# Trade in VA indicators¶

## Background¶

Trade has a double role by firstly allowing consumers to not only demand domestic produce, but also imports and secondly offering income opportunities by exports. The first role can be easily assessed in a CGE framework by reporting import shares on demand. The second one is harder to assess as export revenues comprise both direct value added from the exporting sector and indirect value added comprised in domestic intermediates. In the following, we present the implementation of a well-established framework drawing on Leontief Multiplicator analysis into the post-processing of CGEBox to assess the income generate role of exports.

We start with an illustrative example of an open economy with 2 two sectors and no foreign savings. Imports serve in our example only as intermediates inputs are not detailed by commodity:

Agr | NonAgr | |
---|---|---|

Agr share | 0,1 | 0,05 |

NonAgr share | 0,4 | 0,5 |

Import share | 0,2 | 0,1 |

VA share | 0,3 | 0,35 |

Output | 30 | 80 |

VA | 9 | 28 |

Final demand incl. Exports | 23 | 28 |

Exports | 2 | 12 |

Final domestic demand | 21 | 16 |

The example is balanced as the export revenues of 14 =2+12 are equal to
the value of imports (,2\cdot 30 + ,1\cdot 80)=12. The question is about the
contribution of the exports (or domestic sales) to value added. Based on
usual Leontief approach, we first calculate (I-A), where I is the
identity matrix and A the matrix of *domestic* input coefficients:

In our example that yields the following 2x2 table:

0.9 | -0.05 | |
---|---|---|

-0.4 | 0.5 |

Inverting that matrix delivers the Leontief multiplies (I-A)^-1:

1.1627907 | 0.11627907 |
---|---|

0.93023256 | 2.09302326 |

Multiplying the value added shares of the sectors with the Leontief multipliers delivers the VA multipliers for each commodity:

0.6744186 | 0.76744186 |
---|---|

If we now multiply these with final demand and export, we derive the VA contribution of the demand contributions:

Final domestic demand contribution | 26,4418605 |
---|---|

Export contribution | 10,5581395 |

Total Value added |
37 |

Which are equal to the value added as reported in our simple SAM and, as the SAM is balanced also equal to final domestic demand. The aim is now to implement the above steps into the CGEBOX framework.

## Post-Model processing¶

As a first step, we define (I-A) as follows, where the p_results parameter was populated before from the model results. Note that we are using the “V” field which captures value (= quantity x price):

Next, we use the “INVERT” utility from GAMS to define (I-A)^{-1}:

From there, we calculate multipliers for each primary factor – commodity combination:

Which can be aggregated to yield value added multipliers

Using these multipliers and export volumes allows to calculate the VA contribution of exports:

Further code lines not shown here aggregate the information over regions and commodities.

## GUI¶

In order to generate the information, the “GUI” output option must be switched on as well as the “Trade in VA indicators” checkbox:

That combination produces a table under the theme “trade”:

Which reports both the multipliers and the contribution of trade to value added. Additionally, the share from export related value added on total income is reported:

As seen below, the table also provides detail by factor: