(ii) Deriving constant price estimates of GDP: An illustration of chain-linking

Transcription

1 Case Sudies (ii) Derivin consan price esimaes of GDP: An illusraion of chain-linkin 1. Inroducion The Office for Naional Saisics 1 esimaes ha for 2006 he oal expendiure on oods and services produced by firms wihin he Unied Kindom was approximaely 1,290 billion which is 1.29 rillion. We beer know his expendiure as Gross Domesic produc or GDP. I involves expendiure by households, firms and overnmen in boh he UK and overseas. In 2005 he UK s GDP is esimaed a approximaely 1,226 billion or 1.23 rillion. This means ha GDP increased beween 2005 and 2006 by approximaely 64 billion. This is an increase of 5.2% 2. The increase of 5.2% in he oal value of expendiure on oods and services produced wihin he UK does no mean ha he volume of oods and services consumed increased by 5.2%. Ye, as economiss we ofen wan o commen on wheher we are producin and consumin ever reaer quaniies of oods. Amons he ways in which i is possible o measure our sandard of livin is o look a he producion or consumpion of oods per person. Bu, oal expendiure depends no only on he quaniies of oods and services purchased, bu also he chared. So if we wan o compare he volume of demand for a counry s oods and services over ime hen we have o conrol for price chanes. Lookin across he whole rane of oods and services we produce, his means conrollin for risin. In his case sudy we look a how by usin a echnique called chain-linkin economiss are able o make inferences 1 Naional Saisics Online can be accessed a hp:// 2 =64,000/1,226,000 * abou he volume of oods and services consumed. The need for a echnique o make meaninful comparisons abou he volume of oupu is apparen when one bares in mind he sheer variey of wha is produced. Chain-linkin involves fixin he of differen caeories of oods and services a a momen in ime. To underake chain-linkin requires informaion abou he expendiure on roups of commodiies and heir price levels. This is used o produce a consan price series for iems of expendiure before bein areaed o produce a consan price series of GDP. This series is also referred o as real GDP. 2. Illusrain chain-linkin The approach adoped o enerae a volume series for an iem of expendiure is called chain-linkin. To illusrae annual chain-linkin we will consider how consan price series for wo iems of household consumpion are compiled. In pracice, his process has o be repeaed for he remainin consumpion by households, he consumpion by firms and overnmen, and for he consumpion of Briish oods and services by foreiners. Finally, a consan price series is creaed for impors consumed by Briish households and firms and by he UK overnmen. Impor expendiures are hen subraced in order o derive he consan price esimae for GDP. Table 1 displays informaion relain o expendiure by households in he UK on frui and veeables. In 2003 he expendiure by households in he UK on frui was 4,752 million ( billion), while ha on veeables was 8,595 ( billion). Auhored by Dr Dean Garra, Noinham Tren Universiy, for JISC DEL II Projec Pae 1 of 5

2 Case Sudies Table 1: Expendiure, m, and price relaives, frui and veeables Year Exp on frui Price relaive for frui Exp on veeables Price relaive for veeables , , , , , , , , Source: Consumer Trends, Office for Naional Saisics and Auhor s Calculaions Adjacen o he expendiure fiure for frui and for veeables is a fiure known as he price relaive. The price relaive measures he price level his year relaive o he price level las year, P /P -1. If i exceeds 1 hen he price level his year is reaer han las year. A price relaive of less han 1 indicaes ha he price level has fallen. A price relaive of 1 indicaes ha he price level has no chaned. From Table 1, we observe ha in 2003 he price of frui was imes ha in 2002, so ha he annual rae of price inflaion for frui was 1.54%. In 2003 he price of veeable was imes ha in 2002, so ha he annual rae of price inflaion for veeables was 2.38%. For each year we can re-calculae he expendiure on veeables and on frui based on he levels of he previous year. For insance, we can calculae 2002 expendiures a 2001 and 2003 expendiures a veeables in 2003 a 2002 is calculaed as 8,595/1.0238, which is 8,395m. By holdin a heir 2002 levels we can calculae he percenae chane beween 2002 and 2003 in he real expendiure on frui and on veeables. This percenae chane in consan price expendiure is our measure of he percenae chane in volumes consumed. Since expendiure a consan 2002 for frui increased by 4.26% 3 while fallin by 0.92% 4 for veeables, we can refer o he volume of food consumpion havin increased by 4.26% and he volume of frui expendiure havin fallen by 0.92%. Table 2 overleaf complees he exercise of esimain consan and curren price expendiures for boh commodiy roups. The fiures in bold are curren, while he fiures o he lef of hese are expendiures a he previous year s. To do his we simply divide he mos recen expendiure, E, by he price relaive. We can wrie his as (1) E P P 1 Consider aain To re-calculae he expendiure on frui and on veeables a 2002 we divide he expendiure oals for 2003 by he price relaives. Hence, he expendiure on frui in 2003 a 2002 is calculaed as 4,752m/1.0154, which is 4,680m. The expendiure on 3 =((4, )/4489)* 4 =(8,395-8,473)/8,473)* Auhored by Dr Dean Garra, Noinham Tren Universiy, for JISC DEL II Projec Pae 2 of 5

3 Case Sudies Table 2: Expendiures a curren and previous year s, m Frui Ve Frui Ve Frui Ve Frui Ve Frui Ve ,911 7,723 4,242 8, ,442 8,615 4,489 8, ,680 8,395 4,752 8, ,293 8,853 5,109 8,739 Source: Consumer Trends, Office for Naional Saisics and Auhor s Calculaions We can now complee he exercise of comparin expendiures in he curren year when price levels are held a hose of he previous year wih expendiure in he previous year. The resuls are shown in Table 3. These fiures ac as our esimaes of he chane in he volume of consumpion. Table 3: % chane in consan price expendiures Frui Veeables The final sep in chain linkin is o enerae a consan price series based on a sinle year s. This paricular year is known as he base year. To do his we use he expendiure numbers for he base year and hen apply he percenae chanes in consan price expendiures. Consider he case of enerain a consan price series for frui consumpion a consan Frui expendiure in 2003 was 4,752m. We now wish o apply he percenae rowh raes in Table 3. To see how we do his we need o recall he eneral formula for a percenae chane. Le be he percenae chane in variable from he las period, -1, o he curren period,. (2) = 1 1 To apply percenae chanes oin backwards from he base year we need o rearrane he formula so ha he subjec is -1 (3) 1 = 1 + To apply percenaes oin forwards from he base year we need o rearrane he formula so ha is subjec is (4) = Usin (3) we can show ha he expendiure on frui in 2002 a consan 2003 is 4,558m (5) ( 4,752 m ) = 4,558 m Usin (4) we can show ha he expendiure on frui in 2004 a consan 2003 is 5,293m (6) 4,752 m ( ) = 5, 293 m Table 4 complees his exercise for boh frui and veeables. Table 4: Frui and veeable expendiure, m, consan 2003 Frui Ve Frui and Ve ,353 8,477 12, ,558 8,675 13, ,752 8,595 13, ,293 8,853 14, UK GDP a curren and consan Consan price series are areaed o derive consan series for household consumpion, privae and public invesmen, overnmen final consumpion, expors and impors. These in urn are areaed o enerae a consan price GDP series. Auhored by Dr Dean Garra, Noinham Tren Universiy, for JISC DEL II Projec Pae 3 of 5

4 Case Sudies Char 1 shows GDP a curren and consan 2003 for he Unied Kindom since The wo series are equal in 2003 because he underlyin price levels are hose in The consan price series for GDP is herefore an esimae of wha he value of GDP would have been if he of oods and services were hose in Char 1: UK GDP, millions 1,400,000 1,200,000 1,000, , , , ,000 GDP a consan 2003 GDP a curren By inserin he appropriae values ino (7) we find ha beween 1870 and 2006 he volume of GDP in he Unied Kindom rew a an annual rae of 1.86%. (8) = 1,199.2 b 1 = b 0186 However, he rae of oupu rowh is no smooh. Char 2 shows he percenae chane in real GDP from year-o-year. 6 Despie he volailiy over he period as a whole, we do observe a relaive robusness and sabiliy of rowh afer he early 1990s. Conras his, for insance, wih he period followin World War I when he UK economy conracs sharply wih annual falls in oupu approachin 10% Sources: (i) Feinsein, C.H., Naional Income, Expendiure and Oupu of he UK Cambride: Cambride Universiy Press (fiures from ); (ii) Naional Saisics (fiures from 1955) Noe: Fiures up o 1920 include Republic of Ireland. The sinificance of he consan price GDP price series is ha i shows ha he volume of oods and services produced by Briish firms has increased over ime. The value of GDP in 1870 a consan 2003 was 97.3 billion. By 2006, his had risen o 1,199.2 billion or almos 1.2 rillion. We can measure he lon-run rowh of real GDP by calculain an annual compound rowh rae. 5 This is he year-on-year rae of rowh which accouns for he rowh in oupu from he firs year o he las year. I is calculaed by subracin 1 from he resul of akin he nh roo of he relaive value in he final year, V, o ha in he firs year, A, where n is he number of years in he period bein considered. 1 (7) = ( V n ) 1 A Char 2: Annual rowh in real GDP, % % chane Source: Auhor s calculaions usin daa from Char 1 Tasks The followin is informaion from Consumer Trends. I deails UK household expendiure on rail ranspor and is price relaive, i.e. he raio of he curren price level relaive o he previous year. Expendiure on rail services, m Price relaive, P /P , , , , Use his informaion o calculae (i) Rail expendiure a consan In he case sudy Economic rowh: Wha facors maer? some of he possible influences on lon-run economic rowh are considered. 6 Wih annual daa, he annual percenae chane in real GDP is calculaed as RGDP RGDP 1 * RGDP 1 Auhored by Dr Dean Garra, Noinham Tren Universiy, for JISC DEL II Projec Pae 4 of 5

5 Case Sudies (ii) Rail expendiure a consan 2005 (iii) The annual rowh raes for nominal and real rail expendiure Auhored by Dr Dean Garra, Noinham Tren Universiy, for JISC DEL II Projec Pae 5 of 5