PSC. Research Reports. Population Studies Center. Mary Arends-Kuenning

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1 Mary Arends-Kuenning Changes in Female Labor Force Participation in Brazil : Pushed by Need or Pulled by Opportunity? Report No Research Reports PSC Population Studies Center University of Michigan

2 The Population Studies Center at the University of Michigan is one of the oldest population centers in the United States. Established in 1961 with a grant from the Ford Foundation, the Center has a rich history as the main workplace for an interdisciplinary community of scholars in the field of population studies. Today the Center is supported by a Population Research Center Core Grant from the National Institute of Child Health and Human Development (NICHD) as well as by the University of Michigan, the National Institute on Aging, the Hewlett Foundation, and the Mellon Foundation. PSC Research Reports are prepublication working papers that report on current demographic research conducted by PSC associates and affiliates. The papers are written by the researcher(s) for timely dissemination of their findings and are often later submitted for publication in scholarly journals. The PSC Research Report Series was begun in 1981 and is organized chronologically. Copyrights are held by the authors. Readers may freely quote from, copy, and distribute this work as long as the copyright holder and PSC are properly acknowledged and the original work is not altered. PSC Publications Population Studies Center, University of Michigan S. University, Ann Arbor, MI USA

3 Changes in Female Labor Force Participation in Brazil : Pushed by Need or Pulled by Opportunity? by Mary Arends-Kuenning Research Report No July 1997 Abstract: During the 1980s, Brazil experienced declines in GDP growth per capita and chronic inflation so severe that the 1980s have been called the lost decade. The period also coincided with a steady increase in female labor force participation. Worsening economic conditions for families occurred at the same time that women who had experienced greater educational opportunities entered the labor force. This paper examines how women increased their labor force participation in response to the country s weak macroeconomic situation and in response to their increased educational attainment. Using a series of large household surveys, the Pesquisa Nacional por Amostra do Domicilios, I develop a fixed effect methodology to distinguish long-term cohort-educational effects from short-term responses to changes in income and wages. The analysis shows that educational attainment can explain much of the trend in female labor force participation, but that women also responded to shocks in household income and were more likely to enter in years where average household income was below the mean. Women with high levels of education appear to be more sensitive to these types of income shocks. Changes in income can explain up to fifty percent of the increase in female labor force participation between 1976 and 1990 for all women and twenty percent of the increase for married women. Over the long term, educational levels explain between 49 and 70 percent of the variance among cohort life time participation rates. Datasets used: Pesquisa Nacional por Amostra do Domicilios (PNAD): Brazil, 1976, 1978, The Author Mary Arends-Kuenning, Berelson Fellow, Population Council, 1 Dag Hammarskjold Plaza, New York, NY marends@popcouncil.org Acknowledgments This paper was written as part of my dissertation while I was a graduate student at the Population Studies Center, University of Michigan. I am grateful to David Lam, Charles Brown, John Bound, Debbie Reed, Suzanne Duryea, Lien Tran and participants at the University of Michigan Economic Demography Seminar for extremely useful comments and suggestions. Financial support for this research was provided by an NICHD training grant and the Mellon foundation. An earlier version of this paper was presented at the 1995 Population Association of America meetings, San Francisco, CA.

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5 Introduction During the 1980s, Latin America experienced declines in GDP growth per capita and chronic inflation so severe that the 1980s have been called the "lost decade." However, female labor force participation increased steadily during this period. This experience contrasts with the United States, where large increases in female labor force participation occurred along with increases in real wages. Many sociologists in Latin America have explained the phenomenon as an "added worker" effect, where females have been pushed into the labor market in order to maintain family incomes (See Gladwin 1993). In contrast, Lam and Levison (1992) have found in preliminary work that increases in female labor force participation in Brazil have not been very responsive to the business cycle and instead reflect a trend of increased educational attainment. Whether the increase in female labor supply is due to an added worker effect or is a result of increases in education is an interesting question because of the implications for the future for Latin American countries. If the increase in women working reflects an added worker effect, we would expect it to decline again once Latin American economies resume growth. If it is part of a secular trend, female participation will continue to increase in the future. This paper investigates the increase in female labor supply that took place in Brazil from 1976 to 1990 in a dynamic context. I examine the effects of education, wages, household income and household composition on female labor supply in order to explain the paradox of increasing labor supply during a time of wide swings in real wages. Women s Economic Situation in Brazil in the 1980s Figure 1 shows the macroeconomic cycles that Brazil experienced in the 1970s and 1980s (Estatistica do Brasil). GDP per capita grew at an annual rate of 5 percent on the average during the late 1970s. In 1980, the indicators took a sudden turn for the worse, bottoming out in 1983 when GDP per capita was at 87 percent of 1980 levels. Recovery peaked in 1987 (bringing GDP per capita back to 1980 levels) and then GDP declined again in The Cruzado plan was enacted in 1986, instituting a general freeze on wages and prices. It also increased the wages of minimum-wage workers by 15 percent (Cardoso and Helwege, 1992). Real wages rose for all workers as a result of the Cruzado plan, but the poorest workers experienced the largest increase. Throughout these macroeconomic upheavals, female labor force participation steadily increased. Figure 2 graphs female labor force participation by age for several years, using the data from the Pesquisa Nacional por Amostra de Domicilios (PNAD), an annual household survey conducted by the Fundacao Instituto Brasileiro de Geografia e Estatistica (IBGE). The line represents the proportion of women that are n years old in year x who reported they were working or looking for a job during the survey week. Participation increases steeply from age 15 to 20, levels off until about age 40, and then begins to decline. In the earliest year, 1976, participation begins to decline for women in their early twenties. The profile has steadily shifted upward especially for women aged 35 to 45, implying that older women are increasing their participation over time. In 1976, the participation rate for women aged 40 was about 35 percent; by 1990, the rate had increased to about 55 percent. The cross sectional graph gives an overview of how female participation rates have

6 2 changed over time. Using a series of cross sectional data, it is possible to trace out the path of female labor force participation over the life cycle. If the sample is chosen randomly in each year, cohorts can be followed; women who were 15 in the 1976 cross section were 16 in the 1977 cross section. Figure 3 shows female labor force participation rates following cohorts across the 14 year period. The cohorts include three birth years. Each cohort s participation profile lies above the older cohort s profile. For example, at age 37, the participation rate of the cohort born from 1939 to 1941 was approximately.42, while the 1949 to 1951 cohort had a participation rate of about.56 at the same age. In the United States, women increased their labor force participation in response to increases in real wages, especially due to increased demand for clerical labor (Goldin, 1990 and Smith and Ward, 1985). In Brazil, the increase during the late 1970s and 1980s took place in a time when real wages were erratic, but declining in most of the years. Figure 4 shows the path of log wages for women aged 30 to 45 for 6 separate educational levels. 1 The six educational levels are 0 years of education, 1 to 3 years of education, 4 to 7 years of education, 8 to 10 years of education, exactly 11 years of education, and 12 or more years of education. The fourth, eighth and eleventh years correspond to diploma years in the Brazilian system. The graph shows log wages normalized to 1981 wage levels. For most educational groups (except for the 8 to 10 year group), log wages were stable or increasing during the late 1970s, but then declined in 1983 and Wages began to recover in 1985 and reached a high in 1986, the year of the Cruzado plan. Comparing 1985 and 1986, the gain in wages was especially high for women with 1 to 3 years of education. After the 1986 peak, real log wages again declined for all age groups, with a slight recovery in 1989 and a subsequent drop. The group that suffered the largest overall declines in real wages is that with 8 to 10 years of education. The group that maintained log wages closest to the 1981 level was women with 12 or more years of education. Female labor force participation was increasing in the period prior to 1976 as well. Labor force participation rates for women aged 10 and above were.14 in 1950,.17 in 1960,.19 in 1970 and.27 in 1980 (Anuario Estatistica 1991). The period from 1964 to 1980 was a period of high growth in GDP. The increases between 1976 and 1990 can be viewed in the context of the earlier increases in female labor force participation. As women increase their participation, younger cohorts expect to have higher participation in the labor force. This will encourage younger women to obtain more schooling to prepare for greater labor force attachment. 2 One potentially important component of the increase in female labor force participation during the 1976 to 1990 period is the increase in women s educational attainment. Figure 5 1 One problem in determining real wages in Brazil is the very high and erratic inflation rates experienced during the 1980s. The PNAD data references the week in which the survey question was asked. The income questions in the survey ask "What was your monthly salary the week of (date) to (date)?" The deflator used pertains to the month of the survey. In 1982 the survey was asked over a four month period, so the average inflation rate was used. The source of the deflators is Estatisticas Historicas do Brasil Tables 5.4 and 5.9 and Anuario Estatistico do Brasil 1991 p The analysis of increases between the 1976 and 1990 period within the context of increases since the 1950s is beyond the scope of this paper. 2

7 3 presents the educational distribution of Brazilian women by cohort with data from the 1990 PNAD. The 1923 to 1925 and the 1929 to 1931 cohorts look very similar at the higher levels of education. About 7 percent of the women in these cohorts had at least a high school education. Subsequent cohorts show steady increases in educational attainment. Thirty-four percent of the 1959 to 1961 cohort had at least a high school education. The percentage completing grade school also increased from 12 percent for the oldest cohort to 50 percent for the youngest cohort. To summarize, Brazil s macroeconomic cycles have coincided with large swings in real wages. This paper analyzes the effects of education, wages, household income and household composition on female labor supply and tries to explain why labor supply increased in the midst of these changes in wages. Comparing 1976 and 1990, women s wages have stagnated or declined at all educational levels. Therefore, the increase in female labor force participation cannot be explained by increases in real wages that pull women into the labor market as occurred in the United States. However, this stagnation in real wages has coincided with large increases in women s educational levels. An increase in educational attainment implies that lifetime wages will be higher, increasing the opportunity cost of not working. The negative effect of education on fertility reinforces the effect of education on labor supply through higher wages. Education, apart from increasing the opportunity cost of children because it increases labor market wages, also has an independent effect on fertility because it encourages autonomy and encourages women to be more comfortable with modernity and contraceptive technology, specifically. Women with higher levels of education also have healthier children. If parents rely on children to provide insurance for old age, their fertility will depend on how many adult children they desire to provide support in the future. Therefore, declines in child mortality would tend to decrease fertility as a higher proportion of children born survive to adulthood (Summers, 1992 and Schultz, 1990). Declines in fertility imply more time available to work in the labor market. Another factor that may have increased participation is the decline in family income as household heads experienced declines in their real wages. The Added Worker Effect If women did increase their labor force participation in response to the macroeconomic difficulties of the 1980s, labor economists would describe this response as an added worker effect. Mincer (1962) first described the added worker effect in his work on the labor force participation of married women, but it could be applied to child labor as well. His model assumes that families act so as to maximize an aggregate utility function, with members taking action to maximize total family utility. The family bases their maximization problem on permanent family income. If there is an exogenous change in income, for example due to the husband s unemployment (or in the case of Brazil a large reduction in real wages due to inflation) families will maintain consumption by running down assets or by incurring debt. However, if assets are low or not liquid, it may be preferable to make the adjustment to a drop in family income by increasing income rather than reducing spending. For the family, the adjustment of home production or leisure may be more flexible than consumption or borrowing, so that the wife or children may temporarily work in the paid labor force as an alternative to borrowing, dissaving, or cutting consumption. According to Mincer, the increase in participation of wives or children will occur only in response to short run changes in income. In the long run, families will adjust their permanent 3

8 4 income estimates downward and reduce consumption. 3 So in a recession, two forces pull female labor force participation in opposite directions: The decrease in wages during a recession tends to decrease participation because the probability that the market wage exceeds the reservation wage decreases, but the shortfall in income tends to increase participation because the family s strategy may be to send more members into the paid labor market. If the added worker effect dominates, female labor force participation rates should increase in a recession and then fall during the recovery. As women expect to spend a higher proportion of their lives in the paid labor market, the added worker effect should decline in importance. Their participation will not depend as much on other family members decisions. Also, if marriages are becoming less stable, women would be expected to spend more time working as insurance against the failure of a marriage (Becker 1991). There has been an increase in the number of women in informal unions over this period, and informal unions are more unstable than civil or religious marriages (Greene and Rao 1992). The Model and Estimation Strategy For this study, I require a model that will allow me to distinguish long-term trends from responses to changes in the macroeconomic situation of Brazil. One way to think of the problem is to distinguish between characteristics that are not changing over the period (fixed effects) and characteristics that are changing from year to year. If education is completed, education can be thought of as a fixed effect, as is the year of birth. Income, wages, and the number of young children in a household can change from year to year. Heckman and MaCurdy (1980) have developed a model that distinguishes between responses to temporary and permanent changes in income and wages. It is a model that looks at married women s labor supply over the life cycle. Because it is impossible to observe income and wages for an individual over the entire life cycle, Heckman and MaCurdy advocate an individual fixed effect approach where the fixed effect represents the marginal utility of wealth λ. The family maximizes a single utility function over its life cycle: T [ it it it it] t Vit = ( 1 + ρ ) δ C + γ L t = 0 i α ω (1) where C is consumption, L is time spent at home (in home production or leisure) and δ and γ are weights that vary over time and with each individual. i indexes family members and t indexes time. The weights allow a unit of leisure to provide higher utility at certain points in the life cycle, for example γ it would be high for married women during prime childbearing years. Utility is additively separable. The budget constraint is 3 This does not take into account the fact that families may want to maintain a given standard of living rather than reduce their consumption permanently. Families may be willing to forego household production to obtain more market goods. 4

9 5 A( 0) + ( 1 + r) W H = ( 1 + r) C i T T t t t it it t it (2) t = 0 i t = 0 i where A i represents assets at time 0, W it is the wage available to each family member in each period, and H it is hours worked by each family member in the market in each period. The interest rate, r t, varies over time. The total number of hours is fixed and each family member decides to participate in the paid labor force if utility from doing so exceeds utility from not participating. Each family member takes the other members hours and wages as exogenous, so for example, a husband s income is exogenous to the wife s decision. If a family member participates, his or her hours of time spent at home will equal L it = t ( 1 + p) Witλ t ( 1 + r) γitω The solution for time spent at home given in equation (3) is put into the utility function in equation (1) and compared to utility obtained when no time is spent in the labor market. Taking logs of equation (3), and writing a separate equation for W it and γ it : ln Wit = Xitβ + ε tw (4) ln γ it = Zitφ + σi + εtr where X represents characteristics that affect the wage in the paid labor market, Z represents characteristics that affect tastes for remaining in the home such as the presence of young children, and σ i represents an individual specific taste for working outside the home. A family member will participate in the paid labor market if 1 ω 1 εtw εtr Xitβ + Zitφ + σ i ln λ + t[ln( 1+ rt ) ln( 1+ ρt )] + ln ω + ( ω 1 )ln L (5) which is the condition that the market wage exceeds the reservation wage. Note that the other family members' wages or earnings will not enter into the individual's labor force participation decision except through the marginal utility of wealth, λ. Lambda summarizes all the information about lifetime wages and property income that an individual uses to determine current consumption and labor supply. Under conditions of certainty, λ will be fixed over the life cycle. Using a fixed effect approach summarizes the information known to the individual and means that the researcher does not have to know wage profiles and income profiles for all household members. The second order conditions for the maximization problem imply that ω will be less than 1. Equation (5) implies a probit structure at the level where individual women are deciding whether to participate in the labor force. This analysis examines the behavior of cohorts of women over time, and therefore, the individual data is aggregated by cohort and educational group. It will be easier to aggregate over all of the women within a cohort-educational level group if the equation for labor force participation is linear. Therefore, equation (5) is transformed as a linear equation for female labor force participation: flfp = α + fi + Xitβ + Zitφ + t[ln( 1 + rt) ln( 1 + ρt)] + eit (6) where f i can be interpreted as an individual fixed effect f i = ln λ ln ω + σ i (7) If the permanent income model is correct, other family members earnings should have no impact on a woman s labor force participation when including λ in the regression. The significance of other family members earnings in a regression of female labor supply becomes a test of the added worker effect. Some other implications of the model are that if the wage increases in one period of a woman s life, she will be more likely to participate in that period. Another implication (3) 5

10 6 is that if she is working, she will work more in that period than she would have otherwise, and she will then increase time spent at home in other periods. Therefore, the response to wages reflects intertemporal substitution when λ is fixed. The probability that a woman will participate in the paid labor force is increasing in the marginal utility of wealth and decreasing in her tastes for staying at home. If there is a permanent shift in demand for the woman s skills, the effect on life cycle labor supply is ambiguous. An increase in wages over the whole life cycle would decrease the marginal utility of lifetime wealth and increase the demand for time spent at home. However, the increase in the wage profile also increases the opportunity cost of staying home which would increase the time spent in the paid labor force. Complicating the analysis for women is the sample selection problem. Since many women do not work in the labor market, they do not have observed wages in the data set. Since I am interested in calculating the labor supply responses for all women, not only working women, it is necessary to try to predict what the non-working women would earn in the labor market. This can be done by applying coefficients from a wage regression of working women to the human capital characteristics of non-working women. However, it is likely that women who work have either higher tastes for work or higher ability for market work than women who do not work in the market and the researcher does not observe these attributes. Therefore, using the returns associated with working women will overstate what the average woman with given education and experience will earn. I discuss this below. The Data and Background This study uses the Pesquisa Nacional por Amostra de Domicilios (PNAD), an annual household labor market survey collected since The PNAD surveys about 100,000 households each year until 1985 and about 60,000 households per year from 1986 until Women who were born between 1920 and 1961 in each of 12 PNAD surveys are included in the analysis. These women were aged 15 to 56 in 1976 and 29 to 70 in The number of women in this group varied from 96,433 in 1978 to 46,260 in 1990 and the number of married women varied from 61,113 in 1982 to 31,229 in Like Smith and Ward (1984), who used the United States Current Population Survey, I use the repeated cross sectional data to create a pseudo-panel. 4 For each year, I take the means of the variables included in this study by cohorteducational level groups. For example, the analysis compares the participation rate for women who were born between 1959 and 1961 who have 8 to 10 years of education in the 1976 PNAD with the participation rate for women born between those years with the same education in the 1978 PNAD. Fourteen cohorts and 6 educational groups are included for a total of 84 groups. I regress the changes in this rate for the 84 groups on changes in mean household income, mean 4 Using a series of large cross sections like the PNAD data sets may provide better estimates than real longitudinal data. Since the population is sampled randomly every year, there is no risk of attrition bias which is a common problem with longitudinal data (Deaton 1985). The use of longitudinal data also can exacerbate measurement error bias. With the large numbers of observations in each PNAD, it is possible to reduce measurement error by taking the means by well-defined groups. 6

11 7 wages and other variables for the same group. This method allows the researcher to follow women who were born in a given year who have a given level of education over time, and aggregate them into cohorts. Domestic servants who were living with their employers are excluded from the analysis because no data was collected about their families. Also, domestic servants have income in room and board that is not captured in the surveys and it is difficult to calculate a wage. Rural households are excluded from the study because of the difficulties in 1) determining whether rural women are participating in the market or not, 2) quantifying the value of agricultural production and the number of hours worked to determine income and wages, and 3) constructing accurate price indices. The proportion of women in the sample living in urban areas did increase over time. In 1976 the proportion of women aged 15 to 56 who lived in urban areas was.68 while in 1990, the proportion of women aged 29 to 70 living in urban areas was.78. The biggest changes came for women with the lowest level of education and from the youngest cohorts. For example, for the cohort born between 1956 and 1958 with no education, 29 percent lived in urban areas in 1976 and 55 percent in Of the women in that cohort with 11 years of education, 96 percent lived in urban areas in 1976 while 94 percent lived in urban areas in In both years, the proportion of women living in urban areas for the three highest educational categories in every cohort was above 90 percent. If the women who lived in urban areas in 1976 and 1990 are similar in unobserved characteristics to the women who moved from rural to urban areas between 1976 and 1990, then, with random sampling, migration would not affect the relationship between wages and labor supply. However, in the typical story, migrants are moving from rural areas to urban areas because they desire to work. In economic terms, this means that these women have a lower reservation wage or that they have higher ability in market work. Their migration to urban areas can be imagined as a supply shock, which will decrease wages. A decrease in wages can be observed with an increase in labor supply if the migrants have a lower reservation wage than the natives. Some of the natives who were working before will leave the labor market. If the net effect is an increase in labor supply by all the women in the urban area, the change in labor supply would appear to be responding negatively to changes in wages. Similarly, if migrants have lower household incomes than natives and they are more likely to work, the data will show an increase in labor supply corresponding to a decrease in income. The effect will appear to be an income effect, but it is really a compositional effect. Therefore, if migrants have lower reservation wages than natives, migration will tend to bias the coefficient on wages downward and the coefficient on income upward. The effects described above arise only from differences in reservation wages between natives and migrants. However, migrants may differ from natives in labor market ability and this will also affect the relationship between wages and labor force participation. Whether the migrants are higher in ability than the urban natives is not certain as time continues. As migration continues from rural to urban areas, the new migrants are less able than the earlier migrants within the same cohort because those with the highest incentives to move and work in urban areas will leave the rural areas first. In trend terms, the ability of the urban population would be increasing at first (while high ability rural workers move to urban areas), and then leveling off, and then decreasing (as the last rural workers move to urban areas). If these changes in the error term are correlated with changes in the wages, then estimates of wage elasticity will be biased. 7

12 8 However, the variation in wages and income due to macroeconomic shocks must swamp the variation that could come from migration. The macroeconomic shocks are exogenous to individuals who are making labor supply decisions and they must be greater than supply shifts due to migration. Figure 4 shows that wages follow no clear trend that would be consistent with a steady migration from rural to urban areas. Family level variables are used to proxy the aspects of household structure that are determinants of the reservation wage such as the number of young children in the household. The data record family members in relationship to the family head. Unfortunately, marital status is asked directly of respondents in only three years. Therefore it is not possible to tell directly if a woman is married if she is not the household head or married to the household head. Also, it is not possible to distinguish between religious and civil marriages and informal unions. The family variables are constructed in the following way: women are classified as married if they are coded as spouses of family heads or they are coded as family heads and there is someone coded as the spouse. They may be in formal or informal unions. The children are counted at the family level. The method will tend to miss married women who live with parents or in-laws. By comparing the marital status in years where it is asked directly with marital status from the constructed variable, it is possible to tell what the bias will be. Under-counting of marriages is most likely for younger and older women who are less likely to be household heads or their spouses. Preliminary results find that marriage is stable over the years in the analysis and that the constructed variable is close to the reported marital status in 1977 and 1978 (they differ by about one percentage point in each age group). There is a slight declining trend in marriage rates over the whole period. The proportion of women aged 35 who are married varies from 74 to 78 percent in the fourteen cross sections of PNAD data; the proportion varies from 26 to 30 percent for women aged 20, and from 13 to 18 percent for women aged 18. Whether women are choosing to live in unions and the timing of union formation does not seem to be changing very much. However, it is likely that informal unions have been increasing. Whether assortative mating is changing is another story that this paper does not examine. The children variables include the number of children aged 0 to 3 and aged 4 to 6 within the family. If there is more than one adult woman in the household, it is not possible to tell who the parent of the child is. However, the labor supply of women also depends on the presence of nieces and nephews; families with several adult women may decide to have one of the adult women take care of all the family s children. Therefore, the analysis includes the number of women older than 15 in the household as a regressor. Overview of Econometric Analysis The econometric approach draws heavily on a paper by Smith and Ward. Smith and Ward (1985) adapt Heckman and MaCurdy s method in a study of female labor force participation in the United States from 1950 to They use CPS microfiles and tables to simulate a panel so that they can follow cohorts of women across time. Because the analysis requires several steps, this section describes the analysis and explains the reasons for each step. First of all, I take the 12 cross sections of PNAD data for the years 1976, 1978, and 1981 through I exclude 1977 and 1979 because those years do not include household level variables that are used as instruments. There was no PNAD available in 1980, because 1980 was a census year. For each cross section, four separate OLS wage 8

13 9 regressions are estimated. First, equations for all women born between 1920 and 1961 are presented, both corrected and uncorrected for sample selection. Then separate analyses are presented for married women of the same ages, both corrected and uncorrected for sample selection. The sample selection correction method used is a two-step procedure and involves a linear probability model described by Olsen (1980). To clarify the issues, Table 1 describes which variables are included at each stage of the procedure. In the cross section, the variables control for household composition, region, marital status, income and include 84 cohorteducational level dummies. The cohort-educational level dummies are an interaction of three birth year cohorts (a total of 14 cohorts) with six educational levels--no education, 1 to 3 years, 4 to 7 years, 8 to 10 years, 11 years and 12 or more years. They correspond to the fixed effects shown in equation (6). The reason I chose the year of birth and educational level as the fixed effects was that if education has been completed, these variables are not changing from year to year. Year of birth and educational level may reflect tastes for working in the paid labor market. Also, life cycle wage profiles and income profiles are highly correlated with educational levels. Women with high educational levels tend to marry men with high educational levels, which will give women more access to resources. Younger cohorts may also have different expectations about life cycle wages and income than older cohorts. The cohort-educational level groups are the units for aggregating the data and comparing across the cross sections. The sample selection correction is described more fully in the next section. Having estimated the four wage regressions in each year, I use the coefficients to predict wages for all women within a cohort-educational level cell whether an individual woman is working or not. Then, I take the means of all the relevant variables by the 84 cohort-educational level groups. 5 For each of the groups, there are 12 observations--one for each year of the cross section giving a total of 1008 potential observations. These cohort-educational level cell means are used to estimate a dynamic equation as given by equation (6). I regress the proportion of women in each cell who are in the paid labor force on the cell means of the explanatory variables and on a set of cohort-educational level dummy variables. This is a least squares dummy variable formulation, and is identified off of changes within a group over time--for example changes in the participation rate for a group is a function of changes in household level income for that group. Having estimated equation (6), the coefficients of the cohort-educational level dummies (the f i terms in the equation) can be regressed on education and the wage profile to see how education affects participation over the entire life cycle. All of the stages are discussed in more detail below. 5 When grouping the data across the cross sections, it is important to choose a group that is fairly homogeneous but is large enough so that each group contains enough observations so that results are not driven by outliers (Deaton 1985). That is why the groups were chosen in six educational groups and 14 cohorts. For all women, each cell in each year had a minimum of 17 observations. The mean was 831 women per cell, with only 6.7 percent of the 996 cells including less than 100 women. For married women, each cell in each year had at least 15 observations. The mean cell size was 569 women, with only 11.6 percent of the 960 cells including fewer than 100 women. 9

14 10 Estimating Predicted Wages For each year, I estimate a separate wage function. The coefficients from the wage functions are used to predict wages for both working and non-working women. I include the years of 1976, 1978, and 1981 to 1990 because of the availability of variables used as instruments. I estimate a wage function for all women and also for married women only both using Olsen s correction for sample selection (1980) and using OLS. In Olsen s procedure, the first step is running a linear probability regression for whether an individual woman is in the paid labor force or not. A woman is defined as being in the labor force if she reported earnings and hours worked in the survey week. She works if the wage she can obtain in the labor market exceeds the value of her time at home, or reservation wage. In equation form: w= β X + u (8) w*= γ Z + v (9) where w* is the reservation wage, which is a function of Z, variables that increase household productivity and X are variables that affect the market wage. A woman will work if w > w*, or βx + u > γ Z + v (10) βx γ Z > v u (11) The wage equation will be w = βx + E( u βx γ Z > v u) (12) To use Olsen s correction, it is assumed that the v s are distributed uniformly over [0,1]. To estimate equation (12), suppose wages are observed if γz + v > 0. Then the probability that v >-γz will equal 1 -γz and the wage equation will be w = βx + E( u v < γ Z) (13) w = β X + ρσ u 31 ( γ Z) (14) and γ is estimated by the linear probability model. For women who do not work outside the home the model is w = β X + ρσ u 3( γ Z) (15) For the system of equations to be identified, it is necessary to have a regressor that belongs in the participation equation but not in the wage equation (Z) and a regressor that belongs in the wage equation but not the participation equation (X). One advantage of the Olsen correction over the Heckman (1979) correction is that the latter has a non-linear function in the first stage. Identification in the Heckman method could arise only from the functional form. Since the Olsen correction is linear, identification can only arise from the exclusion restrictions. In the first stage of the Olsen specification, the linear probability model, I regress a dummy variable for whether a woman is employed in the paid labor force on variables representing the composition of the household, access to public goods, region, and income, net of the woman s earnings. When estimating the linear probability model for all women, the variables include log of family income net of the woman s earnings divided by the number of people in the family older than 10 to control for family size, whether the household has indoor plumbing, and household composition variables including a dummy for marital status, the number of children in the family aged three and younger, the number of children aged four to six, and the number of women aged 15 and older who may be available for child care (Table 1). I include region in the regression to control for labor market opportunities available to women. The percentage of total 10

15 11 employment in the textile industry in the state where the woman lives is a regressor that represents the demand for relatively unskilled female labor. It is included in the linear probability model, since it is a determinant of the wage 6. The first stage regression also includes cohorteducational level dummy variables. Each cohort includes three birth years. There are fourteen cohorts and six educational levels for a total of 84 cohort-educational level dummies. 7 The omitted category is women who live in the northwest region who were born from 1959 to 1961 (the youngest cohort) and have no education. Age was not included because in the single year cross section, it is not possible to separately identify cohort and age. Given the year of birth of a woman in the sample, both her cohort and her age are determined. Variables that theory predicts will increase the probability of participating in the labor market include education, and the number of women in the household aged 15 and older. Women who belong to higher educational levels will have higher participation than women in the same cohort with less education. Education increases productivity in the market and in the home. The increase in the opportunity cost of staying at home tends to outweigh the increase in productivity in the home. Income net of the woman s earnings would have a predicted negative effect on labor force participation because at higher income levels, an individual demands more leisure. I assume here that family income is exogenous and that family composition is exogenous. 8 Indoor plumbing is a good that has a public good component. The infrastructure has to be in the community to get plumbing into the home. Having plumbing may allow women to finish their household responsibilities more rapidly, freeing up time to work in the labor force. However, plumbing may represent wealth because families must pay for tubing on their property in order to get indoor plumbing even if the infrastructure is in place in the neighborhood. They may also move to neighborhoods because of the availability of public services. For plumbing to be a valid instrument, it must be true that women did not participate in the labor market in the past in order to obtain indoor plumbing. These variables may be correlated with the error term in the wage equation. The number 6 The rationale for using the percentage employed in the textile industry as an instrument is that once women decide to participate in the paid labor market, they do not care which industry they work in. The presence of a textile factory in an area raises the demand for female labor, but does not affect participation independently of the factory s effect on wages. 7 The specification includes the interaction terms because they are the variables used to determine the groupings for the dynamic model. The interaction terms are in fact a function of education, cohort and age. In a single year, it is not possible to separately identify age and cohort effects. An estimate of age effects will represent an age profile for a given cohort if the shape of all age profiles is the same across cohorts. 8 If family composition is not exogenous, suppose that there are bad times. As a consequence, younger adult children move in with their parents. We would observe an increase in family income available to the children. Income effects would be underestimated if, when times are bad, adult children move home and continue working. Income effects are overestimated if adult children move home and stop working. If children leave home in order to work, this will overstate income effects. 11

16 12 of children is likely to be correlated with a woman s "taste" for staying at home, which is part of error term v. If families decide to have their members specialize in either market or non-market work, then income exclusive of the woman s earnings will be correlated with the error term in the wage equation. Family members who specialize in non-market work are unlikely to have worked in the labor market in the past, which affects labor market experience, which theoretically affects wages. Women who have a higher taste for working in the market may encourage relatives to come and live with them in order to care for their children. This taste for work would also tend to increase her wage. The wealth indicated by indoor plumbing may have resulted from labor force participation in the past. Unfortunately, the PNAD data sets do not have variables that would make better instruments. Therefore, both sample selection corrected and uncorrected results are presented. For married women, the regressors in the linear probability equation are log family income net of the woman s earnings, the husband s education, whether the husband is unemployed, whether there is indoor plumbing, the number of children aged 3 and younger, the number of children aged 4 to 6, the number of women aged at least fifteen, regional dummies, the percentage of employment in the textile industry in the woman s state, and the 84 cohorteducational level dummies. It is a helpful exercise to try to think of expected biases in the uncorrected results. Sample selection bias is likely to be more of a problem for women with low levels of education because a smaller percentage of them are in the labor market than women with high levels of education. The women who do work who have low educational levels are likely to have higher ability or aptitude for working (unobservable characteristics) than the women who do not work who also have low educational levels. Assuming that women who do not work will earn the same return on human capital as the women that do work will tend to overstate wages for the population of women with a low level of education; therefore, uncorrected wage regressions are likely to under predict rates of return to education. If the biases of returns to the explanatory variables were constant over time, it would be possible to say that observed wages are moving in the same direction as the predicted wage for the entire population. However, since more women are entering the labor force over time, it is likely that selectivity is changing, and therefore so is the bias. Complicating the analysis further is the possibility that wages are not always moving in the same direction, as shown by Figure 4. For example, if we know that women with low educational levels have upwardly biased predicted wages, the bias is decreasing over time, and that real wages have been rising, labor supply elasticity for these women is likely to be overestimated in a standard labor supply equation. Over time, the path of the biased predicted wages will be less steep than the path of real, unbiased wages, giving a greater estimated response of hours to the change in biased predicted wages. Conversely, if real wages have been falling, labor supply elasticity will be understated. Therefore, since we are looking at changes over time, the bias is difficult to determine. Real wages are rising and falling from year to year and it is not certain how the sample selection bias on returns to education is changing. Having estimated the linear probability equation in order to calculate (1-γZ), and -γz, the next step is to estimate the wage equation. The wage equation includes the 84 cohort-educational level dummy variables. Four regional dummies control for the cost of living. The percentage of employment in the textile industry in each of twenty-seven states is a proxy for demand for female labor. The appendix presents the linear probability of working regression and wage 12

17 13 regression estimates for 1976 and 1990 to give an idea of the results for the beginning and end of the twelve years included in the analysis. Note that for all four wage regressions--all women in 1976 and 1990 and married women in 1976 and the coefficient of the Olsen correction is positive and significant, indicating that the correlation between the error term in the participation equation and the error term in the wage equation is positive. Unobserved characteristics that increase the probability of participation for women also tend to increase the market wage. The signs of the variables in the participation regressions are as expected, except for the indoor plumbing variable, which has a negative sign and is significant in the 1976 participation regression for all women and is not significant in the other participation regressions. This indicates that indoor plumbing is a proxy for wealth in the cross section. Also, in the married women s regression, the dummy variable for husband s unemployment is negative and insignificant in both 1976 and 1990, which is evidence against the added worker effect. The 84 cohort-educational level dummy variables, which the appendix does not present, show that participation increases with education and that younger cohorts are more likely to participate than older cohorts. Being from a younger cohort also tends to increase wages. To test for a separate effect of cohort apart from education level on participation, I ran two regressions on the sample that had both married and unmarried women for the 1976 and 1990 PNADs. In addition to the variables presented in the appendix, one regression had 16 years of schooling dummy variables (model a), and one had the schooling dummy variables plus cohort dummy variables (model b). An F test comparing models b and a confirms the significance of the cohort dummy variables at the one percent level in both 1976 and Comparing the Actual and Predicted Wage Paths Having estimated the wage equations, it is possible to predict wages for all women in the relevant sample. Figures 6a through 6f trace the wage path that the average woman who was aged 30 to 32 in 1976 would have experienced through 1990, with a separate graph for each educational group. The graphs present the path for women in this age group because female labor force participation peaks between the ages of 30 and 46. Each graph shows separate paths for the observed mean wages for working women only, predicted wages for all women excluding the sample selection correction, and predicted wages for all women including the sample selection correction. The paths are normalized so that the value of the predicted wage in 1981 without the sample selection correction is equal to 0. Therefore, the axis can be interpreted as the percentage difference in wages compared to the 1981 predicted wage without the sample selection correction. It is striking that none of the paths follow a typical concave wage profile in age. Wages were volatile during the 1976 to 1990 period, including predicted wages. Suppose women who worked in the labor market had higher ability than women who did not work. Then, the average predicted wage without sample selection correction calculated for all women, whether working or not, would be higher than the average predicted wage with sample selection correction. This is the case shown in the figures. As education increases, the difference between the two predicted wage paths decreases. Sample selection matters less for high educational levels than for low educational levels. Also, it appears that sample selectivity decreased slightly until about 1983 and then increased in the late 1980s. This may indicate that returns to ability have been increasing in Brazil over the late 1980s. 13