# An Open-Source R Package for Building and Using US Environmentally-Extended Input-Output Models
## 3 Results  
A single-region, summary level (73 commodities and 71 industries) USEEIO model, _USEEIOv2.0.1s_, is used as the example to demonstrate and discuss selected results in this section. The model is built with 2018 Summary IO data, 2010-2017 environmental flow data and a collection of indicators used with other v2 models like USEEIO v2.0.1-411 [18]. Total impact (direct + indirect) coefficients by sector, i.e., \(N\) (see Equation (19)), are examined through the _plotMatrixCoefficient_ function. Results of three impact categories, including acidification potential (ACID), greenhouse gases (GHG), and freshwater withdrawals (WATR), are presented in Figure 1. It should be noted that coefficients of these impact categories are generated using LCIA characterization factors from the TRACI2.1 method [33]. The _farms_ sector has the largest ACID (0.02 kg SO\({}_{2}\) eq/USD) and WATR (460 kg/USD) coefficient, and the second largest GHG coefficient (2.4 kg CO2 eq/USD)--only smaller than that of the _utilities_ sector (2.8 kg SO\({}_{2}\) eq/USD), which is carbon intensive due to primarily fossil fuel-based electric power generation in the US. _Utilities_ also has a notably large WATR coefficient (230 kg/USD), for the same reason. Energy intensive sectors including resource exploitation (i.e., _oil and gas extraction_ and _mining_), manufacturing, transportation, and waste management sectors have relatively large GHG coefficients. This illustration provides a clear view of total impact coefficients by sector in the model year. With more environmental flow data over years, multiple snapshots of the illustration could reflect changes in impact coefficients potentially caused by technological advancement in industries, or structural changes in the economy. Ranking sectors based a composite score of selected total impacts associated with total US demand is an effective means to identify prioritization opportunity in practices, such as the EPA's Sustainable Materials Management program. Comparing rankings is another form of model validation that incorporates the demand vectors and the indicators, as well as the matrices. The composite score for the rankings is calculated as a sum of fractions of sector impact relative to total impact across all sectors, by each selected indicator. This is represented using Equation (36), where \(s\) represents this score and \(t\), calculated in Equation (37), is a vector of the column sums of the given \(LCIA\) (see Equation (25)) matrix. \[s=(LCIA\hat{t}^{-1})i \tag{36}\]  
\[t=i^{\prime}LCIA \tag{37}\]  
The first ranking uses \(LCIA_{d}\) with the US production vector (left in Figure 2), while the second ranking is performed with \(LCIA_{f}\)(see Equation (27)), along with the US consumption vector (right in Figure 2). The sets of commodities in the top 20 from the two rankings (left and right in Figure 2) are nearly identical, with some notable substitutions and some exchanging of places. _Farms_, _utilities_, and _construction_ are in the top places in both rankings, but the orders and the distance (darkness of shade) separating _Construction_ from the other commodities are different. _Food and beverage and tobacco products_ is not in top 20 in the impact ranking created with \(LCIA_{d}\) and the US production vector (left), but is in the top place in the other impact ranking created with \(LCIA_{f}\) and the US consumption vector, as the latter calculation captures impacts, e.g., human health--respiratory effects (HRSP), associated with the use phase of commodities, e.g., tobacco. Figure 1: Total impact coefficients by commodity for acidification potential, greenhouse gases, and freshwater withdrawals. Figure 2: Top 20 commodities by composite impact score for USEELOv2.0.1s calculated using the total US production demand vector and the direct perspective (**left**), and using the total US consumption demand vector and the final perspective (**right**). Darker shade indicates a relatively higher score.