Female Employment and Structural Transformation

Transcription

1 Female Employment and Structural Transformation Rachel L. Ngai London School of Economics and CEP (LSE) Barbara Petrongolo Queen Mary University and CEP (LSE) February 2012 Abstract The rise in female participation to the labor market and the labor reallocation from manufacturing to services are two of the most remarkable stylized facts of the post-war period. Motivated by these facts, we propose a model of labor allocation across three sectors: goods, services and home production, in which women have a comparative advantage in the production of services, both in the market and in the household. Productivity growth is faster in market sectors than in home production, and, within the market, it is faster in manufacturing than in services. Goods and services are poor substitutes, which gives rise to structural transformation. On the other hand, market services are good substitutes to home production, which drives marketization. Realistic differences in productivity growth across sector can predict an important share of the rise in women s market hours, the rise of services in the economy and the marketization of home production. 1

2 1 Introduction One of the most remarkable changes in labor markets since World War II is the rise in female employment rate. For example, in the US the employment rate of prime age women has more than doubled from about 35% in 1945 to 77% at the end of the century (see also figure 1 for the pattern across OECD countries during ). These developments have generated a large literature on the causes, characteristics and consequences of the increase in female involvement in the labor market. The main explanations put forward include a number of "supply-side" stories, and namely introduction of oral contraceptives (Goldin and Katz, 2002), cheaper home appliances (Greenwood et al., 2005), changes in society s views about the role of women s work (Fernandez et al., 2004), and the increase in the return to experience for women (Olivetti, 2006). During the same period, another dramatic change in labor markets across OECD is the reallocation of labor from manufacturing into services. See Figure 3 for the structural transformation pattern across OECD countries during Our objective is to investigate the role of structural change for our understanding of the rise in female hours of market work. The interaction between structural transformation and female employment has been largely overlooked in the literature. But there are at least two reasons why the structural transformation can contribute to the rise in female market hours of work. First, service jobs have traditionally been perceived as more appropriate for women since the early 20th century, as they involved safer, cleaner working conditions and shorter working hours than jobs in factories (Goldin, 2006). While these factors may have become less relevant later in the century, other factors have been suggested to imply that women still have a comparative advantage in the service sector, like the relatively higher use of communication skills than in manufacturing, and the less intensive use of heavy manual skills (Galor and Weil, 1996). This comparative advantage is reflected in the initial allocation of women s hours of market work. In 1970, 76% of market hours for a typical working woman in the US were supplied to the services sector, whereas the corresponding figure for men was only 56%. As the process of structural transformation implies an expansion of the sector in which women may have a comparative advantage, this could have an important consequences for the evolution of women s hours of market work. The second reason is related to the allocation of women s total work, including home production. In 1965, women in the US spent on average 60% of their total working time in home production, corresponding to roughly 33 hours per week, while men spent only about 11 hours in home production (see American Time Use Survey). Household work typically included child care, cleaning, food preparation, and in general activities that can be potentially marketized in the service sector. So if the expansion of the service sector makes it cheaper to outsource these services, one should expect a reallocation of women s 2

3 working time from the household to the market. Previous work by Ngai and Pissarides (2008) has shown that the interaction of structural transformation and marketization is crucial for the evolution of aggregate market hours over time. However, gender differences are noteworthy because, underlying the aggregate changes, the rise in market hours of women has been accompanied by a fall in market hours of men. Given that men are mainly working in the manufacturing sector while women are mostly engaged in home production or in the service sector, the combination of structural transformation and marketization can be potentially important in understanding the different trends in market hours across genders. We focus our analysis on the US experience since the late 1960s. This choice is mostly motivated by data availability, as the US Current Population Survey (CPS) allows us to analyze both the industry structure and the employment rates of various demographic groups since We will first document the increase female market hours during the period and the parallel rise in the share of services. Motivated by these stylized facts, we construct a dynamic model with three sectors (goods, services and home production) and two genders, whose input are imperfect substitutes in all sectors. The driving force is uneven productivity growth across sectors. Typically, productivity growth is faster in market sectors than in home production, and, within the market, it is faster in manufacturing than in services. Goods and services are poor substitutes, which gives rise to structural transformation. On the other hand, market services are good substitutes to home production, which drives marketization. Our goal is to quantify the contribution of the structural transformation and marketization to the rise in female market hours of work. To confront the model with the data, in addition to the use of CPS, we will also use the American Time Use Survey to understand how home production hours are changing across different activities. The speed of marketization of certain home activities depends on the cost of the corresponding substitutes in the market. Thus the fall in hours in the production of a given home good should be related to the expansion of the corresponding market sector. This can potentially help to differentiate our mechanism from alternative stories which would instead cause a generalized increase in female participation in all market sectors. The paper is organized as follows. The next section describes our data set and documents the increase in both female participation to the labor market, relative women s wages, and the share of services in the US economy during Section 3 proposes a model of a three-sector economy and shows predictions for the gender intensity in each sector and the gender wage ratio. Section 4 proposes a calibration of the main parameters in the model, and Section 5 shows the quantitative predictions of uneven productivity growth for the main variables of interest. 3

4 2 Data and stylized facts In order to construct evidence on the evolution of women s position in the labor market and on the process of structural transformation we use micro data from March Current Population Surveys (CPS) for survey years 1968 to Evidence on non-market work by both genders will be obtained from Time Use Survey Data. Our working sample obtained from the CPS includes individuals ages (both inclusive), who are not in full-time education, retired, or military. Our key labor input variable is represented by working hours. Annual hours are obtained from information on usual weekly hours and the number of weeks worked in the year prior to the survey year. Until 1975, weeks worked in the previous year are only reported in intervals (0, 1-13, 14-26, 26-39, 40-47, 48-49, 50-52), and to recode weeks worked during , we use within interval means obtained from later surveys. Similarly, usual weekly hours in the previous year are not available for , and thus we use hours worked during the survey week to measure usual weekly hours in the previous year. For individuals who did not work during the survey week we imputed usual weekly hours using the average of current hours for individuals of the same sex in the same year. Both adjustment methods have been previously applied to the March CPS by Katz and Murphy (1992). Our wage concept is represented by hourly earnings, obtained as wage and salary income in the previous year, dividied by annual hours. Figure 1 provides evidence of the rise in the labor market involvement of women over the past four decades, by showing trends in the average usual weekly hours of women and the gender annual hours ratio. Women were working around 17 hours per week in the late sixties, and their working hours increased steadily until a 25 hours peak in 2000, and have slightly fallen since. This steady increase, coupled with a decrease in men s weekly hours from 40 to 30 hours per week, has implied a doubling in the gender hours ratio, from about 42% in 1968 to 84% in Figure 2 shows the evolution of the female to male wage ratio, using raw hourly wages, unadjusted for characteristics. Women s hourly wages remained stable at around 63% of male wages until about 1980, and then started risign steadily until reaching just about 80% in When using hourly wages corrected for human capital (age and age squared, race and four education groups), the rise in the gender wage ratio is only slightly attenuated, from 64% in 1968 to 77% in The combined increase in female hours and wages raised the female wage bill from 30% to two thirds of the male wage bill. The increase in female market hours since the late 1960s was accompanied by a substantial decline in female home production hours, from 38.5 in 1965, to 30.0 in 2003 (see Aguiar and Hurst ). Another salient labor market development over the last few decades was the process of structural transformation from manufacturing into services. This is shown Figure 3, which 4

5 Women's usual weekly hours Gender annual hours ratio (x100) Year W omen's usual weekly hours Gender annual hours ratio (x100) Figure 1: Women s usual weekly hours, and women s to men s ratio in annual hours (x100), Female to Male hourly wage ratio Year Figure 2: Female to male ratio in gross hourly wages, unadjusted for characteristics, The wage ratio is obtained that exp(ln ln ),whereln and ln are average log female and male wages, respectively. 5

6 Service sector hours share (x100) Survey year Figure 3: The weight of the service sector in the total economy, measured by the share in total annual hours worked. plots the share of annual hours worked in the service sector. 1 The weight of the broad service sector in the total economy rises steadily from 57% in 1968 to 77% in Figure 4 shows the trend in the gender hours ratio in the goods and service sectors, respectively. 2 As one would have expected, the hours ratio has always been substantially higher in the service than in the goods sector, but the key fact emerging from the Figure is that most of the increase in the overall hours ratio is happening within the service sector, where female hours rose from just above 60% of male hours, to 110%. By contrast, in the goods sector, the gender hours ratio rose initially from 23% in 1968 to 33% in 1992, but then fell back to 26% by the end of our sample period. Figure 5 plots corresponding series for wage ratios, showing that both the level of women s wages relative to men s wages and their upward trend was very similar across sectors.model There are two types of consumption objects in the economy, goods and services. Goods (including agriculture and manufacturing products) can only be produced in the market while services can be produced either in the market or at home. Let sector 1 be the market goods sector, sector 2 be the market service sector and sector 3 be the home sector. Production in all sectors involves only labor but each with its own sector-specific productivity index () 1 This include the following broad industries: Transportation; Telecommunications; Wholesale and retail trade; Finance, insurance and real estate; Business and repair services; Personal services; Entertainment; Health; Education; Other professional services; Public administration. 2 We simply defined as part of the goods sector all broad industries that are not included in the service sector, i.e. Agriculture; Mining; Construction; Manufacturing; Utilities. 6

7 gender hours ratio (x100) Survey year services goods Figure 4: Gender ratios of annual hours worked in the service and goods sectors (x100), gender wage ratio (x100) Survey year services goods Figure 5: Gender ratio in gross hourly wages (unadjusted) in the goods and service sector,

8 The model The economy consists of a unit measure of representative male agents and a unit measure of representative female agents. Each male has one unit of time endowment, which can be allocated into three sectors at any time : goods, market services, and home sector. Each female has time endowment and (). 3 Males and females are endowed with () and () units of human caiptal, respectively. As we abstract from capital, the model is essentially static. Its simple dynamics follows directly from the exogenous evolution of sector-specific productivity growth, gender-specific time endowment and gender-specific human capital. We therefore omit time subscripts. 3.1 Firms Production in sectors 1 and 2 only involves effective labor,where 1 2 indexes sectors, according to,where denotes sector output and denotes labor productivity. Effective labor is defined as a CES aggregator of male and female labor inputs: ³ ( ) 1 +(1 )( ) 1 1 (1) where capture the comparative advantage of the female labor input in sector and 1 indicates that female and male labour inputs are highly substitutable. 4 3 We focus on time allocation across work in the market and home, thus abstract from decision on time allocation into leisure, sleeping and personal care. The value of H will be calibrated using the CPS population sample (see Calibration Section). 4 The production function implies that: 1 Note that if, i.e. when two genders are perfect substitute, the relative ratio of marginal productivity are due to differences in human capital or comparative advantage due to gender-specific technology or institution such as law 1.Thefirst component is directly observable while the second component is not directly observable. Violante et al (2011 JPE) allows both to change over time in their accounting exercise for gender wage gap and female labour supply. They interpret growth in as an exogenous gender-specific technical change. We, however, start with the premise that part of their exogenous gender-specific technical change can be understood as the process of structural transformation, so we restrict to be constant. 8

9 Profit maximization implies 1 ; (1 ) 1 (2) and relative labor demand is given by: 1 (3) 1 Combining (1) and (3) gives the following the expression 1 " # (4) 3.2 Household We consider a simple household model, in which a household consists of a male and a female who maximize a joint utility function, defined over two types of consumption goods and : ( ) ³ 1 +(1 ) 1 1 (5) where can be purchased directly from the market sector 1 and can be either purchased from the market sector 1 or produced at home, and is defined as ³ 1 2 +(1 ) (6) We assume 1 so that goods and services are poor substitutes while home services and market services are goods substitutes. Home production has a similar structure as market production defined in(1): ; 3 ³ 3 ( 3 3 ) 1 +(1 3 )( 3 3 ) 1 1 (7) The main difference between market production (1) and home production (7) is the different returns to to human capital. This could be motivated e.g. by different usefulness of communication skills and the ability to operate capital in the home and market sectors. The household budget constraint is given by (1 3 )+ ( 3 ) (8) where is the time endowment of females relative to males. 9

10 The first order conditions associated to the household maximization problem are: ( 1 ) : ( 2 ) : ( 3 ) : The gender ratio in sector 3, 3 3 can be obtained from expression (3), having set 3and the expression for 3 ( 3 3 ) canbesimilarlyobtainedfrom(4). Wenextdefine the implicit price of home production similarly as for market production in (2): ³ (9) We can now derive demand for all goods. For service goods, using first order conditions for 2 and 3 we obtain 2 3 (10) Across goods and services, we combine the corresponding first-order conditions to obtain ( ) Finally, using (6) we can rewrite the above as " # 1 (11) To determine the female input in home production hour, 3, we rewrite the budget constraint as: 3X 3X which implies à 3X ! 1 (12) where 3 ( 3 3 )( 3 3 ) is female s income share in home production and ( )( ) is relative expenditure on goods and Female labor supply is simply obtained as 3 10

11 3.3 Market Equilibrium We can now solve for the equilibrium gender wage gap and the remaining labor allocation for and 1 2 using (2), labor market clearing ; (13) and goods market clearing ; 1 2 (14) Relative Prices and Expenditure Using (2) and (9), we can derive the relative prices as Moreover, and using expression (4), 1 Ã!1 ³ 1+³ 1 ; (15) 1 ³ 1+³ 1 1 where 1 2 for Substituting (16) into (15) gives the following result: 1 ; (16) Lemma 1 Given 1 if is increasing in This results is intuitive: it says that, if sector is more female intensive (because females have a comparative advantage in it) than sector, then an increase in female relative wages will increase the relative price of its output Relative expenditures 12 and 23 can be determined using the household consumption allocation (11) and (10). In particular, the choice between home and market services implies (17) 1 which captures the extent of marketization of services, and namely a higher 23 means that a larger share of services is marketized. The choice between market goods and market service implies " # 1 (18)

12 which captures the extent of structural transformation between goods and services, and namely a declining 12 is consistent with a rising service economy. In the calibration section, we will calibrate to match the female intensity in the three sectors using data on time allocation for 1968, the initial year in our sample. As one would have expected, we find In this case the interpretation of Lemma 1 is that rising relative female wages imply rising 2 1 and 3 2 Given 1 this result in turnshowsupasrising 23 and falling 12 In other words, rising female relative wages contribute to both the processes of marketization and structural transformation Time Allocation and Gender Wage gap We finally turn time allocation to solve for the equilibrium gender wage gap. As the gender ratio of labor inputs in all sectors is given in (3), we just solve for the female time allocation. Using market clearing conditions and the production functions gives ( ) ( ) 123 Using (15), this condition can be rewritten as 1 1 ( ) ( ) 123 (19) Combining (19) and the labor market clearing condition for females, we can solve for the demand for female home production time as " ( 1 1 ) ( 3 3 ) 3 # ( 3 3 ) (20) 3 ( 3 3 ) We can now solve for the equilibirum gender wage gap by equating the demand in (20) with the supply in (12), 3X ( 1 1) 3 3 ( 3 3) ( 3 3) 3 3 ( 3 3) + (21) And using equilibrium wage (2) and the production function, we can solve for 3 : 3 3 Thus the equilibrium gender wage gap satisfies ³ 1 1 ³ (22) (23)

13 where () is an implicit function of given ( ) (definedin(4)),whichcaptures the equilibrium female intensity in sector and (defined in (17)-(18)), which captures equilibrium expenditure relative to the value of home production. Lemma 2 Female labour supply and the gender wage gap depend on the extent of both structural transformation and marketization. The result can be seen directly from equation (20) and (23). Changes that are genderneutral such as shocks to sector-specific productivity can trigger marketization and structural transformation, which in turns affect female market hours 3 and the gender wage gap Finally, we turn to marketization and structural transformation in terms of hours as opposed to expenditure. Marketization can be expressed in terms of hours as ³ ³ and, using (19), this amounts to Similarily for structural transformation: Ã ( 2 2 ) 1+ 2! 2 (24) 3 ( 3 3 ) Ã ( 1 1 ) ( 2 2 ) ! (25) Lemma 3 When and are identical across sectors, are identical across sectors, and marketization and structural transformation in goods and hours are independent of gender-specific parameters( ). The proof of Lemma 3 follows straight from equation (3) for, equation (16), and equations (17)-(18). 4 Calibration Our model abstracts from the human capital accumulation decision, and in the quantitative exercise we simply match the growth in and to th egender evolution of human capital observed in the CPD. Specifically, we estimate wage equations on the CPS for , including a female dummy, age and its square, a race dummy, education dummies and year dummies. The schooling categories are: high school dropout (), high school completed 13

14 (), some college (), and college completed (). We the use the coefficients on the education dummies to construct the human capital index for men in each year as ( +exp( ) +exp( ) +exp( ) ) where the 0 are shares of the male population within each schooling category, and the 0 are the associated coefficients from the wage regression (dropouts being the excluded category). An analogue expression gives Using these indices, we find that the gender ratio in human capital has risen from 0.98 to 1.02 during , and we use these numbers to calibrate growth in We finally assume 3 3 for all periods, implying that the usefulness of human capital for females and males is identical in the home sector. We take the changes in female time endowment relative to male in the model as given. This change can be due to changes in the gender mix in the population, or changes in genderspecific leisure time, sleeping and personal care (or more generally time allocation other than market and home production). Our model is silent about both forces, thus our strategy is to choose the growth rate in that matches changes in both. During the period , the gender ratio in the population according to the CPS decreases from 1.15 to 1.086, while the gender ratio in tottal hours of work rises from to 1.12 (using information from both CPS and American Time Use Survey). Together they imply a growth factor for () equal to , thus we set () to be a constant in the computation. Taking the evolution of the human capital accumulation as given, the objective of the quantitative exercise is to investigate the importance of structural transformation and marketization in accounting for the rise in female labour supply and rise in gender wage gap. Two sets of crucial parameters are the elasticity parameters and the relative sectoral productivity growth rates. We take 2503 from the literature on structural transformation and home production (see Ngai and Pissarides 2008). The elasticity of substitution between male and female labor inputs,, is estimated on the CPS using data on hours and wages by gender aggregated at the state level. Specifically, our regression equation is ln ln (26) where and are average wages by gender in state and year and are the corresponding aggregate hours, and are control for human capital, and and represent state and time fixed-effects, respectively. Human capital indicators are gender-specific vectors of proportions of college graduates, high-school graduates with some college and high school graduates, and 2 denotes the vector of associated parameters. As labor supply is potentially endogenous with respect to wages, we instrument the hours ratio 14

15 by its lagged value. Equation (26) is estimated for , as information on state of residence is only available in a consistent form from 1977 onwards. The estimate obtained for 1 is , corresponding to an elasticity of substitution of In a further specification we control for gender- specific human capital indicators, obtained as ratios between male and female proportions of college graduates, high-school graduates with some college, and high school graduates without college. This somewhat lowers the estimated elasticity of substitution to 8.4. In the simulations that follow we adopt a benchmark value for of 10, and perform some robustness checks using values around this benchmark. The main driver for model dynamics is the difference in sectoral productivity growth.notethat is not the same as actual labor productivity growth, as labor productivity is based on total hours of work by both genders combined, while is productivity of effective labor, as defined in equation (1). In the Appendix, we explain the mapping of actual labor productivity growth into using the data on gender intensity from CPS. We find the implied growth rates as 1 23% and 2 14% The quantitative exercise is simple. We match the initial gender wage gap and initial time allocation of genders across market and home activities. We then feed in the relative productivity growth for each sector and the relative human capital growth to predict the evolution of the gender wage gap and female labor supply until the end of the sample period. The exact calibration procedure is described in the Appendix. In brief, we choose to match the initial gender wage gap. We then set to match the inital within-sector gender hours ratio using (3), given data on relative human capital, the gender wage gap and the within-sector gender hours ratio (are these actual or predicted?) Finally, we choose the initial relative productivity to match the allocation of hours across sectors. We show in the Appendix that the dynamics of the model depends on two growth rates, 12 and ˆ where is the growth in female human capital, which is equal to 05% overthesampleperiod. Givenvalues 1 and 2 we obtain 12 09% To obtain ˆ 23 we need a measure of 23 i.e. the difference in productivity growth between the service and the home sector. As the latter is not available, for our benchmark case we set 23 04%, which is equal to TFP growth in the service sector. This implicitly assumes that the home sector has zero TFP growth. We also consider the case in which i.e. the only difference between the service and the home sector is due to the usefulness of human capital. We will conduct sensitivity analysis with regard to both 12 and 23 To summarize, the baseline parameters are Table1: Baseline Parameters 12 ˆ % 0.9% 15

16 5 Quantitative Results 5.1 Baseline Results Table 2 reports quantitative results. Using the baseline parameters, the replicates very well female market hours as a proportion of total hours. In the data, an average female allocates 30% of her total working hours to market work in 1968, and this proportion rises to 45% by The model prediction for 2009 is 43%, implying that the model explains about 88% of the increase in female s market hours. The model is also doing a very good job at predicting the rise in services. In the data, the share of hours in services increases from 0.57 to The model predicts an increase to 0.72, i.e. it accounts for 75% of the observed increase. This is an improvement over Ngai and Pissarides (2008) calibration, which explains about 70% of the rise in services in a model without a gender dimension. 5 The main value-added of our framework to the literature on structural transformation are the predictions of the dynamics of hours of work for males and females separately, and the change in the gender ratio within each sector. The model gives a reasonable account for changes in gender ratio within each sector. In the data, the ratio of female to male hours increases from 0.23 to 0.26 in the goods sector, from 0.63 to 1.11 in the service sector, and it declines from 3.98 to 1.88 in the home sector. The model predicts this ratio to be 0.29 in 2009 in the goods sector, 0.79 in the service sector and 3.52 in the home sector. Thus the model over-predicts the increase in the gender ratio in the good sector, explains 34% of the increase in the service sector and 22% of the decline in the home sector. The model is, however, not doing a good job in explaining the rise in female relative wages. In the data, the wage ratio increase from 0.64 to 0.77, while the model predicts an increase to 0.65, equivalent to only 6.5% of the observed increase. This paper is among the very few papers that allow both the gender wage ratio and female market hours to be endogenously determined. In this literature, Heathcote et al. (2011) also aim to replicate theriseingenderwageratioandfemalemarkethoursinamodelinwhichfemaleandmale labor inputs perfect subsitutes ( ). This assumption delivers a one-to-one mapping between the (1 ) ratio and the equilibrium wage ratio. Thus Heathcote et al. (2011) can calibrate the growth rate in (1 ) to exactly match the observed rise in the wage ratio, and interpret the growth in as exogenous, gender-specific technical change. In our baseline model, we do not allow to change exogenously. Our calibrated s satisfy (in actual numbers, 0.36, 0.38 and 0.42), reflecting the comparative advanage of females in services and home production. We then predict the aggregate in the market (i.e. think of as a combination of 1 and 2 ) to be rising as labor reallocate from the goods to service sectors. Quantitatively, though, this proposed mechanism is not strong enough to 5 Another closely related paper is Rogerson(2008), which chooses parameters to match the evolution of US service employment shares exactly, then use these parameters to predict European outcomes. 16

17 produce a substantial rise in the aggregate explaining why we fall short of explaining the riseinthegenderwageratio. Ifweweretointroducesomeexogenousgrowthin 1 and 2, say 0.1% per year 6, the gender wage ratio would increase to 0.68, which amounts to about 30% of the observed increase. This would also improve model predictions for the gender hours ratio in both the service and home sectors, and for the fall in male market hours. However, in this case the model would overpredict female market hours and the gender ratio in the goods sector. 5.2 Mechanisms at Work There are two major forces at work for the increase in female market hours and the change in the gender wage ratio, namely the rise in female human capital, which is useful in market production, and structural transformation, as women have a comparative advantage in producing services. These mechanisms are related to the forces at work in Heathcote et al (2011), who find that skill-biased and gender-biased demand shifts are important for understanding the rise in female market hours. We do not model skill-biased demand shifts, and consider as exogenous the rise in relative female human capital. We, however, model gender-biased demand shifts as an outcome of structural transformation, insofar women have a comparative advantage in services. To understance the contribution of these two forces, we conduct two counter-factual experiments. In the first, we shut down the human capital channel by setting 1 in all sectors, and leaving 12 09% and ˆ % In the second, we shut down the structural transformation channel by setting but allow for human capital to be useful for market production only, i.e. ˆ 23 05% The results are shown in Table2,row2and3. Bothexperimentssuggestthattheincreaseinrelativefemalehuman capital contributes to about two-thirds of the increase in female market hours and almost theentireriseinthewageratio. So far we have assumed that human capital is only useful for market production. We now relax this assumption and allow human capital to be equally important at home. In other words, we set and in all sectors, and ˆ Rows4and5nowshow a different picture about the relative power of structural transformation vs. human capital. In particular, the whole increase in female market hours is due to structural transformation, whereas the rise in the wage ratio continues to rely on the improvement in relative women s human capital. But the overall effect on female hours is much weaker than in the baseline case, as the model now only predicts 20% of the rise in female market hours. Therefore, the assumption that human capital is only useful in market production is crucial both in 6 Note that if we follow Violante et al by choosing the ratio of to match the average annual growth rate of the wage ratio, which is 0.4% in the data, the implied growth rate for will be about 0.3%. 1 17

18 terms of the overall predictive power of the model and the decomposition of trends in female market hours into their two driving forces. Finally, we examine the role of alternative values for productivity growth 12 and 23 We first assess the role of faster productivity growth in the goods sector by setting it equal to productivity growth in the service sector, 12 0 but keeping productivity in both market sectors higher than in the home sector, i.e % as in the baseline case. Row 6 in Table 2 shows that the prediction on the wage ratio and female hours are not affected at all but as one would expect the model fails to capture the rise in the service share, explaining only less than half the rise. An important message from this counter-factual experiment is that while the gender dimension is important for explaining the rise in services, higher productivity growth in services does not seem drive the rise in female employment. Finally, we examine the role of the assumption that productivity growth is higher in the market service sector than the home sector by setting 23 0 while keeping Row 7 in Table 2 shows that the predicted rise in female market hours is substantially reduced from 75% to 50% data, though the model predicts a slightly higher increase in the wage ratio, from 6.5% to 10%. This experiment demonstrates that productivity improvement in market sectors over home production is an important factor driving the rise in female market hours. 6 Conclusions to be written 7 Appendix 7.1 Calibration Here we give details on (1) how is chosen to match the initial gender wage gap and (2) how productivity growth differences and female human capital growth are used in the calibration. To determine by definition we have X X Substituting 3 using household supply in (12) gives where ( ) 3 (27)

19 Equation (27) cam be simplified as ( ) ³ Note given data on initial time allocation ( ) 123 and gender wage gap can compute and 1 ³ we Thus (1) is obtained given initial time allocation and initial gender wage gap. Finally, we choose the initial relative productivity to match initial marketization and structural transformation. Using computed and the data, we derive which give values for à +(1 ) From marketization (17), we can write ³ ³ 1! 1 1 (28) so together with (28), we can compute an effective relative productivity ˆ Similarly from structure transformation (18), we can write where (29) " # so together with (28), we can compute ˆ (30)

20 Let ˆ ˆ ˆ be the growth rate of ˆ and by definition we have ˆ ; ˆ (31) where isthegrowthinfemalehumancapital. We next describe how we obtain 1 and 2 Using KLEMS 2008 March release, we compute the real labour productivity growth in service and non-service sector,,where ( + ); (32) where is the real value-added of sector and is the hours of work by gender Using KLEMS data, is simply real value-added per hour. We find 1 255% and 2 148% so the difference across the two sectors is 1.07%. To link to in the model, rewrite (32) as ( + ) ; where is the CES form of male and female labour hours as in the model (1), so we have ( + ) We can rewrite it as + wherewecanobtainthefirst two terms directly from the data and the last term from the model, where is derived in (4) and as shown in the Calibration section, the initial level of can be derived from (??). To summarize, the growth rate we are interested in is (33) where + is the intensity of female hours in sector and To compute growth rate of using (??) h i (1 ) where is the ratio of efficiency hour across gender, so 1 (1 ) ³ (1 ) 1 +(1 ) ³

21 So substituting into (33), the final formular is or as + + +(1 ) (1 ) +(1 ) (1 ) +(1 ) ³ 1 ³ 1 ³ 1 ³ 1 ³ ³ (1 ) 1 ³ +(1 ) 1 Together with the average from from KLEMS, we can calibrate using CPS data related to gender, i.e. the growth rate of human capital for each gender & and hours ratio across gender if we know. As mentioned previously, is calibrated to initial observation using the equilibrium condition of the model as in (??), which requires information on the initial wage ratio. If we stick with the assumption that is constant, then we will just use this level of for the computation of The worksheet computeai in the excel file do the conversion and find 1 231% and 2 141% so the difference across the two sectors is 0.89%. Given 12 and ˆ 23 we have the time series of ˆ together with and () we are ³ now ready to derive the path of gender wage gap () from (21), female labour supply using (12) and share of service sector using (25). References [1] Aguiar, Mark and Erik Hurst (2007). Measuring Trends in Leisure: The Allocation of Time Over Five Decades. Quarterly Journal of Economics 122: [2] Fernández, Raquel and Alessandra Fogli (2004). Mothers and Sons: Preference Formation and Female Labor Force Dynamics. Quarterly Journal of Economics 119: [3] Goldin, Claudia (2006). The Quiet Revolution That Transformed Women s Employment,Education,andFamily.American Economic Review, Papers and Proceedings 96: [4] Goldin, Claudia and Lawrence F. Katz (2002). The Power of the Pill: Oral Contraceptives and Women s Career and Marriage Decisions. JournalofPoliticalEconomy100:

22 [5] Greenwood, Jeremy, Ananth Seshadri and Mehmet Yorukoglu (2004). Engines of Liberation. Review of Economic Studies 72: [6] Heathcote, Jonathan, Kjetil Storesletten and Gianluca Violante (2010). The Macroeconomic Implications of Rising Wage Inequality in the United States. Journal of Political Economy 118: [7] Ngai, Rachel L. and Christopher A. Pissarides (2008). Trends in Hours and Economic Growth. Review of Economic Dynamics 11: [8] Katz Lawrence F. and Kevin M. Murphy (1992). Changes in Relative Wages, : Supply and Demand Factors. Quarterly Journal of Economics 107: [9] Olivetti, Claudia (2006). Changes in Women s Aggregate Hours of Work: The Role of Returns to Experience. Review of Economic Dynamics 9:

23 Table 2 Data and model predictions wage share of women's men's women's women's gender gender gender ratio services hours: hours hours: hours: ratio: ratio: ratio: market/ market/ goods/ services/ goods services home total hours total hours services home data data baseline model % explained no human capital growth model % explained no structural transformation model % explained human capital useful at home model % explained human capital useful at home model no structural transformation % explained prod growth goods prod growth services model > prod growth home 0 % explained prod growth goods > prod growth services model prod growth home 0 % explained