Until quite recently, most OECD countries rebased their constant price estimates every five or ten years, such that the latest base year coincided with the reference year. Consequently, their constant price estimates were additive for recent years and the derivation of the contributions to the growth of GDP was straightforward.

Most OECD countries now derive their quarterly volume estimates by rebasing annually and chain-linking. (Canada and the US use Fisher’s ideal index and the rest use the Laspeyres index. Canada rebases quarterly). Nearly all the remaining countries intend to make the change soon.

For most countries that rebase annually or quarterly their volume estimates are no longer additive, and so the simple formula cannot be used.

Annual chain-linking and its implications for contributions to growth

Countries have adopted different ways of overcoming this problem:

Australia and the UK re-reference their volume estimates to the latest base year every year. Hence their volume estimates are additive for recent years and the simple formula applies.

Other countries using the Laspeyres index calculate contributions to growth using estimates expressed in the prices of the previous year, which are therefore additive, but it means having five quarters in previous year’s prices.

Canada and the US derive weights that can be applied to the growth rates of the components.

Annual chain-linking and its implications for contributions to growth

The problem for the OECD, Eurostat and other users is that it is now difficult, if not impossible, for them to derive contribution to growth data that are exactly the same as those derived by NSOs and the questionnaire does not include them.

Hence, the OECD and Eurostat request countries to supply these data for Tables 0101, 0102, 0104 and 0105 (i.e. 0101 and 0102 of the new questionnaire).

Countries have adopted different ways of dealing with this problem:

Differencing the most closely associated chain-linked series, i.e. closing and opening values for inventories, exports and imports for external balance.

Do not derive chain-linked volume estimates of such series.

Deriving annual chain-linked volume estimates for series that can change sign

Differencing chain-linked series to obtain the target series assumes an additive relationship between the three series that is invalid, and so this approach can only give an approximate estimate of the target series. However, it seems plausible to believe that the approximation will be better the closer the relationship between the three series is in terms of price and volume relativities.

Given that inventory levels generally change by only a small percentage over a quarter, the composition of the seasonally adjusted levels of inventories will generally be almost the same in consecutive quarters, implying a near-additive relationship between the chain-linked estimates of opening and closing levels and the difference between them.

Deriving annual chain-linked volume estimates for series that can change sign

Three countries that use the recommended approach are Canada, UK and US. Table 1 compares their published annual estimates of chain-linked changes in inventories with estimates derived as GCF – GFCF:

The difference between the two estimates generally grows the further they are away from the reference year. At 30 years from the reference year the difference often exceeds the magnitude of the published estimates.

Sometimes abrupt changes can occur, as it did between 1981 and 1982 for Canada.

Importance of deriving chain-linked estimates of changes in inventories

While contributions to growth of GDP are useful they are not an analytical substitute for actual volume estimates of changes in inventories.

Early 1980s recession in Canada (* Contributions to growth derived using simple formula)

Early 1980s recession in Canada – cont. (* Contributions to growth derived using simple formula)

Denmark and Iceland directly chain-link changes in inventories

Czech Republic uses GCF-GFCF

Netherlands by total final expenditures with and without changes in inventories. See comparison with GCF-GFCF in Table 1.

Results of the survey Table 3 – quarterly changes in inventories

Sweden calculates changes in inventories in prices of the previous year and then scales up according to GDP.

Most countries derive quarterly current price estimates of changes in inventories directly from survey data, but quite a few derive them residually.

Of the former group, a few countries have described in detail how they go about deriving the national accounts estimates from the raw book value data collected from surveys. Others provided much less detail.

Derive chain-linked volume estimates of changes in inventories by differencing chain-linked opening and closing levels. If no levels, consider deriving them.

For those using inventory survey data (quarterly or annual), how well founded are your assumptions about the inventory valuation practices of businesses?