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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

\(d_{i}^{1}\)

\(d_{i}^{s}\)

\(d_{i}^{n}\)

 

\(c_{i}^{r,r} = \frac{{z_{i}^{r,r} }}{{d_{i}^{r} }}\), \(c_{i}^{s,r} = \frac{{z_{i}^{s,r} }}{{d_{i}^{r} }}\)