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In my view, a new state-of-the-art is emerging in the economic accounting of GHG emissions. Emissions from operations and value chains will increasingly be quantified using top-down methods that are less process- and more results-oriented, fuzzier but more accurate, bigger, less mathematically complex, and also less transparent to laypeople. I’m a big fan of the new models, because they commit fewer errors of omission in their estimations of “Scope 3” GHG emissions, and are therefore less biased than lifecycle method. I will attempt to interpret the new methods so as to make them more transparent and understandable, and possibly even fun for both scientists and laypeople. My lay readers are strongly encouraged to push past the places that they don’t understand in order to capture the spirit of the thing, even if the mathematical details seem too abstract or advanced. Please leave me comments on what is not clear.
The methods are known to economists as input-output models, and they’ve been around in other forms for quite some time. Historically, input-output models have been applied to the industrial production of goods and to flows of capital between industries. The guy who invented the input-output method, Wassily Leontief, won the Nobel prize in economics for his contribution, which made possible the derivation of a general equilibrium economic theory. Now, start-up companies in Silicon Valley, regional economics think tanks like the Association of Bay Area Governments, and other entities interested in GHG emissions are increasingly making use of this method to express the embodied energy consumption and GHG emissions in the flows between different parts of the economy. These players are scaling their models from single company operations to national economies and back again. Examples of input-output systems include corporate operations, corporate value chains, customer ecosystems, entire industries, geographic regions such as the Bay Area, and national accounts. This blog entry will stick with industrial Sectors as economic black boxes with financial and environmental inputs and outputs, and no transparent process inside.
Through some mathematical wizardry, the economist “inverts” a matrix table of Sector inputs and outputs. The result of the economist’s mathemagic looks like this:
Example Input-Output Results*
| Sector |
Example of Sector |
Total Purchase |
Indirect Purchase |
Value Added |
CO2e Emitted |
| Energy Generation |
Power Utilities |
1,730,000 |
350,000 |
1,000,000 |
10500 Metric Tonnes |
| Wholesale Trade |
Wholesale Gas Stations |
1,550,000 |
230,000 |
1,000,000 |
279 Metric Tonnes |
| Retail Trade |
Grocery Stores |
1,390,000 |
260,000 |
1,000,000 |
381 Metric Tonnes |
| Air Travel |
Airlines |
2,090,000 |
530,000 |
1,000,000 |
1810 Metric Tonnes |
*Carnegie Mellon University Green Design Institute. (2009) Economic Input-Output Life Cycle Assessment (EIO-LCA) US Dept of Commerce 1997 Industry Benchmark (491) model [Internet], Available from: [Accessed 5 Jul, 2009]
These numbers are real. They are available from Carnegie Mellon University’s Green Design Institute’s input-output model, which uses United States National Accounts Data for 1997. Other data options are available, and custom projects can be modeled by selecting a basket or portfolio of purchases.
How did the economist calculate CO2 emissions? By treating the environment like a “Sector” of its own – conceptually and mathematically – a Sector in which there are inputs and outputs to the Environment Sector in the form of greenhouse gases rather than money or jobs. The same can be done for other air pollutants, for energy, and for toxic releases. What do the terms mean? Indirect economic activity is the amount spent on the Sector’s value chain. For example, let’s say that I’m a grocery store in Retail Trade. My entire inventory is a direct expenditure. But the processes that led to the products in my inventory are all a part of my value chain. Perhaps there is a metal can maker who sells cans to the company that cans tomatoes who then sells canned tomatoes to me. By adding canned tomatoes to my inventory, I just made an indirect purchase of some cans ex-tomatoes, and that part of my value chain, including everything upstream of the can, is an indirect purchase that is reflected in the table. The economist can therefore estimate how much of the GHG emissions from the Sector were the result of direct purchases.
In a sense, this accounting is a total accounting that spans a range of influence and accountability, from what a company can directly influence and is responsible for, to the farthest reaches of its value chain. The method implicitly holds a company responsible for the entire economy, which seems a little unfair. But most importantly, the method double counts. You see, my indirect emissions are someone else’s direct emissions. Perhaps I have a contractor or supplier who buys gasoline. Those are indirect emissions to me; they are direct emissions to my contractor. If we both claim responsibility for those emissions in the context of a regulated national carbon market, then we’ve double counted. So while this is a very powerful and inclusive method in the sense that it captures your entire value chain, it puts too much responsibility for emissions on the shoulders of the consumer at all levels and by all definitions, and too little responsibility on the shoulder of producers. To be fair, we should lop each and every transaction in half and call it a 50/50 split that directly reflects the handshake effect of a free market in which two counterparties choose to do business.
But, there’s a problem. The full economic accounting outlined above is very simple and straightforward to implement: I take my corporate ledger, which is kind of like a budget, organize it by Sector, and then scale the CO2e values in the table above up or down depending on how much money I spent. So if $2.38 million spent on electric power bills results in 10500 metric tonnes of CO2e, then I can divide by that and multiply by how much money I actually spent, right? Easy. Wrong. Because as easy as that method is, it double counts, and therefore it implicitly holds you accountable for the entire U.S. economy right down to the extraction of minerals from the Earth. That seems a little unfair. After all, your suppliers share half the responsibility for making certain unsustainable choices.
So, the alternative is to explicitly model each and every implied transaction in your value chain, lopping each one in half and adding it to the total until the total converges to within a fraction of a percent and you can call it a day with a complete value chain modeled. That’s a lot of computing power. And that’s why private companies are moving into this space, because building those models is a value add.
Note: don’t get scared that you need to know all of your own value chain transactions. You may have thousands to millions of value chain transactions and you cannot possibly map them all. The good news is that the National Accounts data described in the above table will map the transactions for you, by breaking each Sector of production into its corresponding Sectors of consumption. All you need to do is provide the algorithm; the data have been provided for you.
The good news is that I intend to do this and make it open source, or at least free online. I’ll begin with the ledger from the undergraduate solar car project that I contributed to as an undergraduate student at Yale. I’ll simulate what Team Lux’s budget must have been, and then cascade the impacts of each purchase decision upstream through the value chain, taking half the CO2e value of each transaction, until the answer converges. And, I intend to create a nice online GUI and tutorial. The results will be combined with a life cycle analysis of sustainable solar car design and implementation, and will include some Value Scenarios that assess the value of Team Lux’s stakeholder relationships as it was positively and negatively impacted by the effects of time, pervasiveness, and systemic on the uses of solar technology. I don’t yet have a firm time frame for providing this, but I’ll stake my job search on it.
So, to review. There’s a new state-of-the-art that quantifies the GHG emissions of entire value chains. It’s called input-output modeling. At first glance, it seems to allow corporations to estimate their emissions using nothing but their ledger and some simple scaled numbers by Sector. But, the method double counts, by holding companies accountable for the entire economy, including the half of each value chain transaction that is the responsibility of the seller. The solution is to explicitly model each value chain transaction explicity, in cascading fashion, lopping off half the emissions associated with each transaction. The good news is that you don’t have to know your value chain inside and out in order to do this, because the National Accounts dataset will map those transactions for you.
For more information on input-output modeling, go to the mother lode: eiolca.net.
There is also a Wikipedia page on input-output modeling and Wassily Leontief.
Thanks for reading!
p.s. I had originally written this blog entry as a transferable skill set primer for atmospheric scientists like myself. That approach didn’t work too well, but I’ll just make a few key points here for atmospheric modelers. First, economic input-output is a form of linear programming, but the Bayesian inversions that you know and love are definitely not linear programming! Don’t get the two confused. Atmospheric inverse models are nonlinear. The problem that I describe above is indeed a matrix inverse problem, because it assumes that each Sector’s output is a linear combination of inputs from other Sectors. But, it is an analytical matrix inversion as far as I know, rather than a statistical Bayesian problem that is underdetermined and inexact and requires an a priori guess. Hope that helps! Good luck in skill building.
