Introduction of chain-linked volume measures in the Quarterly Spanish National Accounts General National Accounts Unit National Statistics Institute May, 2
1 Introduction Modern market economies are characterised by the performance, over a specific period of time, of a high number of transactions that involve the production and sale of goods and services (mainly products). The value in current terms of each of said transactions is obtained by multiplying the amount produced or exchanged of the product in question by its corresponding unitary price. Thus, for a specific time interval (e.g., a year or a quarter) the total value of the transactions that take place in a given economy results from adding up the individual values of all the transactions performed over said period. The comparison of said values in time, generally, results from combining variations in the exchanged amounts and modifications regarding the prices at which the transactions have been performed. Consequently, from a statistic and economic point of view, it is interesting to note the extent to which said nominal variations are due to one or another factor, breaking down the nominal variation as regards volume and price. This double statistic and analytical need has given way to two types of measurements that isolate the effect of variations in amount from variations in prices: estimates at constant prices and chain-linked volume measures. The latter provide a more accurate estimate of the economic phenomenon linked to the production and exchange of amounts of products. Thus the INE, following recommendations issued by Eurostat and other international statistics institutions, has applied this measurement system when compiling National Accounts, both yearly and quarterly. In the first place, the different assessment systems are set out: at current prices (section 2), at constant prices of a base year (section ), at prices of the previous year alongside the corresponding chain-linked volume measure (section 4). Hereunder is a chain-linked indices methodology applied to the data published for the 2-24 accounting series at constant prices for 1. Finally, the European Union legal framework that sustains the introduction of this new assessment system is also analysed. 2 Valuation at current prices As aforementioned, valuation at current prices is obtained aggregating current exchanges values for all products of the economy. The following table presents an example including hypothetical data on two products (A and B) for three years (, 1 and 2).
Table 1: Exchange value at current prices 1 Product Price Quantity PQ Price Quantity P1Q1 Price Quantity P2Q2 A B 4 1 18 1 6 11 66 28 Total 4 Valuation at constant prices for a year (fixed base) Interannual variations in the previous table result both from modifications in the amounts exchanged of A and B, and variations in their respective prices. In order to isolate the former from the latter, the valuation at constant prices assesses exchanges in terms of the valid prices for a certain period, called the "base period." The following results are obtained by taking year as the base year, for example: Table 2: Exchange values at constant prices for year 1 2 Product Price Quantity PQ Price Quantity PQ1 Price Quantity PQ2 A B 4 1 28 2 2 1 6 11 2 28 44 Total 4 1 Adopting a set year for the valuation implies that, to the extent that the exchange structure for said year is modified over time 1, the corresponding assessment loses relevance and significance, from both economic and statistic viewpoints. Consequently, in order to update quantification structures, base year changes are performed periodically. Valuations at prices for the previous year (mobile base) and chainlinked volume measures. If the loss of relevance of the base can be solved by modifying the base year periodically, the ideal solution is to update said base with the same frequency that the estimate is calculated. This operation obtains valuations at prices of the previous year, called "links," which appear in the following table: 1 Given the changes in relative prices; modifications in the exchange patterns brought about by changes in technology or preferences; modifications in products exchanged, etc.
Table : Exchange values at prices of the previous year 1 2 Product Price Quantity PQ Price Quantity P1Q1 PQ1 Price Quantity P2Q2 P1Q2 A B 4 1 28 18 1 6 11 66 18 28 Total 4 Link 1 12. 1. As valuations have always been performed considering consecutive pairs of years, creating a homogeneous series that represents the whole sequence of years requires the chain-linking of all yearly links. Said chain-linking is obtained by multiplying each annual link as an index by the chain accumulated up until the previous year. The chain obtained using this method is obviously an index number. Therefore, its conversion to monetary terms is performed by multiplying it by the value at current prices for a specific year, called "reference year". The following table considers year as the reference period: Table 4: Chain-linked index: basic and monetary expressions r 2 Product Price Quantity PQ Price Quantity P1Q1 PQ1 Price Quantity P2Q2 P1Q2 A B 1 28 2 18 2 1 6 11 66 18 4 28 Total 4 Link 1 12. 1. Chain-linked index 1 12. 16.2 Monetary valuation 4.8 where: (/4) x 1= 12. (/) x 1= 1. 12.x1.= 16.2 4x12. = 4x16.2 =.8 Conversely to what occurs with the valuation at constant prices in which the reference year and the base coincide, it must be noted that they are not equivalent in the system for valuation at prices of the previous year. Thus, the reference year defines the scale for the chain-linked index (setting it at 1), whilst the temporal base is mobile, with as many bases as consecutive pairs of years. Therefore, as a whole, the chain-linked valuation lacks a fixed base (mobile base). Applying the methodology generates a loss of additivity in the chain-linked volume measures (except in data corresponding to the years considered as the mobile base and the immediately subsequent year). Losing additivity implies that, for example, the addition of the components of the Gross Domestic Product () does not coincide with the latter (except in the data corresponding to the years considered as the mobile base and the immediately subsequent year). In general, a variable assessed considering chain-linked volume measures does not add up to the elements that compose it which have been equally assessed via chainlinked volume measures. Losing additivity is a direct consequence of the
mathematical properties of the valuation system. Therefore, discrepancies do not reflect any deterioration whatsoever regarding quality in the measuring process. The following table considers four products (A, B, C and D) and two ways of aggregating them: Z=X+Y, where X=A+B and Y=C+D and V=A+B+C+D. All years, except for the reference year () and the following year (1), show a discrepancy between both forms of composing totals Z and V. Table : Chain-linked index: loss of additivity 1 2 Product Price Quantity PQ Price Quantity P1Q1 PQ1 Price Quantity p2q2 p1q2 A B 1 28 2 18 2 28 1 6 11 66 18 4 X=A+B 4 Link 1 12. 1. Chain-linked index 1 12. 16.2 Monetary valuation (X) 4.8 C D 1114 84 6 1411 84 66 1614 144 6 8 6 Y=C+D 1 161 16 214 14 Link 1.8 12. Chain-linked index 1.8 11. Monetary valuation (Y) 1 16 16. Z=X+Y 182 11 2.6 V=A+B+C+D 182 214 11 26 Link 1 14. 124. Chain-linked index 1 14. 1.4 Monetary valuation (V) 182 11 28. Z=X+Y Monetary 182 11 2.6 valuation (V) 182 11 28. difference 1. In order to facilitate analysis and estimates, the reference is modified each time a new datum is published, always ensuring that the last year is additive. Modifying the reference changes the levels of the whole series, but preserves growth, as appears in the following table, referring exclusively to products A and B and their aggregate (X) that are included in table : Table 6: Chain-linked index with reference modification Refe- 1 2 rence Chain-linked index 1. 12. 16.2 Monetary valuation 4...8 Δ - 2.. Chain-linked index 8.2 1. 1. 1 Monetary valuation 41.4.. Δ - 2.. Chain-linked index 6.8 2.6 1. 2 Monetary valuation 42.6 4.. Δ - 2..
Counterfactual assessment of the National Accounts The table hereunder is a numerical example comparing the data published at constant prices for 1 for the main demand aggregates (SNA 1 Base), with those that would have been obtained if the chain-linked methodology had been applied to said figures. FIXED BASE 1 Domestic FCE on food, beverage and tobacco Domestic FCE on items other than foodstuffs FCE NPISH FCE PAs GFFC in capital goods GFFC in construction GFFC in other products Variation in stocks Export of goods Export of non-tourist services Import of goods Import of non-tourist services 1 IQ TP IV 21 IQ IP IV 21 IQ n> TV IQ IP IV 24 CONSTANT CONSTANT CURRENT CONSTANT CURRENT CONSTANT CURRENT CONSTANT CURRENT CURRENT 6,4, 12.64 1. 1.82 6,84 6,21 12. 14.8 1. 66,4 81,684 11.8 1.6 1.86 6,61 86,468 11. 1.4 14.8 68,66 661 2, 12,66 12. 1. 1. 248 1,2 11. 8 1.1 1.14 282,84 48.2 12. 1.4 1.88 2,611 68,44 1.1 12.4 16.18 2,1 1,4,6 4, 11. 1.2 1.1,82 4, 14.2 1.6 18.1 8 4,6 14.64 14.1 1.1 4,14, 11.8 1. 1.2 4,2,6,2 1,8 1. 1.1 16.8,261 11,14 14.1 1. 1.8 11,244 128 1.8 1.8 1.41 1,18 1, 14.8 2 14.66 1. 11,2 146,4 41,2 4,66 8.82 11.1.82 4,812 4.4S 4. 11.62 6.8 8,88 4, 11. 11.1 12. 8,4 44,8 1.8 12. 18.1 41,26 4884 68, 8,66 1. 1.46 111. 2,61 2,4 1.2 1.2 11.8 6,422 12.8 14. 16. 11.,8 11,88 14.4 1.86 112.66 8,2 128,2 2,22 2,11 1.66 1.6 1.4 2, 26, 1.1 14. 1.8 21,62 2,114 1. 1.44 18.6 22,24 1,61 1.2 1.1 11.6 22, 4.2 18 2,22 8. 12. 8.21 1,61 1,6 11.4 12.16 112.86 1824 2,18 124.18 14.1 12.8 2,26 2,82 16. 24.2.6,42 112 11,26 126, 12.6 12.6 14.4 116 12,221 12. 8.8 12.6 11,1 1611 1..6 1.1 12,814 14,12 16. 8 8.8 1.1 12,8 148,8 2 2,1 2,216 111.1 12.8 114.2 22,44 26,4 1. 1.16 16.8 2,2 28,44.42 12. 11.6 2,11 28, 8.8 12. 11.1 22,8 228-144,2-164,2 1.26.8 1.8-148,6-16,16 1. 8. 11. -1,1-11,6 1.16.68 14.8-161,6-1,8 1.8 12.88 11. -1.68-2,42-2,124-2, 16.4 14. 111.22-24,2 -,66 1. 11.8 12.6-24,1 -,8 12.2 11.16 1.1-2,1-1,81 1. 6 12. 1.2-2,61 -,16 2,61 61,41 12.8 14.1 1.11 4446 6,2 12.2 14. 16.8 6,61 688 12. 14.1 16.61,6 44,4 12.6 14.44 1.24 8,8 8,62 GROUPING FCE GFC where: IQ = volume index IP = price index IV = value index 41,1 4,441 12. 1. 16.42 4418 2,2 12.4 12,4 16,61 12. 14. 16.84 16.66 16,18 11. 1,221 14, 1.6 12.2 16. 18.18 18,61 1. 6-16,126-11,288 1. 1.44 14.2-1,426-1,82 1. 6 2,61 61,41 12.8 14.1 1.11 4446 6,2 12.2 1.46 1.8 44,4 844 12.8 1.26 16.24 46,621,61 1.2 1.4 16. 482,12 6,84 14.1 16. 18,4 1. 1.44 1. 18.61 14,221 1,264 1.4 1.4 11.41 11,26 22,48 1.2 1.6 142, 164.4 1.1 1. 1.24 146,1 16,812 1.6. 14.6 1,218 18,28 8.61 11.6-18,682-22,6 14..8 14.6-18,21-211, 18. 12. 111. -22-26,8 14. 16.8 6,61 688 12. 14.1 16.61,6 44,4 12.6 14.44 1.24 8,8 8,62
The indices with the highest level of break down are taken as the interannual indices: CHAIN-LINKED INDICES Domestic FCE on food, beverage and tobacco Domestic FCE on items other than foodstuffs FCE NPISH FCE APs GFFC in capital goods GFFC in construction GFFC in other products Variation in stocks Export of goods Export of non-tourist services Import of goods Import of non-tourist services 2 21 IQ IP IV CONSTANTES IQ período anterior CORRIENTES IP IV CONSTANTES IQ IP período anterior CORRIENTES IV CONSTANTES IQ IP IV período anterior CORRIENTES CORRIENTES. 12,64 1, 1,82 2.626 6.21 12,8 14,8 1,.8 81.684 11,8 1,6 1,86 8.1 86.468 11, 1,4 14,8 12.66 12, 1, 1, 21.4 1.2 11, 1,1 1,14.66 48.2 12, 1,4 1,88.86 68.44 1,1 12,4 16,18 4. 11, 1,2 1,1 4.4 4. 14,2 1,6 18,1 4.2 4.6 14,64 14,1 1,1.14. 11,82 1, 1,2 1.8 1, 1,1 16,8 111.66 11.14 14,1 1, 1,8 11.86 12.8 1,8 1,8 1,41 128.6 1. 14,8 14,66 1, 4.66 8,82 11,1,82 4.2 4.48 4, 11,62 6,8 4.4 4. 11, 11,1 12, 44.1 44.8 1,8 12, 18,1 8.66 1, 1,46 111, 88.4 2.4 1,2 1,2 11,8.81 12.8 14, 16, 11, 1.64 11.88 14,4 1,86 112,66 2.11 1,66 1,6 1,4 26.4 26. 1,1 14, 1,8 2.88 2.114 1, 1,44 18,6 2.88 1.61 1,2 1,1 11,6 2.22 8, 12, 8,21 1.888 1.6 11,48 12,16 112,86 2.1 2.18 124,18 14,1 12,8 2.1 2.82 16,8 24,2,6 126. 12,6 12,6 14,4 12.48 12.221 12,,8 12,6 16.12 16.11 1,,6 1,1 141.48 14.12 16,2 8,8 1,1 2.216 111,1 12,8 114,2 2.8 26.4 1, 1,16 16,8 2.4 28.44,42 12, 11,6 28.181 28. 8,8 12, 11,1-164.2 1,26,8 1,8-16.61-16.16 1, 8, 11, -1.48-11.6 1,16,68 14,8-18. -1.8 1,86 12,88 11, -2. 16,4 14, 111,22-28. -.66 1, 11,8 12,6 -.6 -.8 12,2 11,16 1,1-1.61-1.81 1, 12, 1,2 61.41 12,8 14,16 1,11 62.814 6.2 12,1 14,42 16,8 66.12 68.8 12, 1, 16,61 16.2 44.4 12,84 14,2 1,24 22 2 PIE GROUPING: FCE GFC 4.441 12, 1, 16,42.41 2.2 12,4 1,46 1,8 4. 8.44 12,88 1,26 16,24 4.86.61 1,2 1,41 16, 16.61 12,8 1, 16,84 161.4 16.18 12,4 14,22 16, 1.2 1. 1,2 14,2 18,61 184.22 1.264 1,2 1,8 11,41 14. 1,2 12,2 16, 1.48 18.61 1, 1,2 1,6 16.62 164.4 1,1 1, 1,24 16.68 16.812 1,,4 14,6-11.288 1,8 1,4 14,2-18.2-1.82 1,1 8,6 11,6-2.84-22.6 14,, 14,6-212.11-211. 18,4 12,8 111, 61.41 12,8 14,16 1,11 62.814 6.2 12,1 14,42 16,8 66.12 68.8 12, 1, 16,61 16.2 44.4 12,84 14,2 1,24
The following differences appear when comparing volume indices obtained for the grouping of four components, using both systems: INDEXES FCE* GFC 2 21 22 2 24 1. 12. 12.4 12.88 1.2 1. 12.8 12.4 1.2 1.2 1. 1.2 1. 1. 1. 1. 1.8 1.1 14. 18.4 1. 12.8 12.81 12. 12.84 FIXED BASE 1 FCE* GFC DIFFERENCES FCE* GFC 2 21 22 2 24 1. 12. 12.4 12.8 1.2 1. 12. 11.6 1.44 1.4 1. 1.6 1.6 1.1 1.6 1. 1. 1. 14. 18. 1. 12.8 12.2 12. 12.6 2 21 22 2 24.......1.28.8 -.12... -.4 -.1..1 -.2 -.4 -.14....8.16 * differences appear as of the fourth 6 Legal framework Chain-linked volume measurements in Spanish National Accounts are envisaged in European Commission Decision number 8/1, establishing their compulsory nature in the transmission of data from National Statistics Institutes to the Statistical Office of the European Union, EUROSTAT. Throughout 2, the following EU countries will include chain-linked volume measures in their National Accounts: Germany, Austria, Cyprus, Denmark, Slovakia, Spain, Finland, France, Greece, Holland, Italy, Lithuania, Luxembourg, Malta, Poland, Portugal, Czech Republic, United Kingdom and Sweden. These measures are also applied in Australia, Canada, United States, Japan and New Zealand, among others. There is no equivalent legal framework for Quarterly National Accounts. Nevertheless, to maintain consistency, Eurostat and other international statistical institutions such as the International Monetary Fund (IMF) and the Organisation for Economic Cooperation and Development (OECD), among others, have recommended their implementation. The methodology applied for the quarterly accounts requires a series of special technical considerations that are detailed in a specific document. 8