2 Real gross domestic product compared with real gross domestic income

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Economic theory and statistical practice dictate that nominal gross domestic product (GDP) and nominal gross domestic income (GDI) are equal so that value added is equal to the value of purchases. However, the inflation-adjusted real measures can differ significantly when the volume of production and the volume of domestic purchases grow at different rates. Because GDP and GDI are equal in nominal terms, differences between real GDP and real GDI stem from deflator choice.

Real GDP is a measure of the price-adjusted flow of income generated by an economy in terms of the goods and services produced. It is a production-based measure. Its deflator accounts for price changes so that the resulting volume measure only changes when inputs or productivity change. While this feature makes real GDP a measure of real value added, it prevents real GDP from illuminating how relative price shifts affect the volume of goods and services that can be purchased with that income.

The GDI deflator allows relative price changes to affect the number of goods and services that may be purchased in an open economy. The GDI deflator achieves this by deflating net exports by one price index, rather than exports and imports separately. Deflating net exports directly leads to a real series that is different from the implied real net exports that come from subtracting real imports from real exports. The difference between the implied and the directly deflated real net exports is the change in the purchasing power of domestic production.

A decision about which price index should by used to value net exports must be made. The System of National Accounts 1993 (SNA93) does not explicitly preclude any method for deflating net exports. It does, however, note that:

There is a large but inconclusive literature [about selecting which price index to use to deflate net exports], but one point on which there is general agreement is that the choice of [that index] can sometimes make a substantial difference in the results. Thus the measurement of real GDI can sometimes be sensitive to the choice of [the price index] and this has prevented a consensus being reached on this issue.

SNA93, no. 16.153

This paper follows Kohli (2006) by using the final domestic demand (FDD) deflator because recent research suggests that it allows for a broader range of relative price changes and has fewer measurement issues—it alleviates concerns that arise when unit price indices are used for export and import price deflators (Silver 2007). The FDD deflator is one of the options put forward in SNA93, which makes it a real income measure that is officially recognized by the Organisation for Economic Co-operation and Development, World Bank, International Monetary Fund, United Nations and Commission of the European Communities. Unlike other options, Kohli's (2006) derivation shows that a trading gain based on the FDD deflator is consistent with an economy that engages in trade and has a current account imbalance. It is, therefore, consistent with the general equilibrium models of Corden and Neary (1982) and Corden (1984), and with the dependent economy model of the balance of payments.

Using the FDD deflator provides more information than other options by allowing the decomposition of the trading gain into terms-of-trade effects and an effect from the change in the relative price of traded to non-traded goods. Because some regions, such as the Canadian provinces or European Union member states, are affected by policies that transfer funds from richer regions to poorer regions, both relative price effects are crucial for understanding real income growth.

The terms of trade represents the volume of domestic goods and services that must be forgone to acquire a foreign good or service. A shift in the terms of trade, therefore, represents a real change in the volume of goods and services that an economy can purchase with what it produces. Terms- of-trade improvements have an impact analogous to productivity growth (Diewert and Morrison 1986).

The relative price of traded to non-traded goods and services has been referred to as the real exchange rate and as the Salter ratio, after W.E.G. Salter (1959) who placed the role of relative price changes between non-tradable and tradable goods at the centre of balance of payments adjustments. This paper follows Corden's (1992) example and refers to the price ratio as the Salter ratio to avoid confusion.

Changes in the relative price of tradable to non-tradables (the Salter ratio) can lead to changes in the income earned from, or spent on, net exports. Over time, this can lead to changes in the expenditure patterns of domestic agents by making tradables relatively more or less attractive. As a result, changes in domestic demand, inflationary pressures, unemployment rates and net exports can occur when the Salter ratio changes. The outcome from a change in the Salter ratio is more complex than terms-of-trade changes and depends on the source of the change (export, import or domestic prices), the relevant elasticities, the magnitude of the changes and the net export balance. Nevertheless, changes in the Salter ratio lead to changes in domestic purchasing power.

To illustrate how real GDI measure captures the trading gain, consider the following derivation which is based on Kohli (2006). It shows how, by deflating nominal GDP using two different deflators, it is possible to mathematically decompose the trading gain into terms-of-trade and Salter-ratio effects.

The GDP deflator is calculated as the weighted average of movements in FDD prices (i.e., consumption prices, investment prices and government expenditure prices), export prices and import prices where imports enter with a minus sign. By denoting ln( P_{Y t , / t −1} ) as the Törnqvist index value for the GDP deflator, it can be written as

where FDD , X and M represent final domestic demand, exports and imports; and the weights are calculated as each aggregate's share of nominal GDP,

and are averaged across t and t −1 :

Given the deflator, real GDP growth is defined as nominal GDP growth minus deflator growth:

By assumption, the real GDI deflator growth equals FDD deflator growth:

Real GDI growth is calculated in the same manner as real GDP growth. In the event that one does not need to decompose the trading gain into its components, it is possible to directly deflate nominal GDP with the FDD deflator to calculate real GDI. Using the FDD deflator, real GDI growth is equal to nominal GDP growth minus FDD deflator growth:

The trading gain from relative price changes that occur between t and t −1 is calculated as the difference between the real GDI growth and real GDP growth,

that reduces to the difference between GDP deflator growth and GDI deflator growth—i.e., to the difference between domestic price and import/export prices:

Since real GDP and real GDI are closely related, it is possible to calculate real GDI growth as real GDP growth plus the trading gain:

In order to calculate real GDI growth as the sum of production changes (real GDP) and relative price changes (the trading gain), an estimate of trading gain growth is necessary. By decomposing the trading gain into a terms-of-trade ( ToT ) effect and a Salter ratio ( E ) effect, it is possible to calculate changes in the trading gain as follows:

• Define terms-of-trade growth as :

Define growth in traded prices as:

• Define growth in the Salter ratio as:

Using these definitions and (2), it can be shown that trading gains are the weighted sum of the Salter-ratio and terms-of-trade movements:

By combining (3) and (4), the decomposition of real GDI growth becomes

Description

The weights attached to the Salter ratio and terms of trade have economic interpretations. The sign of the Salter ratio weight, 

Description

, is positive (negative) when the trade balance is in surplus (deficit), while its magnitude captures the size of the surplus (deficit) relative to nominal  GDP. The weight attached to terms-of-trade growth, , is the average value of trade as a proportion of nominal GDP. Real GDI in economies that are more open to trade is more susceptible to terms-of-trade shifts while a larger trade imbalance makes real GDI more susceptible to Salter ratio movements. Regions are often more susceptible to Salter ratio changes than countries are, because transfers from richer to poorer regions can lead to relative trade imbalances.

Because relative price changes play an important role in the evolution of real GDI, it can behave quite differently from real GDP. For instance, suppose that there is a ceteris paribus appreciation of the nominal exchange rate that lowers the price of imports. All else being equal, the appreciation means that less domestic income is spent purchasing foreign goods, which raises nominal GDP. Since the GDP deflator adjusts to account for price change, the volume measure of GDP will not change, or may decline, if domestic production is displaced.

The real GDI deflator, on the other hand, allows the nominal appreciation to affect the volume of goods and services that may be purchased. When the nominal exchange rate appreciates, it lowers the price of traded goods relative to non-traded goods (a shift in the Salter ratio). The appreciation simultaneously lowers export revenues and import costs. The net effect depends on whether net exports are in surplus or in deficit (Kohli 2006). Additionally, the import price falls relative to the price of exports (a terms-of-trade improvement), allowing the economy to transform each export into more imports. As a result, real GDI growth differs from real GDP growth.

When the effect of the appreciation on economic aggregates is examined, further differences between real GDP and real GDI materialize. First, while real GDI has increased, there may be no accompanying increase in the volume ofimports. In reality, there is no guarantee that an increase in real GDI from trading gains will lead to an accompanying increase in real domestic expenditures if additional expenditures must come from this source. The increase may, instead, translate into lower exports or greater savings. The relative price shifts cause a re-allocation of expenditures that is captured in real GDI changes but not necessarily in real GDP changes.

Second, if the lower import price is allowed to affect import volumes, economic theory suggests that import volumes will rise. If the rise leads to substitution away from domestic production, the increased level of imports will tend to lower real GDP. Real GDI, however, increases. The paradoxical result is that a nominal exchange rate appreciation can lower real GDP while raising real GDI (Kohli 2004).

² . The gross domestic product deflator also includes inventories and a statistical discrepancy. These are omitted from the analytical section.