Appendix 11D Balancing of provincial trade flows

The provincial balancing of trade flows – both international and inter-provincial – is calculated using the Input-Output Tables (IOT) framework. The following accounting identities are used to constrain trade flows within the Input-Output Tables.

1. In each province and for each commodity, total domestic supply (DS) must be identical to sales to the rest of the world (international exports (XW)), to other provinces (interprovincial exports (XP)) and to its own province (PS). Total domestic supply (DS) is defined as the value of production (PR) plus shipment out of the inventories¹ of producers, wholesalers and retailers (Δ-INV). Equation 11D.1 reflects this, where i is for provinces or territories and x stands for commodities.

   Equation 11D.1

   DS_i,x = XW _i,x + XP _i,x + PS _i,x

   where,

   DS_i,x = PR_i,x + Δ-INV_i,x

   hence,

   PR_i,x + Δ-INV_i,x = XW _i,x + XP _i,x + PS _i,x

2. In each province and for each commodity, total domestic demand (DD) must be identical to purchases from the rest of the world (international imports (MW)), from other provinces (interprovincial imports (MP)) and from its own province (PS). Total domestic demand is equal to final domestic demand (FDD) (personal expenditure, capital formation and current government expenditure) plus intermediate domestic demand² (IDD) plus additions to inventories³ (Δ+INV) of producers, wholesalers and retailers. Equation 11D.2 reflects this, where i is for provinces or territories and x stands for commodities.

   Equation 11D.2

   DD _i,x = MW _i,x + MP _i,x + PS _i,x

   where,

   DD _i,x = FDD _i,x + IDD _i,x + Δ+INV _i,x

   hence,

   FDD _i,x + IDD _i,x + Δ+INV _i,x = MW _i,x + MP _i,x + PS _i,x

3. In each province and for each commodity, total domestic supply (DS) minus total domestic demand (DD) equals total exports (X = XW + XP) minus total imports (M = MW + MP). This yields a measure of net trade (NT) by province and by commodity. Equation 11D.3 reflects this, where i is for provinces or territories and x stands for commodities.

   Equation 11D.3

   DS _i,x - DD _i,x = NT _i,x

   where,

   NT _i,x = (XW _i,x + XP _i,x ) - (MW _i,x + MP _i,x)

4. For each commodity, the sum of international exports (XW) and imports (MW) by province are identical to their national counterparts. Equation 11D.4 and Equation 11D.5 reflect this, where i is for provinces or territories and x stands for commodities.

   Equation 11D.4

    

   Equation 11D.5

   

5. For each commodity, interprovincial exports (XP) and imports (MP) are identical when summed over all provinces since one province's exports are another province's imports. Equation 11D.6 reflects this, where i is for provinces or territories and x stands for commodities.

   Equation 11D.6

   

   Goods purchased outside Canada and re-exported to the rest of the world are not part of the provincial identities. They are recorded as a separate element, a trade flow from the rest of world to outside Canada.⁴

Collectively, those identities form an accounting framework for adjusting source data, for filling data gaps and for analyzing the quality and consistency of the information used in the derivation of trade flow estimates. These identities are respected for each commodity, for each year at the lowest detail possible (about 725 commodities that are latter aggregated to 679 commodities).

Back to

• Appendix 11C Level of detail for the trade in goods
• 11 International and inter-provincial trade in goods and services

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Notes

1. This is known as inventory withdrawals in the Input-Output Tables.

2. This would correspond to inputs into the production process.

3. This is known as inventory additions in the Input-Output Tables.

4. While re-exports are excluded from the international imports and exports as part of the international and interprovincial trade flows program, they are included in the comparable estimates in the provincial expenditure-based gross domestic product program.