Female Labor Participation Behavior in Japan: Theory and Evidence. A general equilibrium model is constructed to explain an empirical evidence of the

Transcription

1 Female Labor Partcpaton Behavor n Japan: Theory and Evdence Yoko Furukawa Tomohko Inu Abstract: A general equlbrum model s constructed to explan an emprcal evdence of the lnkage between female labor partcpaton and the busness cycle n Japan. We present a conjecture on why the dscouraged worker effect has become weak n recent Japan. The man mplcaton s that ncome nequalty affects the movement of female labor supply, and wdenng ncome nequalty s a possble cause that leads to the weak correlaton between female labor partcpaton behavor and the busness cycle. JEL classfcaton: E4, J, O4, O53. Key words: female labor partcpaton, busness cycle, housework, ncome nequalty. 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 Chyoda-ku, Tokyo, Japan, E-mal:nu@eco.nhon-u.ac.jp

2 . Introducton In the past recessons, the number of dscouraged workers was large n Japan, and women made up a large share of dscouraged workers. The female labor partcpaton rate tended to move pro-cyclcally to the busness cycle. That s, the female labor partcpaton rate rose when the economy expanded and fell n a recesson. Therefore, the unemployment rate remaned substantally lower than that of other ndustralzed countres. In the current prevalng economc stagnaton, however, the female workers tend to stay n the labor market and the unemployment rate s rsng rapdly. Here, one queston arses. In the past recessons, female workers had a tendency to leave the labor market and engage n housework. Why has the net dscouraged worker effect become smaller n the recent recesson? In other words, what causes a change n the balance between the added worker effect and the dscouraged worker effect n the recent stagnaton n Japan? The trend of female labor supply has been analyzed n many researches. Shmada and Hguch (985) and Tachbanag and Sakura (99) provded emprcal analyses usng Japanese macroeconomc data. Most of the researches about the female labor supply are focused on only the supply sde of female labor whle female labor supply s determned not only by each household decson but also by the wage level offered by the producton sector. In the prevous researches, the demand sde s rarely examned wth a few exceptons ncludng Benhabb et al. (99) and Ros-Rull (993). In ths paper, we combne both the producton sector and the household decson to analyze the relatonshp between the busness cycle and female labor supply n a general equlbrum model as the benchmark of the emprcal works. Then, usng a general equlbrum model, the mechansm of female labor supply can be smply analyzed and an mplcaton of the lnkage between female labor partcpaton and the busness cycle s explctly provded n ths paper. The model n ths paper shows that the role of housework n each household determnes whch effect, the dscouraged or the added worker effect, domnates the economy. See OECD (993).

3 We construct a model that shows the relatonshp between female labor partcpaton and the growth of the economy. One producton sector wth two factors s consdered n ths paper, male and female labors. The framework heavly depends on the analyss provded by Wong (995) that showed how the growth of varous factors contrbutes to changes n the economc envronment n a small and open economy. We examne the household decson of female labor supply by usng the CES utlty functon that was shown n Zabalza (983), consderng each household preference between housework and labor market partcpaton of women. A dstngushng feature of usng the CES functon s that t allows for an easer emprcal analyss, as stated n Zabalza. However, t s not suffcent to focus on the lnkage between female labor partcpaton and the busness cycle to explan the recent change n Japanese female labor partcpaton behavor. We notce that the ncome level of each household that affects the decson of female labor partcpaton s dfferent from the busness cycle that represents the aggregate movement of the economy. Swngs of the busness cycle do not necessarly lead to ncreases or decreases n the ncome level of each household n the equal growth rate. It s worth ntroducng the ncome dstrbuton nto the analyss n order to nvestgate the ssue of female labor partcpaton and the busness cycle theoretcally and emprcally. The most mportant contrbuton n ths paper s that the ncome nequalty s a possble source of the recent change n female labor supply n Japan theoretcally, and our emprcal nvestgaton usng Japanese macroeconomc data supports the theoretcal conjecture. Ths paper suggests that the household preference, whch s determned by the ncome level of each household, may have caused the smaller dscouraged worker effect n the recent recesson. Ths ndcates that the wdenng ncome dstrbuton s a cause that the net effect of unemployment has been changed from past recessons and the recessons n 990s. Tachbanak(998) clamed that there was ncrease n ncome nequalty n the recent Japanese economy, partly due to the asset bubble occurred n the late 980 s. Snce the controversy about the wdenng ncome nequalty exsts, ths paper consders the cross-regonal dfference n the ncome dstrbuton and female labor supply to examne the theoretcal framework. 3

4 The rest of the paper s organzed as follows. In Secton, we explore a basc model and ts mplcatons to descrbe the tendency of female labor supply n Japan. Secton 3 demonstrates a statstcal estmaton by usng Japanese cross-regonal aggregate data to examne adequacy of the theoretcal conjecture descrbed n Secton. The concludng remarks and suggestons of further research are gven n Secton 4.. 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 assumed to partcpate n the labor market, and low-sklled workers choose labor market partcpaton or housework. The aggregate producton functon s gven n the form of Cobb-Douglas functon. That s, θ θ Q = AL L, 0< <, () where Q s aggregate output, and A s the productvty whch represents the level of technology, knowledge captal, and so on. Productvty s treated as an exogenous parameter. It s assumed that all markets n ths economy are perfectly compettve, and prces are perfectly flexble. Let us denote the wage rate of labor by w, and the equlbrum condtons for the two types of labor become as follows. w = θ Q L, w θ ) = ( Q L. () Under perfect competton, frms producng postve outputs earn zero economc proft, whch means, Let Q = wl + wl. (3) yˆ dy y represent the rate of growth of any varable y. Dfferentatng equaton (), (), and (3), and rearrangng terms allow us to obtan Aˆ = θwˆ + ( θ ) w, (4) ˆ Takng nto account that the elastcty of techncal substtuton of the aggregate 4

5 producton functon s equal to -, the change n each wage rate can be wrtten as follows; = Aˆ ( θ )( Lˆ ˆ ), (5) ˆ L w = Aˆ + θ ( Lˆ ˆ ). (6) ˆ L w The economy under analyss has contnuum households measured by one. Each household has L, the amount of labor, and L, the amount of labor. Each household derves utlty from famly ncome (or goods consumpton) and housework. Defne I as the famly ncome and h as the hours of housework by labor. Each household s preference s gven by ε ε ε h U = I +, >0, <, for all, (7) α where and are parameters. The parameter expresses the weght on housework relatve to ncome, whle determnes the elastcty of substtuton of the utlty functon. Usually, preference between consumpton and housework s strongly affected by the wealth level of the household. In ths model the parameter s assumed to represent the scale of household s ncome level 3. Convexty of the ndfference curve requres that <, whle negatve slope s assured f >0. The hours for housework are nterpreted as the hours for cookng or dong laundry nstead of purchasng meals or usng laundry servces n the market, for example. The budget constrant of each household can be wrtten as follows. I w L + w L h ). (8) ( To smplfy the problem, savng s not consdered n ths economy. Labor workers are consdered to be frmly attached to the labor force over tme, and labor workers, who are low sklled and mostly consst of females, are consdered to allocate ther tme to work or to do housework. These assumptons are mposed to capture the household decson easly. The maxmzaton of (7) subject to (8) wth respect to h and I gves the resource allocaton functon of each household 3 Ths assumpton s renforced by the statement of Pssardes (000, p.70). 5

6 h I = ε ( α w ). (9) The behavor of labor s characterzed n terms of a crtcal housework-ncome rato. A labor ndvdual wll partcpate n the labor market 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, t s defned as ( X ) α = exp, (0) where X s a random varable, whch s assumed to be normally dstrbuted wth zero mean and varance σ, ~ N( 0, σ ) X. Now, denotng α = { } α, can also be thought as the parameter whch expresses the ncome dstrbuton. In ths paper, the defnton of asset ncludes human captal as well as non-human captal such as money and land. It s natural to consder the asset dstrbuton to analyze the decson of the labor supply n each household, because usually, the preference of each household s nfluenced by ts wealth, and the decson of labor to engage n housework or to work depends on the levels of household ncomes and ther own assets. A labor ndvdual 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, the non-partcpaton rate of labor, denotng P(NP), can be expressed as follows. [( h I ) ( L w )] P( NP) = prob L. () Substtutng (9) and (0) nto (), the non-partcpaton rate can be wrtten as ( ) P ( NP) = F, () Y NP where F( ) s the standardzed cumulatve normal dstrbuton functon, and YNP s defned as Y NP [( ε )ln w + ( ε)ln L ln w ( ε) L ] = ln. (3) σ Then, the change n the non-partcpaton rate can be wrtten as follows: dp( NP) = f NP ε w σ ( Y ) {( ) w } ˆ ˆ, where f ( Y ) = df( Y ) dy. From the assumpton of ε<, t s easy to see that the 6

7 non-partcpaton rate s ncreasng n w and decreasng n w. Now we can 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 lnkage between the growth of 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, that s, L ˆ = 0 n ths model. The aggregate amount of supply of labor should be equal to demand n the producton sector, and t s gven as follows, L = ( L ) h d, (4) NP where NP s defned as { ( h I ) ( L w )} aggregate supply of labor s measured by, dl = NP dh d α NP =. Usng Lebnz rule, the growth of L = NP ( L h ) ( ) I wˆ wˆ wˆ w h d w w L + wl ˆ ε w L + wl. (5) By usng (5), (6), and (5), we have Lˆ ε = C Aˆ 0, (6) ε where C 0 NP I h d ( w L w L ) L NP + w ( L h ) h ε ( θ ) I h d + ( w L + w L ) L ε ( w L + w L ) NP L d, and C 0 > 0. 4 Also, the lnkage between the non-partcpaton rate of labor and the ε ( θ ) 4 Remember 0< < and ε<. In ths case, 0 < < ε w ( L h ) h w ( L h )( h L + L ) d = d w L + w L L w L w L L ( ) ( ) NP NP + and 7

8 growth of productvty can be solved by usng (5) and (6), that s, ε dp( NP) = C Aˆ, (7) σ where C w ( L h ) h I h d ( w L + w L ) L ( w L w L ) = f ( YNP ) d, L NP NP + C > 0. Equaton (7) descrbes the response of the household sector to a fluctuaton of the economy. Consderng both the demand sde and the supply sde of female labor, we can evaluate a smple relatonshp between female labor partcpaton and the productvty growth n the economy. The relatonshp s affected by the parameters and σ. In the case where 0< <, 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. Ths s called the dscouraged worker effect. If s negatve, and goods consumpton and housework are less substtutes for the household, the female labor partcpaton rate moves opposte to the productvty growth. Ths s known as the added worker effect. In addton to that, a smaller σ enlarges the nfluence of the productvty growth upon the female labor partcpaton rate. Ths suggests that the partcpaton rate wll change more when σ s small and less f σ s large. Ths parameter represents the degree of the ncome dstrbuton n ths model. For nstance, when s postve, the dscouraged worker effect becomes large n a recesson f the ncome nequalty s slght (σ s small), and n contrast to that, the dscouraged worker effect becomes small f the ncome dstrbuton s wdely spread. The characterzatons of the relatonshp between labor supply and the productvty growth descrbed above comes from the followng mechansm of household = NP w ( L h ) wl d + ( w L + wl ) L w L + wl Thus, 0 C should be postve n ths model. However, an excepton would arse f the elastcty of techncal substtuton of the producton functon s very small. That s, the producton functon s dfferent from the one n ths paper. In that case, there s a set of the elastcty of techncal substtuton and the elastcty of substtuton between consumpton and housework that causes the coeffcent C0 to be negatve.. 8

9 utlty dervaton. In ths model, ncome s consumed for goods consumpton only and savng s not consdered. The consumpton-housework rato represents the labor resource allocaton n the household over the busness cycle. If s postve and 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 of consumpton goods n a market 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. Therefore, the dscouraged worker effect appears. However, f s negatve, sustanng the ncome level s mportant when the economy s n the recesson. Low-sklled workers tend to partcpate n the labor market rather than to conduct housework, and the consumpton-housework rato ncreases and the added worker effect appears n ths case. Notably, the parameter σ, whch s nterpreted as the ncome nequalty, affects the partcpaton behavor of labor. When the ncome dstrbuton s wdely spread, the net effect of the productvty growth upon the partcpaton rate of labor s small and vce versa. Accordng to equaton (7), σ determnes the scale of the mpact by the busness fluctuaton on labor. The parameter σ can be consdered as a multpler that mples the relatonshp between the busness cycle and partcpaton of labor. That s, the smaller σ enlarges the net effect of the productvty growth on the partcpaton rate, and the partcpaton decson s not strongly nfluenced by a productvty shock when σ s large. Ths characterzaton can be explaned by the followng mechansm. The threshold that determnes the labor partcpaton decson of labor becomes narrow when the ncome nequalty s large. The productvty shock does not have an mpact strong enough to change the partcpaton behavor of labor f the ncome dstrbuton s wdely spread. For nstance, a rch household remans rch and a poor household remans poor even f there s a productvty shock n the economy that causes the changes n wage levels of both labor and labor, and t s exactly mddle class households that are strongly nfluenced by the economc stuaton. There s a small number of households that reconsders labor s behavor dependng on the busness fluctuaton when the ncome dstrbuton s large. In 9

10 contrast to that, many workers who are labor may swng between engagng n housework and partcpatng n the labor market when the ncome dstrbuton s small and there are many mddle class households n the economy. Also, t should be carefully noted that not σ but determnes whch effect, ether the dscouraged worker effect or the added worker effect, domnates the economy, and σ s the parameter that enlarges the net effect whch s determned by. The model has mplcatons about emprcal evdence of the recent change n the lnkage between female labor supply and the busness cycle. The theoretcal framework suggests that the wdenng ncome dstrbuton may be a possble cause that has lead to the recent change n female labor partcpaton behavor, n whch female labors tend to reman n the labor market despte the economc stagnaton. The wdenng ncome nequalty has caused many mddle class households to be poorer, whch forces many female labor to be nvolved n the labor market even when the busness cycle moves downward n the economy. The model also suggests that the substtuton between goods consumpton and housework has changed from the past recessons to the current recesson, whch may be a cause that led the added worker effect to exceed the dscouraged worker effect n the recent recesson. Ths ndcates that goods consumpton and housework are gettng less substtutve n the economy. For example, n the past, a housewfe sewed a shrt nstead of purchasng one n the market, but nowadays sewng a shrt s no more a part of housework. As a result, there s no choce but to go to a shop to look for a shrt. To sustan the ncome level s more valuable than to engage n housework n an economc stagnaton n recent Japan. Estmaton of the female labor force partcpaton rate On the bass of the theoretcal model constructed n the prevous secton, we proceed to nvestgate the effect of ncome dstrbuton on the female labor force partcpaton rate. The estmaton perod s 990 to 999. There were major revsons of the Equal Employment Opportunty Law Between Men and Women n 985 and 999, and by lmtng the estmaton perod to the 990s, we hope to avod that the estmaton results are heavly nfluenced by these large nsttutonal changes. Panel data for nne Japanese regons (Hokkado, Tohoku, Kanto, Hokurku, Toka, 0

11 Knk, Chugoku, Shkoku and Kyushu), over the ten-year perod s the bass for the emprcal nvestgaton. 5 The dependant varable n our model s the log of the change n the female partcpaton rato, denoted by LDFPt. The rato s calculated as the female labor force dvded by the female populaton aged 5 and older. 6 We consder three dependant varables: the log of the ncome dstrbuton (denoted by LGINIt), the year-on-year change n the job openngs/applcatons rato (denoted by DJOBt), and the annual macro-economc Total Factor Productvty (TFP) growth rate (denoted by GTFPt). We calculated Gn coeffcents for each regon usng data from the Survey of Household Economy (sc) and use these coeffcents as proxes for the ncome dstrbuton n the regons. The job openngs/applcatons rato n each regon s calculated usng data from the Report on Employment Servce (sc) and s ncluded n our model to capture short-run varatons n the demand-supply gap. The TFP growth rate s drectly taken from Hayash & Prescott (00). 7 Our basc model ncludng these varables s gven by the followng equaton: LDFPt= LGINIt+ DJOBt+ GTFPt Based on the theoretcal model presented n the prevous secton, we expect a negatve ncome dstrbuton coeffcent. In addton to that, t s assumed to obtan postve coeffcents on both the job openngs/applcatons rato and the TFP growth rates, accordng to the prevous researches. 8 We estmated three types of equatons, as shown n table, and all equatons are estmated usng both the fxed ( wthn ) and the random effect methods. The last column n the table gves Hausman test results and from these results, we can conclude that the random effect method s the approprate estmaton. All the coeffcents have the expected sgns, and notably, the 5 A lst of the prefecture ncluded n each of the regons and more detals of the data used n the model can be found n the Appendx. 6 Because we cannot take the log of a negatve number, s added to all the calculated changes n the ratos. 7 Ths s the macro TFP growth rate, snce regonal TFP growth rates are not avalable. 8 See Shmada and Hguch (985), Tachbanag and Sakura (99), and Can (966).

12 coeffcents on ncome dstrbuton are statstcally sgnfcant. Hence, we conclude that the wdenng ncome dstrbuton had a negatve mpact on the female labor partcpaton rato n Japan durng the 990s. Hausman test Equaton number LGINI t DJOB t GTFP t GTFP t- (CHISQ). Concludng remarks Ths paper has provded a theoretcal and emprcal analyss on female labor supply and the growth of productvty n a closed economy to analyze the emprcal facts on the recent change n female labor partcpaton. Income nequalty s the key to understandng the lnkage between female labor partcpaton behavor and the swngs of the economy. Recently n Japan, the labor partcpaton rate, partcularly the female labor partcpaton rate, has not declned snce the 990s. Ths ndcates that the dscouraged worker effect has not strongly domnated n the economy, unlke from the prevous recessons. Accordng to the model provded n ths paper, t may be possble to state that the wdenng ncome dstrbuton s a cause to weaken the dscouraged worker effect n the recent prevalng recesson. The model s estmated by usng Japanese cross-regonal data on partcpaton, on the busness cycle, and on ncome nequalty n the 990s to provde a check on the result obtaned n the theoretcal framework. The emprcal analyss shows that small ncome nequalty enlarges the dscouraged worker effect. Ths ndcates that the

13 theoretcal conjecture s vald n understandng the recent change n female labor partcpaton behavor. The theoretcal framework provded n ths paper wll help us to understand female labor supply and the recent hgh unemployment rate n Japan. Hopefully the model constructed n ths paper wll be useful n understandng the ssues of the productvty growth and female labor partcpaton behavor n other ndustralzed countres. References J. Benhabb, R. Rogerson, and R. Wrght (99) Homework n Macroeconomcs: Household Producton and Aggregate Fluctuatons, Journal of Poltcal Economy, vol. 99 no. 6, G. G. Can (966) Marred Women n the Labor Force: An Economc Analyss, The Unversty of Chcago Press. F. Hayash (000) Econometrcs, Prnceton Unversty Press. F. Hayash and E. Prescott (00) The 990s n Japan: A lost decade, Revew of Economc Dynamcs, 5, Y. Hguch (00) Economcs of Employment and Unemployment, Nhonkezashnbunsha Tokyo. (n Japanese) OECD Employment Outlook, Pars. Pssardes (000) Equlbrum Unemployment Theory, second edton, MIT Press, 000. J.-V. Ros-Rull (993) Workng n the Market, Workng at Home, and the Acquston of Sklls: A General-Equlbrum Approach, The Amercan Economc Revew, vol. 83 no.4, H. Shmada and Y. Hguch (985) An Analyss of Trends n Female Labor Force Partcpaton n Japan, Journal of Labor Economcs, vol.3 no., s T. Tachbanak (998) Dstrbuton of Economc Well-beng n Japan, Iwanam-shoten, Tokyo. (n Japanese) T. Tachbanak and K. Sakura (99) Labour Supply and unemployment n Japan, European Economc Revew, 35,

14 R. H. Topel. (997) Factor Proportons and Relatve Wages: The Supply-Sde Determnants of Wage Inequalty, Journal of Economc Perspectves, vol., no., K. Wong (995) Internatonal Trade n Goods and Factor Moblty, MIT Press. L. M. Wooldrdge (00) Econometrc Analyss of Cross Secton and Panel Data, MIT Press. A. Zabalza (983) The CES Utlty Functon, Non-Lnear Budget Constrants and Labour Supply: Results on Female Partcpaton and Hours, The Economc Journal, 93, 3-3. Appendx Female Labor Force Partcpaton Rato = (Female Labor Force by regon)/(female Populaton aged 5 years and older by regon) Data Source: Labour Force Survey, Statstcs Bureau, Mnstry of Publc Management, Home Affars, Posts and Telecommuncatons. Job Openngs/Applcatons Rato = (Actve job openngs by regon)/(actve applcatons by regon) Data Sources: data for : annual (Fscal year) data from Yearbook of Labour Statstcs, Mnstry of Health, Labour and Welfare. data for annual (calendar year) data from Todofuken no Ksotoke 998 (Basc Statstcs by Prefecture), Statstcal Informaton Insttute for Consultng and Analyss. Fscal year data for s converted nto calendar year data by applyng the followng equaton: Xcalendar(t) = Xfscal (t )*(9/) + Xfscal (t)*(3/). Gn Coeffcent = 0.*( *A+ *B + *C + *D + ) 4

15 where A = average annual earnngs wthn the ncome category sum of average annual earnngs of all ncome groups; B sum of average annual earnngs wthn the ncome categores and sum of average annual earnngs of all ncome groups; C sum of average annual earnngs wthn the ncome categores,, and sum of average annual earnngs of all ncome groups; D = sum of average annual earnngs wthn the ncome categores,,, and sum of average annual earnngs of all ncome groups. Data Source: Survey of Household Economy, Statstcs Bureau, Mnstry of Publc Management, Home Affars, Posts and Telecommuncatons. TFP growth rate Data Source: Hayash & Prescott 00 Regonal Classfcaton Regon Prefectures Hokkado Hokkado Tohoku Aomor, Iwate, Myag, Akta, Yamagata, Fukushma Kanto Satama, Chba, Tokyo, Kanagawa, Ibarag, Tochg, Gunma, Yamanash, Nagano Hokurku Ngata, Toyama, Ishkawa, Fuku Toka Gfu, Shzuoka, Ach, Me Knk Shga, Kyoto, Osaka, Hyogo, Nara, Wakayama Chugoku Tottor, Shmane, Okayama, Hroshma, Yamaguch Shkoku Tokushma, Kagawa, Ehme, Koch Kyushu Fukuoka, Saga, Nagasak, Kumamoto, Ota, Myazak, Kagoshma, Oknawa Note) In our calculaton of the Gn coeffcent for Kyushu, we dd not nclude data for Oknawa prefecture because we were unable to fnd an approprate weght for the aggregaton. 5