## 3 Methodology
### Demand-Side Model  
In the IO table, the total output (\(X_{i}\)) of sector \(i\) consists of the sum of intermediate demand (\(z_{ij}\)) and final demand (\(Y_{i}\)). Intermediate demand, \(z_{ij}\), can be expressed as \(a_{ij}X_{j}\) using \(a_{ij}(=z_{ij}/X_{j})\), which is called the input coefficient. Let \(A\) be the matrix composed of input coefficients, \(X\) be the matrix composed of total output, and \(Y\) be the matrix consisted of final demand. If the identity matrix \(I\) is included and a little manipulation is performed, the following equation, which is widely used in IO analysis, is derived. \[X=(I-A)^{-1}Y \tag{1}\]  
The model represented by Equation (1) is called a demand-side model, and the output (\(X\)) to satisfy the final demand (\(Y\)) can be obtained through the model. \((I-A)^{-1}\) is called the Leontief inverse matrix or production-inducing coefficient matrix. This is because the components of the matrix are \(a_{ij}=\partial X_{i}/\partial Y_{j}\), which represents how much the total output of sector \(i\) changes due to the one-unit change in final demand for sector \(j\). Through this model, the production-inducing effect, value-added creation effect, wage-inducing effect, and employment-inducing effect can be derived. In this study, as mentioned above, four effects of investment or production in the NG supply sector are obtained by the exogenous specification of the sector. The NG supply sector is referred to as \(K\) for convenience. First, the production-inducing effect, which means the amount of production that one unit of production or investment in sector \(K\) induces in other sectors, is derived as follows [43; 44]. \[\Delta X_{e}=(I-A_{e})^{-1}(A_{K}^{e}\Delta X_{K}) \tag{2}\]  
\(\Delta X_{e}\) refers to the amount of output change in other sectors due to the total output change of the sector \(K\), \(\Delta X_{K}\). \((I-A_{e})^{-1}\) is the Leontief inverse matrix created by excluding the column and row containing the sector \(K\) in the input coefficient matrix [45]. \(A_{K}^{e}\) is a column vector excluding elements of sector \(K\) among column vectors representing sector \(K\) in the input coefficient matrix (\(A\)), and \(X_{K}\) represents the total output of sector \(K\). In other words, \((I-A_{e})^{-1}A_{K}^{e}\) represents the production-inducing effect of one unit of production or investment in sector \(K\). Second, the value-added creation effect refers to how much production or investment in one unit in the \(K\) sector leads to value-added in other sectors. When the value-added coefficient matrix, which means the proportion of value-added in the total input, is multiplied by Equation (2), the value-added creation effect calculation formula is derived as follows. \[\Delta V_{e}=\hat{A}_{e}^{V}(I-A_{e})^{-1}(A_{K}\Delta X_{K}) \tag{3}\]  
\(\Delta V_{e}\) is a column vector consisting of changes in the value added in other sectors except for the sector \(K\). \(\hat{A}_{e}^{V}\) is the diagonal matrix of the value-added coefficient matrix excluding sector \(K\). Third, the wage-inducing effect refers to wage changes caused by one unit of production or investment in the sector \(K\) in other sectors. The wage coefficient (\(w_{i}\)) is defined as \(w_{i}=W_{i}/X_{i}\), which is the wage amount (\(W_{i}\)) of the sector \(i\) divided by the total output (\(X_{i}\)). By removing the row corresponding to sector \(K\) from the wage coefficient matrix and multiplying the diagonalized matrix \(\hat{W_{e}}\) by Equation (2), an equation for calculating the wage-inducing effect of an increase in investment or output in sector \(K\) on other sectors is derived as follows. \[\Delta W_{e}=\hat{W}_{e}(I-A_{e})^{-1}(A_{K}\Delta X_{K}) \tag{4}\]  
Fourth, the employment-inducing effect refers to the number of people employed in other sectors when the final demand for sector \(K\) increases by KRW 1 billion.