Session 4.2: Price and Volume Measures

Transcription

1 Session 4.2: Price and Volume Measures Regional Course on Inegraed Economic Saisics o Suppor 28 SNA Implemenaion Leonidas Akriidis Office for Naional Saisics Unied Kingdom Conen 1. Inroducion 2. Price and Volume: concep and measures 3. Developing relevan deflaor 4. Qualiy change in price indices 5. Price and Volume Indices 6. Chain-linking and re-referencing 7. Double v. Single deflaion/exrapolaion

2 1. Inroducion: Covered in 28 SNA chaper 15; A very useful handbook used in he UK Naional Accouns and in Europe is he Eurosa Handbook on price and volume measures 3 1. Inroducion Uses of price and volumes daa: Comparing economy over ime Comparing differen economies a he same ime 4

3 1. Inroducion Deermined by a marke Non-marke producs? Differen ypes of prices: Basic price Producer price Purchaser price Published price indexes (CPI, PPI, ) 5 2. Prices and Volume Quaniy Value, price and quaniy are linked by he fundamenal equaion: This equaion is valid only for homogeneous producs 6

4 2. Prices and Volume Homogeneous producs Homogeneous producs are producs for which i is possible o define unis which are all considered equivalen and which can hus be exchanged for he same moneary value A homogeneous produc consiss of unis of he same qualiy 7 2. Prices and Volume Volumes Seems easy when he produc is simple - jus a physical quaniy (one on of coal or one cup of coffee.) Bu volume also includes qualiy : more value for money Volume = quaniy * qualiy 8

5 2. Prices and Volume Decomposing values Value = Volume x Price Value Volume Price Can also express his as: => deflaion 9 2. Prices and Volume Consan prices The noion of volume is inroduced o eliminae he effec of price changes on a se of producs This effec can be offse by calculaing wha he value of he se of producs would have been if here had been no changes in prices 1

6 3. Developing relevan deflaors Deflaors for marke oupu Bes mehod: deflaion by appropriae producer price indices: basic prices adjusmens for qualiy changes exac correspondence o producs o be deflaed conceps according o naional accouns (or an indicaor proven o be equivalen) Developing relevan deflaors Deflaors for marke oupu Alernaive mehods: less appropriae PPIs, CPIs, volume indicaors Unaccepable mehods: inpu mehods, secondary indicaors, inappropriae price indices To be applied o specific producs firs 12

7 Agriculure Usually price*quaniy approach so all daa are available. Some remaining issues: Producion process spread over more han one accouning period Seasonal prices Subsidies 13 Manufacuring Usually PPIs available Unique producs large equipmen: ships, planes, special machines Compuers 14

8 Consrucion Wide range of producs new consrucion improvemens Unique producs -> model prices Producion process spread over more han one accouning period 15 Wholesale and reail rade services Trade margins: no direc prices paid for rade services Assumpion used: volume of oupu equals volume of sales How o measure qualiy of rade services, eg. supermarke versus shop-on-he corner 16

9 Transpor and communicaion Transpor: passenger-kilomeres and onnekilomeres are accepable mehods Take accoun of subsidies Empy bus problem Communicaions: differeniae household and business purchases 17 Banking Two pars: explici charges and FISIM For explici charges price indices can be developed This is no he case for FISIM are he use of volume indicaors (deleed sock using general price index) and price ha is base year ineres raes 18

10 Non-marke services Examples - healh, educaion, defense, adminisraion Difference beween individual and collecive services Measuremen of oupu in curren prices 19 Measuring a consan prices? Disinguish beween: Inpu-based mehods - deflaing inpus Oupu-based mehods - measuring volume of oupu using indicaors 2

11 Educaion One definiion quaniy of eaching received by sudens, adjused o allow for qualiies of he services provided, for each ype of educaion Wha does his mean? Quaniy of eaching Adjused for qualiy Type of educaion 21 Healh One definiion he quaniy of healh care received by paiens, adjused o allow for qualiies of service provided, for each ype of healh care Looks similar o educaion Wha is quaniy? 22

12 Collecive services Difficul o define oupu, bu no impossible: Tax sysem Social Securiy Public adminisraion? Use of aciviy indicaors Measuring qualiy Qualiy change in price indices Examples of qualiy physical characerisics accompanying services locaion iming Price discriminaion 24

13 4. Qualiy change in price indices Depends on he ype of produc, bu generally: Mached models Opion pricing Overlapping Exper judgmen Hedonics Price and Volume indices Comparing base and curren periods The value of a se of producs in he curren period is: 1 1 v p Vol The volume can be defined as: 1 i i q i p 1 i i q i The volume index is: 1 p i i q i IVol p q i i i 26

14 5. Price and Volume indices Table 1 Car Producion Year Year 1 Price Quaniy Value Price Quaniy Value Value ( $/un.) (No.) ( $) ( $/un.) (No.) ( $) (year $) (1) (2) (3) = (1)*(2) (4) (5) (6)=(4)*(5) (7)=(1)*(5) Model A Model B ,8 54 Values in column (6) are in curren prices showing a 14 percen increase over year (index = 18/45 = 24) Values in column (7) are a consan prices of year, hey reflec changes in quaniy and/or qualiy. Values a consan prices are an aggregaed volume measure, expressed in money erms and addiive Price and Volume indices The average of he proporionae changes in he price (or volume) of a specific se of goods and services beween wo periods of ime 28

15 5. Price and Volume indices The Laspeyres philosophy ime periods and quaniy (volume) relaives q/q weighs : share in oal value of period Laspeyres volume index (arihmeic mean of quaniy relaives) L q v q p q q v pq Price and Volume indices The Laspeyres philosophy ime periods and price relaives p/p weighs of period Laspeyres price index L v p p v pq P pq 3

16 5. Price and Volume indices Laspeyres Volume Index Formula The change from he base year in consan prices or he raio of he curren year volume o he base year volume in able 1 may be expressed in index form as: LQ = 54 x 1 / 45 = 12. This is also called Laspeyres (fixed-base) volume index (LQ ). Mahemaically: LQ Q, Q, Q, Noe: he wo componens of he index are ADDITIVE The Laspeyres volume index can also be wrien as: qi, LQ w, (2) i i q V i, i p i, q i, i p i, q i, (1) where w i,o is he base period weigh, i.e. he iems share in he oal value in he base period Price and Volume indices The Laspeyres philosophy Table 2 Year Year 1 Price Quaniy Value Weigh Quaniy Quaniy ( $/un.) (No.) ( $) (w ) (No.) relaives (QR) w *QR (1) (2) (3) = (1)*(2) (4)=(3)/ (3) (5) (6)=(5)/(2) (7)=(4)*(6)*1 Model A % Model B %

17 Paasche Price Index Formula To facor he change in he value of car producion from year o year 1 arising from price changes. ake he raio of he value of oupu in curren prices in year 1 o he value of oupu in year 1 measured in consan prices (prices of year ) (and muliply i wih 1 o conver o an index form): PP = 18 x 1 / 54 = 2. Shows 1 percen increase or doubling in prices The above raio is also called he Paasche price index (PP ). Algebraically: PP V Q, i p i, q pi, PP 1 w, (2) i i pi, where w i, is he curren period weigh, i.e. he iems share in he oal value in he curren period i, i p i, q i, (1) or 33 Paasche Price Index Formula According o he laer formulaion, PP is derived as follows from he daa in able 1: Table 3 Year Year 1 Price Price Value Weigh ( $/un.) ( $/un.) ( $) (w 1) Price relaives (PR) w 1 *PR (1) (2) (3) (4)=(3)/ (3) (5)=(1)/(2) (6)=(4)*(5)*1 Model A %.5.44 Model B %.5.6 1,8.5 PP = 1/ (w 1 * PR) = (1/.5) x 1 2. The raio of any aggregae in curren prices o he aggregae in consan prices yields an implici Paasche price deflaor Price measures for he main naional accouns aggregaes are (always) derived implicily 34

18 5. Price and Volume indices Value, Volume and Price Indexes The change in he curren price value of car producion from year o year 1 in our example can be expressed algebraically as: V p i i qi p i i q V,,, i, Muliplying and dividing by i p i, q i, gives: V p,,,, ) * ( i i qi p i i q V i ( p i i, qi, p i i,qi, Value index = Laspeyres Volume index * Paasche Price index / 1 V V 1 /1 LQ PP The volume and price effecs of value change are muliplicaive When V and V are known and PP is available he Laspeyres volume index can be derived indirecly from above formula a process called price deflaion 2 ) Price and Volume indices Value, Volume and Price Indexes Anoher se of volume and price indices may be obained saring from he change in he curren price value of car producion from year o year 1: Muliplying and dividing by i p i, q i, gives: V V V V i p i, or Value index = Paasche Volume index * Laspeyres Price index / 1 PQ can be obained by inflaing he base period values using he ofen available LP and hen dividing he curren price value by his amoun. q i, ( pi, qi, o pi,qi, ) * ( pi, qi, pi, qi, ) i p i, q i, i i i i V V 1 LP PQ /1 IMF Saisics Deparmen JVI/QNA/L11 : 36

19 5. Price and Volume indices Laspeyres, Paasche and Fischer Laspeyres: weighs of period Paasche: weighs of period Fischer: geomeric mean of Laspeyres and Paasche Price and Volume indices Laspeyres, Paasche and Fischer Value index = Laspeyres volume index * Paasche price index = Paasche volume index * Laspeyres price index = Fischer volume index * Fischer price index 38

20 Example Value in 25: 12 Paasche price index 24-25: 125 Volume 25 in prices of 24: 96 Laspeyres volume index 24-25: 12 Value in 24: 8 Value change = 2% * 25% = 5% Price and Volume indices CPIs, PPIs: all Laspeyres price indices Define precise bundle of goods and services & obain heir value shares in base year (for weighing) Observe monhly prices, by going o shops, magazines, inerne, ec. Calculae index 4

21 6. Chain-linking and re-referencing When a fixed base Laspeyres is used over a long run of periods, he weighs become progressively ou of dae and irrelevan. Chain-linking is simply he limiing case in which he weighs are updaed each period. No fixed base year bu moving base year: always use weighs of previous year o calculae growh raes (Previous Year Prices - PYPs) Chain year-on-year growh raes ogeher o obain consan price daa Non - addiiviy will occur in consan price series Chain-linking and re-referencing Base and reference period Base period he period ha provides he weighs for he index Reference period he period for which he index has he value 1 42

22 6. Chain-linking and re-referencing Re-Referencing Table 6 Index (reference period 2=1) Growh rae (percen) New Index (reference period 21=1) (1/12) (11/12) (12/12) (13/12) Growh rae (percen) Noe: Growh rae remains he same Re-referencing shifs focus o new reference year Values of he oher periods are now compared wih he value in his year 6.Change of Base Year. Effec on growh raes Table 7 Growh rae (percen) Values in curren prices Wool Price Quaniy Value Muon Price Quaniy Value TOTAL Value Values in consan prices of 2 Wool Muon TOTAL Values in consan prices of 25 Wool Muon TOTAL Values in consan prices of 21 Wool Muon TOTAL

23 7. Double v. Single deflaion/exrapolaion Bes mehod: double deflaion/exrapolaion GVA is derived as oupu less inermediae consumpion a consan prices, boh obained separaely Alernaive mehod: Single exrapolaion GVA is exrapolaed using oupu daa GVA is exrapolaed using employmen daa Single deflaion GVA is deflaed using oupu deflaor GVA is deflaed using he wage index GVA is deflaed using a general price index, e.g. CPI Illusraion of Double Deflaion Mehod Double Deflaion Example 23 Curren prices Price indexes Consan (2) prices GO IC GVA PPI ICI GO IC GVA ( $) ( $) ( $) (2=1) (2=1) ( $) ( $) ( $) (1) (2) (3)=(1)-(2) (4) (5) (6)=(1)/(4)*1 (7)/(5)*1 (8)=(6)-(7) Mining 7,3. 3,8. 3, , , ,78.7 Manufacuring 12,8. 6,3. 6, , ,58.3 3,86.7 Toal 2,1. 1,1. 1, , , , Curren 23 prices GVA volume GVA implici GVA index deflaor ( $) (2=1) (2=1) (9) (1)=(8)/(9)*1 (11)=(3)/(8)*1 Mining 1, Manufacuring 3, Toal 5, GO: Gross Oupu IC: Inermediae Consumpion GVA: Gross Value Added PPI: Producer Price Index ICI: Inermediae Consumpion price Index

24 7. Illusraion of Single Indicaor Mehods Primary daa Dae Oupu a curren prices Inermediae consumpion curren i Value added curren prices (1) (2) (3)=(1)-(2) 2 3,2 2, ,94 2, ,68 2,7 98 Dae Oupu a consan 2 prices Paasche price deflaor for oupu Oupu volume index (4) (5)=(1)/(4)*1 (6)=(4) / 32 * 1 2 3, , , Illusraion of Single Indicaor Mehods Single exrapolaion Dae Value added 2 Laspeyres volume index oupu Value added consan 2 prices (6) (7)=8*(6) / *1. = *.938 = *.969 = 775. Single deflaion Dae Paasche price deflaor for oupu Value added curren prices Value added consan 2 prices (5) (13)=(1)-(2) (14)=(13)/(5) * /1. = /.98 = /1.187 = 825.5