Assessing the adequacy of measures of Australia s price competitiveness and structural change

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1 MPRA Munich Personal RePEc Archive Assessing he adequacy of measures of Ausralia s price compeiiveness and srucural change Don Harding Universiy of Melbourne Sepember 21 Online a hp://mpra.ub.uni-muenchen.de/3383/ MPRA Paper No. 3383, posed 4. June 27

2 Assessing he adequacy of measures of Ausralia s price compeiiveness and srucural change Don Harding Melbourne Insiue, The Universiy of Melbourne. Sepember 21 Absrac There are a plehora of measures of Ausralia s inernaional price compeiiveness. This aricle provides a praciioners guide o hose series. The currenly available measures of inernaional price compeiiveness are found o be deficien. A heoreically sound measure is suggesed and compuer code is supplied o consruc esimaes. 1

3 1. Inroducion The Reserve Bank of Ausralia (RBA) and he Treasury consruc several measures of Ausralian price compeiiveness. 1 The RBA real rade weighed index of exchange raes (RTWI) has no been made public bu, Dungey and Joiner (2) provide a spreadshee ha may be used o calculae a RTWI using he RBA mehodology. 2 Given his plehora of measures of inernaional price compeiiveness here is scope for a guide for praciioners ha reviews hese indexes. In his paper I discuss he underlying economic conceps, assess how well hese indexes approximae hese economic conceps, assess he qualiy of he index consrucion and make available improved procedures for consrucing hese indexes. A useful saring poin is o noe ha one migh conver foreign price indexes ino Ausralia dollars and hen ake an average of hese prices. Alhough here are many ways o make an average, he focus on ineres is on relaive prices and hus a rade weighed geomeric average is a naural measure. Assume for he momen ha all daa is available coninuously and le w i () represen counry i s rade share, e i () and p i () represen he logarihm of i s bilaeral exchange rae wih he $A and he logarihm of he relevan price index respecively. Consider he index I A () which is consruced as he logarihm of he relevan Ausralian prices p A less he logarihm of he geomeric mean of foreign prices convered o Ausralian dollars. Then I A () measures he raio of Ausralian prices o a rade weighed index of foreign prices convered o $A. I A N () = p w () ( p ) + e () ) A i= 1 i i ( (1) Such an index is of some use for descripive purposes bu he main focus of ineres is on why i changes i over ime. Differeniaing equaion (1) wih respec o ime yields he insananeous change in he geomeric mean of prices. () dp () () de () N N di A A dpi i dwi = wi () + [ pi ( ) + ei () ] (2) d d i= 1 d d i= 1 d The firs erm in equaion 2 measures he insananeous change in Ausralia s price compeiiveness, a rise in his componen means ha Ausralian goods have become more expensive relaive o foreign goods indicaing a decline in compeiiveness. The second erm measures how he change in he counry srucure of rade has affeced he raio of Ausralian prices o he average of foreign prices. Clearly, economic heory requires ha we separae hese wo effecs since oherwise we would confound price effecs wih quaniy effecs. Thus in assessing he various measures of compeiiveness he main crieria will be minimizing he approximaion errors made when rying o measure hese wo componens. The relevan heory is discussed in secion 2. The size of he approximaion errors depends no only on he mehod of index consrucion bu () 1 Treasury s real exchange raes are available from hp:// 2

4 also on he paern of movemens in counry rade shares, and exchange raes. Informaion on hese is provided in secion 3 of he paper. The RBA s nominal TWI is evaluaed in secion 4 and he several measures of inernaional price compeiiveness (real TWIs) are evaluaed in secion 5. Conclusions are presened in secion Theoreical consideraions in consrucing indexes of price compeiiveness and srucural change The approximaion errors, alluded o in he inroducion, arise because daa on prices, exchange raes and rade shares are no available in a coninuous record bu insead are recorded a discree (quarerly) inervals. Thus we need a link beween he unobservable coninuous ime daa in equaion (2) and he observable discree daa on exchange raes prices and rade shares. This link is made via he wo inegral equaions (3) and (4) ha define he change from he beginning of he period (quarer) o he end of he period in he divisia index of price compeiiveness( IC ΔIC divisia = K k = 1 1 wi () dei d divisia () dp () + ) and srucural change index i d () d (3) divisia IS. K divisia dwi ΔIS = { () ()} pi + ei d (4) 1 k = 1 d The index number problem hen, is o obain good approximaions o hese inegrals above. In discussing hese approximaions i is useful o focus on he following discree approximaions made for various values of α in he inerval o 1. Δ ln IC ΔIS α α = = K k = 1 K k = 1 [ αw + ( α ) w ]{ Δp + Δe } k 1 1 [ α{ pk 1 + ek 1} + ( 1 α ){ pk + ek }] Δwk k i i (5) (6) Choice of he values,.5 and 1 for α yield a riniy of index numbers:! α = 1 yields Lasypeyres indexes of prices and srucural change.! α = yields Paasche indexes of prices and srucural change.! α =. 5 yields Törnqvis indexes of prices and srucural change. I is well known 3 ha he Lasypeyres and Paasche indexes are firs order approximaions o he divisia price and srucural change indexes. Tha is hey produce second and higher order errors. Tha is he Lasyperes 2 The RBA also publishes a nominal rade weighed index of exchange raes. 3 Diewer 1976 and 1981; Guerrieri and Milana 1995; Denny and Fuss (1983). 3

5 and Paasche indexes do a poor job of separaing he price compeiiveness and srucural effecs. The Törnqvis index in conras is a second order approximaion and hus produces hird and higher order approximaion errors. Thus i does a far beer job a separaing he price compeiiveness and srucural effecs. Caves, Chrisensen and Diewer (1982a,b) show ha he Törnqvis index mainains is high degree of approximaion even if he underlying aggregaion funcion is shifing in a non-homoheic way. Given ha i is relaively sraigh forward o calculae, i seems ha bes pracice is o compue Törnqvis indexes of price compeiiveness. 3. Some feaures of bilaeral exchange raes and counry rade shares Trade weighed exchange raes combine bilaeral exchange raes and rade shares. Insigh ino he magniude of he aggregaion problem is obained by examining hese specific measures. For example, if bilaeral exchange raes conain a significan common componen hen small aggregaion errors will be incurred. However, as shown in Figure 1, in an average quarer, one half of currencies appreciae agains he $A while he oher half depreciae. 4 Moreover, he proporion of currencies ha are appreciaing agains he $A varies considerably over ime. The marked variaion in he proporion of currencies agains which he Ausralian dollar is appreciaing also highlighs he flaw in focusing on any single bilaeral rae. Figure 1. Proporion of currencies agains which $A appreciaed in he quarer, June 197 o June 2 Proporion of currencies (22 counries) agains which $A appreciaed (per cen) Jun-7 Jun-75 Jun-8 Jun-85 Jun-9 Jun-95 Jun- 4 Based on he 22 counries ha comprise Ausralia s larges rading parners. These comprise, Unied Saes, Unied Kingdom, Belgium, France, Germany, Ialy, Neherlands, Sweden, Swizerland, Canada, Japan, New Zealand, Saudi Arabia, Taiwan, Hong Kong, India, Indonesia, Souh Korea, Malaysia, Singapore, Papua New Guinea, China. 4

6 Even wih he direcional paern of bilaeral exchange rae flucuaions shown in Figure 1, consrucion of a rade-weighed index of exchange raes would be relaively sraighforward if he magniude of he flucuaions were small. However, he larges bilaeral appreciaion of he $A in a quarer averages 8.3 per cen while he larges bilaeral depreciaion averages 5.9 per cen. Moreover as is shown in Figure 2 here are subsanial flucuaions around hese averages. Indeed, he larges appreciaion of he $A was 82 per cen agains he Indonesian Rupiah in March 1998 while he larges bilaeral depreciaion was 4 percen agains he Indonesian Rupiah in December Moreover as is shown in Figure 3 he sandard deviaion of bilaeral exchange raes varies considerably and has been as high as 19 per cen during he Asian crisis. Figure 2. Maximum, minimum and arihmeic average of he change in bilaeral $A exchange raes for Ausralia s 22 larges rading parners, June 197 o June 2 Percenage change over previous quarer 1 8 Larges appreciaion in he quarer Larges depreciaion in he quarer Jun-7 Jun-75 Jun-8 Jun-85 Jun-9 Jun-95 Jun- When consrucing rade weighed exchange raes he objecive is o separae he movemen in exchange raes from he change in he counry srucure of rade. If counry rade shares are consan his problem does no arise. Unforunaely consrucion of TWIs for Ausralia is complicaed because is rade shares are changing over ime. Specifically, here is a change away from rade wih he counries ha represened Ausralia s big four rading parners in 197 and owards increased rade wih Asia (See Figure 4). 5

7 Figure 3: Sandard deviaion of percenage changes in Ausralian bilaeral exchange raes wih 22 counries Sandard deviaion of change in bilaeral raes for 22 counries Sandard deviaion across counries and ime is 3.4 per cen Jun-7 Jun-75 Jun-8 Jun-85 Jun-9 Jun-95 Jun- 8 Figure 4. The changing regional paern of Ausralia s rade, March 197 o June 2 Per cen of bi-direcional rade Unied saes, Japan, Unied Kingdom and Germany Asia including Japan Mar-7 Mar-75 Mar-8 Mar-85 Mar-9 Mar-95 Mar- 6

8 I is also insrucive o examine movemens in he sandard deviaion of counry rade shares shown in Figure 5. To inerpre ha figure, noice ha if N represens he number of counries hen (since rade shares add o 1) he average rade share is 1/N. Thus, he sandard deviaion of rade shares is N 1 1 σ = Si. N i= 1 N 2 Noe ha σ is minimized wih value zero when all he rade shares are equal o 1/N. Thus from Figure 5 we can conclude ha Ausralia s rade is concenraed wih some large rading parners bu, he fall in he sandard deviaion since he mid 198s signals increased dispersion of rade. Tha is, Ausralian rade has been shifing from a few counries wih large rade shares o many counries wih smaller rade shares. Figure 5. Sandard deviaion of Ausralia s rade shares, March 197 o June 2 Sandard deviaion of bi-direcional rade shares (per cen) Mar-7 Mar-75 Mar-8 Mar-85 Mar-9 Mar-95 Mar- In summary, he preceding discussion suggess ha he paern of movemens in Ausralia s bilaeral exchange raes and rade shares is such ha consrucion of boh nominal and real TWI s needs o be underaken wih considerable care so as o avoid making large approximaion errors. These consideraions srenghen he case for using he Törnqvis index o consruc real and nominal TWIs. 4. The RBA s measure of he nominal and real rade-weighed exchange raes The RBA publishes a nominal rade-weighed index of exchange raes ha is repored in he financial media 7

9 and is widely used in financial markes and in economeric models of he Ausralian economy. This measure was iniially consruced as an arihmeic mean of exchange raes. In Ocober 1988 he Bank followed inernaional pracice and moved o calculaing he TWI as geomeric mean of exchange raes. Raher han recalculaing he TWI on he new mehod he Bank chose o splice he new geomeric mean series ono he old arihmeic mean series a 3 Sepember Thus, i is very difficul o know how o inerpre he TWI as produced by he Bank. I is no suiable for use in economeric work as he ime series properies of he arihmeic and geomeric means are quie differen. Each year since 1988 he Reserve Bank has updaed he weighs used o calculae he TWI. However, i follows a pracice of calculaing he TWI for he smalles number of counries ha cover 9 per cen of Ausralia s rade in he year for which he weighs were calculaed. Each year he TWI so calculaed is spliced o he previous year s TWI. Wha his means is ha he counries on which he TWI is based change over ime. Again his limis he usefulness of he RBA measure of he TWI. As shown in Figure 6 here are significan differences beween he published RBA measure of he TWI and he preferred Törnqvis measure of he TWI. 5 For example, A June 2 he deviaion beween he wo indexes was abou 1 percenage poins. Moreover, he unusual weighing paern and year o year variaion in counry coverage of he RBA measure inroduces significan quarer o quarer variaion in he difference beween he wo indexes. 5 Gauss code for consrucing Törnqvis indexes is available from he auhor on reques. 8

10 Figure 6. Deviaion beween he RBA measure of he nominal TWI and he preferred Törnqvis index based measure, March 197 o June 2 (per cen) 16 Exen o which RBA TWI deviaes from bes esimae of rade-weighed nominal value of he $A (Per cen) Mar-7 Mar-75 Mar-8 Mar-85 Mar-9 Mar-95 Mar- 5. Assessmen of official measures of Ausralia s exernal price compeiiveness 5.1. The RBA real TWI The RBA s Real TWI (like is nominal TWI) is based on a Laspeyres-ype index excep ha annual rade weighs from he previous financial year are used raher han he weighs from he previous quarer. Thus for he year 1999/ he RBA uses he rade weighs from 1998/99. In principle he RBA published nominal TWI and is unpublished real TWI can be decomposed as follows. 6 TWI RBA = Törnqvis index measuring price compeiiveness effec + Törnqvis index of srucural change in rade paerns + measuremen error from use of Lasyperes index + measuremen error from using ou-ofdae rade shares. As shown in Figure 7 hese measuremen problems mean ha here are significan differences beween (my esimae of) he RBA s unpublished real TWI and he preferred Törnqvis index measure of he real TWI. A June 2 he RBA measure of he real TWI is oo high by abou 14 percenage poins when compared o he Tornqvis index measure. 9

11 Figure 7. Alernaive measures of he $A real rade-weighed exchange rae, March 197 o June 2 $A real rade-weighed exchnage rae - CPI Basis, (March 197=1) Real TWI RBA Basis Real TWI (Tornqvis) Mar-7 Mar-75 Mar-8 Mar-85 Mar-9 Mar-95 Mar The Treasury s hree measures of he real exchange rae The Treasury publishes hree measures of he real rade-weighed exchange raes ha compare domesic and foreign consumer prices, implici price deflaors and real uni labour coss respecively. The Treasury indexes share he same problem as he RBA s measure in ha hey are based on Paasche index numbers. However, he Treasury s measures cover only 4 of Ausralia s larges rading parners he Unied Kingdom, he Unied Saes of America, Germany and Japan. In 197 hese rading parners accouned for 68 per cen of Ausralia s exernal rade. Bu his share has declined over ime; by 1997 hose counries accouned for only 46 per cen of Ausralia s exernal rade. Thus he Treasury measures are becoming obsolee and poenially misleading. Inspecion of Figure 8 shows The Treasury measure of he real exchange rae differs significanly from he preferred Törnqvis index and significanly oversaes he real exchange in he 197s. More recenly he Treasury s measure of he real TWI oversaes he improvemen in Ausralia s exernal price compeiiveness by abou seven percenage poins. Thus he Treasury series moves from a 5 per cen overesimae in 1996 o a seven per cen underesimae currenly. This is a oal shif in measuremen error of 12 percenage poins in four years. 6 This decomposiion is only achievable in principle because of he oher wo problems wih he RBA measures, namely he changing counry composiion and he splicing of he arihmeic mean index o he geomeric mean index. 1

12 Figure 8. Deviaion beween he Treasury measure of he real TWI and he preferred Törnqvis index based meaure, March 197 o June 2 Exen o which he Treasury real TWI deviaes from he bes esimae of he real TWI (per cen) Mar-7 Mar-75 Mar-8 Mar-85 Mar-9 Mar-95 Mar- I is also of some ineres o examine he effec of srucural change in Ausralia s rading paerns. As is shown in Figure 9, over he 199 s Ausralia s rade has moved owards counries agains which he real $A is appreciaing. This shif in rade paerns couneracs o some exen he simulus ha comes from improved price compeiiveness over he same period. Figure 9. Effec of he changed counry srucure of rade on he Ausralian real TWI, March 199 o June Index March 199= Mar-9 Mar-92 Mar-94 Mar-96 Mar-98 Mar- 11

13 6. Conclusions The RBA and Treasury produce several nominal and real TWIs. However, I have shown ha hese measures are poor approximaions o he economic conceps of ineres. I have provide a formula and compuer code o consruc more accurae approximaions. When properly measured, he real rade weighed exchange rae is beween 7 and 14 per cen below official esimaes. This suggess ha Ausralia is significanly more price compeiive han suggesed by official esimaes. I have also consruced a index ha measures he srucural effec ha arises because of changes in he paern of Ausralia s rade. I urns ou ha his shif in he paern of Ausralian rade is owards counries agains which he bilaeral $A real exchange rae is appreciaing. This srucural effec hen works agains he price improved price compeiiveness of Ausralia. References Abramowiz, A. and I.A., Segun (1972), Handbook of Mahemaical Funcions, Dover Publicaions, New York. Caves, D.W., L.R., Chrisensen and E.W., Diewer (1982a), Mulilaeral comparisons of oupu, inpu and produciviy using superlaive index numbers, Economic Journal, vol. 92, pp Caves, D.W., L.R., Chrisensen and E.W., Diewer (1982a), The economic heory of index numbers and he measuremen of inpu, oupu and produciviy, Economerica, vol. 5, pp Denny, M., and M., Fuss (1983), A general approach o inernaional and inerspacial produciviy comparisons, Journal of Economerics, Vol 23, pp Diewer, E., (1976), Exac and superlaive index numbers, Journal of Economerics, vol. 4, pp Dixi, A.K., and V., Norman (198), Theory of Inernaional Trade, Cambridge Universiy Press. Dungey, M.H. and A. Joiner (2), Dwyer, J., and P., Lowe (1993), Alernaive Conceps of he Real Exchange Rae: A Reconciliaion, Reserve Bank of Ausralia, Research Discussion Paper 939. Guerrieri, P., and C., Milana (1995), Superlaive indexes of price compeiiveness and effecive exchange raes, In: B., Quinieri (Ed.), Paerns of Trade, Compeiion and Trade Policies, Avebury. Jones, M.T., and J., Wilkinson (199), Real Exchange Raes and Ausralian Expor Compeiiveness Reserve Bank of Ausralia, Research Discussion Paper 95. Tardii, A., (1996), Modelling he Ausralian Exchange Rae, Long Bond Yield and Inflaionary Expecaions, Reserve Bank of Ausralia, Research Discussion Paper 968. Woodland, A.D., (1982), Inernaional Trade and Resource Allocaion, Norh Holland. 12