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Internal review draft us methods#7

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WesIngwersen wants to merge 32 commits intopublic-review-draft-US-methodsfrom
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Internal review draft us methods#7
WesIngwersen wants to merge 32 commits intopublic-review-draft-US-methodsfrom
internal-review-draft-US-methods

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@WesIngwersen
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@WesIngwersen WesIngwersen commented Feb 25, 2026

First proposed complete draft for Cornerstone team review.

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@WesIngwersen WesIngwersen self-assigned this Feb 25, 2026
@WesIngwersen WesIngwersen added the documentation Improvements or additions to documentation label Feb 25, 2026
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FYI for internal team I put some draft documentation that I extracted from this paper to hold off until more full model documentation in the team-in repo
https://github.com/cornerstone-data/team-in/tree/main/temp/draft_papers

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The procedures for the after redefinitions industry output estimation for non-IOT years is new. I validated the matrix algebra here, assuming a square Make table with identical cols and rows so diagonal is primary production.

https://github.com/cornerstone-data/methods/blob/main/paper-support/validate-after-redef-output-equations.ipynb


Brian Tobin, [briantobin-99](https://github.com/orgs/cornerstone-data/people/briantobin-99)

This paper describes the methodological approach to building the detailed United States national environmentally-extended input-output (EEIO) model that is to be integrated into the Cornerstone (CS) global EEIO model, v1.0.
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Shall we adopt year-based versioning convention, since it'd be more convenient to users?

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This paper describes the methodological approach to building the detailed United States national environmentally-extended input-output (EEIO) model that is to be integrated into the Cornerstone (CS) global EEIO model, v1.0.
v2026.

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Shall we adopt year-based versioning convention, since it'd be more convenient to users?

Suggested change
This paper describes the methodological approach to building the detailed United States national environmentally-extended input-output (EEIO) model that is to be integrated into the Cornerstone (CS) global EEIO model, v1.0.
v2026.

I strongly prefer semantic versioning for the model itself.

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I strongly prefer semantic versioning for the model itself.

I hear you. It makes sense to use semantic versioning for the model then year-based versioning for data product release.

- _Noncomparable imports_ (BEA S00300)
- _Rest of the world adjustment_ (BEA S00900)

_Customs duties_ are tariffs or taxes collected on imports. BEA defines _Rest of the world adjustment_ as "values for exports and imports that have offsetting adjustments to personal consumption expenditures (PCE) and government". _Noncomparable imports_ are "(1) Services that are produced and consumed abroad, such as airport expenditures by U.S. airlines in foreign countries; (2) services imports that are unique, such as payments for the rights to patents, copyrights, or industrial processes; and (3) services imports that cannot be identified by type, such as payments by U.S. companies to their foreign affiliates for an undefined “basket” of services". [BEA IO Manual](https://www.bea.gov/resources/methodologies/concepts-methods-io-accounts).
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_Customs duties_ are tariffs or taxes collected on imports. BEA defines _Rest of the world adjustment_ as "values for exports and imports that have offsetting adjustments to personal consumption expenditures (PCE) and government". _Noncomparable imports_ are "(1) Services that are produced and consumed abroad, such as airport expenditures by U.S. airlines in foreign countries; (2) services imports that are unique, such as payments for the rights to patents, copyrights, or industrial processes; and (3) services imports that cannot be identified by type, such as payments by U.S. companies to their foreign affiliates for an undefined “basket” of services". [BEA IO Manual](https://www.bea.gov/resources/methodologies/concepts-methods-io-accounts).
[BEA IO Manual](https://www.bea.gov/resources/methodologies/concepts-methods-io-accounts).

This last piece is not sentence.

| ' | symbol that indicates the transposition of a matrix of vector | |
| - | bar over to represent a variable before transformation into CS conventions | |

We start with the Make table from BEA, $\bar{V}$, and the Use table from BEA, $\bar{U}$.
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needs to start a new line after this sentence

We use matrix algebra to describe the treatment of the economic data to construct the US IOT.
Variables are defined in Table 3.

### Table 3. Variables.
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Why do some variables boldfaced and some not?

$$ W = \hat{\chi}^{-1} V\hat{q}^{-1} $$

The Use table is normalized by industry output and then post-multiplied by $W$ to get $A$ in commodity by commodity format.
This method for creating the $A$ matrix is based on the _industry- technology_ assumption, wherein the manufacture of the primary and any secondary commodities by an industry uses the same production requirements, and the commodity requirements are based therefore on the mix of industries that produce that commodity, weighted by their relative share of total commodity output. See [Input Output Analysis by R. Miller and P. Blair 2022](https://doi.org/10.1017/9781108676212).
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This method for creating the $A$ matrix is based on the _industry- technology_ assumption, wherein the manufacture of the primary and any secondary commodities by an industry uses the same production requirements, and the commodity requirements are based therefore on the mix of industries that produce that commodity, weighted by their relative share of total commodity output. See [Input Output Analysis by R. Miller and P. Blair 2022](https://doi.org/10.1017/9781108676212).
_industry-technology_


## Preparing the GHG Data for use with the IOT
The first step is to create the matrix of direct GHG emissions per commodity, $B$ from the $E$ matrix of GHGs by industry.
This requires some adjustments due to the differences in data years of the IOT and the GHG data and the need to align the data with commodities and not industries.
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@WesIngwersen I see you are describing the adjustment of industry output used in B here, would you think we should pair it up with the adjustment to A matrix, if we decide to apply some, in this section? Or in an earlier section?

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I think it needs to go in the earlier section for just the economic IOT

WesIngwersen and others added 2 commits February 27, 2026 15:56
Co-authored-by: Mo Li <mo@watershedclimate.com>
Co-authored-by: Mo Li <mo@watershedclimate.com>
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