THE USE OF CHAIN INDICES IN THE NETHERLANDS. Sake de Boer. Jan van Dalen. Piet Verbiest

Transcription

1 THE USE OF CHAIN INDICES IN THE NETHERLANDS Sake de Boer Jan van Dalen Pie Verbies December, 1996 Paper o be presened a he Conference on Measuremen problems and economeric modeling, Isiuo Nazionale di Saisica, Rome, January The views expressed in his paper are hose of he auhors, and do no necessarily reflec he views of Saisics Neherlands. The auhors would like o hank Ger den Bakker and Seven Keuning for heir useful commens on earlier versions of his paper. BPA no : DFB.PNR Noanr. : DFB-PNR Saisics Neherlands Deparmen for Naional Accouns P.O. Box JM Voorburg The Neherlands 1

2 1. Inroducion An imporan purpose of he compilaion of naional accouns is measuring changes in economic variables. Changes in he producion and use of goods and services are caused by a combinaion of wo facors: a change in price and a change in quaniy and qualiy (in naional accouns ofen denoed as: volume change). Par of he work on naional accouns is he decomposiion of value changes ino volume changes and price changes. The mos imporan purpose is he esimae of real growh raes (volume indices). The second goal is he esimae of price changes (deflaors). An imporan characerisic of his work when embedded in a naional accouns framework is ha volume indices and deflaors of various variables and a differen levels of aggregaion are inerrelaed in a sysemaic way. This is achieved by using supply and use ables or inpu-oupu ables as an inegraing and balancing framework. Price and volume indices of aggregaes are always compiled from price and volume indices of individual goods and services. Direc observaion of price and volume changes of aggregaes is - by definiion - impossible. Nearly all iems in he naional accouns are aggregaes or aggregaes of aggregaes. Examples of he laer are oal household consumpion expendiure, oal impors and oal expors, bu also oal oupu and oal inermediae consumpion of indusries. So he quesion rises how price and volume changes of individual goods can be added o price and volume changes of aggregaes. Various mehods are available o solve his problem. Differen index formulae are available wih differen weighing schemes. So one has o make a choice. I is beyond he scope of his paper o discuss in deph he heoreical and pracical consideraions wih respec o his choice. For a broader discussion of he heoreical and pracical consideraions wih respec o he choice of index number formulae and weighing schemes he reader is referred o e.g. Allen (1975) and o Al e al. (1986). Besides aggregaes, special aenion mus be paid o a number of balancing iems. Mos imporan of course is GDP. GDP is he difference beween wo aggregaes: oal oupu value and oal inermediae consumpion of goods and services by all indusries. Hence price and volume changes of GDP are he resul of he price and volume changes of oal oupu and of oal inermediae consumpion of all indusries ogeher. Since oal oupu and oal inermediae consumpion are aggregaes whose volume and price changes are a resul of changes a a deailed level, price and volume changes of GDP are also a resul of changes a a deailed level. 2. The choice of index number formulae. Mos counries - including he Neherlands - use a combinaion of a Laspeyres volume index and a Paasche price index. For he formulae we refer o annex I. Characerisic for he Laspeyres volume index is ha he volume changes of individual goods are weighed ogeher wih he value in a former year (he "base year"). Characerisic for he Paasche price index is ha he price changes of individual goods are weighed ogeher wih heir value in he curren year. The deflaed values derived wih his index formula combinaion can easily be explained as "values in prices of he base year". Alernaive soluions for he weighing problem are e.g. he combinaion of a Paasche volume index and a Laspeyres price index and he combinaion of a Fisher volume index and a Fisher price index. All hose combinaions have in common ha here is a decomposiion in price and volume changes wihou 2

3 residuals. The Fisher volume index is he geomeric mean of he Laspeyres and Paasche volume indices; he Fisher price index is he geomeric mean of he Laspeyres and Paasche price indices. 3. Fixed or changing weighing schemes. Applying he Laspeyres volume index number formula, volume changes are weighed wih he values in a "base year". Nex quesion is which year should be chosen as he base year. Generally speaking here is a choice beween a fixed base year and a changing base year. The laer mehod is ofen called he "mehod of chain indices". Wih he mehod of fixed weighs for a series of years, he weighs are derived from a single year in he pas. An advanage of his mehod is ha in longer series of values in consan prices deflaed pars of aggregaes exacly add up o he deflaed aggregae. However, a very serious disadvanage is ha volume changes of aggregaes are calculaed wih oudaed weighs. This disadvanage is especially severe when relaive prices change rapidly. As a resul economic growh is ofen significanly overesimaed. Applying he chained Laspeyres volume index means ha weighs change every year and are derived from he previous year. Since hose weighs are more up-o-dae, a beer approximaion of he "real world" volume changes is obained han wih he mehod of fixed weighs. Time series resuls can be obained by muliplying separaely esimaed year-o-year volume indices: hence he name chain indices. An imporan advanage of he chain index mehod is ha he above menioned overesimaions of growh raes are avoided. There is also a disadvanage: in ime series in consan prices he deflaed pars of an aggregae no longer exacly add up o he deflaed aggregae. As a resul "mahemaical discrepancies" will appear ha canno be removed wihou disurbing he underlying "acual" volume and price movemens. The conras beween fixed weigh mehods and changing weigh mehods is o a cerain exen no absolue bu only exiss in relaive erms. Even counries ha apply fixed weighs, periodically change he weighs and choose anoher base year. In chaining he sub-series hey also have a non-addiiviy problem. Confroned wih he choice beween fixed weigh and changing weigh mehods, a preference for yearly changing weighs is expressed in recen inernaional guidelines. The following quoaions are from SNA and ESA. SNA-1993 says: (secion 16.41) " If he objecive is o measure he acual movemens of prices and volumes from period o period indices should be compiled only beween consecuive ime periods. Changes in prices and volumes beween periods ha are separaed in ime are hen obained by cumulaing he shor-erm movemens: i.e., by linking he indices beween consecuive periods ogeher o form "chain indices". Such chain indices have a number of pracical as well as heoreical advanages. For example, i is possible o obain a much beer mach beween producs in consecuive ime periods han beween periods ha are far apar, given ha producs are coninually disappearing from markes o be replaced by new producs, or new qualiies. Chain indices are also being increasingly demanded by economiss and ohers for analyical purposes and are being increasingly used for special purpose indices, such as consumer price indices, in order o have indices whose weighing srucures are as up-o-dae and relevan as possible". 3

4 ESA-1995 says: (secion 10.62) "The preferred measure of year o year changes in volume is a Fisher volume index which is defined as he geomeric mean of he Laspeyres and he Paasche indices. Changes in volume over longer periods being obained by chaining, i.e. by cumulaing he year o year volume movemens. (secion 10.64) "Chain indices ha use Laspeyres volume indices o measure changes in volume and Paasche price indices o measure year o year price movemens provide accepable alernaives o Fisher indices." Bu ESA-1995 says: (secion 10.65) "Alhough he preferred measure of volume and price is a chain index, i mus be recognized ha he lack of addiive consisency can be a serious disadvanage for many ypes of analysis." (secion 10.66) "I is herefore recommended ha disaggregaed consan price daa, i.e. direc valuaion of curren quaniies a base-year prices, are compiled in addiion o he chain indices for he main aggregaes." 4. Shor hisory of deflaion pracice in he Neherlands For he aferwar period, Saisics Neherlands has published annual esimaes of values in consan prices and volume indices of naional accouns variables from 1948 onwards. In addiion, for he period 1900 o 1920 annual volume growh raes of naional produc are available. In 1987, new macro economic daa for he period 1921 o 1939 have been published. Recenly, new volume changes and deflaors for ha period have been published as well. In he aferwar period, wo periods can be disinguished wih respec o he esimaion mehods: 1948 o 1980 and 1981 up o presen o 1980 For his period daa have been published for GDP, impors, expors, domesic final demand caegories and value added of indusry groups. The level of aggregaion was high; e.g. he number of indusry groups a he beginning was 5 and laer on 14. The esimaes were carried ou in consan prices of fixed base years (successively 1953, 1958, 1963, 1970 and 1975). The deflaion was carried ou afer he esimaes in curren prices had already been finished. Generally speaking curren values were deflaed a a raher deailed level (and wih various index number formulae). However, he balancing of he esimaes ook place a a very high level of aggregaion o presen During he 70s here arose a need for more coherence beween saisics of values, volumes and prices. The co-ordinaion insrumen should be he inpu-oupu ables. A he ouse he ideas wen o a sysem of fixed weigh price indices. In he discussions he mos imporan user of naional accouns daa, Neherlands Bureau for Economic Policy Analysis (CPB), has played a very imporan role. CPB has always (wih one excepion) consruced models based on values in prices of he previous year. During he ime ha Saisics Neherlands did no ye provide ha kind of daa, CPB iself compiled he daa. Because of he daa requiremens for heir more complicaed and more disaggregaed models he CPB was and is srongly in favour of a sysem of chained (Laspeyres) volume indices and chained (Paasche) price indices. This could be realized in a series of inpuoupu ables in prices of he previous year. An imporan moivaion of he CPB's opinion can be found in 4

5 heir bad experiences during he oil-crises in he 70s wih he use of fixed weigh indices and values in consan prices of a fixed base year in heir model a ha ime. The resul of he discussions has been recorded in a common paper of Balk (Saisics Neherlands) and Eijgenraam (CPB) in They concluded ha here was a need for a dynamically defined price index number; in such a heory more-period-indices are defined as a chain of single-period-indices; for singleperiod-indices from a heoreical poin of view so-called superlaive indices are preferable (Diewer, 1978); good approximaions are he Tornqvis and Fisher indices; for single-period-indices also Laspeyres and Paasche indices are expeced o be good approximaions. The resul of he discussions during he lae 70's has been ha from he reporing year 1981 onwards wo imporan mehodological (and also organizaional) changes have been inroduced in he Duch naional accouns. The firs is ha for various variables in he naional accouns ime series of volume indices and deflaors have been calculaed by chaining he year-o-year indices. The basis for his was he compilaion of inpu-oupu ables (from 1986 onwards replaced by supply and use ables) in consan prices of he previous year. An imporan organizaional change was ha from 1981 onwards, he annual inpu-oupu ables in curren prices and in prices of he previous year, value changes, volume changes and price changes have all been compiled simulaneously (see De Boer and Broeserhuizen, 1986). As a resul, yearly Laspeyres volume changes are available, weighed wih he values of he previous year, in combinaion wih Paasche deflaors. The advanage of using chain indices and he relaively minor disadvanage of he resuling non-addiiviy of consan price series has also been elaboraed by Al e al. (1986). A presen, he annual Naional accouns publicaions of Saisics Neherlands conain he following ime series: values in curren prices, annual volume growh raes, volume indices, annual price changes, indices of deflaors and values in prices of a base year (recenly: 1990). The series of volume indices and deflaors are chain indices derived from muliplying he annual changes. The values in prices of a consan base year are calculaed wih he help of chained volume indices. Hence in his case, sub-series are non-addiive o aggregaes in our publicaion. 5. Opinion of users of Neherlands' naional accouns. The auhors have asked a number of insiuions in he Neherlands ha use naional accouns daa for model consrucion abou heir opinion on he choice beween fixed weigh indices and chain indices. In addiion heir experience wih he use of chain indices provided by Saisics Neherlands has been enquired. The CPB is he mos imporan user of naional accouns daa in he Neherlands. I played an imporan role in he discussions preceding he inroducion of chain indices in he Neherlands (see secion 4). The CPB had and sill has a srong preference for chaining single-period- indices based on annually changing weighs. In heir opinion, values in consan prices for a longer period, based on fixed weighs, yield meaningless daa. They say ha heir experience wih he use of chain indices is excellen. For hem, he non-addiiviy of values in consan prices is no problem. Discrepancies from aggregaions are no eliminaed. Oher users ha have been approached are Neherlands Economic Insiue (NEI), Groningen Universiy and The Neherlands' Cenral Bank. 5

6 I is he opinion of he model builders a NEI ha chain indices are a good base for he consrucion of economic models. However, i is necessary ha model builders carefully "une" he specificaion of heir models o he characerisics of he daa. They hink ha he ofen menioned problem of he aggregaion discrepancies is no a real problem, bu a maer ha calls for special aenion when presening he daa o he public. Researchers a he economic faculy of Groningen Universiy don' use consan price series a all. Their macro-economic models require figures on volume changes. So he issue of non-addiiviy is no relevan for hem. If only consan price figures were available, hese could only be used if hey yielded he correc volume indices. The deparmen for moneary and economic policy of The Neherlands Cenral Bank (DNB) says ha indices wih annually changing weighs have he advanage of a srong connecion wih acual developmens. Hence his deparmen has no problems wih Saisics Neherlands pracice. The deparmen for economic research of DNB uses annual changes as well as values in curren and consan prices in heir macro-economic models. If here are problems wih mahemaical discrepancies in model resuls, he soluion mosly is found by an adjusmen of he changes in socks. 6. Resuls from changing versus fixed weighing schemes and differen index number formulae. SNA-1993 saes: (secion 16.43) "In general, Laspeyres indices, wheher volume or price, end o increase more (or decrease less) han Paasche indices, bu if fixed base indices are replaced by chain indices, he index number spread beween Laspeyres and Paasche is likely o be grealy reduced. The relaionship beween a fixed base index and he corresponding chain index is no always he same, however, as i mus depend upon he pahs followed by individual prices and quaniies over ime". SNA-1993 saes: (secion 16.44) "If individual prices and quaniies end o increase or decrease monoonically over ime i can be shown ha he chain Laspeyres will end o increase less han he fixed weigh Laspeyres while he chain Paasche will end o increase more han he fixed Paasche. In hese circumsances, herefore, chaining will reduce he index number spread, possibly almos eliminaing i." We will illusrae he differences beween he resuls of differen mehods for he esimaion of real annual growh raes on he basis of Duch daa. We presen resuls for wo periods. Firsly, we have made alernaive esimaes for he period , based on deailed daa in he supply and use ables in curren prices and in consan prices of he previous year for ha period. Secondly, we give some resuls from he sensiiviy analysis ha Den Bakker made for he inerwar period ( ) of he influence of he choice of he index number formulae and he choice of he weighing scheme (see Den Bakker, 1991). We discuss he resuls of alernaive esimaes shorly in his secion. For a more comprehensive discussion and more resuls we refer he reader o annex II (period ) and annex III (period ). 6

7 Period In he Duch supply and use ables, 250 indusries, 850 commodiies and 10 final demand caegories are defined. Supply and use ables are available for he period For he years , he value in curren prices, he value in prices of he previous year, he volume index and he deflaor are available for every cell of he supply and he use able. For our calculaions, he price and volume indices of he cells are considered as individual indices (of course his is an assumpion: almos every cell of he supply and use ables is already an aggregae). A higher levels of aggregaion indices are calculaed wih differen index number formulae and wih fixed and changing weighing schemes. Table 1 gives he resuls of he alernaive esimaes of he growh raes of GDP and he corresponding ime series of volume indices. The reader will find similar resuls for impors and final expendiure caegories in Annex II. The resuls in he column "Paasche (weighs, 1986)" are obained by deflaion wih fixed base (1986) Laspeyres deflaors and henceforh will be called "fixed weigh Paasche volume indices". Table 1. Volume growh raes (/-1) and ime series of Gross Domesic Produc (marke prices) according o differen index number formulae ( ) Volume growh raes (%) Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986), 1986) ,4 1,4 1,4 1,4 1, ,4 2,6 2,6 2,6 2, ,8 4,7 4,6 4,4 4, ,2 4,1 4,0 3,9 3, ,3 2,3 2,2 2,2 2, ,0 2,0 2,0 2,0 2, ,3 0,8 0,8 0,8 0,7 Time series of volume indices (1986=100) ,4 101,4 101,4 101,4 101, ,9 104,1 104,0 104,0 104, ,9 108,9 108,8 108,6 108, ,5 113,4 113,1 112,8 112, ,1 116,0 115,6 115,3 115, ,5 118,3 117,9 117,5 117, ,0 119,2 118,9 118,5 118,2 A firs sigh he differences beween he resuls for differen formulae seem o be raher small. However, one mus ake ino consideraion ha hey concern large macro oals. In he Neherlands every 0.1 % of GDP equals abou 600 million guilders (280 million ECU). Secondly, if he differences every year show he same sign (- or +) in a ime series yearly differences, however small, can cause serious long erm 7

8 deviaions. Thirdly, only one year wih a larger deviaion can cause large deviaions in all succeeding years of a ime series. When discussing he resuls we will consider he chain Fisher volume indices as he "sandard" wih which we compare oher resuls. The reason is ha Fisher indices can be seen as good approximaions of superlaive indices ha can be seen as ideal indices from a heoreical poin of view (see also secion 4). The sequence of he columns of he ables in his paper has been chosen such ha a cerain following order of resuls could be expeced: highes growh raes are expeced wih he fixed weigh Laspeyres formula and lowes wih he fixed weigh Paasche formula and he resuls of he chain formulae are expeced o be in beween. The resuls in able 1 and annex II show ha mos subsanial divergences are wih Laspeyres fixed weigh indices (firs column). The Laspeyres, Fisher and Paasche chain ype indices in mos cases yield comparable resuls and he differences beween he Paasche fixed weigh and chain indices are generally speaking much smaller han beween he Laspeyres fixed weigh and chain indices. A remarkable and for he saisical pracice very imporan conclusion which can be drawn is ha, as ESA saes, he Laspeyres chain indices provide good approximaions of he "ideal" Fisher chain indices and ha he Laspeyres fixed weigh indices do less or no a all. This is especially imporan for he cases where he differences beween Laspeyres and Paasche fixed weigh indices and beween he Laspeyres fixed weigh index and he Laspeyres chain index are subsanial. E.g. see: GDP (1988 and 1993). Generally speaking he resuls in able 1 and annex II also bear ou he saemen of SNA ha Laspeyres volume indices yield higher growh raes han Paasche volume indices and ha he differences beween he Laspeyres and Paasche chain indices are smaller han beween he corresponding fixed weigh indices. 8

9 Table 2. Growh raes (/-1) of and value added of hree indusry groups according o differen index number formulae ( ) (%) Agriculure and horiculure Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986), 1986) ,2-4,2-4,5-4,7-4, ,3 5,2 5,1 5,0 4, ,8 7,5 7,1 6,6 6, ,0 9,5 9,2 8,9 9, ,2 2,8 2,0 1,2 0, ,2 4,9 4,4 4,0 4, ,6 2,5 1,5 0,6 3,2 Pero-chemical indusry ,2 1,2-0,8-2,7-2, ,6 5,6 6,3 7,0 8, ,6 4,0 7,3 10,8 8, ,0 6,7 5,8 4,9 8, ,8-8,2-8,3-8,4-6, ,8-1,6-0,9-0,1-2, ,1 2,7 2,8 2,9 2,8 Consrucion of buildings and dwellings ,4 1,4 1,4 1,4 1, ,5 9,6 9,6 9,7 9, ,1 2,2 2,2 2,3 2, ,2 0,1 0,1 0,2 0, ,5-2,4-2,3-2,3-2, ,7-3,8-3,7-3,6-2, ,1-7,4-7,2-7,0-6,6 Table 2 gives he resuls of alernaive calculaions of he annual volume growh value added of hree indusries which play quie a differen role in he Duch economy and are under he influence of quie differen circumsances. Annex II presens similar resuls for oal oupu and inermediae consumpion of hese hree indusries. Agriculure and horiculure This is an indusry which includes very differen aciviies. As a resul of differen volume and price developmens of oupu and inpu in he underlying sub-indusries (livesock raising, arable farming and horiculure) he average producion srucure of oal agriculure can change rapidly. Hence, one can 9

10 expec raher subsanial deviaions of volume indices calculaed wih differen index number formulae, especially for value added, which is, as he balancing iem of oupu and inermediae consumpion, influenced by changes in boh oupu and inpu. Annex II shows ha, wih some excepions for 1991 and 1993, deviaions in oupu and inermediae consumpion are raher modes. Differences in he resuls are more subsanial wih value added (able 2). For chain indices give he bes approximaions of he "ideal" Fisher indices. However, remarkable for 1992 and 1993 he chain Laspeyres and he chain Paasche indices ac relaively badly. Pero-chemical indusry This indusry is raher sensiive o flucuaions on he inernaional markes. Because i absorbs for he greaer par semi-manufacured producs from crude oil refineries, i is also relaively sensiive o subsanial price flucuaions. The consequence is ha he resuling volume growh raes from differen index number formulae show larger deviaions. I should be noed ha he fixed weigh Paasche indices as well as he chain Laspeyres and he chain Paasche indices someimes also show larger deviaions. However, able 2 shows ha larger deviaions again mos frequenly occur wih he fixed weigh Laspeyres indices. As could be expeced he mos subsanial deviaions are found wih value added (a balancing iem). Consrucion of buildings and dwellings This indusry shows srong flucuaions in volume growh raes. However price movemens and changes in producion srucure are raher gradual. This means ha he esimaes of volume growh raes are less dependen on he ype of index number formula. Annex II shows ha gross oupu and inermediae consumpion yield only very small (or no) differences beween he resuls of differen formulae. Table 2 shows ha he same holds in mos cases for value added. However, for 1993 boh fixed weigh indices show subsanial deviaions from he hree chain indices. Period The inerwar figures provide a very ineresing daa se for esing he differences beween growh raes arising from he use of differen index number formulae and weighing schemes. The reason is ha he inerwar period is characerized by large flucuaions in economic growh raes and price movemens. Table 3 gives he average annual growh raes of GDP for hree sub periods during he inerwar period, esimaed wih differen index number formulae. The resuls are derived from Den Bakker (1991). The reader will find more resuls in annex III. 10

11 Table 3. Average annual volume growh raes of GDP a marke prices according o differen index number formulae (Inerwar period) (%) Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1921), 1921) ,2 4,7 4,6 4,5 4, ,7-1,5-1,5-1,6-2, ,5 3,8 3,9 4,0 4,5 An ineresing poin is ha during he years periods of economic growh and decline alernaed. The years 1921/29 and 1934/39 are periods of growh. Table 3 shows ha for hose years he fixed weigh Laspeyres indices give higher volume growh raes han he Paasche indices and also higher growh raes han he chain Laspeyres indices. Furher i is quie clear ha, jus like he resuls for , he chain Laspeyres indices give a much beer approximaion of he "ideal" chain Fisher indices han he fixed weigh Laspeyres indices. The years 1929/34 are a period of economic decline. For hose years he difference beween he fixed weigh Laspeyres and Paasche indices is no sysemaic. However, in mos cases fixed weigh Laspeyres indices show sharper declines han he chain Laspeyres indices. Again a very imporan conclusion is ha he chain Laspeyres gives a much beer approximaion of he chain Fisher han he fixed weigh Laspeyres indices. Also for his period he differences beween he chain Laspeyres, Fisher and Paasche indices are - relaively- small. 7. Non-addiiviy. When using chain indices o consruc ime series of values in consan prices of a cerain base year, he problem arises ha he deflaed pars of an aggregae do no add up o he deflaed aggregae iself. The magniude of his "mahemaical discrepancy" varies wih he way he aggregae is spli up in differen sub groups. In he Duch Naional Accouns he mahemaical discrepancies in consan price ables are no eliminaed, bu hese ables are lef non-addiive. Foo-noes explain he non-addiiviy o he users. In he publicaion Naional Accouns of he Neherlands (see: CBS, 1995) consan price ables are no presened separaely, bu always in conjuncion wih oher ables and in a fixed sequence: curren prices, volume changes, chain volume indices, values a consan prices (by applying hese volume indices). Price changes and chain indices of deflaors are given as well. To give an impression of he order of magniude, able 4 presens mahemaical discrepancies for he supply and disposiion of goods and services. The differences can be quie subsanial. 11

12 Table 4. Supply and disposiion of goods and services a prices of 1986 mln. gld Domesic produc (gross, marke prices) Impors (cif) Mahemaical discrepancy Disposable for final expendiure (gross) Final consumpion expendiure general governmen households Fixed capial formaion (gross) enerprises general governmen Changes in invenories enerprises Expors (fob) Mahemaical discrepancy Toal final expendiure (gross) Concluding remarks In his paper we discussed he use of chain indices in he Neherlands. Duch pracice wih chain indices is from 1980 onwards. In he discussions preceding he inroducion of chain indices, CPB, he mos imporan user of naional accouns daa, played an imporan par making a plea for annually changing weighs and chain indices. CPB sill has a srong preference for chaining one-period growh raes based on annually changing weighs. They call heir experience wih he use of chain indices excellen. Three oher users of naional accouns daa have been asked abou heir opinion on he choice beween fixed weigh indices and chain indices. All of hem say ha chain indices are a good base for he consrucion of economic models. Furher: i is necessary ha model builders carefully une he specificaion of heir model o he characerisics of he daa. 12

13 non-addiiviy need no be a real problem, if researchers give special aenion o he presenaion of he daa o he public. for policy makers i is imporan ha chain indices have a srong correspondence o developmens. acual We also have carried ou a sensiiviy analysis of he choice of index number formulae and weighs in he deflaion of naional accouns daa. For he period alernaive esimaes are presened of he volume growh raes of GDP, privae consumpion of households, gross fixed capial formaion, impors and expors, and for oupu, inermediae consumpion and value added of hree indusries. For he period alernaive esimaes are given of he volume growh raes of GDP. Considering he chain Fisher indices as a sandard, mos imporan conclusions ha can be drawn from hose resuls are: in nearly all cases boh chain Laspeyres and chain Paasche volume growh raes and indices are good approximaions of chain Fisher indices. This affirms he saemen in ESA-1995 (secion 10.64) ha chain Laspeyres volume indices (in combinaion wih chain Paasche price indices) provide accepable alernaives o chain Fisher indices. he resuls show ha mos subsanial deviaions from he chain Fisher indices are found wih he fixed weigh Laspeyres formula. This is very imporan since fixed weigh Laspeyres volume indices ofen are used in consan price esimaion of naional accouns daa. fixed weigh Paasche indices generally speaking ac beer han fixed weigh Laspeyres indices, bu in some cases here are also severe deviaions from he chain indices. 13

14 References Al, P.G., B.M. Balk, S. de Boer and G.P. den Bakker, The use of chain indices for deflaing he naional accouns, Saisical Journal of he Unied Naions, volume 4, number 4, July 1987 p Allen, R.G.D., 1975, Index numbers in heory and pracice, Aldine Publishing Company, Chicago. Bakker, G.P. den, 1991, The choice of index number formulae and weighs in he naional accouns (a sensiiviy analysis based on macro-economic daa for he inerwar period), Naional Accouns Occasional Paper nr. NA-044 (Saisics Neherlands, Voorburg). Balk, B.M. and C.J.J. Eijgenraam, 1979, Aspecen van een saische en dynamische definiie van de prijsindex, Advisory Commiee for he Price Saisics of Saisics Neherlands. Boer, S. de and G.A.A.M. Broeserhuizen, 1986, The simulaneous compilaion of curren price and deflaed inpu-oupu ables, Naional Accouns Occasional Paper nr. NA-013 (Saisics Neherlands, Voorburg). CBS, Naional Accouns of he Neherlands, 1995, Saisics Neherlands, Voorburg. Diewer, W.E., 1978, Superlaive Index Numbers and consisency in Aggregaion; Economerica, vol.46, no 4. Eurosa, 1996, European Sysem of Accouns (ESA 1995). Unied Naions e al., 1993, Sysem of Naional Accouns (SNA 1993). 14

15 Annex I. Index number formulae 1) Fixed weighs Laspeyres volume index pq 0 pq 0 0 = pq q 0 0 q pq Paasche volume index pq pq 0 = pq 0 pq q q Fischer volume index Laspeyres * Paasche 2) Annual changing weighs Laspeyres volume index p p 1 q q 1 1 = p p q 1 1 q q q Paasche volume index pq pq 1 = pq pq q q 1 Fischer volume index Laspeyres * Paasche 15

16 Annex II Resuls Table I gives he resuls of he alernaive esimaes of he growh raes of GDP, impors and final demand caegories. Table II gives he corresponding ime series of volume indices. When discussing he resuls as in secion 6 we will consider he chain Fisher volume indices as he "sandard" wih which we compare oher resuls. The resuls in Table I show ha mos subsanial divergences occur wih Laspeyres fixed weigh indices. The Laspeyres, Fisher and Paasche chain ype indices in mos cases yield comparable resuls and he differences beween he Paasche fixed weigh and chain indices are generally speaking much smaller han beween he Laspeyres fixed weigh and chain indices. A remarkable and for he saisical pracice very imporan conclusion which can be drawn from Table II is ha, as ESA saes, he Laspeyres chain indices provide good approximaions of he "ideal" Fisher chain indices and ha he Laspeyres fixed weigh indices do less or no a all. This is especially imporan for he cases where he differences beween Laspeyres and Paasche fixed weigh indices and beween he Laspeyres fixed weigh index and he Laspeyres chain index are subsanial. See: GDP (1988 and 1993), Consumpion of households (1991), Capial formaion (1992 and 1993), Expors (1988, 1989, 1990 and 1993), Impors (1990, 1991 and 1993). Generally speaking he resuls in Table I also bear ou he saemen of SNA ha Laspeyres volume indices yield higher growh raes han Paasche volume indices and ha he differences beween he Laspeyres and Paasche chain indices are smaller han beween he corresponding fixed weigh indices. Table II presens he ime series of volume indices corresponding wih he annual growh raes in able I. I will no be surprising ha he conclusions ha can be drawn from he resuls in able I and II are quie similar. 16

17 Table I. Growh raes (/-1) according o differen index number formulae ( ): macro oals (%) Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986), 1986) Gross Domesic Produc (marke prices) ,4 1,4 1,4 1,4 1, ,4 2,6 2,6 2,6 2, ,8 4,7 4,6 4,4 4, ,2 4,1 4,0 3,9 3, ,3 2,3 2,2 2,2 2, ,0 2,0 2,0 2,0 2, ,3 0,8 0,8 0,8 0,7 Consumpion expendiure of households ,7 2,7 2,7 2,7 2, ,7 0,8 0,8 0,8 0, ,5 3,5 3,5 3,5 3, ,2 4,2 4,2 4,2 4, ,3 3,1 3,1 3,1 2, ,5 2,5 2,5 2,5 2, ,1 1,0 1,0 0,9 0,9 Gross fixed capial formaion ,9 0,9 0,9 0,9 0, ,6 4,5 4,5 4,5 4, ,0 4,9 4,9 4,9 4, ,7 1,6 1,6 1,5 1, ,2 0,2 0,2 0,2-0, ,8 0,6 0,6 0,6 0, ,5-2,8-2,8-2,9-3,0 Expors ,0 4,0 3,9 3,7 3, ,3 9,0 9,0 9,0 9, ,8 6,6 6,5 6,3 6, ,4 5,3 5,3 5,2 5, ,9 4,7 4,7 4,6 4, ,1 2,9 2,8 2,8 2, ,1 1,5 1,4 1,4 1,4 Impors ,2 4,2 4,0 3,9 3, ,7 7,6 7,5 7,4 7, ,6 6,7 6,7 6,6 6, ,4 4,2 4,2 4,1 4, ,3 4,1 4,1 4,1 3, ,2 2,1 2,0 2,0 2, ,5-2,1-2,2-2,3-2,4 17

18 Table II. Time series of volume indices according o differen index number formulae (1986=100) Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986),1986) Gross Domesic Produc (marke prices) ,4 101,4 101,4 101,4 101, ,9 104,1 104,0 104,0 104, ,9 108,9 108,8 108,6 108, ,5 113,4 113,1 112,8 112, ,1 116,0 115,6 115,3 115, ,5 118,3 117,9 117,5 117, ,0 119,2 118,9 118,5 118,2 Consumpion expendiure of households ,7 102,7 102,7 102,7 102, ,5 103,6 103,6 103,6 103, ,1 107,2 107,2 107,1 107, ,6 111,7 111,7 111,6 111, ,3 115,2 115,1 115,0 114, ,2 118,1 118,0 117,9 117, ,5 119,3 119,2 119,1 118,5 Gross fixed capial formaion ,9 100,9 100,9 100,9 100, ,5 105,5 105,5 105,5 105, ,8 110,7 110,7 110,7 110, ,6 112,4 112,4 112,4 112, ,8 112,7 112,6 112,6 112, ,8 113,4 113,3 113,2 112, ,0 110,2 110,1 109,9 109,0 Expors ,0 104,0 103,9 103,7 103, ,8 113,4 113,2 113,0 113, ,6 120,9 120,5 120,1 120, ,1 127,4 126,9 126,4 126, ,4 133,4 132,8 132,2 132, ,5 137,2 136,6 135,9 135, ,5 139,3 138,5 137,8 137,7 Impors ,2 104,2 104,0 103,9 103, ,2 112,1 111,8 111,6 111, ,7 119,6 119,3 118,9 118, ,9 124,7 124,2 123,8 123, ,3 129,8 129,3 128,9 128, ,2 132,5 132,0 131,4 131, ,2 129,7 129,1 128,5 127,9 18

19 Tables IIIA, IIIB and IIIC give he resuls of alernaive calculaions of he annual volume growh raes of oal oupu, oal inermediae consumpion and value added of hree indusries which play quie a differen role in he Duch economy and are under he influence of quie differen circumsances. Agriculure and horiculure This is an indusry which includes very differen aciviies. As a resul of differen volume and price developmens of oupu and inpu in he underlying sub-indusries (livesock raising, arable farming and horiculure) he average producion srucure of oal agriculure can change rapidly. Hence, one can expec raher subsanial deviaions of volume indices calculaed wih differen index number formulae, especially for value added, which is, as he balancing iem of oupu and inermediae consumpion, influenced by changes in boh oupu and inpu. Table IIIa shows ha, wih some excepions for 1991 and 1993, deviaions in oupu and inermediae consumpion are raher modes. Differences in he resuls are more subsanial wih value added. For chain indices give he bes approximaions of he "ideal" Fisher indices. However, remarkable for 1992 and 1993 he chain Laspeyres and he chain Paasche indices ac relaively badly. Pero-chemical indusry This indusry is raher sensiive o flucuaions on he inernaional markes. Because i absorbs for he greaer par semi-manufacured producs from crude oil refineries, i is also relaively sensiive o subsanial price flucuaions. The consequence is ha he resuling volume growh raes from differen index number formulae show larger deviaions (see: able IIIb). I should be noed ha he fixed weigh Paasche indices as well as he chain Laspeyres and he chain Paasche indices someimes also show larger deviaions. However, able IIIb shows ha larger deviaions again mos frequenly occur wih he fixed weigh Laspeyres indices. As could be expeced he mos subsanial deviaions are found wih value added (a balancing iem). Consrucion of buildings and dwellings This indusry shows srong flucuaions in volume growh raes. However price movemens and changes in producion srucure are raher gradual. This means ha he esimaes of volume growh raes are less dependen on he ype of index number formula. Table IIIC shows ha gross oupu and inermediae consumpion yield only very small (or no) differences beween he resuls of differen formulae. The same holds in mos cases for value added. However for 1993 boh fixed weigh indices show subsanial deviaions from he hree chain indices. 19

20 Table IIIA. Growh raes (/-1) of gross oupu, inermediae consumpion and value added of hree indusry groups according o differen index number formulae ( ) (%) Agriculure and horiculure Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986), 1986) Gross oupu ,4-1,4-1,6-1,8-1, ,9 2,0 1,9 1,8 1, ,3 3,4 3,2 3,0 2, ,8 3,5 3,4 3,2 3, ,2 2,0 1,6 1,3 1, ,0 2,4 2,1 1,8 1, ,5 0,8 0,4-0,1 0,6 Inermediae consumpion ,7 0,7 0,6 0,5 0, ,5-0,4-0,5-0,5-0, ,0 0,2 0,1 0,1 0, ,3-1,6-1,5-1,5-1, ,2 1,2 1,3 1,3 1, ,0 0,1 0,0-0,1 0, ,5-0,6-0,6-0,7-0,3 Value added (basic prices) ,2-4,2-4,5-4,7-4, ,3 5,2 5,1 5,0 4, ,8 7,5 7,1 6,6 6, ,0 9,5 9,2 8,9 9, ,2 2,8 2,0 1,2 0, ,2 4,9 4,4 4,0 4, ,6 2,5 1,5 0,6 3,2 20

21 Table IIIB. Growh raes (/-1) of gross oupu, inermediae consumpion and value added of hree indusry groups according o differen index number formulae ( ) (%) Pero-chemical indusry Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986),1986) Gross oupu ,8 4,8 3,9 3,1 3, ,9 9,7 9,7 9,7 9, ,7 0,6 0,8 0,9 0, ,1 3,3 2,9 2,6 3, ,1-5,3-5,4-5,4-5, ,2-2,6-2,6-2,6-3, ,8-1,8-1,8-1,9-2,2 Inermediae consumpion ,2 6,2 5,9 5,7 5, ,5 11,5 11,3 11,2 11, ,9-1,3-2,3-3,4-4, ,9 1,5 1,7 1,8 1, ,6-4,3-4,4-4,5-4, ,0-2,9-3,0-3,2-3, ,1-2,9-3,0-3,1-3,4 Value added (basic prices) ,2 1,2-0,8-2,7-2, ,6 5,6 6,3 7,0 8, ,6 4,0 7,3 10,8 8, ,0 6,7 5,8 4,9 8, ,8-8,2-8,3-8,4-6, ,8-1,6-0,9-0,1-2, ,1 2,7 2,8 2,9 2,8 21

22 Table IIIC. Growh raes (/-1) of gross oupu, inermediae consumpion and value added of hree indusry groups according o differen index number formulae ( ) (%) Consrucion of buildings and dwellings Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1986),1986) Gross oupu ,1 5,1 5,1 5,1 5, ,2 12,2 12,3 12,3 12, ,6 4,6 4,6 4,6 4, ,5 0,5 0,5 0,5 0, ,5 0,5 0,5 0,5 0, ,2-2,2-2,2-2,2-2, ,4-4,4-4,4-4,4-4,4 Inermediae consumpion ,7 6,7 6,7 6,7 6, ,4 13,4 13,4 13,4 13, ,6 5,6 5,6 5,5 5, ,6 0,6 0,6 0,6 0, ,7 1,7 1,7 1,7 1, ,6-1,6-1,6-1,7-1, ,0-3,1-3,2-3,2-3,3 Value added (basic prices ,4 1,4 1,4 1,4 1, ,5 9,6 9,6 9,7 9, ,1 2,2 2,2 2,3 2, ,2 0,1 0,1 0,2 0, ,5-2,4-2,3-2,3-2, ,7-3,8-3,7-3,6-2, ,1-7,4-7,2-7,0-6,6 22

23 Annex III Resuls Table IVA gives he annual volume growh raes of GDP during he inerwar period, esimaed wih differen index number formulae. The resuls are derived from Den Bakker (1991). Generally speaking for he inerwar period he resuls from he alernaive index number formulae show more differences han for he years The reason is of course ha relaive price and volume changes were more subsanial during he inerwar period. An ineresing poin is ha during he years periods of economic growh and decline alernaed. The years 1922 o 1929 and 1935 o 1937 are periods of seady growh. Table IVA shows ha for hose years (excep 1929) he fixed weigh Laspeyres indices give higher annual volume growh raes han he Paasche indices and also higher growh raes han he chain Laspeyres indices. Furher i is quie clear ha, jus as for , he chain Laspeyres indices give a much beer approximaion of he "ideal" chain Fisher indices han he fixed weigh Laspeyres indices. Besides i is remarkable ha for 1924, 1936 and 1937 he fixed weigh Paasche index as well as he fixed weigh Laspeyres index is higher han all hree chain indices. The years 1930 o 1934 (excep 1933) are a period of economic decline. For hose years he difference beween he fixed weigh Laspeyres and Paasche indices is no sysemaic. However, in mos cases fixed weigh Laspeyres indices show sharper declines han he chain Laspeyres indices. Again a very imporan conclusion is ha he chain Laspeyres gives a much beer approximaion of he chain Fisher han he fixed weigh Laspeyres indices. Also for his period he differences beween he chain Laspeyres, Fisher and Paasche indices are -relaively- small. Table IVB shows he ime series of volume indices of GDP for he years 1921 o Despie srong price and volume flucuaions during ha period he chain Laspeyres and Paasche indices show much similariy wih he "ideal" chain Fisher indices. The highes deviaion is 1.4 %. In conras, he series of fixed weigh Laspeyres indices yields very high deviaions from he Fisher indices and for many years of he series. Highes deviaions are for 1937 (9.1 %) and for 1939 (9.5 %). The series of fixed weigh Paasche indices shows higher deviaions han he chain indices (highes for 1935: 5.2 %), bu he deviaions are less han hose for he fixed weigh Laspeyres. 23

24 Table IVA. Growh raes (/-1) of GDP a marke prices according o differen index number formulae (Inerwar period) (%) Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1921),1921) ,5 6,5 6,1 5,6 5, ,7 2,1 2,0 1,9 1, ,1 7,2 7,3 7,5 7, ,9 3,6 3,3 3,1 3, ,5 6,8 6,7 6,6 6, ,1 4,6 4,6 4,5 4, ,3 4,9 4,8 4,8 4, ,3 2,4 2,3 2,3 2, ,6-1,2-1,1-1,1-1, ,4-4,6-4,5-4,4-5, ,2-0,9-1,1-1,3-2, ,2 0,4 0,4 0,3 0, ,2-1,1-1,3-1,4-1, ,4 2,7 3,0 3,2 2, ,4 5,5 5,3 5,2 5, ,2 5,7 5,8 5,9 7, ,4-3,2-2,9-2,7-2, ,1 8,1 8,3 8,6 9,8 24

25 Table IVB. Volume indices of GDP a marke prices according o differen index number formulae (Inerwar period), 1921=100 Laspeyres Laspeyres Fisher Paasche Paasche (weighs (chain) (chain) (chain) (weighs 1921), 1921) ,5 106,5 106,1 105,6 105, ,4 108,7 108,2 107,7 107, ,3 116,5 116,2 115,8 115, ,9 120,7 120,0 119,3 119, ,1 128,9 128,1 127,3 126, ,8 134,9 133,9 132,9 131, ,1 141,4 140,4 139,3 138, ,4 144,8 143,7 142,5 142, ,0 143,1 142,1 141,0 139, ,0 136,5 135,7 134,8 132, ,3 135,3 134,2 133,1 129, ,0 135,9 134,6 133,5 129, ,7 134,3 133,0 131,6 128, ,7 138,0 136,9 135,9 131, ,9 145,6 144,2 142,9 139, ,9 153,8 152,5 151,3 148, ,7 148,9 148,1 147,2 144, ,9 161,0 160,4 159,8 158,8 25