How do we transform environmental totals by industry into B matrix including price year adjustment?

[WesIngwersen]

Environmental flows come into USEEIO and CEDA as totals by industry. They have to be transformed into B matrix values of coefficents of flows per USD. The steps of these transformations are slightly different in USEEIO v2 models and CEDA models and could result in slight differences in values.

RESOLVED as of 12/11/2025. Use USEEIO method for now and explore other options in medium term.

[WesIngwersen]

In USEEIO, to get from totals by industry into a B matrix value, using an example of a GHG total by an industry for 2023 in a 2017 IO based model like USEEIOv2.6.0-phoebe-23, the steps are:

1. adjust industry output price -- Adjust industry output in 2023 to be in 2017 USD using the ratio derived from the industry gross output chained-price index.
2. divide by adjusted industry output -- create a coefficient or intensity based using the adjusted output eg. kg GHG 2023/2023 industry output in USD 2017.
3. transform into commodity format -- transform it by the market shares to get it into kg GHG 2023/2023 commodity output in USD 2017.

That is the value that goes in the B matrix to use with the 2017 USD A matrix. This is represented in equations 3-6 of USEEIO v2 paper.

[WesIngwersen]

useeior steps

Within constructEEIOMatrices() in BuildModel.R the Totals by sector TbS are transformed into coefficients by sectors CbS

  model$TbS <- do.call(rbind,model$SatelliteTables$totals_by_sector)
  # Set common year for flow when more than one year exists
  model$TbS <- setCommonYearforFlow(model$TbS)
  # Generate coefficients 
  model$CbS <- generateCbSfromTbSandModel(model)
  
  model <- buildEconomicMatrices(model)
  
  # Generate B matrix
  logging::loginfo("Building B matrix (direct emissions and resource use per dollar)...")
  model$B <- createBfromFlowDataandOutput(model)

https://github.com/cornerstone-data/useeior/blob/90f4d7a022a3ecb2043535c30b473cd1068078a8/R/BuildModel.R#L25-L35

Steps 1 and 2 occur within generateCbSfromTbSandModel(), where generateFlowtoDollarCoefficient()
is called for every unique data year in the totals by sector

      for (year in data_years){
        cbs_r_y <- generateFlowtoDollarCoefficient(tbs_r[tbs_r$Year==year, ], year,
                                                   model$specs$IOYear, r, IsRoUS = IsRoUS,
                                                   model, output_type = "Industry")

https://github.com/cornerstone-data/useeior/blob/90f4d7a022a3ecb2043535c30b473cd1068078a8/R/BuildModel.R#L226C1-L229C84

within generateFlowtoDollarCoefficient(), adjustOutputbyCPI() is called to get the adjusted output which constructs an adjustment ratio diving reference year (~IO Year) by output year, then multiplying that by output from output year.

AdjustedOutput$DollarRatio <- AdjustedOutput[, as.character(referenceyear)]/AdjustedOutput[, as.character(outputyear)]
AdjustedOutput[, paste(outputyear, "IndustryOutput", sep = "")] <- AdjustedOutput$Output * AdjustedOutput$DollarRatio

https://github.com/cornerstone-data/useeior/blob/90f4d7a022a3ecb2043535c30b473cd1068078a8/R/IOFunctions.R#L20-L21

Back in getFlowtoDollarCoefficient, the physical flow amount from the TbS (e.g. kg CO2 from 112200) is divided by that adjusted output and that becomes the primary value in the CbS

  Sattable_USEEIO_wOutput$FlowAmount <- Sattable_USEEIO_wOutput$FlowAmount/Sattable_USEEIO_wOutput[, outputcolname]

https://github.com/cornerstone-data/useeior/blob/90f4d7a022a3ecb2043535c30b473cd1068078a8/R/SatelliteFunctions.R#L95

Step 3 occurs in createBfrinFlowDataandOutput() the CbS df is cast into a matrix and then multiplying by the market shares matrix, V_n, to put into commodity format.

createBfromFlowDataandOutput <- function(model) {


  CbS_cast <- standardizeandcastSatelliteTable(model$CbS,model)
  B <- as.matrix(CbS_cast)
  # Transform B into a flow x commodity matrix using market shares matrix for commodity models
  if(model$specs$CommodityorIndustryType == "Commodity") {
    B <- B %*% model$V_n
    colnames(B) <- model$Commodities$Code_Loc
  }
  return(B)
}

https://github.com/cornerstone-data/useeior/blob/90f4d7a022a3ecb2043535c30b473cd1068078a8/R/BuildModel.R#L197-L207

[WesIngwersen]

In CEDA, the steps to get from a total by industry to a B matrix value are, using an example of a GHG total by an industry for 2023 in a 2017 IO based model are:

1. divide by industry output -- create a coefficient or intensity based on the GHG year. eg. kg GHG 2023/2023 industry output in USD 2023.
2. transform into commodity format -- transform it by the market shares to get it into kg GHG 2023/2023 commodity output in USD 2023.
3. adjust commodity output price -- transform that into kg GHG 2023/2023 commodity output in USD 2017 using the ratio derived from the industry gross output chained-price index.

[WesIngwersen]

I'm looking into what I've noted as step 3 in CEDA , above. and it appears to be different. The code appears to be performing an output adjustment (not just a price adjustment) and using summary level data. Here is what I see is happening:

$\frac{2023 commodity GHG}{2023 commodity output in 2023 USD}$ $\frac{2023 commodity output in 2023 USD}{2017 commodity output in 2017USD}$

@MoLi7 It appears, by function name scale_detail_B_based_on_summary_q, that the B adjustment is using summary level data. Can you explain?

def derive_B_usa_non_finetuned() -> pt.DataFrame[BMatrix]:
    E_usa = derive_E_usa()
    # B_usa_2017 has 2022 emissions but 2017 economic data
    b_usa_2017 = derive_B_usa_via_vnorm(E_usa=E_usa)
    # Scale the economic data part of B_usa_2017 to 2022
    B_usa = inflate_B_matrix(
        scale_detail_B_based_on_summary_q(
            B=b_usa_2017,
            original_year=get_usa_config().usa_detail_original_year,
            target_year=get_usa_config().usa_io_data_year,
        ),
        original_year=get_usa_config().usa_io_data_year,
        target_year=get_usa_config().ceda_base_year,
    )

https://github.com/cornerstone-data/bedrock/blob/9eaaf0a39b1cdf0afe030218f38a537955e66e49/bedrock/ceda_usa/transform/eeio/derived.py#L81-L94

def scale_detail_B_based_on_summary_q(
    B: pd.DataFrame,
    target_year: USA_SUMMARY_MUT_YEARS,
    original_year: USA_SUMMARY_MUT_YEARS,
) -> pd.DataFrame:
    B_scaled = B.copy()
    q_summary_base = derive_summary_q_usa(original_year)
    q_summary_target = derive_summary_q_usa(target_year)
    # b_ratio is the opposite of q_ratio because
    # the price value for B is in the denominator
    b_ratio = (q_summary_base / q_summary_target).fillna(1.0)


    summary_to_ceda_v7 = load_bea_v2017_summary_to_ceda_v7()
    for i, val in b_ratio.items():
        if i not in summary_to_ceda_v7:
            continue
        ceda_sectors = summary_to_ceda_v7[i]  # type: ignore
        B_scaled.loc[:, ceda_sectors] *= val


    return B_scaled

[bl-young]

Do we know for sure if this results in different outcomes? Isn't the commodity CPI likely to be derived using the market shares, and so the sequence shouldn't matter?

[jvendries]

Resolution

We will use USEEIO's approach for now given it has been peer-reviewed but we will revisit in the future, specifically on the issue of updating the economic tables to a more recent year (e.g., using nowcasting or conceptually similar approach)

[yyandgin]

Just from the general 3 steps, not sure if USEEIO and CEDA should generate different emissions intensities THERE, though the use of summary level data in CEDA in that specific step is a bit confusing. Sometimes summary level data is used because it comes out sooner than detailed level data, just as a proxy.

A more important cornerstone needs to think about is when or where to apply the price adjustment and what assumptions are involved, for which I refer to another discussion Wes and I had recently:

cornerstone-data/supply-chain-factors#2