the oil is sucked out of the ground faster). But it can only increase production in tired old fields, and it won't bring production back to it's old peak.
Where does the output go? I guess you mean where the product is used? Everywhere. In 99% of all transportation services. And everything is transported. The output also goes to heating and power generation where adequate alternatives exist and will supplant hydrocarbons in the long run. Another important use is in the petrochemical sector where alternatives are hard to see.

Who is this guy Leontieff, and why do I keep bringing his matrices up? The answer after the fold.

Wassily Leontief was a German-born Russian exile who won the 1973 Nobel Prize in Economics for his Input/Output model. According to Wikipedia,

The analytical apparatus is strictly empiricist and reducing bias in the analysis. For this reason, Leontief seems to have been just about the only economist who was equally honored by communist and capitalist economists.

I first encountered Leontief's model as an application of elementary linear algebra when I was a teaching assistant for freshman-level "Linear Algebra for Business" at an American university. Assisting math courses for Business majors was a rite of passage that every mathematics graduate student had to go through for at least (and hopefully at most) one quarter at the beginning of our studies. For the students this example (like most examples of applications in introductory maths textbooks that I encountered over the following 4 years) was a disaster: supposedly the Leontief model would help students understand linear algebra, but instead they were faced with the task of simultaneously getting their heads around matrices and macroeconomics while having no experience or inclination for modelling. So much for trying to make math easier to teach by making it "relevant". </pedagogy rant>

Anyway, I think the Leontief model, painfully simple as it is, is quite useful and instructive. It is also quite limited, but that is mostly because of its linearity. It can easily be complicated beyond tractability, and that is just what I intend to do here. No, really, I'm just kidding.

So, keeping in mind Stephen Hawking's admonition that every equation reduces the number of your readers by half, I won't use any equations. Or not really. But, as you know from my previous writing, I don't like to do that anyway and it's your loss because an equation is worth 1000 words (just look at Archimedes).

The model

The basic building block of the model is a description of an "industry" in terms of one "output" and several "inputs". Like this (if you like chemistry you'll like this)

industry: (input 1) + ... + (input N) -> (output)

The model is parametrised by giving the amount of each input that is needed to produce one unit of each output. This is (the inverse of) the productivity of the given input. What makes this model more interesting than an enumeration of productivity numbers is the idea that every input must be the output of some other process, and conversely every output must be an input as well. This makes the system closed. The full model is obtained by allowing for consumption and trade of the products. It can be used to study the question of how changes in one sector of the economy will affect other sectors.

Leontieff formulated his model to study "general equilibrium", but the model can be used dynamically, and it can even be used as a framework in which "innovation" can be represented by adding new "products" or "industries" to the system, increasing the dimension of the input/output matrix. The possibilities are endless. The model is also great in that if emphasises that the economy contains cycles much like the enviromental cicles of carbon, water, etc, and allows one to study internal consumption, that is, what fraction f what is produced just goes to keep the machine going, as opposed to being enjoyed by the public.

Peak oil: the setup

So, what does this have to do with starvid's question on Peak Oil? Well, I think Leontief's framework allows one to systematically address the question of the effects of Peak oil on the economy.

Peak oil is a prediction that the output of the oil extraction industry cannot increase in the medium term and will likely start declining in the long term. So, we would start by writing an equation (like a chemical formula) for that industry...

oil extraction: (capital) + (skilled labour) + (machinery) + (oil fields) -> (crude oil)

A few questions immediately arise: 1) are "capital", "skilled labour", "machinery" and "oil fields" homogeneous enough, or do they have to be broken down further? 2) what processes and/or industries produce "capital", "skilled labour", "machinery" and "oil fields"? 3) aren't we forgetting waste products? How about the energy to power the machines? 4) how much of each of these inputs is necessary to produce one barrel of crude oil? Are there tradeoffs (e.g., can use more machinery and less labour)? 5) what processes/industries use "crude oil"?

Let's not get carried away into excessive complexity (there is always time to analyse entities into smaller ones and multiply the dimension of the problem) and instead concentrate on questions 2) and 5): where do the inputs come from and where does the output go? For the inputs, take "machinery" for instance

machinery: (capital) + (skilled labour) + (machinery) + (materials) -> (machinery)

and for outputs we have

oil refining: (capital) + (skilled labour) + (machinery) + (crude oil) -> (transportation fuel)
oil refining: (capital) + (skilled labour) + (machinery) + (crude oil) -> (heating oil)
oil refining: (capital) + (skilled labour) + (machinery) + (crude oil) -> (aviation fuel)
oil refining: (capital) + (skilled labour) + (machinery) + (crude oil) -> (petrochemicals)

We can play this game in as much or as little detail as we want (I recommend little detail) by adding new processes/industries as long as there are products that are unaccounted for as either inputs or outputs. At some point, every product will appear at least once as an input and once as an output and we will have achieved closure. Then we can start analysing the impact that changes in one economic sector will have on another economic sector. In particular, for our purposes, we might be able to trace the impact of Peak Oil.

Peak oil: the answer

Questions? Thoughts? Rotten tomatoes?

(Yet another) probably incredibly unreadable modelling thread | 68 comments (68 topical, 0 editorial, 0 hidden)

Re: (Yet another) probably incredibly unreadable m (4.00 / 15)

Questions? Thoughts? Rotten tomatoes?

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Fri Nov 17th, 2006 at 08:33:46 PM EST

Re: (Yet another) probably incredibly unreadable m (none / 0)

How about a 4? :-)

by Fran on Sat Nov 18th, 2006 at 01:06:00 AM EST
[ Parent ]

Re: (Yet another) probably incredibly... (4.00 / 2)

So when you say "linear", and "linear algebra", and like that, you mean that the function

oil extraction: (capital) + (skilled labour) + (machinery) + (oil fields) -> (crude oil)

one legitimate possibility (with a nice match between units and circumstances) would be

1 + 1 + 1 + 1 -> 4,

and that another legitimate possibility would be

1 + 1 + 1 + 0.1 -> 3.1,

or even

1 + 1 + 1 + 0 -> 3.0?

Pretty much everything is locally linear, but the locale is sometimes too small. If we can exploit computers and forget about academic "general equilibrium" (!) ideas, why use a linear model? "System dynamics" is more expressive, but I'd like to know what economists are using these days.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Sat Nov 18th, 2006 at 02:04:51 AM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

Great point, Technopolitical. System Dynamics must be a better tool.
Thanks, Migeru.

by findmeaDoorIntoSummer on Sat Nov 18th, 2006 at 05:04:30 AM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

I am not particularly interested in the linear Leontief model of general equilibrium, but in the analysis of the economy into processes. For one thing, the Peak oil hypothesis seems to me like a statement of nonlinearity.

Anyway, the equation

oil extraction: (capital) + (skilled labour) + (machinery) + (oil fields) -> (crude oil)

is not to be interpreted as a linear equation. '+' means "with" and '->' means "produce(s)". It's like a non-stoichiometric chemical equation such as

(oxygen) + (hydrogen) -> (water)

I am not saying how much of the reactants produces how much of the products and I am not even saying that defintie proportions apply. The analogue of

O2 + 2 H2 -> 2 H2O

with the coefficients involves quantifying the productivity of the factors of production.

One of the interesting insights that allowed Leontief to make a useful model is that he reversed the flow of the "production" equations/processes. Instead of asking "how much of the output can be produced given the inputs?" which, if the quantities are not right will result in some of the inputs being left over, he asked "how much of (input) is needed to produce one unit of (output)?". This is the inverse of the productivity of the input, by the way. The cool thing is that, given the inputs, how much and which outputs arre produced is an indeterminate problem, and not all the inputs may end up being used; but, given the outputs, you know exactly how much of the inputs has been used.

This is why actually none of the equations you has written really is a correct interpretation of how to turn the "process equations" into linear equations. But, then again, all this is true of chemical reaction equations. The symbols '+', '->' and the coefficients have the same meaning. The 1/2 in

(1/2) O2 + H2 -> H2O

means that "it takes 1/2 mole of the (oxygen) input to produce one mole of the (water) output". It does not mean that the amount of water produced is a linear combination of the amount of hydrogen and oxygen present.

So, there is a linear model at the end, but it is not obvious from the presentation of the "process" equations, not even if the "productivity" (stoichiometric) coefficients are given.

As an aside, I think this is clear why this was an insane choice of ancillary topic in the course I was assisting. Maybe there is a diary in there where I pick apart college level mathematics education in the US.

Anyway, the assumption of linearity is implicit in the question "how much of (input) is needed to produce one unit of (output)?", but you can of course replace that with a nonlinear function. I am more interested, however, in the "process equations", which might be represented as a directed graph (with nodes representing processes and arrows representing inputs and outputs).

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:08:12 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 1)

I am more interested, however, in the "process equations", which might be represented as a directed graph (with nodes representing processes and arrows representing inputs and outputs).

H'mmmm.

What you need is a Neural Net.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 04:28:20 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

It's not a neural network, it's a flow network (with conservation laws).

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:52:48 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

Isn't working out stability criteria a complete pig of a problem?

If the model isn't linear then presumably it's pretty much unstable, almost by definition. I suppose a subset of small problems might convege towards something resembling equilibrium. But won't a reality-sized model that assumes time-based relationships between inputs and outputs wobble chaotically all over the place?

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Nov 18th, 2006 at 08:05:41 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

If the model is convex it's stable, almost by definition. Linearity is just a red herring there.

I agree, though, that as soon as you introduce time and, more importantly, delays, you get an entirely different order of complexity. Delayed feedback is really, really nasty in that respect.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 09:34:57 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 1)

I'm glad to hear that we're not talking about a small patch of linearity here, and chemical equations are of course a good example of another of the many uses of "+".
'One' + 'two' = Onetwo, and so on. On the other hand, the case a hand is obviously not stoichiometric, and small variations in the inputs will indeed produce linear changes in the outputs, in a very reasonable model.

Perhaps I should actually break down and look at Leontief's methods. But since I heard that he treated "technology" as a scalar input, I've had a disgust toward the topic.

...Hmmm... Google doesn't think that "process equations" have much to do with "Leontief" (10 hits)....Further digging suggests that Leontief was indeed saying what you and I have trouble believing he'd say:

The neoclassical production function is an explicit function
Q = f(K,L),
where Q = Quantity, K = Capital, L = Labor...
Leontief, the innovator of input-output analysis, uses a special production function which depends linearly on the total output variables....
Widipedia: Input-output model

I'm puzzled.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Sun Nov 19th, 2006 at 04:34:10 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

The "Neoclassical production function" post-dates Leontief by at least 20 years, so the wikipedia article is an attempt looks like an attempt at deducing the Leontief model from general neoclassical principles, with partial derivatives and the whole works. It looks just like the kind of dreadful stuff Paul Samuelson would do. I'm looking at it from a different perspective. The article does say

The inimitable book by Leontief himself remains the best exposition of input-output analysis. See bibliography.

Maybe I should try to get ahold of that. Drew should have easier access to it through his university library.

The wikipedia article also says

Despite the clear ability of the input-output model to depict and analyze the dependence of one industry or sector on another, Leontief and others never managed to introduce the full spectrum of dependency relations in a market economy.

in other words, the program is too ambitious to be practical. For instance

Irving Hock at the Chicago Area Transportation Study did detailed forecasting by industry sectors using input-output techniques. At the time, Hock's work was quite an undertaking, the only other work that has been done at the urban level was for Stockholm and it was not widely known. Input-output was one of the few techniques developed at the CATS not adopted in later studies. Later studies used economic base analysis techniques.

This economic base analysis sounds like a simplification of the Leontief model for tractability, though it appears to have been developed independently. That Leontief was too ambitious to be practical did not prevent people from coming up with even more general (and presumably more intractable) models

In 2003, Mohammad Gani, a pupil of Leontief, introduced Consistency Analysis in his book 'Foundations of Economic Science', which formally looks exactly like the input-output table, but explores the dependency relations in terms of payments and intermediation relations.
...
In a technical sense, input-output analysis can be seen as a special case of consistency analysis without money and without entrepreneurship and transaction cost.

Anyway, it does seem like economics is indeed much harder than chemistry or ecology as I discussed with TBG on a parallel thread.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 04:49:21 PM EST
[ Parent ]

Re: (Yet another) probably incredibly... (none / 0)

OK, I'm de-puzzled. I was reading the relationship backward, and the reverse direction makes perfect sense. It's saying that the amount of each kind of stuff required is the sum of the amounts required for each of the consumers of that stuff. (The flow of stuff is in the opposite direction from the arrows you showed, which corresponded instead to the direction of demand.)

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Sun Nov 19th, 2006 at 04:53:46 PM EST
[ Parent ]

Ack! (none / 1)

I've been somewhat tainted with box modeling, but I never knew Leontief cast economic fluxes into one. I finally get about what you were Starvid harassing with. Fascinating.

by Nomad (Bjinse) on Sat Nov 18th, 2006 at 04:50:56 AM EST
[ Parent ]

Re: Ack! (none / 0)

What do you understand by "box modelling"?

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 10:46:51 AM EST
[ Parent ]

Re: Ack! (4.00 / 2)

To grapple with flux processes in the earth system, the carbon cycle, nitrogen cycle, oxygen cycle, ocean heat distribution, global heat distribution, etc. You define your reservoirs, reservoir times, reservoir conditions, the products that go into the reservoir, the products that come out of them and so on. The reservoirs represent indvidual boxes; you slice the cycle up into different stations, and where needed you subdivide to smaller detail. If you turn this into a mathematical/computational model the transformation from chemical reactions/processes to variables and operators do not alter the basic structure much (though the necessary translation becomes essential).

Understanding the layout of the fluxes aids in predictive qualities - similar to the Leontief matrix as you describe. One difference I see seems that Leontief uses economic components as building blocks, and not reservoirs. Somewhat logical, as geology constantly mucks with the influence of time and kinetics.

by Nomad (Bjinse) on Sun Nov 19th, 2006 at 01:05:03 PM EST
[ Parent ]

Re: Ack! (none / 0)

What you describe seems more like what the System Dynamics people use.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Sun Nov 19th, 2006 at 04:36:01 PM EST
[ Parent ]

Re: Ack! (none / 0)

To me it sounds like thermodynamics.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 04:38:43 PM EST
[ Parent ]

Well (none / 0)

That could be the proper name for it; I've never gone into depth to work with box modelling, and terminology is not my strongest suit (while it should...) It makes sense to see it integrated at lots of fields; it looks a useful concept - even when it creates thinking inside boxes :)

by Nomad (Bjinse) on Sun Nov 19th, 2006 at 06:14:00 PM EST
[ Parent ]

Re: Well (none / 0)

Some nifty diagrams over at Wikipedia: System Dynamics.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 06:18:29 PM EST
[ Parent ]

Re: Ack! (none / 0)

It seems that flows on networks are a basic metaphor underlying models across many disciplines. As category theory suggests that graphs underlie a large part of interesting mathematical structures, this is not entirely surprising.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 04:37:20 PM EST
[ Parent ]

Re: (Yet another) probably incredibly unreadable m (none / 0)

Getting business majors involved in mathematics is bad enough. Throwing macro on top of it...and I'm just amazed their heads didn't explode.

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Sat Nov 18th, 2006 at 05:13:00 AM EST
[ Parent ]

Re: (Yet another) probably incredibly unreadable m (none / 1)

We just did it with 2x2 matrices so their head wouldn't explode, and they still couldn't understand what it was all about, or more importantly why they should care.

The basic flaw in all this is that illustrative examples are only useful if your audience already knows about the subject matter. For instance: I can use exponential growth or an elastic spring to illustrate/introduce ordinary differential equations provided that my audience knows about population growth or mechanics so I can breeze through the modelling and see how the equations arise. But I always found that the ancillary topic that was used to ease in the main mathematical topic was harder for the students than the actual math. It would have been preferable to just do the math in the abstract, because the examples were just confusing.

And the worst were the pre-business students.

But please, don't get me started on pedagogy or on busines majors. I want to have a nice modelling (if incredibly unreadable) thread.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 05:35:44 AM EST
[ Parent ]

Re: (Yet another) (none / 1)

We just did it with 2x2 matrices so their head wouldn't explode, and they still couldn't understand what it was all about, or more importantly why they should care.

In all honesty, in my econometric theory class, I, too, often think "Why the hell do I need to know this given that the damned computers do it for me?" when the lecturer frustrates me. But that usually only happens when I've begun tuning out after classmates begin asking stupid questions.

I've certainly had all of my prejudices about education across the world confirmed by this program. The business majors can't do economics to save their lives. Students from East and South Asia are all incredibly strong with mathematics, but they have no intuition whatsoever, whereas Westerners -- all six of us in my program (five Brits and me) -- are in the exact opposite position. We stumble through the math, but we understand the essential ideas and have actually developed some of our own, which is, in my opinion, far more important in econ.

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Sat Nov 18th, 2006 at 07:24:51 AM EST
[ Parent ]

Re: (Yet another) (none / 1)

We just did it with 2x2 matrices so their head wouldn't explode, and they still couldn't understand what it was all about, or more importantly why they should care.
In all honesty, in my econometric theory class, I, too, often think "Why the hell do I need to know this given that the damned computers do it for me?" when the lecturer frustrates me.

Have you heard of the "Garbage in - garbage out" law of computing?

Anyway, I means that the students couldn't understand a 2x2 leontieff model, or why they should care. The sad part is that the "practical example" was there for the sole purpose of increasing the "relevance" of the material. In actual fact, the material was absolutely irrelevant. And the reason is not that linear algebra is useless necessarily, but that whatever economics courses that these business majors had in their program that used algebra or calculus did not actually have their dependence enforced as a prerequisite. So, people just left the math courses for "later" and took the econ courses or whatever it was, and the professors in those courses just introduced the calculus or algebra they needed and got on with it. So I basically had a freshman class with a roomfull of seniors who had taken the courses which used algebra at least two years prior and forgotten about them because ot their irrelevance to Fraternity life and likely irrelevance to business administration. So the course was useless. And the textbook writer though Leontief's model was a good excuse for 2x2 matrices, and my professor thought that was cute, and I ended up learning something interesting, but my students? No way!

Oh, and what you say about math and intuition reminds me of how I felt taking an advanced Partial Differential Equations in my math degree. I had a good physics background and I could see my pure-math classmates had no idea what that was all about, but had the "professional" traning in functional analysis to follow the class at the ttechnical level. But meaning? No, sir. Same thing with differential geometry.

Bah.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:26:22 PM EST
[ Parent ]

Re: (Yet another) (none / 0)

Rare is the occasion that I find textbooks to be worth the powder to blow to hell. Romer's Advanced Macro is one exception, but the other books I use -- "use" meaning own and have looked over before coming to the conclusion that they were each a waste of perfectly good paper -- have been of no help.

Oh, and what you say about math and intuition reminds me of how I felt taking an advanced Partial Differential Equations in my math degree. I had a good physics background and I could see my pure-math classmates had no idea what that was all about, but had the "professional" traning in functional analysis to follow the class at the ttechnical level. But meaning? No, sir. Same thing with differential geometry.

Oh, you've got to see the level of achievement in stupidity for yourself to fully appreciate it. If it were an Olympic sport, these people would take home the gold everytime. Some of my classmates can run through mathematics like nothing I've ever seen. But trying to get them to make a statement even somewhat bold-sounding about (say) household behavior in multi-period models or the implications of imperfect competition on outcomes in the aggregate is like pulling teeth. They don't even know where to begin.

My "favorite" classes are the (unfortunately mandatory) tutorials, which largely involve the lecturer or professor working through only the first half of one question -- one out of five or six on a problem set -- because of the aforementioned classmates having presumably not looked at the sheet or put in the extra studying time with the lecture notes. (This is what happens when professors spoon-feed students by printing off handouts with all of the notes on them. Arrogance sets in, followed by laziness -- and, in the end, the idiots learn nothing and drag the rest of us down.)

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Sat Nov 18th, 2006 at 07:08:51 PM EST
[ Parent ]

Re: (Yet another) (none / 0)

Okay, I must ask: What is the "garbage in - garbage out" law of computing?

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Sat Nov 18th, 2006 at 07:12:38 PM EST
[ Parent ]

Re: (Yet another) (none / 0)

Garbage In, Garbage Out (abbreviated to GIGO) is an aphorism in the field of computer science. It refers to the fact that computers, unlike humans, will unquestioningly process the most nonsensical of input data and produce nonsensical output. It was most popular in the early days of computing, but has fallen out of use as programs have become more sophisticated and now usually have checks built in to reject improper input.

The last line is an example of hubris.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 07:35:44 PM EST
[ Parent ]

Re: (Yet another) (none / 0)

(that's from wikipedia, by the way)

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 07:36:29 PM EST
[ Parent ]

Re: (Yet another) (4.00 / 2)

... computers, unlike humans, will unquestioningly process the most nonsensical of input data and produce nonsensical output.

and this line is completely false.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sun Nov 19th, 2006 at 02:22:54 PM EST
[ Parent ]

Re: (Yet another) (none / 0)

Which part, the "unlike humans"?

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 03:20:33 PM EST
[ Parent ]

Explication (none / 0)

Humans also unquestioningly process nonsensical input to produce nonsensical output.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sun Nov 19th, 2006 at 03:42:24 PM EST
[ Parent ]

Re: Explication (none / 1)

Computers require syntactically correct nonsensical input to produce ninsensical output. Humans not even.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 03:44:33 PM EST
[ Parent ]

Re: Explication (none / 0)

Homo sapiens is a branch of the ape family, a branch so confident of its superiority that it names itself "Man the wise," flatly denying the evidence of most of its own daily experience.
Cohen and Stewart, The Collapse of Chaos

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sun Nov 19th, 2006 at 04:10:20 PM EST
[ Parent ]

Re: (Yet another) (4.00 / 3)

It's like the equivalent law for economic theories, but mechanised.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Nov 18th, 2006 at 08:08:19 PM EST
[ Parent ]

Re: (Yet another) (none / 1)

"Why the hell do I need to know this given that the damned computers do it for me?"

The computers will certainly give you an answer. But will the answer they give be 1) correct 2) relevant? You won't know.

GIGO is not used much nowadays, because, well, it was a sort of joke--like the old wireless operators' "after careful investigation we discovered the radio transmition was being prevented by a short between the ears."

But with the popularization and multiplication of computers, GIGO is not a joke anymore--it is just everyday life.

The Fates are kind.

by Gaianne on Sun Nov 19th, 2006 at 11:43:46 PM EST
[ Parent ]

Peak oil is all in one equation (4.00 / 4)

oil extraction: (capital) + (skilled labour) + (machinery) + (oil fields) -> (crude oil)

(oil fields) cannot be modellised as an output. Thus you cannot close your model. The question thus becomes: what input can you replace anything that depends on the input (oil fields), so as to finally close the matrix?

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Sat Nov 18th, 2006 at 08:50:56 AM EST

Re: Peak oil is all in one equation (4.00 / 3)

Are you sure of that ? an oil field is the result of plenty of cash and time, spent on hardware and staff roaming hostile parts of the planet in search for oil.

I'm sure oilco's geologist have models of the return on investment of this. We now the curve for the new finds since 100 years, which is logistics with a peak in the sixties, we could guesstimate the amount of cash put in exploration by the majors (I don't think the national oilcos did a lot of exploration until recently, and their playing field is often limited to their borders).

Put in a fudge factor <<1 to model the fact that there has been more continental crust explored than is left to explore and that it will get worst as more cash is poured in the effort.

Wild yet low-risk bet: over time, an exponentially growing amount of cash will be spent to discover an exponentially shrinking amount of oil fields (by cumulative size, the number of stranded fields will be very large on the contrary). So I think we could write:

K.cash -> X bbl oil fields where K=exp(-big time the time integral of oil fields already discovered at the moment under consideration)

Pierre

by Pierre on Sat Nov 18th, 2006 at 10:24:50 AM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

an oil field is the result of plenty of cash and time, spent on hardware and staff roaming hostile parts of the planet in search for oil.

That's covered by capital, machinery and labor inputs. Ultimately, you still need the actualg geological structure, and that one is not going to be an output in a timeframe that makes sense for a purposes. Just define "oil field" in a narrow sense, and you bump against that problem again.

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Sat Nov 18th, 2006 at 01:05:06 PM EST
[ Parent ]

Re: Peak oil is all in one equation (4.00 / 4)

OK, let's restate a definition meaningful for the purpose of this model (after all, Migeru wanted the thread to be unreadable): oil fields come in two flavors, we have pre-existing undiscovered oil fields, in a finite number (as you said, they're only produced in geoligical timescales), this number is unknown but the order of magniture can be estimated quite accurately. These are the inputs to produce "known fields" aka reserves, the other flavor, which goes into Migeru's matrix.

Of course, we are not in a pure Leontieff model since the coefficient of oil discovery will vary over time. The oil itself will change also, making refining less efficient, etc...

But this was to be expected: we are modeling a depletion process, which is irreversible just like entropic decay. The pure leontieff model is reversible if you keep all coefficients constants, it is always conceivable to return to a previous state of equilibrium. Which will not be possible with oil: once it's all CO2 in the stratosphere we won't be able to drive so many hummers...

Pierre

by Pierre on Sun Nov 19th, 2006 at 11:22:04 AM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Who tells you the Leontief model is reversible? Chemical equations are reversible, but not economic processes.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 03:24:18 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

It is in its simplest form: a closed network with constant coefficients over time. You have a number of solutions, which are the equilibrium points, it is entirely static, you may move from one point to the other with external shocks which are not modelled in this basic version itself, and nothing forbids that an opposite shock takes you back to the previous point.

Pierre

by Pierre on Mon Nov 20th, 2006 at 04:45:10 AM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Yes, in that way it is.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Mon Nov 20th, 2006 at 04:48:23 AM EST
[ Parent ]

How about...? (none / 0)

oil prospection: (capital) + (geologists) -> (oil fields)

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:29:43 PM EST
[ Parent ]

Re: Peak oil is all in one equation (4.00 / 2)

Once again (ignoring the mathematics) the models ignore the fact that there is no cost assigned to the depletion of non-renewable resources.

Suppose we wanted to assign a cost to the raw material. Several choices come to mind:

The value that the last barrel in the world will have calculated to present value.
The value of an equivalent amount of energy from a renewable source.
A value set arbitrarily to force development of alternative sources.

Even these models fail when the raw material has no substitute (say Tantalum or Platinum).

Which gives another option:
4. The cost to extract the same amount of material via recycling.

Even these options assume an adequate supply of energy to do something like recycling. The amount of Tantalum in the typical mobile phone is probably on the order of a few grams, how much does it cost to separate it from all the other elements? Obviously at current labor and energy costs it is not economical.

We need new economic models that take into account the finiteness of the plant. So far these are not forthcoming.

Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Sat Nov 18th, 2006 at 12:06:50 PM EST
[ Parent ]

In practice (none / 0)

2 or 4 will be decisive, depending on how easy the substitution can be made.

3 might play a role if there is decisive regulation to modify the equation (but will still just be a artificially modified version of 2 or 4)

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Sat Nov 18th, 2006 at 01:08:34 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

As a static (general equilibrium) model, you're right, but in a dynamic model there's no reason why you can't throw in an equation where "the amount of (oil fields) left" decreases by an amount proportional to the amount of oil extracted.

I have alluded to the parallel with chemical equations in the diary, and developed it in a reply to Technopolitical in a parallel subthread. If Chemistry can take into account rates of reaction, and the depletion of the reactants, why can't we? The equations just describe the processes. There are no cost anywhere yet, I haven't even written down the productivity coefficients explicitly.

Like I say in the reply to Technopolitical, what I want to take away from Leontief analysis is the "graph" of inputs, outputs and processes.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:35:22 PM EST
[ Parent ]

Re: Peak oil is all in one equation (4.00 / 2)

Yes, but you're being algorithmic again.

It's a pretty idea, but it doesn't model the fact that the depletion of reactants, and the creation of pollutants, has consequences for the model. Which means these consequences - which are not trivial - are ignored.

You could say 'Yes, but you can include them in the model.'

But you can't. For example - if you model CO2 as an output, you may (arguably) get the right figure for the amount of CO2. But you will get no information about the impact of CO2 on the environment, because you'd need to include the entire ecosystem, or at least a reasonable analysis of the economic outputs that CO2 produces.

Since no one agrees what those outputs are, you have a problem.

So this is yet more toy economics which - as usual - pays no attention to non-financial realities. And given where we are now, this is a bad thing, not a good one.

Economists and business majors need to be trained to think that externalities are central to any useful model, not peripheral to it. This does the opposite - it creates an illusion of understanding, which will tend to reinforce a distant FT-length view of what's happening in the physical world.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Nov 18th, 2006 at 08:22:12 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Sorry, I don't follow this.

The model pays attention to whatever you put in it. If you want to include the carbon cycle in the model you can. You are limited by your knowledge of the carbon cycle, just like you're limited by your knowledge of specific sectors of the economy.

Is it actually possible to improve our understanding of the carbon cycle and of the climate system to reduce the size of the "problem" that "disagreing on the outputs of CO2" causes, or not? If this kind of stuff is unknowable I would like to know why.

Do you actually think understanding our economic (and ecological) system is impossible?

Even if you don't have information on the environmental impacts of pollution you could include "cleanup" as a sector of the model and ask yourself what would happen if you demanded that all pollution be cleaned up. For instance, what does a carbon-neutral economy look like? If there are econometrists working for governments that have relatively faithful Leontieff models of their countries' economies, they're actually rather close to answering the question of what a carbon-neutral economy looks like for their country. I doubt anyone is asking them that question.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 09:31:14 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 1)

Well, yes. Quite.

So you have a model which isn't actually an - er - model?

What's your definition of a model, exactly? I know that if I use standard models (not to be confused with The Standard Model) in circuit design or bridge building, I'll get an answer that approximates reality in a useful way, subject to some minor and predictable constraints.

When I look at ideas in economics, after I get over the 'You cannot be serious?!' stage, that kind of precision seems somewhat lacking, except for a very tiny subset of very simple problems.

Do you actually think understanding our economic (and ecological) system is impossible?

I think it's a much harder problem than it looks, because unlike engineering or chemistry, economics is mostly psychology and politics.

And as for ecology - ecology is hard. It's much harder than most people seem to even begin to realise. Ironically I think the Leontieff approach is a lot more applicable to ecology than to economics, because the networks and energy flows in an ecosystem don't depend on anyone's opinion. (At least, not until fairly recently.)

What bothers me is that this modelling seems like an appeal to authority, and is only superficially related to the modelling done in real science.

I haven't looked through acres of papers, but I would be mightily surprised if I couldn't find at least one paper that used this model to 'prove' that raising the minimum wage would create unemployment, and another that 'proved' that it wouldn't.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Nov 18th, 2006 at 10:28:17 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Why is "model" a dirty word to you? I agree with you that chemistry is easier than ecology is easier than economics, but I think focusing on the political and psychological side of economics it's hard to get a grip on the eminently physical constraints on "sustainable economics". I still think the economy is still mainly about feeding people and making stuff. When people point out how much oil is used in industrial agriculture they are making a quantitative statement that fits snugly as a matrix element of the Leontief model, namely the "fertilizer + fuel" bit of

industrial agriculture: (capital) + (labour) + (soil) + (fertilizer) + (fuel) + (sunlight) + (water) -> food

So actually, as a quantitative descriptive (as opposed to predictive, your implicit necessary attribute for 'models') tool, I find these kinds of models rather appealing. And I don't understand how this is not related to "modelling done in real science". Anyone professionally involved in an economic sector should be able to give a reality-based estimate of the factors involved and their necessary quantities.

If we want to understand the likely impacts of peak oil, we can either pull things out of thin air or try to undestand on a more concrete level what the flow of oil through the economy actually works. And though that has a psychological and political basis, it is not a psychological or political question. How the flows can be modified is a partly technical, party political, and partly psychological, question, I'll give you that. However, once again, I am interested in the physical constraints that "sustainability" imposes on economics.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 09:06:20 AM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

We need new economic models that take into account the finiteness of the plant. So far these are not forthcoming.

As I point out in various places in this discussion this kind of framework for describing the economy has more than an accidental resemblance to standard representations of ecological cycles (like carbon or water). So maybe the models are not forthcoming, but the framework is there.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sun Nov 19th, 2006 at 10:53:09 AM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Technically a model doesn't have to close; it has to correspond to what you're modeling - the prototype.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 04:10:41 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

That is great, I'll have to chew on it and come up with some cogent answer, but I just want to encourage others to poke as many conceptual holes in this kind of model as they can.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:28:41 PM EST
[ Parent ]

Re: Peak oil is all in one equation (none / 0)

Leontief's model does not strictly require closure, in fact in his application he allowed for consumption and trade. One of the questions that can easily be answered within the linear model is whether a given level of demand can be satisfied, and what the necessary level of production, internal consumption and importation is. This, of course, begs the question of where the necessary imports are going to come from, especially if one is trying to model the global economy.

Take, for instance:

agriculture: (capital) + (labour) + (land) + (sunlight) -> (food)

Land and sunlight are not "outputs". You can always cheat and write

agriculture: (capital) + (labour) -> (food)

arguing that land and sunlight are just subsumed in the productivity of capital and labour, but I think it is more honest to make them explicit inputs and then have to worry about the fact that they cannot be created and so have to appear as an "import" in the model (and where is the necessary "import volume" going to come from?).

The way this is done is by building a matrix whose components are "the amount of (input) needed to produce a unit of (output)". Call this A. Then, if you know the desired level of output (call it x), the necesary inputs (call them y) are given by matrix multiplication y = A x. If x is the (desired? actual?) level of production, y is the internal consumption, that is the part of the produce that is consumed just "to keep the machine going". The quantity x - y is the net product, that is how much is available for final consumption or exports (or storage?). If a component of x - y is negative, you need to import, or have a shortage.

So if "new oil fields" is a factor in the production of "crude oil" you can use the linear model to figure out how many new fields you have to find ("import") in order to meet a given level of demand.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 09:21:23 PM EST
[ Parent ]

Can we put.. (none / 0)

Can we put a non-local term...porfa please..

A hilbert transform.. plese please... I am sure it msut mean soemthing economy.... :)

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sat Nov 18th, 2006 at 08:57:35 AM EST

Re: Can we put.. (none / 1)

The Hilbert Transform of a constant is zero.

A zero Lyapunov Exponent means no information is gained or lost.

Therefore no information is gained by using the Hilbert Transfrom.

je je je je
/
8^0

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 02:27:34 PM EST
[ Parent ]

Re: Can we put.. (none / 1)

i want anon-local functional of the input where it can describe that the dependence of the different outputs is not linear.

In this way a certain output is afunctional of the input and not a pure linear relation...

I will start int his way to make the problem look more like the real world.

Problem is thsi works ina purely amterialsitic world.. but material are mostly irrelevant.. except fro energy..

So maybe thismodel coudl eb useful to energy..

It was a weird though... in anyc ase.

a pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sat Nov 18th, 2006 at 02:40:56 PM EST
[ Parent ]

Re: Can we put.. (none / 0)

I want a non-local functional of the input where it can describe that the dependence of the different outputs is not linear.

How do you see the Hilbert Transform accomplishing this?

I'm not being snarky here. I'm really interested.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 03:33:30 PM EST
[ Parent ]

I was taliking about.. (none / 0)

non local in the sense of the dependeces of one with the other.

So variblae Output z= Hilbert[f(Inputy)](on INput y)

So the output is actually an integral over the dumb variable y and where y_o is the actual value of the input being y_o the varialbe after the integral.

This is what I mena by non-local in the sense that output z depends on all possible values of input y.

it is not local because the funcionality is not linear at all.. SO non-local in the sense of the dependence... although I do not know if this would be of any use at all... do outputs may depend on all possible variable of the input?

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sat Nov 18th, 2006 at 07:18:53 PM EST
[ Parent ]

Re: Can we put.. (none / 1)

It's all nonlocal (or, rather, alocal, with the processes being local) at the moment. Think of it as the "reaction" part of a reaction-diffusion system.

I am also interested in how the economic sector "transportation" is modelled. With so many economists in the house, it would be depressing (but maybe not entirely surprising) if nobody could answer that question according to current economic practice.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:38:23 PM EST
[ Parent ]

Reinventing the Wheel? (none / 0)

If you are insisting on a linear model why not spend a couple of hours in a library researching away? I would be very surprised if research wouldn't uncover an existing, perfectly adequate, linear model. (Tho, amusingly, when I googled for ["Peak Oil" + Leontieff] the top item was a comment on EuroTrib.) Just how that linear model corresponds to the prototype is, of course, a good question. My prediction: Not Much.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 02:20:26 PM EST

Re: Reinventing the Wheel? (none / 0)

Migeru has a comment above that shows I failed to grasp his purpose.

I'd request everyone troll-rate my comment but then I'd deprive him of the opportunity to tell me I'm an idiot. ;-)

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Nov 18th, 2006 at 04:39:36 PM EST
[ Parent ]

Re: Reinventing the Wheel? (none / 0)

My purpose is to reinvent the wheel. I can't learn anything otherwise. Maybe one day I'll invent a wheel that is original.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:42:16 PM EST
[ Parent ]

Re: Reinventing the Wheel? (none / 0)

I am not interested in the linear model, I am interested in the web of processes, inputs and outputs that's behind the Leontieff analysis.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Sat Nov 18th, 2006 at 04:39:54 PM EST
[ Parent ]

incredibly unreadable modelling thread (none / 1)

Great diary, Migueru! Don´t get it. Most of it. Maybe part. Rusty machinery.

Our knowledge has surpassed our wisdom. -Charu Saxena.

by metavision on Sat Nov 18th, 2006 at 03:09:38 PM EST

I like (4.00 / 2)

the sort of equations that say that if the decision-making of a manager depends entirely on the information provided by two under-managers who are right 2/3rds of the time, then the managers decisions will be 4/9ths correct - and he would be better advised to do the opposite of wahtever his underlings propose.

Multiply this throughout an organization and you will realise why 40% of employees do not care whether their companies do well or not because they are run by fatheads.

Mythology beats equations any day of the 8 day week.

You can't be me, I'm taken

by Sven Triloqvist on Sun Nov 19th, 2006 at 03:14:50 PM EST

Re: (Yet another) probably incredibly unreadable m (none / 1)

Via google, I found a very intersting powerpoint presentation for a lecture on a Leontief analysis of oil shocks, by Christian Kerschner of the Institute for Environmental Science and Technology at the Universitad Autonoma de Barcelona [kcurie alert!], and Klaus Hubacek of the Sustainable Research Institute at the University of Leeds.

The paper is called assessing the suitability of input-output analysis for enhancing our understanding of the potential effects of peak oil [PDF, see also the Google HTML conversion].

Regarding starvid's initial motivation which was to rebalance his investment portfolio on the basis of the impact of Peak Oil, page 21 contains the top 10 (relative and absolute) sectors affected by the modelled oil shock, in three countries.

Those whom the Gods wish to destroy They first make mad. -- Euripides

by Carrie (migeru at eurotrib dot com) on Mon Nov 20th, 2006 at 02:56:02 PM EST

Re: (Yet another) probably incredibly unreadable m (none / 1)

Hooray!

Academics are useful after all! ;)

Peak oil is not an energy crisis. It is a liquid fuel crisis.

by Starvid on Tue Nov 21st, 2006 at 01:37:22 PM EST
[ Parent ]

(Yet another) probably incredibly unreadable modelling thread | 68 comments (68 topical, 0 editorial, 0 hidden)

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(Yet another) probably incredibly unreadable modelling thread

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