1 γ λ 1 r 1 ε
< β ≤ + + − (4)
where the first inequality follows from the assumption γ β> .
C. PNAD data and variable description
In this section, I describe the sample from the PNAD data set used in the empirical analysis, and the choice of empirical counterparts to the model variables. The empirical analysis will be conducted on the 1976 and 1996 PNAD surveys of Brazilian households.
The Pesquisa Nacional de Amostra Domiciliar (PNAD) is a series of cross-sections that have been collected annually since 1973 (except for 1980, 1990 and 1991) by the Instituto Brasileiro de Geografia e Estatistica (IBGE). Each cross-section contains over 100000 observations on Brazilian households, and over 300000 observations on individuals. The PNAD is close to a nationally representative sample, though it is not fully representative of rural areas, especially in the remote frontier regions.
The PNAD is mainly concerned about labor market outcomes, but it also has information on some individual demographic variables, including fertility for some specific years. The empirical analysis uses two subsamples, for fertility and for schooling (income) of the adult child. The fertility sample consists of about 18000 married women aged 45 years and over in 1976.
Since information for both the child's and parental schooling in 1976 is available only for families in which children live with their parents, I used information from the PNAD 96 to construct measures of the adult child's schooling and income. This is possible because the 1996 PNAD has information on schooling of parents for household heads and spouses of household heads. The schooling (income) sample consists of about 18000 respondents aged 41-50 in 1996. The rationale for the choice of the latter age range is that it corresponds to the cohort aged 21-30 in 1976, for which I want to gather education and income information.
The measure of fertility used in the paper is the number-of-children-ever born to married women aged 45 years and older. This age range is chosen to have a measure of completed fertility.
The measure of full income (labor income) for fathers used in this paper is the log of average income (labor income) for individuals working on average 40 hours per week during the year. I compute different averages of full-time income (labor income) for male household heads grouped according to some characteristics, such as education, region of residence, and whether they live in an urban or rural area. This measure is computed for
individuals working full-time, and is assigned to all individuals sharing the same characteristics.
Years of schooling of adults aged 41-50 in 1996 is used as the measure of the adult child's human capital. I construct the adult child's income (labor income) measure by first computing different averages of income (labor income) for male household heads working on average 40 hours per week during the year, grouped according to their education, region of residence, and whether they live in an urban or rural area. These full-time income (labor income) averages are then assigned to men and women aged 41-50, according to their characteristics.
I use several control variables, including age and age squared of the husband, wife and oldest child, and the sex of the oldest child. I also use dummy variables for region residence and for whether the family lives in an urban or rural area. The latter may be viewed a proxy for the goods cost of fertility, φ, since the cost of living is usually higher in urban than rural areas.
All regressions use sampling weights available from the PNAD.
0 5 10 5 0
102 4 6
human capital physical capital
fertility
Fertility Policy Function
0 5 10
2 3 4 5
human capital
fertility
Fertility Policy Function (k=2)
0 5 10
2 2.5 3
physical capital
fertility
Fertility Policy Function (h=2) Figure 1-Fertility Policy Functions (baseline parameters)
100 101 102 103 0.8
0.9 1
parental wealth (log scale)
labor share
Labor-Share-Wealth Cross-Section Profile
100 101 102 103
2 3 4
parental wealth (log scale)
fertility
Fertility-Wealth Cross-Section Profile
100 101 102 103
100 102 104
parental wealth (log scale)
adult child wealth (log scale)
Persistence of Wealth Inequality
Figure 2-Cross-Section Profiles at t=0 (baseline parameters)
0 5 10
100 101 102 103 0.8
0.9 1
parental wealth (log scale)
labor share
Labor-Share-Wealth Cross-Section Profile
100 101 102 103
0 1 2
parental wealth (log scale)
fertility
Fertility-Wealth Cross-Section Profile
100 101 102 103
100 102 104
parental wealth (log scale)
adult child wealth (log scale)
Persistence of Wealth Inequality
Figure 4-Cross-Section Profiles at t=0 (lambda=0.4)
0 5 10 5 0
102 4 6
human capital physical capital
fertility
Fertility Policy Function
0 5 10
2 3 4 5
human capital
fertility
Fertility Policy Function (k=2)
0 5 10
2 2.5 3 3.5
physical capital
fertility
Fertility Policy Function (h=2) Figure 5-Fertility Policy Functions (epsilon=0.5)
100 101 102 103 0.8
0.9 1
parental wealth (log scale)
labor share
Labor-Share-Wealth Cross-Section Profile
100 101 102 103
0 5
parental wealth (log scale)
fertility
Fertility-Wealth Cross-Section Profile
100 101 102 103
100 102 104
parental wealth (log scale)
adult child wealth (log scale)
Persistence of Wealth Inequality
Figure 6-Cross-Section Profiles at t=0 (epsilon=0.5)
100 101 102 103 0
5 10
parental wealth (log scale)
fertility
Fertility-Wealth Cross-Section Profile (PNAD 76)
100 101 102 103
100 102 104
parental wealth (log scale)
adult child wealth (log scale)
Persistence of Wealth Inequality (PNAD 76) Figure 7-Cross-Section Profiles (PNAD 76)
102 104 106 108 2
4 6
family income ($,log scale)
fertility
Fertility-Income Profile without Childless (SCF89)
102 104 106 108
2 3 4
family income ($,log scale)
fertility
Fertility-Income Profile (SCF89)
Figure 8-Fertility-Income Cross-Section Profiles (SCF 89)
Table1:baseline parameters
β =0.25 3 r=
ε =0.2 5 A=
λ=0.14 α =0.67 γ =0.33 φ =0.5
Table 2: Fertility regression coefficients
persistence of wealth persistence of labor income
0 0.94
Table 4: Fertility regression coefficients (λ=0.4)
wealth labor income
0 0.25
θ = − θ = −0L 0.22
1 0.01
θ = θ =1L 0.01
2 0.22
θ = θ =2L 0.22
3 0.89
θ = θ =3L .
4 0
θ = θ =4L .
θ∞ =. θ∞L =.
Table 5: Persistence of inequality (λ=0.4)
persistence of wealth persistence of labor income
0 0.52
ρ = ρ =0L 0.45
1 0.35
ρ = ρ =1L 0.28
2 0.19
ρ = ρ =2L 0
3 0.16
ρ = ρ =3L .
4 0
ρ = ρ =4L .
ρ∞ =. ρ∞L =.
Table 6: Fertility regression coefficients (ε =0.5)
wealth labor income
0 0.76
θ = − θ = −0L 0.69
1 0.92
θ = − θ = −1L 0.92
2 0.95
θ = − θ = −2L 0.95
3 0.88
θ = − θ = −3L 0.88
4 0
θ = θ =4L 0
θ∞ =0 θ∞L =0
Table 7: Persistence of inequality (ε =0.5)
persistence of wealth persistence of labor income
0 0.93
ρ = ρ =0L 0.91
1 0.92
ρ = ρ =1L 0.92
2 0.95
ρ = ρ =2L 0.95
3 0.98
ρ = ρ =3L 0.98
4 1
ρ = ρ =4L 1
ρ∞ =1 ρ∞L =1
independent
Notes: (a) All income variables are measured in logs. Standard errors in parentheses. The regressions use sample weights provided by IBGE. N refers to the unweighted number of observations.
(b) The full-time concept of full income is defined as average family income for men who are household heads and work 40 hours per week on average.
Different income averages are calculated for each possible combination of education category, state of residence and whether the individual lives in a urban or rural area.
(c) A constant, the mother's age, its age squared, the father's age, its age squared, the oldest child age, its age squared, the oldest child's sex, a dummy variable for urban areas, a dummy variable for the state in which the family resides and mother's schooling are included in each regression.
(d) * significant at the one-percent level
Table 8: OLS Regression of fertility, adult child's schooling and adult child's income on family income (full-time)- PNAD
76
independent
Table 9: OLS Regression of fertility and adult child's wage on father's wage (full-time)- PNAD 76 and Mulligan (1993)
Notes: (a) All wage variables are measured in logs. Standard errors in parentheses. The PNAD regressions use sample weights provided by IBGE. N refers to the unweighted number of observations.
(b) The full-time wage measure for the PNAD is defined as average hourly wage for men who are household heads and work 40 hours per week on average. Different wage averages are
calculated for each possible combination of education category, state of residence and whether the individual lives in a urban or rural area.
(c) A constant, the father's age, its age squared, the child's age, its age squared and the child's sex are included in each regression.
(d) * significant at the one-percent level
independent
Table 10: 2SLS Regression of fertility and adult child's wage on father's wage (full-time)- PNAD 76, PNAD 96 and Mulligan
(1993)
Notes: (a) All wage variables are measured in logs. Standard errors in parentheses.
The PNAD regressions use sample weights provided by IBGE. N refers to the unweighted number of observations.
(b) The full-time wage measure for the PNAD is defined as average hourly wage for men who are household heads and work 40 hours per week on average. Different wage averages are calculated for each possible combination of education category, state of residence and whether the individual lives in a urban or rural area.
(c) For the Mulligan (1993) PSID data mother's schooling is the fitted value from a regression of mother's schooling on the age variables, father's wage, fertility, a gender dummy and agriculture's share of personal income in the county where the son grew up. For the PNAD, mother's schooling is the fitted value from a regression of mother's schooling on the age variables, father's wage, mother's full-time labor income, a gender dummy , and a dummy variable indicating whether the father lives in a urban area.
(d) A constant, the father's age, its age squared, the child's age, its age squared and the child's sex are included in each regression.
(e) * significant at the one-percent level
** significant at the five-percent level
independent variables
log earnings (PNAD 76)
log earnings (PNAD 76)- age
controls
log earnings (Mincer (1993))
log earnings (Mincer)-age
controls
schooling 0.17 *
(0.0007)
0.18 *
(0.0007) 0.09* 0.09 *
adjusted R
squared 0.45 0.47 0.07 0.14
N 62875 62860
Table 11: OLS Regression of log earnings on schooling (with and without age controls) - PNAD 76 and Mincer (1993)
Notes: (a) Standard errors in parentheses. All regressions include a constant term. The PNAD regressions use sample weights provided by IBGE. N refers to the unweighted number of observations.
(b) The respondent's age and his age squared are used in the regressions displayed in columns 2 and 4.
(d) * significant at the one-percent level