Input-Output analysis adds indirect CO2e, such as energy to mine metals used in machines and fertilizer to grow cloth and food.
"Direct emissions from an industry are, on average, only 14% of the total supply chain carbon emissions (often called Tier 1 emissions), and direct emissions plus industry energy inputs are, on average, only 26% of the total supply chain emissions" http://pubs.acs.org/doi/full/10.1021/es703112w
Input-Output analysis is used by economists to measure how industries directly and indirectly use the products of other industries, such as energy. It is important to use it to measure energy use, and therefore greenhouse gas emissions in many industries, since it adds indirect uses to the direct uses in those industries.
Care needs to be taken that the sector as defined in the IO model matches the work being estimated. Berkeley researchers applied the Carnegie-Mellon EIOLCA model to car manufacturing and found results similar to more detailed item-by-item estimates. An Australian researcher found much lower IO-based estimates for road construction than his item-by-item estimates, probably because the construction sector in his IO model is much wider than road construction and includes activities with lower greenhouse gases. These examples are in the spreadsheet on the Cars tab.
Carnegie-Mellon researchers using IO found much higher greenhouse gas emissions from food production than food companies using methods of the Carbon Trust. These examples are on the Products tab of the spreadsheet. In their EIOLCA.net model, Professor Weber reports in a 16Ap'09 email,
1) Process CO2 emissions [from calcining concrete] are included.
2) pipeline leakage methane is, but hydro[electric] reservoirs are not due to the aggregate electricity sector.
3) air travel is CO2 only due to the uncertainty in contrail effect.
4) LUC [Land Use Change] not included due to lack of data (but it can be included in such a model; the US inventory just doesn't allow us to do it with any resolution).
5) gas flaring is included."
IPCC's Special Report on Renewable Energy Sources does not use input-output analysis, but only studies which try to list direct inputs. They distinguish between "attributional" and "consequential" methods in section 9.3.4, where "consequential" studies are rare and predict the results after the economy changes, for example to include more renewable energy.
Ecoinvent.org is a Swiss organization with estimates of CO2e and other impacts of many industrial processes and products. They charge 1,800 Euros for access. Ecoinvent's public documents imply they do not use Input-Output method, but try to itemize each input, and the inputs for that input, etc. Ecoinvent recognizes that CO2e from capital goods can be substantial, and recommend it be included "where relevant! Criteria need to be defined!" (exclamation points in original). They provide a free example of their information for hard coal, which cites an internal ecoinvent report as its source. It gives 130 grams of CO2e per million joules, 30% higher than EPA gives for direct burning alone. Access is free for schools outside the OECD, so perhaps a researcher there can report more on how their numbers were derived and compare more of their numbers to other sources.