In the 1990s, Japanese economy has experienced a surge in the unemployment rate,

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1 Productvty Growth and the female labor supply n Japan Yoko Furukawa * Tomohko Inu Abstract: In the 990s, Japanese economy has experenced a surge n the unemployment rate, and ths s due partly to the recent change n the structure of the female labor supply. In the past recessons, female workers tended to be dscouraged from partcpatng n the labor market and ths made the Japanese unemployment rate substantally lower than that of the other ndustralzed countres. In the current prevalng economc stagnaton, female workers tended to stay n the labor market, and ths caused the economy to experence a hgher natural unemployment rate. We develop a one-sector model wth two factors of producton, and the female worker chooses ether to partcpate the labor market or to supply housework servces. Our model shows that the change n the degree of the elastcty of consumpton wll contrbute to the ncrease n the female labor partcpaton rato under the economy s stagnaton, and suggests that the role of housework servces n each household has changed n recent years. JEL classfcaton: E4, J, O4, O53. Key words: female labor partcpaton, productvty, added worker effect, dscouraged worker effect. * Yoko Furukawa: The offcal name s Yoko Tsuda. Graduate school of Economcs, Unversty of Tokyo Hongo, Bunkyo, Tokyo, Japan E-mal: ee707@mal.ecc.u-tokyo.ac.jp Tomohko Inu College of Economcs, Nhon Unversty -3- Msakcyou Cyoda-ku, Tokyo, Japan, E-mal:nu@eco.nhon-u.ac.jp

2 . Introducton In the 990s, the Japanese economy has experenced the prolonged economc stagnaton and the hghest level of the unemployment rate. Though t s natural that the unemployment rate rses n the economc stagnaton, the unemployment rate n Japan stayed at a lower level n the past recessons, compared to other ndustralzed countres. Ths s partly due to the structure of the female labor supply. In Japan, the number of the dscouraged workers was large, and dscouraged workers mostly conssted of females. The female workers had a tendency to be dscouraged from partcpatng n the labor market n the past recesson and ths made the Japanese unemployment rate substantally lower than that of the other ndustralzed countres. However, n the current prevalng economc stagnaton, the female workers tend to stay n the labor market and the unemployment rate begn rsng rapdly. One queston arses now. In the past recesson, female workers tend to leave the labor market and engage n housework. Why does the net dscouragement effect become smaller n the recent recesson? In other words, what causes the added workers effect larger that the dscouraged workers effect n the recent stagnaton than the cases n the prevous recessons n Japan? The controversy aganst the added and dscouraged workers effects was shown n Can (966). He provded the emprcal analyss of the net effect of unemployment by usng data from each census year for 940, 950, and 960 for the U.S. Hs emprcal test suggested that the dscouraged workers effect exceeded the added workers effect n the Unted States. A smlar result appeared n Hguch (00), that the dscouraged workers effect was larger than the added workers effect n the past recessons n Japan. However, Hguch also ponted that recently the female labor partcpaton rate does not fall compared to the past recesson although the labor demand declned n the recent recesson. We wll provde why the there s a net effect of unemployment changes from past recessons and the recessons n 990s. Zabalza (983) estmated the female labor partcpaton n Brtan by usng the CES utlty functon. He showed the household decson of the female labor supply by See OECD (993).

3 consderng the choce between housework and labor market partcpaton. Then he provded a functon of the female labor partcpaton rate that allows for easer emprcal analyss. However, most of the researches about the female labor supply examned only the supply sde of female labor. It means that the lnkage between the busness cycle and female labor partcpaton has not been examned theoretcally. In ths paper, we try to analyze the relatonshp between the productvty of the producton sector and the household decson of the female labor supply theoretcally and emprcally. We wll show that the decson of the female labor supply determnes the role of housework n each household, and suggests that the change of the role of housework may be one of the reasons that the dscouraged worker effect s smaller n the recent recesson. We had to develop a model that shows the relatonshp between female labor partcpaton and the growth of the economy. In ths paper, we develop a one-sector model wth two factors of producton, male-female labor. The framework heavly depends on the analyss provded n Wong (995). It shows how the growth of varous factors contrbutes the economc envronment n a small and open economy by usng a two-factor, two-sector model. The explanaton of the Japanese economy s recesson n terms of productvty was formalzed by Hayash and Prescott (000) wth one-sector aggregate model. They argued that slackenng productvty growth s the cause of the Japanese economc recesson. Thus, we consder the sluggsh productvty growth to be the cause of the stagnaton of the economy, and examne the relatonshp between female labor partcpaton and the growth of the Japanese economy. Secton provdes the basc model and ts mplcatons. The concludng remarks and suggestons of further research are gven n Secton 3.. The Model The economy s endowed wth fxed amounts of two types of homogeneous labors, labor and labor. Denote the endowments of labor and by L and L respectvely. Labor s thought to be a hghly sklled worker, and labor s thought to be a low-sklled worker, mostly consstng of female workers. All hghly sklled workers are 3

4 assumed to partcpate n the labor market, and low-sklled workers choose labor market partcpaton or housework. The aggregate producton functon s gven as; Q = AF L, L ), () ( where Q s aggregate output, and A s the productvty whch represent levels of technology, knowledge captal, and etc. Productvty s treated as an exogenous parameter. The producton functon s ncreasng, concave, lnearly homogeneous, and dfferentable n nputs up to the necessary order. It s assumed that markets are perfectly compettve, and prces are perfectly flexble. Let me denote the wage rate of labor by w, and the equlbrum condtons for the two types of labor become as follows. w F = A, (=, ) () L Under perfect competton, frms producng postve outputs earn zero economc proft, whch means, Q = w L +, (3) Let wl yˆ dy y represent the rate of growth of any varable y. Dfferentate equaton (), (), and (3), and rearrange terms to obtan Qˆ = Aˆ + θlˆ + ( θ ) Lˆ, (4) 0 = Aˆ + θwˆ + ( θ ) w, (5) ˆ where θ s labor s share n the producton technology, that means θ w L Q. The assumpton of a zero-economc proft condton requres θ +θ. Defne s as the = elastcty of techncal substtuton of the aggregate producton functon, then the changes of each wage rate can be wrtten as follow; w = Aˆ + ( θ )( Lˆ Lˆ ) s, (6) ˆ w = Aˆ θ ( Lˆ Lˆ ) s. (7) ˆ Now we turn to the household problem. There s a contnuum of households of total measure one. Each household has L, amount of labor, and L, amount of labor. The household derves utlty from famly ncome (or goods consumpton) and The elastcty of techncal substtuton s negatve n a usual producton functon. 4

5 housework. Defne I as the famly ncome and h as hours of housework by labor. Each household preference s gven by ε ε h U = I + α, >0, <, (8) where and are parameters. The parameter expresses the weght on housework relatve to ncome. The budget constrant of each household can be wrtten as follows. I w L + w L h ). (9) ( To smplfy the problem, savng wll not be consdered n ths economy. Labor workers are consdered to be frmly attached to the labor force over tme, although labor workers, who are low-sklled and mostly consst of females, are consdered to allocate ther tme to work or to housework. Then, maxmzng (8) subject to (9), we have h I = αw ε. (0) The behavor of each labor s characterzed n terms of a crtcal housework-ncome rato. An ndvdual who s labor wll go to work f the housework-ncome rato s smaller than L w L. Let us ntroduce a stochastc varaton of the model n the parameter. Snce must be a postve parameter, we defne α = exp(x ), () where X s a random varable, whch s assumed to be normally dstrbuted wth zero mean and varance, σ X ~ N( 0, σ ). Now, can also be thought as the parameter whch expresses the ncome or wage dstrbuton. It s natural to consder the ncome or wage dstrbuton to analyze the decson of household labor supply, because usually, the wves decson to be housewves or to work may depend on the levels of household ncome. An ndvdual who s labor wll not partcpate n the labor market f her housework-ncome rato, assumng that the wage rates are gven for each household, s bgger than L w L. Therefore, denotng P(NP) as the non-partcpaton rate of labor, we have [( h I ) ( L w ] P( NP) = prob L ). () 5

6 Substtutng (0) and () nto (), the non-partcpaton rate can be wrtten as ( X NP P( NP) = F ), (3) where F( ) s the standardzed cumulatve normal dstrbuton functon, and XNP s defned as X NP ln L + ln w ln w ln L. (4) σ ε = The change of the non-partcpaton rate can be wrtten as follows: dp( NP) = f ( X ) ˆ + ˆ NP w w, σ ε where f ( X ) = df( X ) dx. From the assumpton of ε<, t s easy to see that the non-partcpaton rate s ncreasng n w and decreasng n w. Now we would lke to nvestgate the relatonshp between the swngs n the busness cycle and the supply of labor by combnng the producton sector and the household sector. To examne the relatonshp between the growth of the productvty n the economy and the partcpaton rate of labor, we have to calculate the aggregate labor supply. The aggregate supply of labor s L because all the ndvduals who are labor are thought to spend all of ther tme workng to earn ncome. Thus, n ths model. The aggregate amount of supply of labor should be equal to the demand n the producton sector, and t s gven as follows, X NP ( X ) L = F dx. (5) 3 Lˆ = 0 Then, usng Lebnz rule, the ncrease of the aggregate supply of labor s, dl = F ( X ) dx NP NP, λ and, defnng L L, the change rate can be wrtten as, Lˆ ( P( NP) ) wˆ w σ ε = ˆ λl By usng (6), (7), and (6), we have. (6) 3 To be exact, the aggregate supply of labor can be wrtten as follows, L L L X ( ) = [( ) ( )] ( ) NP X ( h ) dh L h F X ( h ) F X ( h dh = F( X ) 0 L = h f ) 0 0 dx. 6

7 ηl ˆ ε = Aˆ, (7) ε λl where η σ ( P( NP) ) ε( θ ) s( ) ε and η > 0. 4 Also, the relatonshp between the non-partcpaton rate of labor and the growth of productvty can be solved by usng (6) and (7), that s, dp( NP) = f ( X ) NP η ˆ L λl ( P( NP) ) ε ( ) ˆ f ( X NP ) λl = A. (8) ε η P( NP) What s nterestng s that the relatonshp between the partcpaton of labor and the growth of the productvty s determned by the parameter, whch ndcates the elastcty of substtuton between goods consumpton and housework, that s, /(- ). In the case where 0< <, the goods consumpton and housework are substtutes, and the postve growth rate of the productvty n the economy leads to a ncrease n the labor nvolvng n the labor market. If s negatve, and the goods consumpton and housework are less substtutes for the household, the growth of productvty n the economy leads to an ncrease n the number of housewves. In other words, f s postve, the dscouraged workers effect exceeds the added workers effect, and f <0, the added workers effect s larger than the dscouraged workers effect. The mplcaton behnd ths fact s as follows. In ths model, all the ncome s consumed for goods consumpton. Thus, the consumpton-housework rato allows us to examne the labor resource allocaton n the household over the busness cycle. If s postve and the goods consumpton and housework are substtutes for the household, the consumpton-housework rato wll declne when the wage level falls compared to the prce level when the economy s n the recesson. As the result, the partcpaton rate of labor decreases, and the labor force moves toward the household sector to equalze the margnal utltes. Thus, the dscouraged workers effect appears. However, f s negatve, to sustan the ncome level s mportant when the economy s n the 4 Remember s<0, 0<θ<, and ε<. 7

8 recesson, then low-sklled workers tend to partcpate n the labor market rather than conductng housework. Therefore, the consumpton-housework rato ncreases and the added workers effect appears n ths case. It s notable that the relatonshp between the low sklled or female labor supply and the busness cycle s determned by the elastcty of goods consumpton and housework. In ths case, the elastcty can be consdered to be the role of housework n the household. To descrbe t smply, the household can derve utlty from ether goods consumpton or housework servces f 0< <. However, f <0, both goods consumpton and housework servce are necessary to derve utlty. Therefore, the role of housework becomes mportant n examne the ssue of the female labor supply. The dscouraged workers effect lowers unemployment rate n the recesson. In contrast, the unemployment rate wll be hgher when there s more added workers effect because the labor supply expands although the labor demand may shrnk because of the stagnaton n the economy. The model n ths paper provdes that the elastcty of substtuton between housework and goods consumpton determnes the net effect of the female labor partcpaton. Ths suggests that changes n the role of housework servces n each household also brng about a change n the net effect of the female labor supply. Then, the tendency of the unemployment s affected by the role of housework servces. Also, notce that the parameter σ affects the partcpaton rate of labor. The partcpaton rate wll change more when σ s small and less f σ s large. Ths parameter represents the degree of the ncome or wage dstrbuton n ths model. For nstance, when s postve, the dscouraged worker effect becomes large n a recesson f the ncome dfference s slght (σ s small), and n contrast to that, the dscouraged workers effect becomes small f the ncome dfference s large. Ths s because the number of so called the mddle class households decreases when the ncome varance becomes large, and the mddle class households are the most strongly affected by the change of the ncome. The choce of the mddle class household s the threshold that determnes the partcpaton rate of labor.. Concludng remarks 8

9 Ths paper has provded a theoretcal analyss on the female labor supply and the growth of productvty n a closed economy. The role of housework servces s the key to determne the female labor partcpaton n the swngs of the economy. The dscouraged workers effect s often observed n the Japanese economy and t leads to a low unemployment rate durng the past recessons. Recently n Japan, however, the unemployment rate has rsen gradually because of Japanese economy has stagnated n the 990s. Ths s partly because the labor partcpaton rate, especally the female labor partcpaton rate, dd not declne n the 990s, that means, the dscouraged workers effect becomes smaller, dfferent from the prevous recessons. Accordng to the model provded n ths paper, t mght be possble to state that the role of housework servces becomes less substtutable for goods consumpton. Although no emprcal analyss s provded, the theoretcal framework provded n ths paper wll help us to understand the female labor supply and the recent hgh unemployment rate n Japan. In addton, ths paper shows that the ncome dstrbuton affects the degree of the net effect of the female labor supply. The net effect, ether added workers effect or dscouraged workers effect becomes nsgnfcant when the ncome varance s small. There s an observaton that ncome dfference becomes large n recent Japan. It also mght be the reason why the female workers tend to stay n the labor market n contrast to the tendency n the past recessons. In the next paper, we wll emprcally examne hgh unemployment rate, the female labor supply, and the change of the role of housework servces n Japan. Further analyss of these ssues wll be shown together n the next paper. References G. G. Can (966) Marred Women n the Labor Force: An Economc Analyss, The Unversty of Chcago Press. F. Hayash and E. Prescott (00) The 990s n Japan: A lost decade, Revew of Economc Dynamcs, 5 Y. Hguch (00) Economcs of Employmen t and Unemployment, Nhonkezashnbunsha Tokyo. (n Japanese) 9

10 K. Matsuyama (99) Agrcultural Productvty, Comparatve Advantage, and Econom c Growth, Journal of Economc Theory, 58. OECD Employment Outlook, Pars. R. H. Topel. (997) Factor Proportons and Relatve Wages: The Supply-Sde Determnaton of Wage Inequalty, Journal of Economc Perspectves, vol., no.. K. Wong (995) Internatonal Trade n Goods and Factor Moblty, MIT Press. A. Zabalza (983) The CES Utlty Functon, Non-Lnear Budget Constrants and Labor Supply: Result on Female Partcpaton and Hours, The Economc Journal, 93. 0