2. Quantity and price measures in macroeconomic statistics 2.1. Long-run deflation? As typical price indexes, Figure 2-1 depicts the GDP deflator,

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1 1 2. Quaniy and price measures in macroeconomic saisics 2.1. Long-run deflaion? As ypical price indexes, Figure 2-1 depics he GD deflaor, he Consumer rice ndex (C), and he Corporae Goods rice ndex (CG) for he period from 1994 o has been frequenly saed ha he Japanese economy suffered from annual one or wo percen deflaion for he period beween 1997 and 2012, and general prices had declined by around weny percen for he corresponding period. However, his order of deflaion canno be observed in general prices of goods/services such as he C for consumpion goods and he CG for corporae goods. nsead, he GD deflaor had declined by abou 17 percen for he period. A grea divergence beween he GD deflaor and he C (or he CG) indicaes ha any facor oher han a change in general prices of goods/services was responsible for a subsanial decrease in he GD deflaor. n his secion, we would like o explore why such a considerable divergence emerged among he Japanese price indexes. Then, we would ask ourselves why people was feeling ha he Japanese economy had suffered from long-run deflaion alhough prices of goods/services did no decline significanly. Before his invesigaion, we make a commen ha here did no emerge any noiceable difference in he endency beween he GD deflaor and he C for he U.S. economy. n he U.S., as shown in Figure 2-2, he

2 2 GD deflaor and he C moved ogeher for he period from 1994 o 2015, alhough he C grew faser han he GD deflaor. suggess ha any facor specific o he Japanese economy migh have caused a difference in he behavior beween he GD deflaor and he C rice levels and relaive prices A definiion of he GD deflaor The GD deflaor is defined as he raio of nominal GD o real GD. One imporan feaure of he GD deflaor is ha given a volume (nominal GD), a quaniy (real GD) is deermined firs, and a price index (GD deflaor) is deermined second. Due o his naure, he GD deflaor is classified as an implici price index. n he case of he C or he CG, on he oher hand, given a volume (nominal value), a price index is deermined firs, and a quaniy (real value) is deermined second. GD How are nominal and real GD compued? Suppose ha GD ( Y ) consiss of expendiures on goods/services as household consumpion (C), fixed invesmen (), governmen consumpion (G), expors (), and impors (). Thus, nominal GD of ime is calculaed as: Y = C + + G + (2-2-1) GD GD C G where s represen price deflaors for GD, household, consumpion, fixed invesmen, governmen consumpion, expors, and impors.

3 3 Since GD concerns how much goods/services are produced domesically, impors are no o be added, bu o be subraced as foreign producion. Nominal expors minus nominal impors,, are called nominal ne expors. As shown below, his subracion of impors from domesic oupu may poenially make he GD deflaor quie differen from he C and he CG. As o he compuaion of real GD, a base year should be picked up; le us choose year 2005 as a base year. Wih all price deflaors fixed a year 2005, real GD of ime is compued as: Y = C + + G + GD GD C G A base year deflaor is usually sandardized a one. Thus, he above equaion is rewrien as: Y = C + + G + (2-2-2) GD Given equaions (2-2-1) and (2-2-2), he GD deflaor GD is defined GD GD as he raio of nominal GD ( Y ) o real GD ( Y ). C G GD = C + + G + C + + G + GD (2-2-3) Because real GD is compued wih prices fixed a a base year, he denominaor of he righ hand side of equaion (2-2-3) is compleely free of any effec of changes in price levels such as C or changes in relaive prices such as. Tha is, any price effec is shu down in consrucing C real GD. On he oher hand, any change in price levels and relaive prices induces raher complicaed effecs on is numeraor, nominal GD. As shown below, nominal GD can be expressed in several ways. G GD GD C Y = C + C + G C + C C C G = C + + G +

4 4 C G = C G + G + G + G G C G = C + + G + C G = C + + G + Tha is, nominal GD is a complicaed funcion of five price levels (,, G, G, ) and en combinaions of relaive prices (,,, G, G, ). C C G,, C C, C, n he righ hand side of equaion (2-2-3), he denominaor is compleely independen of changes in price levels and relaive prices, bu he numeraor is subjec o hose changes. Consequenly, he lef hand side of equaion (2-2-3), or he GD deflaor reflecs changes in boh price levels and relaive prices, which shows up in nominal GD. We will below pay aenion o he fac ha he GD deflaor is influenced by changes in relaive prices beween expors and impors Terms of rade as relaive prices We now focus on a relaive price beween expors and impors. Following a convenion, we define i as. This price raio is ofen called erms of rade, more precisely erms of inernaional rade. When increasing, we describe i as improving in he sense ha domesic economic agens can enjoy spreads hrough foreign rade by exporing domesic goods a higher prices and imporing foreign goods a lower prices. On he conrary, we express a decrease in as deerioraing erms of rade. n he pas wo decades, erms of rade have changes dramaically in Japan. As shown in Figure 2-3, her erms of rade declined subsanially from 1.34 in 1994: o 0.76 in 2008:. Then, hey improved o 0.94 in 2009:, and deerioraed again down o 0.75 in 2014:. However, hey have improved is

5 5 since mid Behind such long-run deerioraion in erms of rade lies a surge in oil prices and losing inernaional compeiiveness in a par of Japanese manufacurers. The former conribued o an increase in impor prices, while he laer caused expor prices o decline. On he oher hand, a recen slump in oil prices since mid-2014 help her erms of rade improve o some exen A definiion of real GD and he GD deflaor Real GD in a simple case As discussed above, real GD is compleely free of any price effec including changes in erms of rade as a consequence of fixing all prices a a base year. n oher words, real GD is no influenced by any change in erms of rade. By he deerioraion of erms of inernaional rade, for example, a par of he value added generaed by domesic producion may no be aribued o domesic players, bu may be leaked o economic agens in foreign counries. Thus, real GD fails o capure such income leakage o foreign counries. Consequenly, wha is recorded as a magniude of domesic producion by real GD may be differen from wha is received evenually by domesic economic agens who conribue o domesic producion. n his way, real GD is a proper measure of domesic

6 6 producion, bu no a proper measure of real aggregae income. We here propose real GD (gross domesic income) as a measure of real aggregae income wih due consideraion for effecs of changes in erms of rade. For his purpose, we sill fix relaive prices among domesic goods by assuming ha deflaors are idenical for household consumpion, fixed invesmen, governmen consumpion, and expors, or = = = =. D C G Then, relaive prices beween domesic goods and impors as erms of inernaional rade. D are defined The above simplifying assumpion is no as resricive as i looks. A reason for his is ha any change in erms of rade among domesic producers is neuralized a he level of a macroeconomy. Suppose ha erms of domesic rade are more advanageous o one domesic producer han o anoher one. Here, a gain of he former producer is cancelled ou exacly by a loss of he laer a he aggregae level. Bu, an income leakage o foreign counry by he deerioraion of erms of inernaional rade canno be cancelled ou even a he aggregae level, and is recorded as a loss of domesic income. As equaion (2-2-2) implies, real ne expors fails o consider any effec of erms of rade. We herefore replace by an alernaive measure of real ne expors. Tha is, we divide nominal ne expors by he domesic D deflaor o compue real ne D expors: D (2-2-4) Because an inverse of erms of rade appears in equaion (2-2-4), an alernaive measure of real ne expors successfully considers effecs of erms of rade. For example, when erms of rade deeriorae, an increase in lowers he above-defined real ne expors ( D D ); his relaive price effecs capure an income leakage o foreign counries. We hen define he rade gains/losses TG as follows: TG = D ( ) (2-2-5)

7 7 By adding he rade gains/losses o real GD ( Y ), is replaced GD by D. A newly defined aggregae Y GD + TG is called real GD ( Y ). GD Noing ha all deflaors are sandardized as one a a base year, we easily demonsrae ha if erms of rade are deerioraing relaive o a base-year level ( < 1), hen he rade gains/losses are negaive ( TG < 0 ), and real GD is smaller han real GD. On he conrary, if erms of rade are improving relaive o a base-year level ( > 1), hen he rade gains/losses are posiive ( TG > 0), and real GD is larger han real GD. n he former case, a difference beween real GD and real GD represens a relaive size of income linkage o foreign counries by he deerioraion of erms of rade. n he laer case, on he oher hand, i represens a relaive size of income inflow o a domesic counry by he improvemen Real GD in a realisic case (incomplee) We nex define real GD in a more realisic case wihou assuming idenical deflaors among domesic goods. We now employ a newly defined deflaor, called he expor/impor deflaor ( ), insead of he expor deflaor ( ) o compue a real value of ne expors. The expor/impor deflaor is defined as follows: = On he oher hand, he rading gains/losses ( TG ) are defined by: TG = ( ) A definiion of real GD ( Y GD ) is he same as in he previous case. Tha

8 8 is, real GD is defined as real GD ( Y ) plus ( TG ); is now replaced by GD in real GD. Again as in he previous case, we can easily prove ha if erms of rade are deerioraing relaive o a D base-year level ( < 1), hen he rade gains/losses are negaive ( TG 0 < ), and real GD is smaller han real GD. Le us ake a look a boh real GD and real GD of he Japanese economy for he period from 1994 o 2015 (see Figure 2-5). As discussed before, erms of rade were deerioraing for he period up o mid Thus, real GD grew slower han real GD. For he period beween 2002 and 2007, which period is known as he longes recovery in he pos war era, real GD grew a 1.8% per year, bu real GD grew a only 1.0% per year. For anoher recovery period from 2009: o 2014:, real GD grew a 2.2% per year, bu real GD grew a only 1.3%. For he period from 2014: o 2015:V during which erms of rade were improving, on he oher hand, real GD (3.0%) grew faser han real GD (1.4%) A comparison beween he GD deflaor and he GD deflaor A nice by-produc of consrucion of real GD is he GD deflaor, which serves as a price index of domesic goods. As discussed before, he GD

9 9 deflaor ( GD ) is defined as nominal GD/real GD, and reflecs no only price levels, bu also relaive prices including erms of rade. A reason for his is ha is denominaor (real GD) is compleely free of any price effec, and he impac of relaive prices included in is numeraor (nominal GD) remains in he GD deflaor. On he oher hand, he GD deflaor ( GD ) is defined as nominal GD/real GD. An imporan difference beween he GD deflaor and he GD deflaor is ha real GD as is denominaor now conrols for erms of rade, and consequenly, he effec of erms of rade is cancelled ou in he GD deflaor. The feaure of he GD deflaor in urn illuminaes ha of he GD deflaor. As shown below, he GD deflaor is decomposed ino he GD deflaor and he impac of erms of rade. GD Y Y = Y Y GD TG = 1+ GD Y GD GD GD GD GD As menioned before, he rade gains/losses decreases as erms of rade deeriorae. Thus, a decline in he GD deflaor eiher a decrease in he GD deflaor as a price index of domesic goods or he deerioraion of

10 10 erms of rade. n oher words, a difference in he behavior beween he GD deflaor and he GD deflaor indicaes he effec of erms of rade. Figure 2-5 depics he GD deflaor and he GD deflaor for he period from 1994 o A difference beween he wo deflaors indicaes ha changes in erms of rade played a big role in deerminaion of he GD deflaor. For he period from 2003:V o 2008:V, he GD deflaor declined, bu he GD deflaor was sable; i implies ha prices of domesic goods were sable, bu erms of rade were deerioraing. For he period from 2014: o 2015:V, on he oher hand, he GD deflaor was increasing, bu he GD deflaor was sable; i indicaes ha prices of domesic goods were sable, bu erms of rade were improving A comparison among differen price indexes aasche indexes versus Laspeyres indexes There are wo classes of price indexes, eiher of which any price index is classified as. One is called he aache index, and he oher is called he Laspeyres index. n he aasche index, a quaniy weigh is chosen a a curren year as follows. L = i= 1 i= 1 p pq i i i 2005 q i n he Laspeyres index, on he oher hand, a quaniy weigh is fixed a a base year as below. = i= 1 i= 1 p pq i i 2005 q i i The GD deflaor is defined as C + + G + C G GD = C G 2005C G Thus, i is classified as he aasche index. The oher deflaors employed in he naional accouns also belong o he aasche index. On he oher hand, he C is one of he mos popular Laspeyres indexes. The CG is also

11 11 classified as he Laspeyres index. We below describe how inflaion (deflaion) raes differ beween he aasche index and he Laspeyres index. Buyers purchase more goods wih lower prices and less goods wih higher prices. Accordingly, goods wih higher (lower) prices end o lower (more) weighs in he aasche index. On he oher hand, all quaniy weighs are fixed in he Laspeyres index. Consequenly, he aasche index deflaes more han he Laspeyres index when some prices are going down, and he former inflaes less han he laer when some prices are going up. n oher words, he rae of inflaion (deflaion) based on he aasche index is lower (higher) han ha based on he Laspeyres index A comparison among he GD deflaor, he GD deflaor, he consumpion deflaor, and he C We have already discussed a difference beween he GD deflaor and he GD deflaor; changes in erms of rade have significan impacs on he GD deflaor, bu lile impac on he GD deflaor. The GD deflaor can serve as a price index of domesic goods/services. The consumpion deflaor does no include impor goods as a subracion erm, and i hen behaves in he same manner as he GD deflaor wihou any direc effec from changes in erms of rade. n sum, he GD deflaor and he consumpion deflaor

12 12 differ from he GD deflaor o he exen ha changes in erms of rade affec he GD deflaor. On he oher hand, like he GD and GD deflaors, he consumpion deflaor belongs o he aasche index. Therefore, in comparison wih he C as he Laspeyres index, he consumpion deflaor ends o generae lower inflaion raes and higher deflaion raes. As shown in Figure 2-6, for he period from 1994 o 2015, he consumpion deflaor indeed declined significanly, bu he C was quie sable. Le us make a comparison among he GD deflaor, he GD deflaor, he consumpion deflaor, and he C for he period from 1997 o 2012, which period is known as he long-run deflaion era. Among he hree deflaors as he aasche indexes, he GD deflaor declined mos; i deflaed a 1.2% per year. Boh he GD and consumpion deflaors declined a lile more moderaely; i deflaed a 0.9% per year. A difference in deflaion raes beween he GD deflaors and he GD/consumpion deflaors reflecs he degree of he deerioraion of erms of rade. On he oher hand, he C as he Laspeyres index declined only slighly. The annual deflaion rae was only 0.2%. A difference in deflaion raes beween he C and he GD/consumpion deflaors is induced by he naure of he Laspeyres index, which end o lower deflaion raes.

13 A comparison beween Japan and he U.S. Coming back o one of our original quesions, le us discuss why he price index behaved quie differenly beween Japan and he U.S. The mos imporan reason for his is ha erms of rade changed quie differenly beween he wo counries. As repeaedly discussed and shown in Figure 2-7, erms of rade coninued o deeriorae for he period from 1994 o mid-2014 excep a few quarers immediaely afer he bankrupcy of Lehman Brohers in Sepember We can hardly observe such long-run deerioraion of erms of rade in he U.S. daa. As shown in Figure 2-7, erms of rade were fairly sable in he U.S. Thus, he facor of erms of rade is almos absen on he U.S. side. Boh he GD and consumpion deflaors behaved similarly; GD deflaor inflaed a 1.9% per year, and he consumpion deflaor increased a 1.8% per year. On he oher hand, he C inflaed a 2.3% per year. As discussed before, he dominance of he C over he consumpion deflaor comes from a difference in he naure beween he Laspeyres and aasche indexes An empirical exercise Try roblem Se 1! (Excel Daa) By solving his problem se, you will undersand how a long-run deerioraion of erms of rade hur he real value of employee compensaion in Japan. You will see how much he deerioraion of erms of rade can explain he fac ha real GD grew, bu real labor income improved quie lile. believe ha many workers fel ha he pas wo decades were he era of deflaion in he sense ha heir purchasing power from labor income did no improve a all.