DBJ Research Center on Global Warming Discussion Paper Series No.37 No.28 (2009) (9/2003)

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1 DBJ Research Cener on Global Warming Discussion Paper Series No.37 No.28 (2009) (9/2003) Wage Differenials and Srucure in he U.S. and Japan, Purchasing Power Pariies for Labor Inpu Koji Nomura and Jon D. Samuels This paper is a preliminary draf and provided for discussion purposes only. Please do no quoe or cie wihou he auhors permission. The views expressed in his paper are hose of he auhors and do no presen hose of he Developmen Bank of Japan or he Research Cener on Global Warming.

2 Wage Differenials and Srucure in he U.S. and Japan, Purchasing Power Pariies for Labor Inpu Koji Nomura and Jon D. Samuels * Absrac: This paper proposes a framework for he cross-counry comparison of labor inpu and measures he relaive price, qualiy, and he purchasing power pariy for labor inpu beween he U.S. and Japan during , based on deailed labor daa crossclassified by sex, age, educaion, class of worker, and indusry in boh counries. Keywords: Purchasing Power Pariy for Labor Inpu, Relaive Price, Relaive Qualiy Koji Nomura: Keio Economic Observaory (Insiue for Economic and Indusry Sudies), Keio Universiy, and CBG Fellow, Kennedy School of Governmen, Harvard Universiy, nomura@sanken.keio.ac.jp; Jon D. Samuels: Kennedy School of Governmen, Harvard Universiy, jon_samuels@ksg.harvard.edu. We also hank professor Dale Jorgenson (Harvard Universiy) for his suppor, and professor Morio Kuninori (Hosei Universiy) and Kimiko Hanabusa (Research Cener on Global Warming, Developmen Bank of Japan) for heir help esimaing Japanese labor daa. This paper is preliminary and we welcome commens.

3 1 Inroducion Across economies, he purchasing power pariy (PPP) is required in order o ranslae daa measured in nominal values in differen currencies ino a common uni. Using he U.S. dollar as he numeraire, he PPP beween he U.S. and Japan is defined by he number of yen required in Japan o buy he same quaniy of goods or services ha one dollar can buy in he U.S. The PPP ranslaes unis no only o a common currency, he U.S. dollar, bu convers values such ha he convered unis are expressed as one dollar s worh of each goods and service. The exchange rae is no sufficien for he ranslaion since i fails o accoun for differen price levels, i convers only o a common currency. The relaionship beween he PPP and he exchange rae in a cross-counry comparison is similar o ha beween he uni price and denominaion in ime-series. The concep of he purchasing power pariy for labor inpu can be defined analogously wih purchasing power pariies for commodiies, which are familiar. As he PPP for commodiies is he raio of own-counry prices a he mos deailed level of commodiy, he PPP for labor inpu is simply he raio of per hour labor compensaion for each ype of worker by counry. We classify workers in he US and Japan ino homogenous ypes and compue he PPP for each ype and for larger groups. Labor inpu purchasing power pariies allow for supplyside comparisons of labor, and are necessary for comparing labor produciviy and oal facor produciviy across counries. In his paper, we measure he purchasing power pariy for labor inpu beween he U.S. and Japan during Our measuremen is based on deailed cross-classified labor daa; Jorgenson daa a Harvard Universiy covers he U.S. and Keio Economic Observaory Daabase (KDB) a Keio Universiy covers Japan. Daa used in our sudy is an updaed version of he daa desribed in Ho-Jorgenson(1999) and Kuroda-Shimpo-Nomura-Kobayashi(1997). Each daa se has labor inpu cross-classified by sex, age, educaion, class of worker, and indusry. From hese deailed caegories, we can consruc indices of consan qualiy labor inpu and measures of he purchasing power pariy for labor inpu. In secion 2, afer we describe briefly he framework for labor inpu in he ime-series comparison, we propose he framework for he cross-counry comparison and consrucing he purchasing power pariy for labor inpu in each caegory and aggregaing o he economy as a whole. In his secion we define he relaive price of labor aking ino accoun he impac of he exchange rae on relaive price levels in he U.S. and Japan, and inroduce a measure of qualiy differences beween he work forces in boh counries. We inroduce our labor daa, homogenize he daases of boh counries over a group of common caegories in secion 3. We discuss he esimaed resuls of he purchasing power pariy for aggregae level labor inpu in secion 4. In addiion, we decompose he conribuions o he growh of he relaive 1

4 price for labor inpu, discuss he relaive per worker price, and compare he relaive prices for differen groups of workers. In secion 5, we presen indusry level deail and describe how variaion in relaive prices by indusy has changed over ime. Secion 6 concludes he paper. 2 Framework 2.1 Time-Series Comparison We begin wih he following noaion. Le E x saecj h x saecj H x saecj c x saecj C x saecj L x saecj p x saecj Q x saecj =number of workers by sex s, age a, educaion e, class of worker c, indusry j, year, and counry x; =average annual working hours by saecjx; =E x saecj hx, hours worked by saecjx; saecj =average hourly labor compensaion by saecjx; =annual labor compensaion by saecjx; =quaniy of labor inpu by saecjx; =price index of labor inpu by saecjx; and, =qualiy of labor inpu by saecjx. This noaion is based on Jorgenson-Gollop-Fraumeni (1987) and Ho-Jorgenson (1999), boh of which measure he labor inpu in he U.S. For our cross-counry comparison of quaniy, price, and qualiy of labor inpu, we expand hese variables concepually and add some noaion laer. A firs, for each counry, we describe briefly he framework for labor inpu in each counry, in order o clarify he relaionship beween he ime-series comparison in each coury and he cross-counry comparison in each year. Firs, he quaniy of labor inpu is assumed o be propoional o hours worked in each caegory, L x saecj = Qx saecj Hx saecj, (1) where qualiy of labor inpu, Q x, is consan for all year. We assume ha labor qualiy saecj for deailed caegories of workers does no change over ime. Tha is, an hour worked by caegory saecj in year equals an hour worked in year + s. By definiion, annual labor compensaion is described in wo ways; hours worked and labor inpu, C x saecj = Hx saecj cx saecj = px saecj Lx saecj. (2) We should make clear he uni of measuremen of each variable. Labor compensaion per year, C x saecj, and per hour, cx, are measured in own-counry currency unis. Consan saecj qualiy of labor inpu Q x is measured in own-counry consan currency unis per hour. saecj 2

5 From equaions (1) and (2), labor qualiy index can be also described as follows, c x saecj = Qx saecj px saecj. (3) Qualiy for labor inpu is defined from he quaniy-side in he Equaion (1) and from he price-side in equaion (3). In he base year T, qualiy of labor, Q x, equals per hour labor saecj compensaion, c x saecjt, and quaniy of labor inpu, Lx, equals per year labor compensaion, saecjt C x saecjt, since px = 1.0 for each counry. saecjt Nex, we describe briefly he framework for he aggregae measure of labor inpu in each counry. Toal labor compensaion in each year and in each counry, C x, is defined as follows, C x = px Lx = p x saecj Lx saecj = C x saecj, (4) saecj where L x and px represens quaniy and price of he aggregae labor inpu, respecively. We define he aggregae measure of quaniy of labor inpu as a Divisia index, L L x = Lx T x exp v x saecj saecj dτ, (5) T saecj saecj L x saecj C x v x saecj = saecj C x, (6) where L x T = Cx a he base year T. T The corresponding price of aggregae labor inpu can be derived by equaion (4) as he raio of oal labor compensaion o he aggregae quaniy of labor. Alernaively, he aggregae price can be derived by equaion (5) and he differencial of equaion (4), as he aggregae measure of price of labor inpu as a Divisia index, p x = Cx L x = exp T saecj v x saecj ṗ x saecj p x saecj dτ. (7) Addiionally, we define oal hours worked and simple average hourly labor compensaion in each year and in each counry as, H x = H x saecj, (8) saecj c x = Cx H x. (9) We can define he aggregae measure of qualiy of labor inpu in wo ways; from he quaniy-side in equaions (5) and (8) and he price-side in equaions (7) and (9), L x = Qx Hx, (10) c x = Qx px. (11) 3

6 I is imporan ha he aggregae measure of qualiy, Q x, depends on year, hough qualiy of labor in each caegory, Q x, does no. In each deailed caegory, because of he assumpion saecj of consan labor qualiy in equaions (1) and (3), he growh raes of labor inpu and hours worked coincide and he growh raes of average hourly labor compensaion and price of labor inpu also coinside. However, he growh rae of he aggregae measure of qualiy of labor inpu, ( Q x /Qx ), is non-zero and measured from he quaniy-side and he price-side as, differenciaing equaions (10) and (11) respecively, * 1 Q x Q x = L x L x Ḣ x H x = ċx c x ṗx p x. (12) The change of aggregae qualiy of labor depends on he change of price in each labor inpu. The labor inpus in each caegory are assumed o be homogeneous over ime, however, he price of he labor, which represens he marginal produc of labor, can be differen. Also, he change of he aggregae qualiy of labor depends on he change of allocaion among labor inpus. In he special case of consan prices of each labor inpu over ime, or equal price changes across all caegories, he movemen of workers across caegories drives he aggregae qualiy of labor. 2.2 Cross-Counry Comparison Now, we describe he cross-counry comparison of quaniy, price, and qualiy of labor in each caegory and a he aggregae level. A firs, we inroduce he quaniy and price of labor, each of which is comparable wih ha in he base counry y,in he reference counry x. Quaniy of labor inpu, L x saecj, in equaion (1) or price index of labor, px, in equaion (3) is saecj sufficien for a ime-series comparison in each counry. However, hey are no sufficien for a cross-counry comparison. Adjusing by he qualiy of labor inpu in base counry, we define he qualiy-adjused quaniy and price of labor inpu in he reference counry, as L x y saecj and p x y respecively. For he cross-counry comparison, he equaions of quaniy and price in saecj (1) and (3) and he balance equaion on nominal labor compensaion in (2) should be redefined as, L x y saecj = Qy saecj Hx saecj, (1) c x y saecj = Qy saecj px y saecj, (3) C x y saecj = Hx saecj cx y saecj = px y saecj Lx y saecj, (2) *1 In measuremen of equaions (5) and (7), we use he discree approximaion by Theil-Törnqvis indices of aggregae quaniy and price of labor inpu. I is imporan o noe ha Theil-Törnqvis index numbers are no ransiive. Then, equaion (12) is saisfied approximaely. 4

7 where he labor compensaions, per year C x y and per hour cx y, in he reference counry are saecj saecj defined by he base counry s currency; C x y saecj =Cx saecj /ex y and c x y saecj =cx saecj /ex y, using annual average exchange rae, e x y. Quaniy and price of labor inpu in he reference counry are evaluaed by he qualiy of labor in he base counry in (1) and (3). Assuming ha he qualiy-adjused labor inpus in each caegory are homogeneous, i is convenien o define he relaive quaniy and price of labor inpu, RL x y and Rpx y saecj saecj, he relaive values of hours worked and per hour labor compensaion, RH x y and Rcx y saecj saecj, and he relaive values of per year labor compensaion, RC x y, based on equaions (1), (3), and saecj (2). Each relaive variable in he reference counry o he base counry can be described as follows, where RC x y saecj saecj = C x y C y saecj RL x y saecj = RHx y saecj, (13) Rc x y saecj = Rpx y saecj, (14) RC x y saecj = RHx y saecj Rcx y saecj = Rpx y saecj RLx y saecj, (15) saecj L x y, RL x y saecj = L y saecj H x c x y, RH x y saecj = saecj, Rc x y saecj = H y saecj saecj c y saecj saecj p x y, Rp x y saecj = p y saecj. (16) By he qualiy adjusing of he quaniy and price of labor inpu in he reference counry, he relaive labor quaniy coincides wih he relaive hours worked and he relaive per hour compensaion coincides wih he relaive price of labor inpu in each labor caegory. The relaive price of labor, Rp x y in equaion (16), defines an index such ha he price of labor saecj inpu in he base counry is se as uniy every year. So, Rp x y represens he price-gap index saecj of labor inpu in boh counries and is no uniy even in he base year. Similarly, we can define he purchasing power pariy for labor inpu in each caegory as follows, PPP x y saecj = ex y Rp x y saecj. (17) If PPP x y for a paricular labor inpu is smaller han he exchange rae ex y saecj, ha is Rp x y saecj < 1, i implies ha he cos of labor services for worker caegory saecj in he reference counry is lower han ha in he base counry. Comparing Japan and he U.S., he purchasing power pariy for labor inpu, PPP J U, is he number of yen required in Japan o purchase he saecj homogeneous labor inpu cosing one dollar in he U.S., and is unis are yen/dollar. * 2 *2 From he viewpoin of measuremen, i is easy o udersand PPP x y is defined by he relaive value of per saecj hour labor compensaion; c x saecj /cy, in equaion (17), because per hour labor compensaions in each caegory saecj and in each counry are direcly observed and he PPP can be measured indepen of he exchange rae. 5

8 Under he assumpion ha prices of each caegory of labor inpu represen he marginal produc of labor in each counry, he PPP of each ype of labor inpu represens he relaive marginal produc of labor. Labor services in each caegory in boh counries are assumed o be homogeneous, however he marginal produc of he labor can be differen in each counry. Equaion (17) can be also described as, Q x PPP x y saecj = saecj Q y saecj p x saecj p y saecj = PPPx y saecjt p x saecj p y saecj. (17) The PPP in each labor inpu consiss of consan relaive labor qualiy and relaive price index of labor inpu in each counry. In he base year T, he PPP coincides wih he relaive labor qualiy in each caegory. In each labor caegory, he PPP and price indices in each counry are ransiive; PPP x y saecjt = Qx saecj /Qy. If we can observe he PPP only in he base year saecj T, he PPP in any year should be measured by muliplying he relaive price index of labor inpu in each counry. Using he PPP for labor inpu, he qualiy-adjused labor quaniy is measured based on he equaion, L x y saecj = C x saecj PPP x y saecj py saecj = C x saecj p x saecj PPPx y saecjt. (18) An annual labor compensaion in Japan, C J, can be ransformed o he labor compensaion, which is comparable wih ha in he U.S., dividing by he PPP. The ransformed labor saecj compensaion in Japan can be realized o labor quaniy, L J U, which is comparable wih ha saecj in he U.S., L U saecj, dividing by he price of labor inpu in he U.S. Alernaively, CJ can be saecj ransformed o he labor quaniy, L J, dividing by he price of labor in Japan. The labor saecj quaniy in Japan can be realized o L J U, dividing by he PPP in he base year. In each labor saecj caegory, he relaive labor quaniy, which is cross-counry comparable, coincides wih he relaive hours worked. Nex, we formulae an aggregae measure of quaniy, price, and qualiy of labor inpu. Using he qualiy-adjused quaniy and price of each labor inpu, oal labor compensaion in equaion (4) is redifined as, C x y = p x y L x y = saecj p x y saecj Lx y saecj = saecj C x y saecj, (4) where L x y and p x y represens he qualiy-adjused quaniy and price of he aggregae labor inpu, respecively. We formulae he purchasing power pariy for aggregae labor inpu as a Theil-Törnqvis index, PPP x y = exp saecj 1 2 (vx saecj + vy saecj )lnpppx y 6 saecj, (19)

9 where v x is defined in equaion (6). The rae of he PPP for aggregae labor inpu, lnpppx y saecj, is defined as he share weighed rae of he individual caegory PPPs where he shares are an average of each caegory s share of labor compensaion in each counry s aggregae labor compensaion. Also, an aggregae measure of relaive price for labor inpu is described as a Theil-Törnqvis index and simply described as, Rp x y = PPPx y. (20) e x y The aggregae PPP in equaion (19) represens he relaive marginal produc of aggregae labor inpu in boh counries, implicily defined by a common ranslog labor aggregaor funcion. Given he wage srucure in he U.S. and Japan, he aggregae purchasing power pariy, PPP J U, is affeced by he allocaion of workers across caegories in each counry since his allocaion deermines he weigh enering he Divisia calculaion. The smaller he PPP in each caegory, he lower he marginal produc of labor in Japan, relaively. If workers in Japan shif o a caegory of labor, he PPP of which is smaller, he aggregae PPP will decrease since he marginal produc of aggregae labor inpu in Japan will decrease. On he oher hand, if workers in he U.S. shif o a caegory of labor, he PPP of which is smaller, he aggregae PPP will decrease since he marginal produc of aggregae labor inpu in he U.S. will increase. In each caegory, he qualiy-adjused labor quaniy is described as he labor quaniy devided by he base-year PPP; L x y saecj = Lx saecj /PPPx y in equaion (18). The aggregae measures saecjt and L x, are defined by equaion (5) as a Divisia index and heir growh of labor quaniy, L x y raes coincide. So, he aggregae measure of he qualiy-adjused labor quaniy is also derived as he aggregae labor quaniy divided by he aggregae base-year PPP in equaion (19); L x y = L x /PPPx y. The equaion of he aggregae measure defined by he quaniy-side in T (10) can be described as follows, where L x y = Q x y H x, (10) Q x y = Qx PPP x y T. (21) The aggregae measure of labor qualiy in he reference counry is adjused by he aggregae PPP in he base year T, which is defined as a Theil-Törnqvis index in equaion (19). In each caegory, he PPP in he base year T coincides wih relaive labor qualiy. In he special case of PPP x y T = Qx T /Qy, he aggregae labor qualiy in he reference counry equals ha in he base T counry; Q x y T each caegory. = Q y, and hen equaion (10) in aggregae level is similar o equaion (1) in T 7

10 Also, he aggregae measure of simple average hourly labor compensaion in (11) can be derived as, using c x y and p x y, c x y = Q x y p x y. (11) From equaions (10) and (11), we can describe relaive value equaions of he aggregae quaniy and price of labor as, where RQ x y RL x y Rc x y = Qx y Q y, RL x y = RQ x y RH x y, (22) = RQ x y Rp x y, (23) = Lx y L y, RH x y = Hx H y, Rc x y = cx y c y. (24) Reflecing he difference of labor allocaion in boh counries in he aggregae measure of relaive conceps, he relaive aggregae labor quaniy, RQ x y, does no coincide wih he relaive aggregae hours worked, RH x y, and he relaive average per hour compensaion, Rc x y, also does no coincide wih he relaive price, Rp x y in equaion (20). Only in he special case of equal PPPs across all caegories, he relaive aggregae qualiy is uniy and he relaive values coincide in each equaion (22) and (23), ie RL x y = RH x y and Rc x y = Rp x y. In equaion (24), Rc x y is defined as he raio of simple average hourly labor compensaions, which are measured by he base-counry currency, in each counry in equaion (9). Addiionally, we can also define purchasing power pariy as a raio of average hourly compensaion of aggregae labor in boh couries as follows, PPP x y = e x y Rc x y. (25) The alernaive measure of he aggregae PPP in equaion (25) represens he relaive marginal produc of aggregae labor inpu in boh counries, defined by he simple aggregaion. If workers in each counry shif o a caegory of labor, he marginal produc of which is higher, he marginal produc of he simple aggregae labor inpu will increase. So, PPP J U increases in he case of a shif in Japan and decreases in he case of a shif in he U.S. If he PPPs, ha is o say he relaive marginal produciviy, in each caegory of labor are equalized, he wo indices of he aggregae PPP in equaions (19) and (25) coincide. The raio beween he simple aggregae index and he Theil-Törnqvis aggregae index reflecs he gap of relaive marginal produc of labor and allocaion of workers across counries. We define again he cross-counry aggregae qualiy index as, RQ x y = Qx /PPPx y T Q y = PPPx y PPP x y = Rcx y Rp x y = RLx y RH x y. (26) 8

11 In each counry, if he PPPs in each caegory of labor are equalized, he rae of he relaive aggregae qualiy, ln(rq x y ), is zero. If workers in Japan shif o a caegory of labor, he marginal produc of which is higher, he rae of relaive qualiy will be posiive. On he oher hand, if workers in he U.S. shif o a caegory of labor, he marginal produc of which is higher, he rae of relaive qualiy will be negaive. In he base year, he PPP means no only a relaive index of labor price bu also a relaive index of labor qualiy. Comparing wih he wo alernaive aggregae PPPs in he base year, PPP x y T is he relaive qualiy index which does no adjus for he srucural difference of labor allocaions in boh counries; PPP x y T adjused by he relaive aggregae qualiy; PPP x y T of relaive price based on simple aggregaion, PPP x y T o daa consrains. However, hey have biases. = Qx T /Qy. On he oher hand, PPPx y is he index T T = (Qx T /RQx y T )/Qy. The aggregae measures T and Rcx y, are frequenry measured due The growh of he relaive aggregae qualiy is described as he difference beween he growh of he aggregae qualiy in he reference counry and ha in he base counry, as follows, RQ x y RQ x y = Q x Q x Q y Q y (27) From equaions (25) and (26), he growh rae in he relaive price for aggregae labor inpu can be decomposed as, Rp x y Rp x y PPP = x y PPP x y RQ x y RQ x y ėx y e x y. (28) 3 Daa For boh Japan and he U.S., labor inpus are cross-classified by sex, age, educaion, class of worker, and indusry. Since each counry s classificaion is differen, he firs sep is o esablish a common classificaion sysem. The common classificaion sysem allows us o compare homogeneous workers. Afer classifying he workers by sex, we proceed o spli he workers by he oher caegories. The U.S. daase is based on hiry six indusries while he Japan daa is based on foryhree. We creae hiry common indusries based on able 1. One of he difficulies in creaing a common indusry classificaion is he reamen of aciviies by public secors. In he U.S. and Japan daa, some public secor aciviies are included in privae indusries wih similar characerisics. For example, in he U.S., governmen run power auhoriies are classified in he elecric uiliies indusry. One indusry wihou a privae secor counerpar is secor hiryfive, govermen enerprise, which consiss almos enirely of Posal Services. A big difference 9

12 Table. 1 Indusry Classificaion Common U.S. Japan 1 1.Agriculure 1.Agriculure 2 3.Coal Mining 2.Coal Mining 3 2.Meal Mining, 3.Oher Mining 4.Peroleum and Gas, 5.Nonmeallic Mining 4 6.Consrucion 4.Consrucion 5 7.Food Producs, 5.Food Producs 8.Tobacco Producs 6 9.Texile 6.Texile 7 10.Apparel 7.Apparel 8 11.Lumber and Wood 8.Lumber and Wood 9 12.Furniure 9.Furniure Paper Producs 10.Paper Producs Prining and Publishing 11.Prining and Publishing Chemical Producs 12.Chemical Producs Peroleum Refining 13.Peroleum Refining, 14.Coal Producs Leaher Producs 16.Leaher Producs Sone, Clay, and Glass 17.Sone, Clay, and Glass Primary Meals 18.Iron and Seel, 19.Nonferrous Meals Fabricaed Meals 20.Fabricaed Meals Machinery 21.Machinery Elecric Machinery 22.Elecric Machinery Moor Vehicles 23.Moor Vehicles Oher Trasporaion Equipmen 24.Oher Trasporaion Equipmen Precision Insrumens 25.Precision Insrumens Miscellaneous Manufacuring, 26.Miscellaneous Manufacuring 17.Rubber and Plasic 15.Rubber Producs Transporaion 27.Railway, 28.Road Transporaion, 29.Waer Transporaion, 30.Air Transporaion, 31.Sorage Communicaion, 32.Communicaion 35.Govermen Enerprises Elecric Uiliies 33.Elecric Uiliies Gas Uiliies 34.Gas Uiliies Trade 36.Trade Finance, Insurance, 37.Finance and Insurance, and Real Esae 38.Real Esae Services, 35.Waer Supply, 36.General Governmen 39.Educaion, 40.Research, 41.Medical Services, 42.Oher Services, 43.Governmen Adminisraion 10

13 beween he U.S. and he Japan daases is he classificaion of services provided by some oher public secors, like educaion, which is classfied ino he U.S. secor hiry-six, general governmen, bu allocaed o he secor hiry-nine, educaion, wih privae indusries in he Japan daase. To deal wih his inconsisency, we aggregae miscellaneous service secors and governmen adminisraion, and move U.S. governmen enerprises o he common secor weny-five, he communicaions indusry, where Japanese posal services are included. The U.S. daa has eigh age classificaions for workers and Japan has eleven. We choose a common classificaion of six age groups as in able 2. Table. 2 Age Classificaion Common U.S. Japan 1.24 years old and less , , , years old , years old , years old , years old , years old and more In boh counries, class of worker is divided ino wo groups: employed, or self-employed and family workers. However, labor compensaion for he self-employed and unpaid family workers is esimaed differenly in he U.S. and Japanese daases. The U.S. daa assumes ha he hourly wage of he self-employed and unpaid family workers equals he hourly wage of he employed. Esimaes of hours worked muliplied imes he wage for he same caegory of employed worker yields an esimae of labor compensaion for he self-employed and unpaid family workers. In he Japanese daa, wage raes of self-employed workers are impued based on daa available for selec indusries o yield an esimae of labor compensaion for he selfemployed group. Furhermore, he wage differenial beween he self-employed and unpaid family workers is esimaed o be he same as he differenial beween full-ime and parime employees. Because of hese differences, we consider only employed workers when measuring he purchasing power pariy for labor inpu. Finally, workers are classified by he educaional aainmen caegories presened in able 3. The definiion of educaional aainmen daa in he U.S. has changed over ime, bu we make use of work done in oher sudies o creae a ime series. We assemble our ime series from four disinc daases, corresponding o definiional changes of he educaional aainmen variable. From , he daa is based on he 1960 decennial census, and fi using published oals from From 1964 onwards microdaa is inroduced and he second breakpoin is 1980, afer which here is addiional deail on graduae educaion. Prior o 1980, he highes educaion caegory was college degree and above. Afer 1980, more deailed daa allows us o spli workers beween hose wih a college degree, and hose wih some graduae 11

14 Table. 3 Educaion Classificaion Common U.S. Japan Male 1.less han high school 1.elemenary school, 2.less 1.less han high school degree han high school degree degree 2.high school degree 3.high school degree 2.high school degree 3.some college 4.some college 1) 3.professional school 2) 4.college degree and 5.college degree, 6.MA and 4.college degree and above above above Female 1.less han high school 1.elemenary school, 2.less 1.less han high school degree han high school degree degree 2.high school degree 3.high school degree 2.high school degree 3.some college and above 4.some college 1), 5.college, 3.professional school 2) degree, 6.MA and above and above Common educaion classificaion in Phase IV ( ) 1) Some college in he U.S. includes junior college, associae degrees, professional school, and hose aending bu no compleing four-year college. 2) In Japan, some college includes higher professional school, junior college, and is equivalens. Those aending universiies bu no compleing are in 2. level educaion. The hird break poin is in 1992 when he definiion of educaion aainmen in he U.S. changed from being based on years of schools compleed o being based on degree obained. For example, prior o 1992 sixeen years of schooling would be equivalen o a BA degree, bu he redefiniion of he daa in 1992 ells us explicily ha he worker compleed a BA degree. In Japan, here are differen levels of deail for he educaional aainmen of males and females. In he common daase, we use he mos deailed level of daa available in he Japanese daa. Male workers are spli ino four educaional groups, while he women are spli ino wo before 1980 and hree afer Afer cross classifying he daa by each of hese characerisics, we have 1260 groups in oal, 720 groups of male employees, and 540 groups of female employees in he phase of he daase. 4 Aggregae Level 4.1 Relaive Price and Qualiy Esimaed resuls of he purchasing power pariy for aggregae labor inpu are in figure 1(a). In each of he four phases, he PPP a he aggregae level is measured every year. The definiion of educaion caegories are differen among four phases, however here are 12

15 8 2435/6798 D/EFG " # %$& (') * +-,/. 0 1 (a) Purchasing Power Pariy! " # %$& # (') *+,.- / :;+ (b) Relaive Price Fig. 1 PPP and RP for Aggregae Labor Inpu 13

16 only sligh discrepancies observed a he overlap years in 1964, 1980, and Hence, we disregard he differences of each phase. In 1960, he PPP for labor inpu a he aggregae level was less han fify yen/dollar in figure 1(a). The relaive price of labor was jus 0.13 because he exchange rae, fixed in hose days, was hree hundred sixy yen/dollar. The labor PPP increased by 6.4 percen annually in 1960s. From he beginning of 1970s, alhough economic growh in Japan slowed, he price of labor inpu in Japan increased relaive o he U.S. unil Beween 1970 and 1975, he annnual average growh rae of he labor PPP was 9.6 percen, which was higher han ha during he Japanease high growh periods of he 1960s. Afer 1975, he PPP for labor inpu decreased moderaely unil he end of he 1980s. Through he middle of he 1990s, he PPP decreased moderaely, reflecing he Japanese depression. In conras o he moderae movemen of he PPP for labor inpu, he annual average exchange rae was more volaile and he yen exhibied rapid srenghening a few imes over he sample period. The fixed exchange rae beween he U.S. and Japan was loosened a he Smihonian Agreemen in 1971 and moved o he floaing exchange rae sysem in Afer dropping he fixed exhange rae, he annual average growh rae of he relaive price for labor inpu was a very high 12.9 percen during From he middle of 1980s, hrough he Plaza Agreemen in 1985, he Japanese yen srenghened rapidly and he relaive price increased by 9.4 percen annualy unil In 1995, during which he yen recorded is sronges rae of in April, he annual average exchange rae was niney-four yen/dollar, and he relaive price of labor inpu in Japan reached is peak, as i was higher by 28.9 percen. Afer 1995, he relaive price declined o below 1.0, reaching 0.97 in Labor services in Japan were slighly cheaper han in he U.S., given he exchange rae of one hundred eigh yen/dollar in Figure 2 shows he qualiy indices of aggregae labor inpu in he U.S. and Japan. The ime series is consruced using he growh raes of labor qualiy in he individual counries and relaive labor qualiy in 1995 as he difference beween aggregae labor qualiy in he U.S. and Japan. During , he average annual growh rae of he aggregae labor qualiy was 0.33 percen in he U.S. and 0.71 percen in Japan. Since he quaniy of he aggregae labor in boh counries increased by 2.11 percen and 2.17 percen respecively, he qualiy change in each counry conribues 15.5 precen of he growh of labor quaniy in he U.S. and 32.4 percen in Japan. *3 In 1995, he relaive qualiy, RQ J U, was The qualiy of labor in 1995 Japan, which was lower by more han 16 percen relaive o he U.S. in 1960, increased faser *3 Here, we compare labor inpus of employees, because of he difficulies of comparison including self-employed and family workers in boh counries as discussed in previous secion. Considering oal labor inpu during , qualiy change conribues more han quaer of growh of labor quaniy in he U.S. and more han half in Japan. 14

17 Fig. 2 Qualiy and Relaive Qualiy of Aggregae Labor Inpu han he qualiy of labor in he U.S. in he 1960s and was 4-7 percen lower afer Decomposiion of Relaive Price We decompose he growh rae of he relaive price for labor inpu ino he conribuion of he PPP for labor inpu, he relaive qualiy, and he exchange rae, by equaion (28). Figure 3 shows he growh rae of relaive price for aggregae labor, as he circle conneced by a doed line, and is conribuions as he cumulaive bars. Overall, he conribuion of he change in he relaive qualiy, which is he difference of qualiy change and efficiency of allocaion of labor in boh counries, was relaively sligh. However, during he Japanese high growh periods unil he beginning of 1970s, he relaive qualiy had a negaive conribuion o he growh of he relaive price, meaning labor moved in a more efficien direcion in Japan compared o he U.S. in his period, as shown in figure 2. I is imporan o noe ha he increase of relaive price for labor inpu was mainly due o he increase of he labor PPP unil he middle of 1970s, and fuher srenghened by he exchange rae unil Also, we can decompose he change in he relaive price in erms of changes in hourly wages in he U.S. and Japan, as in figure 4. In his figure, higher wages or a change of allocaion of workers owards workers wih a higher wage in he U.S., end o decrease he relaive price of labor inpu. We can clearly see how changes in he work force srucure in Japan increased 15

18 ! "#$%&')(* ' (+ '+,.-0/1$%&'*,-(+' 2 3'4 2 ' Fig. 3 Growh of Relaive Price for Labor and Is Conribuions he growh of he relaive price of labor hrough he early 1970 s and how movemens in he relaive price of labor were dominaed by he exchange rae in he lae 1980 s and early 1990 s. Afer he middle of he 1990s, he growh rae of hourly wage in Japan was very small. On he oher hand, he U.S. growh rae expanded gradually. The wage growh in he U.S. pushed down he relaive price for labor inpu, regardless of yen s srenghening afer Relaive per Worker Price As an alernaive o he relaive price of labor inpu per hour, we consider he relaive compensaion of labor per worker, ha is o say he relaive per worker price for labor, as displayed in figure 5. Over he sample period, he relaive per worker price of labor was higher han he per hour relaive price, reflecing he higher average hours worked per worker in Japan. The figure shows ha while he per hour relaive price of labor inpu in Japan caugh up o he U.S. in 1993, he per worker price caugh up in The figure also shows a decrease in he difference beween he wo measures, reflecing a combinaion of increased average hours worked in he U.S. and a decrease in Japan since he middle of 1990s. In 2000, he per hour price of labor was lower by 2.7 percen in Japan, however, he per worker price of labor was 12.0 percen higher in Japan. This figure emphasizes he viewpoin from he employer s perspecive ha per worker prices in Japan are high, and shows he imporance of including 16

19 ! "# $%!&' (*)+-,%,%. / Fig. 4 Conribuion of Each Counry o he Growh of Relaive Price oal hours worked when considering relaive prices. Comparing he relaive price for gross domesic expendiure by OECD *4 and he relaive per worker price, as in figure 5, shows ha he gap beween he relaive price for GDP exeeded he relaive price for labor over he enire sample. This gap indicaes he difference of real purchashing power beween he U.S. and Japan. Labor income per worker in Japan surpassed he U.S. in 1987, however, he real purchasing power in Japan was beneah ha in he U.S. because of he higher price for domesic expendiure. In 1970, he relaive price for GDP, 0.683, was higher han he relaive price of labor, and he he relaive price per worker, In 1995, when he exchange rae was niney-four yen/dollar, he relaive price for GDP was 1.807, above he relaive price of labor, and he price per worker, By 2000, he gap beween he prices subsided as he relaive price for GDP was 1.443, sill higher han he relaive price of labor, he he price per worker, *4 Annual Naional Accouns - volume I - Exchange Rae, PPPs, and Populaion, Vol 2003 release 02. The daa is available from OECD Naional Accouns Saisics, 17

20 "!#%$&'# ( *)+#-,./0!1#.$&'# "!#324"65178:9:4"; < Fig. 5 Relaive per Worker Price for Labor 4.4 Relaive Price by Sex, Age and Educaion We can compare he purchasing power pariy for labor inpu of differen groups by aggregaing over a subse of he deailed ypes of labor. We derive esimaes of he PPP by sex by aggregaing over age, educaion, and indusry. Formally, in equaion (19) he sex dimension, s, is se o eiher male or female, and we aggregae over he oher caegories. The relaive price of labor inpu by gender is simply he gender specific PPP divided by he annual exchage rae as in eqauion (20). The purchasing power for labor inpu by gender is presened in figure 6. Over he enire sample period he relaive prices of male and female labor inpu followed a similar paern. In 1960 he relaive price for males was 0.14, while he relaive price of females was 0.11, meaning female labor was relaively cheaper in Japan han in he U.S. Boh rended upwards beween 1960 and 1978 as he series converged o 0.69 and 0.68, for males and females, respecively. In 1979 he relaive price of female labor acually was slighly above he relaive price of male labor. From 1979 hrough 1985 he relaive price of boh groups rended downwards, alhough he relaive price of male workers increased slighly in Over he same ime period he relaive price gap opened up a bi, as he relaive price of female labor became cheaper, bu he difference remained small unil From 1985 o 1995, he relaive price of male labor increased rapidly, wih a few downward swings in 1989, 1990, and Over he same ime period, he relaive price of female labor 18

21 Fig. 6 Relaive Price for Aggregae Labor Inpu by Sex inpu increased, bu no as rapidly, and he price acually showed a seep dip in As a resul, he relaive price gap beween male and female labor increased. In he firs half of he 1990s, boh indices crossed 1.0 for he firs ime, he male group did so in 1991, and he female group crossed in Boh series reached heir peak in 1995 when he relaive price of male labor was 1.33 and he relaive price of female labor was From he relaive prices of male and female labor decreased, showed a small increase in 1999, hen seled a 0.99 and 0.93, respecively, in While considering he changes in he relaive prices by gender over ime, i is also imporan o consider he paricipaion raes of male and female workers. In he U.S., he role of women in he workforce became more imporan. The share of women as a share of oal workers, and he share of women who chose o work increased seadily. Paricipaion raes by age changed over ime. Prior o 1970, he age group had he highes paricipaion rae, bu by 1980 he group had he highes paricipaion rae. Furhermore, he effec of child-bearing on he paricipaion rae of women diminished over ime, and by 1990 he were almos no signs of a negaive impac of child-bearing years on he paricipaion rae of women. In addiion o more women workers, he growh rae of labor compensaion of women increased significanly in he lae 1970 s and early 1980 s, oupacing he growh rae of labor compensaion of men. While he role of women increased in he U.S., he role of women in he workforce remained very limied in Japan. Paricipaion raes did no increase a he same rae as in he U.S. and 19

22 gains in wage raes were minimal. However, here does appear o be some evidence ha he changes ha occured in he U.S. in he lae 1970 s and early 1980 s are saring o ake place in Japan. In he period, he growh of labor inpu supplied by women acually exceeded he growh of labor inpu supplied by men. Going forward, if his srucural change is allowed o coninue, and is suppored by policy and insiuional facors, women workers could play a significan role in he fuure growh of he Japanese economy. Fig. 7 Relaive Price for Aggregae Labor Inpu by Age In addiion o consrucing relaive prices of labor inpu by sex, we consuc relaive prices by age in figure 7 and educaion in figure 8. Like he relaive price by gender, he relaives prices of labor inpu by age followed a similar paern over he sample period. Prices increased from , dipped somewha prior o 1985, increased rapidly unil 1995, hen fell off a bi hrough From , he wage group wih he highes relaive price was he group. The and groups, which had very similar relaive prices over ime, were he nex highes. The labor inpu in under 24 and groups was relaively cheaper in Japan han in he U.S., almos over he enire sample period. The relaive price of he eldes group, hose over 65, was high relaive o he oher age groups unil he middle of he 1980s, compared o he period afer he las half of he 1980s when he relaive price of he eldes group was one of he cheapes of all he age groups. 20

23 1 *!"#!!"#! $%&!!!!&!"#!& '() (a) Male!"#! $%!"#!& '() *,+.- $%!"#! * + - %/0!!0 '() * + - (b) Female Fig. 8 Relaive Price for Aggregae Labor Inpu by Educaion 21

24 The relaive price of labor inpu by educaion is ploed in wo panels; (a) and (b) in figure 8, represening he educaional classificaion of males and females. The relaive price of labor inpu by educaion followed a similar paern o he relaive price by gender and age. For males, he relaive price was generally inversely proporional o educaional aainmen. In he years , he male group wih he highes relaive price was hose wih less han a high school degree, while prior o 1985 hose having some college had he highes relaive price. For he female group, he relaive price of labor inpu did no vary much by educaion aainmen in he years From 1960 o 1980, he relaive price of hose in he less han high school group was higher. 4.5 Index Numbers for Relaive Price In his secion, in order o consider he effec of he Theil-Tornqvis aggregaion, able 4 compares he resuls of aggregae relaive price for labor using differen aggregaion schemes. Here, we compare each index number; Theil-Törnqvis; Rp x y, Laspeyres, Paasche, Fisher, Suvel, and simple aggregaion; Rc x y. Since he Laspeyres index is defined by using he weigh of he base-counry, he U.S., i is upward biased. The Paasche index is he opposie case. The Theil-Törnqvis index we acceped is beween he Laspeyres and Paasche and very similar o he Fisher index, which is a simple geomeric average of boh indices. Suvel index numbers saisfy a circular es, which he ohers do no saisfy. The measured Theil-Törnqvis index is also similar o he Suvel index. The index by simple aggregaion; Rc x y was downward biased over he enire sample period. In our erminology, he downward bias means ha he relaive qualiy, RQ x y in a paricular period, beween he U.S. and Japan was over one. The relaive qualiy reflecs ha he labor allocaion in he U.S. was more efficien han ha in Japan. Consequenly, in aggregae measures of relaive price based on simple aggregaion, as is frequenly done due o daa consrains, he PPPs are underesimaed in he case of more efficien labor allocaion in he base counry. Table. 4 Comparison of Indices for Relaive Price Theil-Törnqvis Laspeyres Paasche Fisher Suvel Simple

25 5 Indusry Level Finally, we presen deailed indices of he relaive price of labor by indusry. Figure 9, 10, and 11 show he relaive prices of labor inpu by indusry for 1960, 1970, 1980, 1990, 1995, and In 1960, all of he indusry relaive prices of labor inpu ranged beween 0.0 and The lowes relaive prices were in he Oher Mining, Apparel, Miscellaneous Manufacuring, Consrucion, and Lumber and Wood indusries. The indusries wih he highes prices were Elecric Uiliies and Perolem and Coal, bu here was no much deviaion by indusry. The sandard deviaion was In 1970, he sandard deviaion increased o Oher Mining coninued o have he lowes relaive price, Apparel had he second lowes price, and Prining and Publishing had he hird. Agriculure showed a huge increase in he relaive price of labor inpu, and had he highes price of any indusy in Elecric Uiliies and Coal Mining were he wo indusries wih he nex highes relaive price of labor inpu. From 1970 o 1980, as he exchange rae peg loosened and he yen became sronger, he relaive prices by indusry coninued o increase overall. Agriculure coninued o be he mos expensive in 1980, followed by FIRE, and Elecric Uiliies. Oher Mining coninued o have he lowes relaive price of labor inpu. The variaion of prices by indusry increased, as he sandard deviaion increased o The gap in prices by indusry coninued o grow hrough In 1990, all indusry relaive prices were below 1.0, bu mainained heir upward rend. The Agriculure indusry was surpassed by Communicaion as he mos expensive indusry. Peroleum and Coal, Trade and Coal Mining were indusries wih compariively high relaive prices of labor inpu. Oher Mining coninued o be he relaively cheapes indusry, followed by Transporaion, Precision Insrumens, and Apparel. Beween , as he yen srenghened from o 94.06, mos of he relaive prices of labor inpu were above 1.0, indicaing relaively higher labor coss in Japan. Peroleum and Coal had he highes relaive price of labor inpu, followed by Communicaion, and Trade. Oher Mining, Moor Vehicles, and Precision Insrumens, he only indusries wih a relaive price of labor inpu of less han one, were he indusries wih he lowes relaive price. By 2000, wih he weakening of he yen, he rend owards higher prices had reversed. Nineeen of he hiry indusries had relaive prices below 1.0, wih he lowes in he Oher Mining, Leaher Producs, Precision Insrumens, and Chemical indusries. Of he eleven indusries ha had relaive prices above 1.0, he highes prices were in he Coal Mining and Peroleum and Coal indusries. Looking a he Moor Vehicle and Elecric Machinery indusries, we observe he diversiy of change of he relaive price by indusry. In he Elecric Machinery indusry, he relaive price dropped from 1.16 in 1995 o 0.80 in On he oher hand, he relaive wages for workers in he Moor Vehicle indusry changed, as he average 23

26 E =1*! C F G! " $# %$&' & # () *,++ # -).0/ 1 &02 & % '$ + "' & # ' &'/ #! 1!.3 '$ & # '$.4 &05-1! "'$ & # &09 # # '.: 80; # %$ / &; # <! 8 = <! 8 < ">0! # "! )() # =1? +$ ' # 0@ #.: # ; # #)< A (" # = B, # 9, #"B, # (" & %@ C5=! 6 D # (a) 1960 E =)*! 5C,FG H! " $# %$&' & # () *,++ # -).0/ 1 &02 & % '$ + "' & # ' &'/ #! 1!.3 '$ & # '$.4 &05-1! "'$ & # &09 # # '.: 80; # %$ / &; # <! 8 = <! 8 < ">0! # "! )() # =1? +$ ' # 0@ #.: # ; # #)< A (" # = B, # 9, #"B, # (" & %@ C5=! 6 D # (b) 1970 Fig. 9 Relaive Price for Labor Inpu in Indusry Level(1) 24

27 E =)*! 5C,FG H! " $# %$ &' & # () *,+ + # -).0/ 1 &02 & % '$ + "' & # ' &' / #! 1!.3 '$ & # '$.4 &05-1! "'$ & # &09 # # '.: 80; # %$ / &; # <! 8 = <! 8 < ">0! # "! )() # =1? +$ ' # 0@ #.: # ; # #)< A (" # = B, # 9, #"B, # (" & %@ C5=! 6 D # (a) 1980 E =1*! 5C F< G! " $# %$ &' & # () *,+ + # -).0/ 1 &02 & % '$ + "' & # ' &' / #! 1!.3 '$ & # '$.4 &05-1! "'$ & # &09 # # '.: 80; # %$ / &; # <! 8 = <! 8 < ">0! # "! )() # =1? +$ ' # 0@ #.: # ; # #)< A (" # = B, # 9, #"B, # (" & %@ C5=! 6 D # (b) 1990 Fig. 10 Relaive Price for Labor Inpu in Indusry Level(2) 25

28 E F!G H I J K L M'N0J O M'PQ R S T U V! " #!$% $ &' ( ) +**,'-/. 0 $/1 $ 2 # %! * % $ % $%. 0-3 %! $ %! -4 $/5,0 %! $ " $/9 % -: 8/; ) #!. $; < 8 2 = < 8 < >/ '&' =0? *! % /@ -: ; '< A & * " -/-/ = B+ ) 9+B+ & $ 2 #@ C5= 6 D (a) 1995 E FG H I J K L M'N0J O M0PRQ S T U T T V! " #!$% $ &' ( ) +**,'-/. 0 $/1 $ 2 # %! * % $ % $%. 0-3 %! $ %! -4 $/5,0 %! $ " $/9 % -: 8/; ) #!. $; < 8 2 = < 8 < >/ '&' =0? *! % /@ -: ; '< A & * " -/-/ = B+ ) 9+B+ & $ 2 #@ C5= 6 D (b) 2000 Fig. 11 Relaive Price for Labor Inpu in Indusry Level(3) 26

29 "! #$!% & '! (! #)(+*",!% Fig. 12 Indusry Variaion of Relaive Price for Labor Inpu wage for moor vehicle workers in he U.S. decreased from As a resul, he labor PPP increased. The weakening of he exchange rae ouweighed he increase of he PPP, so he ne effec of he increase of he PPP and he exchange rae was a small decrease in he relaive price of labor inpu from 0.99 in 1995 o 0.94 in Over he ime period he sandard deviaion rended updwards from o in 2000, as seen in figure 12. On he oher hand, he coefficien of variaion decreased over ime, reflecing he convergence of price levels for labor inpu in he U.S. and Japan. From his measure, he indury discrepancy of he relaive price shrinked gradually. 6 Conclusion In his paper, we propose he framework for he cross-counry comparison of labor inpu and measure he relaive price and qualiy and he purchasing power pariy for labor inpu beween he U.S. and Japan during , based on deailed cross-classified labor daa; Jorgenson daa a Harvard Universiy covers he U.S. and Keio Economic Observaory Daabase (KDB) a Keio Universiy covers Japan. We observe: The price of aggregae labor inpu in Japan was slighly less han fifeen percen of ha in he U.S. in he beginning of he 1960s. However, i caugh up he U.S. level in 1993 and he wage raes in boh counries are almos equivalen, when he exchange rae is abou one hundred five yen/dollar, which is he purchasing power pariy for aggregae 27

30 labor inpu in The increase of relaive price for labor inpu was mainly due o he increase of he PPP for labor inpu unil he middle of 1970s, and was fuher srenghened by he exchange rae unil The aggregae qualiy index of labor in Japan, which was lower by more han 16 percen relaive o he U.S. in 1960, increased faser han he qualiy of labor in he U.S. in he 1960s and was 4-7 percen lower afer The labor compensaion per worker, ha is o say he per worker price of labor, in Japan surpassed ha in he U.S. in 1987, six years earier han he caching up period from he viewpoin of he relaive price, reflecing he higher average hours worked per worker in Japan. The relaive price for female labor was relaively lower han ha for male. The gap of he relaive price beween male and female labor shrank during he lae 1970s, however i increased from he beginning of he 1980s. The labor inpu in under 24 and groups was relaively cheaper in Japan han in he U.S., almos over he enire sample period. Afer he las half of he 1980s, he relaive price of he eldes group, hose over 65, was also one of he cheapes of all he age groups. For males, he relaive price was generally inversely proporional o educaional aainmen. In he years , he male group wih he highes relaive price was hose wih less han a high school degree. For he female group, he endency was simliar o males hough he gap is relaively sligh. By compuing aggregae PPP using differen index numbers, we conclude he Theil- Törnqvis index was measured similar o he Fisher index and he Suvel index over he sample period. On he oher hand, he index by simple aggregaion was downward biased over he enire sample period. The purchasing power pariies for labor inpu esimaed in his paper are used for an indusry-level comparison of labor produciviy and oal facor produciviy beween he U.S. and Japan. 28