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Table 1 Flow matrix of product i (O–D matrix)

From: Estimation of the contribution of exports to the provincial economy: an analysis based on China’s multi-regional input–output tables

  Destination
1 n
Source 1 \(z_{i}^{1,1}\) \(z_{i}^{1,s}\) \(z_{i}^{1,1}\)
n \(z_{i}^{n,1}\) \(z_{i}^{n,s}\) \(z_{i}^{1,n}\)
  Total \(d_{i}^{1}\) \(d_{i}^{s}\) \(d_{i}^{n}\)
  \(c_{i}^{r,r} = \frac{{z_{i}^{r,r} }}{{d_{i}^{r} }}\), \(c_{i}^{s,r} = \frac{{z_{i}^{s,r} }}{{d_{i}^{r} }}\)