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Scottish Economic Statistics 2004
A1 Annual Chain-linking of the Scottish GDP Index
Introduction
Julie Ramsay, Scottish Executive
The publication of the Scottish GDP index for 2003 Q3 on 11th February 2004 introduced a major change of methodology for estimating economic growth. The adoption of annual chain-linking - in line with European requirements - brought the Scottish index into line with the UK GDP index, following the Office for National Statistics' (ONS) introduction of the new methodology in September 2003.
This article explains the reasons for this change in methodology, and discusses some of the revisions caused to the series as a result.
Background
The purpose of the Scottish GDP index is to provide an indicator of growth in the volume of gross value added 3 in the Scottish economy - also referred to as real terms growth or growth in constant prices. This gives a measure of whether output is increasing, without regard to changes in prices.
Data are collected to reflect the volume growth in gross valued added for more than 270 industries in Scotland. It can be difficult to obtain value added data on a quarterly basis so proxy indicators are used where value added data are not available. Examples of proxies used include: deflated turnover, deflated production, the volume of a good or service sold or produced and, for some parts of the public sector, employee numbers. These estimates are converted to indices referenced to 100.
The GDP index is produced by combining the indices for each of these industries to generate an estimate of how the economy as a whole is growing. The introduction of the new methodology relates to the final part of this process - the aggregation of indices for individual industries into an overall index of GDP.
Previous Methodology
Prior to February 2004, the GDP index was compiled using a fixed-base weighted methodology. A weight was calculated for each industry based on its share of total GVA. The base year used for the weights was updated at five-yearly intervals to give a new structure of weights. Indices using earlier weight structures were linked by choosing an appropriate link year between the two base years and using the ratio of indices to rescale previous indices to the latest base year. The most recent base year used for weights was also used as the indexing reference year.
The latest weights year used under this methodology was 1995. Under this system the weights applied to the latest quarter's estimates would be at best 3 years out-of-date - 2000 weights would have been introduced for 2003 Q3 had we stayed with the fixed base methodology - and at worst 8 years out-of-date - 1995 weights were being used for 2003 Q2.
There were a number of problems with this approach:
- For industries where the contribution to total GVA is changing rapidly, a volume measure based on a weight which is several years out-of-date can be "over-weighted" if price fall was steeper than volume growth or volume contraction was steeper than price increases. Similarly, it can be "under-weighted" if price fall was less steep than volume growth or price increase was steeper than volume contraction.
- Rebasing at five-yearly intervals can lead to large revisions.
- Turnover is commonly used as a proxy for quarterly GVA under the assumption that the turnover to GVA ratio remains stable over time. This assumption becomes less valid as time passes.
- Under the fixed-base methodology, the choice of link year is subjective and the most appropriate link year to use can vary from one industry to another.
New Methodology
The new methodology - annual chain-linking - differs from fixed-base weighting in that the base year is updated every year instead of every five years. Indices are then linked on the 4th quarter of each year.
The main advantages include:
- Annual weights are more up-to-date and therefore more relevant to the current economic situation.
- Rebasing revisions should occur less often. Although the initial introduction of chain-linking caused substantial revisions to the index, it is expected that the yearly update of weights year will cause less revisions.
- Chain-linking reduces the inaccuracies caused by the assumption of a stable relationship between GVA and turnover. Using annual weights, the assumption only has to stand from one year to the next.
- Every year becomes a link year, so there is no subjective choice.
However, there is a drawback. Chain-linking leads to a loss of 'additivity' in estimates before the last base year. Industry level indices prior to 2000 cannot be aggregated to the total simply by applying their weights.
On the whole, the advantages of chain-linking far outweigh the disadvantages and it is considered to be a superior method for the measurement of short term GDP.
Box A1.1 Calculation of Weights |
Industry weights are calculated based on their share of total Scottish GVA in current prices and are expressed in 'parts per thousand' of the whole economy. The current price GVA for an industry will be affected by changes in both prices and volumes in that industry. For example, if prices and volumes are both increasing then current price GVA will rise. Similarly if prices and volumes decrease, current price GVA will fall. However, current price GVA can fall despite increasing volumes if prices are decreasing at a greater rate. Annual industry weights have been calculated using a range of data sources. Industry shares are allocated according to Regional Accounts GVA shares, and broken down to detailed industries using Input-Output tables and Annual Business Inquiry GVA data. |
Effects of Chain-linking on Growth Estimates
In some industries the use of more recent weights caused the estimates of growth to increase, and caused others to decrease. The following are two examples of such industries. 4
Retail
The effect of chain-linking on the retail sector was to decrease estimates of GVA growth. Average quarterly growth between 1995Q1 and 2003Q3 dropped from 0.8% under the fixed-base methodology to 0.7% when the chain-linking methodology was implemented.
C hart A1.1: Retail GVA Index 1995Q1 - 2003Q3
The difference is clearer if we separate the time series into sections. Between 1995Q1 and 2000Q2 there is considerably less growth using the chain-linked index than the fixed-base index (average quarterly growth of 0.7% with chain-linking compared to 1.6% fixed-base). From 2000Q2 onwards the chain-linked index produces higher growth estimates (+0.7% on average compared to -0.4% with the fixed-base index).
It is necessary to look at the sector in more detail to identify the cause of these differences. There are three detailed series within retail: food retail, non-food retail and other retail (including non-store retail and repair).
C hart A1.2: Detailed GVA Indices for the Retail Sector 1995Q1 - 2003Q3
Food and non-food retail follow a fairly similar pattern over the period but other retail is markedly different with a period of high growth between 1999 and 2001 followed by sharp decline from 2002 onwards. Other retail is clearly driving the majority of growth in the earlier period of the fixed-based index for retail as a whole. From 2002 onwards its steep decline is balanced by moderate growth in non-food retail and results in a fairly flat picture at the sector level.
However, other retail does not have as great an effect on the chain-linked index for the retail sector. The chain-linked index appears to be closer to the patterns shown in food and non-food retail over the whole period.
The reason for this difference is due to weights. Chart A1.3 details the GVA weights used for each series in the 1995 fixed-base index and the 2000 weights 5 used in the chain-linked index. The weights for all 3 series have fallen between 1995 and 2000 but, in relative terms, other retail has fallen most significantly. This has reduced the effect of other retail on the overall retail index and increased the effect of food and non-food retail, explaining why the chain-linked index now follows a similar pattern to these two indices.
C hart A1.3: Retail GVA Weights, 1995 and 2000
An examination of price changes over time can explain the fall in relative weight (chart A1.4). The main period of growth in the volume index for other retail was between 1999 and 2001. However, over the same period of time prices experienced a sharp fall which continued into 2003. By contrast, prices in food retail have increased steadily since 1995.
C hart A1.4: Price Deflators for the Retail Sector 1995Q1 - 2003Q3
As a result of the falling prices, the relative weight of other retail has fallen and its influence on the retail industry as a whole has been reduced. This has had a negative effect on the growth estimate for the period 1995Q1 to 2000Q2 and a positive effect on the growth estimate for the period 2000Q2 to 2003Q3.
Electronics & Instrument Engineering
The introduction of chain-linking led to an increase in the estimated GVA growth in electronics & instrument engineering (E&IE). Average quarterly growth between 1995Q1 and 2003Q3 increased from -0.5% using the fixed-base index to +0.1% using the chain-linked index.
C hart A1.5: E&IE GVA Index 1995Q1 - 2003Q3
The two methods result in similar growth estimates for the period from 1995Q1 until 2001Q2 (average quarterly growth of 1.4% with the chain-linked index and 1.2% with the fixed-based index). After this point the chain-linked index shows higher growth (or less decline) than the fixed-base index (average quarterly growth of -3.6% compared to -5.2%).
Again it is necessary to look at trends at a more detailed level to identify the cause of the change. Chart A1.6 breaks the index down into more detailed industries 6.
Box A1.2 |
Industries are grouped according to the Standard Industrial Classification of Economic Activities (SIC). The SIC codes for E&IE are as follows: |
30 | manufacture of office machinery & computers |
31 | manufacture of electrical machinery and apparatus not elsewhere classified |
32.1 | manufacture of electronic valves and tubes and other electronic components |
32.2 | manufacture of television and radio transmitters and apparatus for line telephony and line telegraphy |
32.3 | manufacture of television and radio receivers, sound or video recording or reproducing apparatus and associated goods |
33 | manufacture of medical, precision and optical instruments, watches and clocks |
Between 1995Q1 and 2001Q2 the fastest growing industry was SIC 30 (office machinery & computers) which grew by an average of 2.9% per quarter. SIC 32.1 (electronic valves and tubes) also grew strongly over this period - by an average of 1.1% per quarter.
The most interesting period, however, is the period from 2001Q2 onwards as this is where the fixed-base and chain-linked indices diverge. All five industries declined over this period, but the two strongest growing industries in the earlier period also experienced the steepest decline in the latter period. SIC 30 had an average quarterly growth of -8.4% and SIC 32.1 had -3.1% between 2001Q2 and 2003Q3.
C hart A1.6: Detailed GVA Indices for E&IE 1995Q1 - 2003Q3
Comparing the detailed indices to the overall E&IE indices in chart A1.5 it becomes clear that the fixed-base index was heavily influenced by SICs 30 and 32.1 - following a similar pattern of steep growth and steep decline - and less influenced by SICs 31 and 33 - which remained fairly stable after 2001 - and SIC 32.2/32.3 which actually increased post 2002. Although the chain-linked index follows a similar pattern until 2001, it appears to take more account of these SICs after this point.
The weights help to explain this (chart A1.7). SICs 30, 32.1 and 32.2/32.3 all have decreasing weights between 1995 and 2000 whereas SICs 31 and 33 increase their weights. The total weight for E&IE fell over the period, but the sharp falls in SICs 30 and 32.1 led to a reduction in their influence on the sector as a whole, balanced by an increase in the relative influence of SICs 31 and 33 whilst SIC 32.2/32.3 remained unchanged.
C hart A1.7: E&IE GVA Weights, 1995 and 2000
The weights of SICs 30 and 32.1 fell between 1995 and 2000 despite their high volume growth, because prices fell so sharply - particularly in SIC 30 (chart A1.8). The 1995 weights failed to take this price fall into account and were therefore over-weighting SICs 30 and 32.1 and therefore overstating the decline since 2001.
C hart A1.8: Price Deflators for E&IE 1995Q1 - 2003Q3
Overall Effect on GDP
These two examples provide some insight into how the introduction of chain-linking had different effects across industries. On the whole, more industries were positively affected by the change than were negatively affected and as a result the effect of chain-linking on growth estimates for the economy as a whole was positive.
Chart A1.9 compares the overall GVA index under the fixed-base and chain-linking methodologies. Over the period since 1995Q1 average quarterly growth increased from 0.3% using the fixed-base index to 0.5% using the chain-linked index.
C hart A1.9: GVA Index 1995Q1 - 2003Q3
Between 1995Q1 and 2001Q2 there is no real difference between the two indices with both estimating average quarterly growth as 0.5%. However, there is a clear difference from 2001Q2 onwards, with the chain-linked index estimating average growth of 0.5% per quarter compared to 0.0% under the fixed base index.
This divergence in the latter part of the time series makes sense. The use of updated weights had more impact on estimates for 2001 onwards as these are the furthest away from the 1995 weights which were used in the fixed-base index. For the first few years the 1995 weights were adequate but, as time passed, became less relevant to the current situation and therefore were providing a less accurate estimate of GVA growth.
In the case of the Scottish index, updating weights from 1995 to 2000 led to an increase in the estimates of GVA growth. Chain-linking does not always have a positive effect, however, and future updates of base years could equally result in a downward revision to growth estimates, although the size of any future reweighting revisions are expected to be considerably smaller than those observed following the initial introduction of chain-linking.
The weight structure for the Scottish index will be updated to a 2001 base year on publication of 2004Q2 results on 27th October 2004.
Conclusion
The introduction of chain-linking methodology to the quarterly Scottish GDP index resulted in an upward revision to growth estimates from 2001 onwards. This happened because the 1995 weights had been overestimating the importance of declining industries such as E&IE, whilst underestimating the importance of growing industries such as business services and financial services. The size of revisions were quite large in some cases as the weights were being brought forward by 5 years. In future weights will be updated annually and the resulting revisions will be smaller.
The adoption of annual chain-linking has brought the Scottish methodology into line with the UK and other countries allowing international comparisons to be made on a more equal basis. It is widely accepted that it represents a more reliable, accurate and up-to-date measure of economic growth than the previous fixed-base methodology.
References
Amanda Tuke and Geoff Reed (2001) "The effects of annual chain-linking on the output measure of GDP" Economic Trends No. 575 pp37-53
Amanda Tuke (2002) "Analysing the effects of annual chain-linking on the output measure of GDP" Economic Trends No. 581 pp26-33
Robin Lynch (1996) "Measuring real growth - index numbers and chain-linking" Economic Trends No. 512
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