Testing the Mincer Model Hypotheses for Brazil∗ - FGV EPGE

Testing the Mincer Model Hypotheses for Brazil∗

Rodrigo Leandro de Moura

EPGE/FGV-RJ†

Abstract

Many estimates of rates of return for education have been produced, based on the Mincer’s

model. But some of the hyphoteses (linearity and separability), so that the ("mincer") school

coefficient is interpreted as rate of return, are tested and rejected. When relaxing such hypothe-

ses, we estimate the internal rates of return (Becker, 1975) and we get biases that arrive to 14

percentile points in relation to the “mincer coefficient”. Thus, the magnitude of these returns

is much lower than the papers based on Mincer’s model.In the estimates we incorporate the

sample design of PNAD and correct the problem of bias of sample selection.

Key-words:returns to schooling, sample selection, sample design, local non-parametric linear

regression.

JEL Code: I20, J24, C14, C42

1 Introduction

The decision to accumulate human capital (education, on-the-job training, health, etc.) depends

upon the correct assessment of the returns. One way of measuring the returns is through the use

of the internal rate of return (IRR), a central concept in the theory of human capital, developed in

the analysis of the individual’s decision to invest in human capital. This measure was developed in

Becker (1975, hereinafter referred to as Becker) and Shultz (1963). In their analysis, the individual

invests in human capital through a comparison of the flows of benefits and costs, from which he takes

∗Article accepted for publication in the Brazilian Economic Review (Revista Brasileira de Economia), 62(1):1-47,

2008. I wish to thank Carlos Eugênio da Costa, of the EPGE/FGV, for various comments and guidance in the

preparation of this article; Petra Todd, of the University of Pennsylvania, for making available the R codes that were

important for some of the tests in this article; Luis Henrique Braido and Luis Renato Lima, of the EPGE/FGV,

and all of the other participants in the Research Seminars at the EPGE for their various suggestions and criticisms,

Breno Néri, a doctoral candidate at New York University for his help with a routine; Elaine Toldo Pazello, of the

FEA-RP/USP, for her suggestions; Maurício Lila, Djalma Pessoa and Pedro Nascimento Silva, of the IBGE, for their

help regarding PNAD and the Census and all of the participants of the XXVIII Meeting of the Brazilian Econometric

Society (SBE), where a preliminary version of this paper was presented. Finally, I wish to express my appreciation

for the comments of an anonymous referee. Any remaining errors are the sole responsibility of the author.†Ph.D. in economics from the EPGE/FGV-RJ. Lecturer of economics at FGV-RJ. E-mail: rodrigolean-

[email protected] or [email protected].

1

a discount rate that makes them equal. Becker shows that a risk-neutral agent who is maximizing

his wealth will tend to concentrate his investments at an early age, because: (i) with the passage of

time the individual has a shorter period of time to recover the return on his investment in human

capital and (ii) the opportunity costs increase with the increase in the level of human capital. In this

paper we will focus on only one component of human capital: education. Individuals with higher

levels of education tend to have higher incomes. This is logical, since with a greater accumulation

of education there is a tendency to improve skills, knowledge and health, all factors that increase

worker productivity. And this last tends to equalize earnings in a perfectly competitive market1.

Therefore the accurate calculation of the IRR depends on the estimates of the individuals’s earnings

profile over their life cycle.

Nevertheless, in the empirical literature, various estimates of rates of return have been re-

ported, based on the seminal models of Mincer (1958 and 1974, hereinafter Mincer I and Mincer

II, respectively) that derive the following salary equation: :

lnY (s, x) = α+ βs+ γx+ δx2, (1)

where, Y (s, x) represents income adjusted for hours of work, s represents years of study and x rep-

resents experience. This coefficient β is known as the mincerian coefficient (or return) on education.

Heckman (2005) points out that in the United States, there are several apparent empirical puzzles,

such as: high mincerian returns to education vis-à-vis other investments; and given this, a slow

response in enrollment by recent cohorts of individuals. But according to Heckman, Lochner and

Todd2 (2006, hereinafter HLT), few of these estimates represent true rates of return. Many of the

assumptions of the Mincer model that turn the mincerian coefficient into an internal rate of return

(TIR) are valid only under very restrictive conditions. Thus, the study of returns to education

must invariably start with Mincer’s original models where these assumptions must be tested.

In Brazil various studies consider the mincerian coefficient as a rate of return, but none of

these studies performed any tests on the assumptions. Meanwhile, various studies have already

performed tests of linearity (Hungerford and Solon, 1987; Jaeger and Page, 1996; and Heckman et

al., 1996b), and more recently parallelism (HLT) in the United States, rejecting these assumptions,

which are crucial for the interpretation of the coefficient as a return to education. The IRRs

can therefore be seen as an opportunity cost for investing in education in comparison with other

alternatives. And, contrary to the “mincerian” returns, the IRR takes into account costs (direct

and indirect). Therefore, only when the assumptions of the Mincer model are satisfied, and under

some additional restrictions, can we say that the IRR is equal to the mincerian coefficient. Some

of these assumptions are: that the working lifetime is the same for all individuals independent

of their educational level; during the period of education individuals do not work; the only costs

incurred are the opportunity costs, in other words, the income from the labor market foregone

1Obviously there are other (non-monetary) benefits derived from the learning process, but according to Becker,

the results point to the secondary importance of these other benefits.2An earlier version of this paper was circulated under the title: Fifty Years of Mincer Earnings Regressions.

2

during the period of schooling; that uncertainty does not exist; agents are risk neutral; there are no

imperfections in the credit market; linearity in schooling and separability between schooling and

experience (parallelism). Therefore, based on similar data and the same structure of the Mincer

model, we tested for the last two assumptions and rejected both hypotheses. In this case, then,

the mincerian return might be better understood as a rate of growth in market wages due to the

increase at the margin in years of study, or even as the marginal cost of education.

Then we estimated the IRRs, using the mincerian coefficients as references, and we showed that

the bias is relatively high when we relax the assumptions of linearity and parallelism. We obtained

biases that reached to a little more than 14 percentage points, when comparing the mincerian

returns (17.29%) to the IRR (3.03%) for the Masters and Ph.D. degrees when compared with an

undergraduate degree. Various studies in Brazil do not take into account these assumptions and,

consequently, their estimates are inaccurate and the degree of this discrepancy is relatively large,

which could lead to distorted or poorly understood conclusions. In addition, we relaxed other of

the above-mentioned assumptions as well.

We used two econometric techniques: parametric and nonparametric regressions. The test for

linearity used the first and the test for parallelism used the second. The calculation of the IRRs

involves the use of both instruments. In all of the estimates, we used PNAD (Brazilian Household

Sample Survey) (This is from the IBGE website) and Census data. With regard to the PNAD data,

we could not assume a random independent and identically distributed sample because the survey

sample is very complex. Therefore we incorporated the sample design of the PNAD3, which could

be considered a positive addition to the empirical literature for Brazil4. In addition, we corrected

the problem of bias in the sample selection that occurs because some individuals choose not to work

because the market wage is lower than his reserve wage. This modification could also be considered

a positive addition, given that even recent studies, such as HLT, do not incorporate this feature,

which changes the magnitude of the IRRs, Thus, we compare estimates made without correction,

incorporating the sample design, and estimated by the two-stage estimation procedure developed

by Heckman (1979)5.

This paper follows the following structure: section 2 presents a selective review of the literature;

section 3 shows, through a simple model, the relationship between the IRR and the mincerian

coefficient; section 4 presents the methodology and results for the linearity and parallelism tests;

section 5 describes the methodology, results and discussion of the IRRs and section 6 offers some

conclusions.3This point will be discussed in greater detail in section 4.2.4With regard to the census, the incorporation of the sample design was not possible. The variables that permit

the incorporation of the samples on the census are considered “classified data” by the IBGE and for this reason they

are not revealed.5The correction of the sample selection bias was done only for the parametric models. For the non-parametric

models it was not possible, because of the great complexity and size of the procedure. This adjustment was proposed

by Das, Newey and Vella (2003) and could be incorporated in future research.

3

2 Review of the Literature

The selective review of the literature presents international and national evidence with regard to

articles where the Mincer and the concept of the IRR are applied.

International Evidence — Mincer In a recent review, Card (1999) points out that studies

that relate education and earnings are almost always heavily based on the Mincer models. But

the functional form of Mincer’s model has raised various issues. Card has already shown that

one way of estimating earnings could be through the use of nonparametric techniques, such as a

general function of years of education and age. In the same vein as the parametric estimations,

Murphy and Welch (1990) show that a linear term of the years of education and a third or fourth

order polynomial for experience leads to a significant improvement in adjustment. An important

factor highlighted by these two studies is that the parametric model has problems in adjusting the

precise form of the profiles of earnings-age (experience) for US data because it tends to skew the

estimated rate of growth in worker earnings with a given level of education, in relation to the value

of the sample. This occurs because of the lack of specification of the model. Another problem that

emerges from these models is a reduction in the parsimony when cubed and fourth power terms

are added to the specification, leading to a problem of increased multicollinearity in the estimates.

These problems can be overcome using nonparametric estimation techniques.

Meanwhile, Card emphasizes the high degree of explanatory power of the mincerian model.

According to Park (1994), in the United States, the linear term for education is well suited to the

data. But there is evidence contrary to the linear model pointed out by Hungerford and Solon

(1987), Belman and Heywood (1991), Jaeger and Page (1996) and Heckman (1996), that make

estimates based on the mincerian model with such additional non-linearity components as, for

example, dummy variables for the years when the course of study was concluded to capture the

“sheepskin effect”6. An F test for the nonlinear terms strongly rejects the linear model.

Psacharopoulos (2004, 1994, 1985) revises the estimates for the rate of return based on the min-

cerian model for various countries, obtaining rewards for education in the Latin America/Caribbean

and sub-Saharan Africa areas — low and medium income countries — that are higher than the average

return worldwide. In addition, during the last 12 years the average mincerian returns worldwide

have declined by 0.6%, while the average level of education has increased7.

Brazilian experience - Mincer With regard to Brazil, various studies have estimated and

considered the mincerian coefficient to be the rate of return. Most of these studies relax the

6The “sheepskin effect” captures the effects of greater returns because of having obtained a degree. This “sheep-

skin” can be interpreted as signal of productivity for which the market contracts the worker.7The reference period depends on the country, varying from 1970 in Morocco to 1998 for Singapore and the

Philippines. Some of these estimates were obtained by the author from other articles. Psacharopoulos (2004) points

out that these comparisons are not exact due to differences in methodology and in the sample size.

4

assumption of linearity, estimating a spline function for years of study, as for example in Leal and

Werlang (1991). Blom et al. (2001) is a recent study that estimates current mincerian returns

for Brazil, using the Mincer II model, but relaxing the linearity assumption by using a spline

function with knots for the years when the cycles are concluded. The authors, using regressions

of the average and quantile conditions, find that there is a wide dispersion of the returns among

the different quantiles at all levels, with the exception of the third level. They suggest that this

dispersion could be due to uncontrolled factors (quality of the school, social capital and unobserved

abilities) related to the returns and that his estimated model will permit the interaction between

education and other terms such as experience, which would relax the parallelism assumption.

Sachsida, Loureiro and Mendonça (2004), using the PNAD for 1996 and various accumulated

years (1992 - 1999), calculate the mincerian return using Mincer II, but correcting for some sources

of bias, such as: sample selection, endogeniety of the education variable and the unobserved ability

of the individual. Soares and Gonzaga (1999), using the 1988 PNAD, test for the existence of duality

in the Brazilian labor market, and a sense of the existence of different salary structures associated

with “good” occupations (linked, for example, to greater returns to education, among other factors)

and “poor” occupations. These two studies, as well as that of Loureiro and Carneiro (2001) are some

of the few that relax the linearity and parallelism assumptions, but apply a functional form to the

equation. The results of these studies point to the significance of the term for interaction between

time in the labor force and years of education, therefore rejecting the assumption of parallelism.

Other studies where the principal objective is not to estimate rates of return, use the Mincer

model in their analyses. Fernandes and Menezes (2000) examine the evolution of inequality of

earnings from work, utilizing a mincerian regression (Mincer II) to which some controls are added,

and relax the assumption of linearity for the years of study. The mincerian return on education, in

this study, is an important explanatory factor in the reduction of inequality, principally between

1990 and 19918.

International Evidence - IRR Focused specifically on the IRR, Becker resolves one important

question relating to earnings-costs-rates of return: the difficulty in isolating the effect of the earnings

8Given the enormous range of studies on returns to education based on the mincerian model, it was not possible

to describe them in detail. But other recent studies that use the Mincer model should be mentioned, such as:

(i) Resende and Wyllie (2006) and Loureiro and Carneiro (2001) that correct for the problem of sample selection

bias by using a linear function for education, where the first controls for quality of education using the PPV between

1996 and 1997, and the second uses PNAD for 1998, and concludes that there are salary differences between rural

and urban laborers and discrimination by race and gender.

(ii) Ueda and Hoffman (2002) estimate the returns to education using least-squares and instrumental variables and

using linear and nonlinear specifications, including socioeconomic variables. They use the PNAD for 1996.

(iii) Silva and Kassouf (2000) examine the degree of segmentation and the labor market, correcting also for the

problem of sample selection, but using a multinomial logit model for the estimation of the selection equation, in order

to differentiate the unemployed and employed workers in the formal and informal sectors. They use the PNAD for

1995.

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derived from a change in returns or a change in the amount invested in education. In the context of

a static model, in which investment is confined to a single time period, and the returns to all of the

remaining periods, Becker argues that the cost and the rate of return are easily determined taking

only the income stream. To accomplish this, he compares the flow of earnings from two different

levels of education, one with investment in the first period and the other that does not require a

lump sum investment. The cost of investment in education would be the net income forgone. This

is the context we use in our model for estimating the IRR9.

Schultz (1964) had already pointed out that the costs should be considered in the analysis of

investment in education. These costs extend beyond the monthly tuition expenses, annuity fees and

others, where the salaries forgone make up a significant part of the cost. In the context of economy

of the whole, the costs incurred by the schools (maintenance of infrastructure, depreciation and

services) are relevant, while in the context of the individual decision, the direct and indirect costs

of the student are more important. Of these latter costs, Schultz emphasizes the cost of the time

the students spent in school, where they are estimated by using the income foregone while students

are in school. Since there does not exist a perfect equivalent from which we can extract the income

stream for the case of the individual who attends, or does not attend, school, we have to take as a

reference point individuals with similar characteristics, but who are in the workforce.

Psacharopoulos (2004), also estimates the IRR, both private and social, for various countries,

and points out that the Latin America/Caribbean and sub-Saharan Africa regions are the ones

with the highest returns for all levels of education. Psacharopoulos (1994) points out that the

IRR method is the most appropriate but also says that this methodology has been replaced by the

Mincer II methodology because of the lack of a base with a sufficiently large number of observations

for a given cell for age-educational level for the construction of well-behaved earnings-age profiles

(concave and non-intersecting). But these arguments have been weakened given the wide range of

bases that currently exist.

Brazilian Evidence - IRR With regard to Brazil, Langoni (1974) was one of the first to estimate

the IRR for Brazil, based on Schultz (1964) and Becker. He calculated the direct costs (the cost

of infrastructure of the school and its depreciation, teacher salaries and student expenses) and

indirect costs (income foregone by students because they have left the labor market, and capital of

the school, measured by the interest sacrificed by the teaching institution). Note that the author

included costs of the school, which is of interest for the social rate of return, but not for the private

rate of return, which does not include these components10. To calculate the IRR, it is necessary

to measure income profiles by experience (age), Langoni does this by using sample means and not

9Future research could include dynamic analysis. The problem here is the lack of a database in Brazil that

accompanies individual through his time in school and, at least, for a part of his working life and would therefore be

able to measure the investment decision by the agent.10Langoni (1974) apparently does not incorporate taxes on the side of benefits, which would be more correct in

estimating the social rate of return.

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through regression11, using cross-sectional data. The IRRs for 1960 and 1969 vary from 48.1% to

32% for illiterates; from 23.8% to 19.5% for middle school as opposed to primary school; and from

14.8% to 21.3% for high school as opposed to middle school; and from 4.9% to 12.1% for college

compared to high school. Barbosa and Pessoa (2006) update Langoni’s work using his methodology.

We show the equivalence between the IRR and the mincerian coefficient below.

3 The equivalence between the IRR and the "mincerian coeffi-

cient"

Mincer I and Mincer II arrive at the same model, but for different reasons. Mincer I uses the

principle of compensating differentials to explain why individuals with different levels of education

receive different income streams over their life cycles. Mincer II assumes that these individuals

can invest in human capital after education (through, for example, on-the-job training) to acquire

or improve their skills, expand their information set regarding their occupation and increase their

potential income. Mincer II obtains the same exact equation (1), while Mincer I has the same

functional form, but without the term for experience.

Therefore, in this section we show that, under certain assumptions, the mincerian coefficient

β for the equation (1) is equal to the IRR for education. Let Y (x, s)equal the annual income

for an individual with x years of work experience and s years of education, and l equal the total

time working. The direct and indirect assumptions in the Mincer model to demonstrate this

equivalency12 are: (i) a neutral risk agent that maximizes the present value of expected income

over the lifecycle, (ii) where l′(s) = 1 (in other words where the time in the workforce is equal for

all individuals independent of their level of education), (iii) that the only costs incurred are the

opportunity costs, in other words, the deferred income from the labor market during the period

of schooling, (iv) that uncertainty does not exist, (v) that the individuals enter the labor force

one period after concluding their studies, (vi) that the individuals do not work while they are

studying, (vii) that there are no imperfections in the credit market, (viii) that after obtaining a job

individuals do not return to school, that the functional form for income will be (ix) the (log) linear

for education and (x) (in level) are multiplicatively separable between education and experience.

This last assumption does not permit interaction between education and experience and maybe

better visualized by rewriting the equation (1) to obtain the following production function for

11The problem with sample means is that it is less efficient, in terms of greater variance, than the estimator of

minimum least squares. Thus, the graph of the income-experience (age) profile, by level of education, according

to the regressions tests to be extremely smooth, while the sample means does not show any smoothness, and may

present spurious relationships between the variables. We can overcome this problem using nonparametric regressions

that do not impose a functional form that regresses one variable against another, which imposes a causal relationship

between the endogenous and exogenous variables, while the sample means do not.12This equivalency is shown also in HLT and Willis(1986), which they derive for the case of continuous time.

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human capital::

Y (x, s) = λ(s)θ(x),

where, λ(s) = λ(0)eβs, and θ(x) = eγx+δx2. Thus, we have ∂ lnY (x,s)

∂s∂x = 0, in other words, in-

come log, which is parallel to experience among the various levels of education (the assumption of

parallelism)..

Willis (1986) also points out an additional assumption for the economy as a whole: that the

economy and the population who are in (long-run) steady-state equilibrium, with no changes for

aggregate productivity, and a constant rate of growth in population, such that the present value of

income for the lifecycle is one for a representative individual. Thus, the individual maximizes the

present value of his income flow by choosing the discrete quantity of years of education:

max{s}s0

l∑

x=0

Y (x, s)

(1 + r)s+x.

assuming parallelism and linearity during the years of study, i.e., Y (x, s) = λ(0)eβsθ(x), θ(x) <

∞, where we have as a first-order condition:

l∑

x=0

Y (x, s+ 1)

(1 + r)1+x−

l∑

x=0

Y (x, s)

(1 + r)x= 0,

[λ(0)eβ(s+1)

1 + r− λ(0)eβs

]l∑

x=0

θ(x)

(1 + r)x= 0.

Forr �= (−1, 0) we have:

λ(0)eβ(s+1)

1 + r− λ(0)eβs = 0,

eβs − 1 = r.

Thus, for equivalency to be valid, the principal assumptions are linearity and parallelism. These

assumptions will be tested. Anticipating the results, we see that they are rejected, which is reason

for their relaxation, as well as assumptions (ii), (iii) e (vi) in addition.

4 Testing The Mincer Hypotheses

In the following subsection we discuss some of the limitations to our approach of using cross-

sectional data. In the next subsection would present the data and some preliminary statistics.

Then we show the methodology for testing the linearity and its results and in the last part of the

section we present the methodology for testing parallelism and its results.

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4.1 Discussion

As pointed out by HLT, the use of cross-sectional data leads us to an assumption that could be

relatively strong. But individuals base their decisions on investment on ex ante analysis, on the

experience—earnings profile of older individuals of active working age. This is one version of the

assumption of rational expectations in which individuals forecast their expected income based on

the earnings profile of older individuals (Heckman, 2005). Thus, it does not take into consideration

that these individuals might anticipate future changes in the price of education, for example. It

should be pointed out, however, that the fact that individuals based their human capital investment

decisions on the experience of older individuals is valid because there is no perfect counterfactual

from which can be extracted the income flow for the case of the individuals who attend and do not

attend school. Thus, we must take individuals with similar characteristics as a reference.

In addition, the use of cross-sectional data, according to Card (1999), is valid if it reflects

differences in real productivity that are not due to differences in the inherent ability of the individual

or that might be correlated with education through the differences in income flows. This problem,

endogeniety, has been intensively examined in the literature; and recently, Sachsida, Loureiro and

Mendonça (2004) have estimated mincerian returns, correcting for various sources of bias in Brazil.

It should be pointed out that the bias caused by ability and other factors that are not present does

not exceed 10% of the value of the mincerian coefficient for the US (Card, 2001). For Brazil, Binelli

et al. (2006) show that this bias, which originates in non-observed heterogeneity, is relatively small

for the respective returns.

4.2 Data and Descriptive Statistics

PNAD, because it deals with a “complex” sample survey, needs special care. For that reason, we

will briefly discuss the literature that explains and incorporates the sample design of the survey

and warn of the consequences of the failure to take this into consideration.

Sample Design The costs of conducting a sample survey based on a simple sample design are

very high. For this reason, according to Chromy and Abeyasekera (2005), complex sample de-

signs are used to control these costs. According to Yansaneh (2005), a complex sample design

involves stratification, multistage sampling (conglomeration or cluster) and different probabilities

of selection. With regard to conglomeration, the selected observations in the first stage generally

are called the primary sampling unit (PSU). The PSUs can be divided into urban and rural areas,

and in some countries, they are divided by geographic or administrative areas. The observations

selected for each PSU are called second stage units (SSU), and within these groups a third stage

(TSU), and so on, successively. Generally speaking, the second stage units are households or fam-

ilies, and the third stage are the individuals. Stratification is generally applied to a stage of the

sample, in which the units are partitioned (into first, second, and third stages) into subgroups that

are mutually exclusive. These units are generally selected with probabilities proportional to their

9

size (for example, the number of families or individuals belonging to a PSU), and therefore may

be unequal in each stage. Thus, according to Pessoa and Silva (1998) and the IBGE (2004), the

PNAD complex sample design uses a sample stratified by State (FU), and smaller regions within

the States. The selection of municipalities within each stratum is done with unequal probabilities,

proportional to size, where there are municipalities included in the sample with a probability equal

to 1 (called auto-representative municipalities). The second stage units are census sectors and, sim-

ilarly a selection of these sectors within each municipality is done with probabilities proportional

to the number of households in each sector according to the most recent Census data available. In

the final stage households are selected in each of these sectors, with equal probabilities. All of the

individuals living in each household of the sample are surveyed.

However the studies in general do not take account of these factors, starting from basic assump-

tions that could only be valid when all of the data are obtained through simple random sampling

with replacement or, similarly, independence and equal distribution (iid). In general, the data

obtained in surveys by sample, such as the PNAD, do not permit these assumptions to be used

(Silva, Pessoa e Lila, 2002).

Various economic studies do not consider the complex sample design when estimating variance,

in the construction of confidence intervals and tests for assumptions, generating, according to Lum-

ley (2004), skewed estimates, which a rigor wind up invalidating the usual tests of the assumptions.

Thus, their results are inaccurate, and can result in a change that is merely quantitative and may

be qualitative, when changing the (non-) significance of the estimated parameters. Therefore, this

study also makes a contribution to this question, by incorporating the sample design of the PNAD.

Sample and Descriptive Statistics Therefore, in all of the tests we performed we use the data

from PNAD from 1992 through 200413, and from the Census data for 1970, 1980, 1991 and 2000.

Thus, we were able to perform the tests of linearity without having to correct the estimates and

comparisons when incorporating the PNAD sample design. The same procedure was used in the

calculation of the IRRs that involve nonparametric and parametric specifications.

The subpopulation used in the linearity test was: white male individuals between 24 and 56

years of age, who were not in school, with a work week of more than 36 hours and less than 44

hours, with positive income14 equal to less than 100 times the minimum wage in reais, excluding

workers in the public and agricultural sectors and workers producing for their own consumption,

construction for their own use and unpaid labor.

The exclusion of agricultural workers and public employees is to the fact that the salary structure

is different from the market. The removal of those attending school is for the purpose of comparison

with the mincerian model which assumes that the individual enters the labor market one period

13Except for the years 1994 and 2000, when the survey was not held. In addition, in 2004, the IBGE included rural

areas in the North, which previously had not been incorporated. So, for the purposes of comparison with other years,

we did not use the data from the rural area in the North in 2004.14When we corrected the bias in the sample selection, we included those who were not working.

10

after completing school.

In addition, we see that in the fifth column of tables 1 — 2 in the appendix that only around

10% of the workers study, but this percentage has been increasing over the years. Among those

who work and study, the majority are men and among the men they are white. But these groups

have declined relatively in recent years. The age limits can be seen in the ninth and 12th columns

of the tables. The large majority of workers are 24 or more years of age and this has increased

during the last two decades at the cost of other age groups. In addition to being the largest group,

this age group has an average income of around R$1000 in real terms15, approximately 100% and

400% more than the second and fourth age groups, respectively. Thus, the non-inclusion of the

smaller groups in the tests at in the calculation of the IRRs includes a relatively small part of the

opportunity costs of the income foregone16. With regard to the limit of 56 years, observe that

within the universe of retirees, the vast majority are more than 56 years old. The average age of

this group is around 63- 66 years. However, this is a measurement that overestimates the actual

age of workers when they retire, which is due to the lack of a variable for correctly measuring this

point.

The restrictions on hours for full-time work is due to the fact that, according to Freeman (1986),

the human capital investment model proposed by Becker states that the individual should decide

if he will attend school and invest in education or seek full-time work in the labor force every year.

Other major studies, such as Murphy and Welch (1992, 1990), that are based on the mincerian

model to estimate the income profile of individuals, also limit the sample to full-time workers.

With regard to the exclusion of women, we can cite two reasons here: (i) women enter the

labor market later, at average of between 14 and 15 years, while men enter the labor force one

year earlier; (ii) Cameron and Heckman (2001, apud Sachsida, Loureiro and Mendonça, 2004), in a

study of the sources of ethnic and racial disparity in school enrollments, consider only men, because

their decisions regarding education are less complicated by conditions of fertility.

4.3 Test for Linearity

In the test for linearity, three different specifications were used. In general form, we estimated:

lnY = α+ β1x+ β2x2 + β3s+ specificationk + e , k = 1, 2, 3, (2)

where, Y is the hourly wage17. In the specification 1, we used a spline function:

specification1 =∑15j=1 βjSj , (3)

15 Income in this article was adjusted by the INPC (Consumer Price National Index) to prices for November 2004.16This point is discussed again in section 5.2 where we discuss the assumptions used in the calculation of the IRRs.17More precisely: Y =(income from principal employment) / (number of hours worked x 4) . Note that for the

Census of 1980/1970 the number of hours worked are available only by groups. Thus the values assumed follow the

table below. With the exception of the upper and lower bounds, the values refer to the average for each hourly group.

11

where, Sj, j = 2, ..., 15, is a dummy and the individual has S � j years of education. These

dummies capture the returns to education, permitting discontinuities and changes in inclination

after each year of study completed. In specification 2, we use a cubic function:

specification2 = β4S4 + β5S8 + β6S11 + β7S15 + β7S2 + β8S

3, (4)

where, but we also include some variables that capture discontinuities18, a definition similar to

equation (3). Finally, we estimate the specification 3 more broadly, which permits us to obtain

estimates of each grade completed. Thus, we do not use more years of education, rather whether the

individual completed a given grade. We also opted for the specification, given that some individuals

receive diplomas (Middle School, High School, etc.) 19 with more or fewer years of study than the

majority of students. For this, we replace S in equation (3) withe variable degree20. E assim a

especificação 3 é descrita como:

specification3 =∑4j=1 β3+jEFj+

∑8j=5 β3+jEFj+

∑3j=1 β11+jEMj+

∑4j=1 β14+jSUPj+β19MD.

(5)

The variables EFj, EMj , SUPj and MD are dummies if the individual has Degree � j. This

logic has shown the same technical features as in specification 121.

Thus, we did a F test on the coefficients of the specifications described above in order to test

the null hypothesis that favors the linear model, against the alternative hypothesis that is more

favorable to nonlinearity in the returns.

It is important to note here the differences between the specification of the years of schooling

(specification of equation 5) and the specification of the years of education (specification of

equation 3 and 4). The years of education variable, in the PNAD, is derived from the grade level

variable (i.e., years of schooling variable). Therefore, someone who studied through the fourth

Because of the division by groups, the sample for 1980/1970 includes only those individuals from 40 to 48/49 hours.

Census 1980

Work-Hours Groups Value Considered

less than 15 hours 15

from 15 to 29 hrs 22

from 30 to 39 hs 34.5

from 40 to 48 hs 44

equal or more than 49 hrs 49

Census 1970

Work-Hours Groups Value considered

less than 15 hours 15

from 15 to 39 hs 27

from 40 to 49 hs 44.5

equal or more than 50 hrs 50

18Specification 2 is based on Hungerford and Solon (1987), that captures the effect of the diploma on the years of

completion with reference to school levels (primary [S4], middle [S8] school, high school [S11] and college [S15]).19Abbreviations will be used herein for this article:

NEDUC : no education, :PRE preschool, : EFj :j-nth grade of Primary School, EMj : j-nth grade of High School,

: SUPj :j-nth grade of College, MD: Master’s/Doctorate. The grades Primary School and Middle School together

are referred to as Elementary School in Brazil.20Degree are given the following values: 0, never studied, 1 preschool or literacy, 2 first grade a primary school, 3

second rate of primary school and so on up to 17 for those who have studied at the Masters or Doctorate level.21The relevant dummies were excluded to avoid perfect linear dependency in the matrix regressions.

12

grade of primary school necessarily has four years of education, in other words, this variable does

not capture directly delays or those students who repeat grades. Meanwhile, someone who has

never attended school or someone who has only attended preschool, is given the same value of 0

years of education, so that these two groups are not differentiated in the specification of years of

education, while in using specification of the grades (years of schooling) it is possible that they can

be differentiated. We also note that six years is assumed to be the age at the start of education

and this is taken as a reference base. Another factor is that PNAD has a maximum limit of 15 or

more years of education. Thus, there could be differences for someone who attended both college

and graduate school courses. In addition, the specification for grade level takes into consideration

whether or not the individual finished his course. With regard to the Census, we have the same

structure, but the variable years of education is more divided, having as its maximum value 17 or

more years of study, with the exception of the years 1970 and 1980, where this variable does not

appear and therefore we estimated only the specification of grade level for these years.

4.3.1 Sample Selection

In Subsection 4.2 the sample to be used was specified conditioned by the explanatory variables, in

other words, filtered by race, gender, age, etc. The problems of bias in the sample selection could

appear to impact the sample of the dependent variable, if only individuals with a positive salary are

considered. The problem of sample selection emerges from the fact that we are unable to observe

the supply of hourly wages for individuals who are not working, in other words, when this wage

offered is less than the reserve wage of the individual. Thus, some individuals decide not to work,

but, as already mentioned in subsection 4.1, we assumed that their wage supply was also taken into

consideration by those who are making the decision of how much they should accumulate years of

education, because that “excluded” individuals are at an age where they are active in the labor

market. The failure to incorporate these individuals will bias educational returns.

To correct this bias, we use the two-stage estimation procedure developed by Heckman (1979,

henceforth heckit), in which we estimate in the first stage, a probit using the entire sample with

a dummy as a dependent variable if the individual is employed. This is the so-called selection

equation. Thus, we obtain an inverse Mills ratio, and estimate the wage equation using this ratio.

The “t” test for the parameters of the inverse Mills ratio is a valid test for the null hypothesis of

the nonexistence of bias in the selection22.

For the selection equation, we use in addition to the co-variables from the salary equation, the

number of children, a dummy for marriage, income not originating from work, a dummy if the

individual belongs to an union, and dummies for the states of residence23.

22The null hypothesis implying the assistance of a bias and a sample selection is rejected.23The number of children is calculated directly only for women. Thus, to calculate this variable for men, would

identify the children present in the family, where the father is the head of the family or the person of reference. For

the marriage dummy, we proceed in the same fashion, calculating the value of one for persons that are head of

the family, since for the PNAD this variable is not exist. A variable for unions was not included in the regressions

13

4.3.2 Results

Tables 3 — 6 in the appendix show the results of the test for linearity for the specifications as

defined. Under all of the estimated specifications, the null hypothesis that the coefficients in the

non-linear terms are null is rejected. In addition, for all of the specifications, note that the value of

the statistic presents a tendency that leads us to conclude that the assumption of linearity in the

Mincer model has become less and less valid , leading to poor specifications in the models that use

it. With regard to the Census, the F statistic is elevated to one of the first specifications, while in

the most recent it oscillates, at a high level.

Comparing the adjustments made in the models, note that the inclusion of the sample design

and the correction of bias in the sample selection using heckit, reduces the F test statistic, but not

to the point of rejecting the null hypothesis for linearity of education.

Therefore, we strongly reject the hypothesis of linearity for Brazil, which by itself invalidates

the consideration of the mincerian coefficient as a return on education.

4.4 Test for Parallelism

Initial estimates of income as a function of experience for various levels of education will be prepared.

To obtain these estimates, we estimate the following equation:

y = f(x) + u,

such that E[u|x] = 0 and E[u2|x] < ∞, which implies that E [y|x] = f(x). therefore, an estimate

for f(x) provides an estimate for the average of y conditional on x. For us to estimate f(x), we use

the global parametric approach which imposes a functional form on f(x)24. Thus, we can impose

f(x) = ax + bx2 + cx3, or a higher order polynomial. The disadvantage of this method is that

the larger the order of the polynomial, the greater are the problems inherent and multicolinearity,

where the estimates lose precision and parsimony. In addition, these techniques are sensitive to

“outliers”, given the fact that the estimates of each point depend on the entire sample. But one

of the larger problems with the parametric methods is the imposition of a functional form on the

model to be estimated, which could create problems of poor specification. Thus we start from a local

approach, using the local non-parametric linear regression method. The idea of using this method

is to minimize in a neighborhood around the points of our grid (x0), the sum of the quadratic

residuals, weighted by the form and width of a sequence of kernels{K(xi−x0hn

)}ni=1

(Härdle, 1990).

Thus for a random sample {xi}ni=1 i.i.d., we have::

(m(x0), b(x0)

)= argmin

m,b

n∑

i=1

[{yi −m− b(xi − x0)}

2Ki

],

with census data, because it’s not covered. And for the Census of 1970, the income from non-labor sources was not

included because only the income from the principal occupation is available.24These methods would be, for example, a global polynomial approximation and splines, with the latter already

having been used in linearity tests.

14

in which, Ki = K(xi−x0hn

)is a quartic kernel25 and hn is a bandwidth, such that hn

n−→∞−→ 0. For

the first-order conditions we obtain::

m(x0) =∑ni=1 yiWi (x0) , (6)

where, Wi (x0) =Ki

[∑ni=1 (xi − x0)

2Ki

]− (xi − x0)Ki [

∑ni=1(xi − x0)Ki]

∑ni=1Ki

[∑ni=1 (xi − x0)

2Ki

]− [∑ni=1(xi − x0)Ki]

2.

Thus, m and b are estimators for f(x0) and f′(x0) respectively

26. The null hypothesis for the

test for which of the profiles of the log experience-earnings are parallel among different years of

education is:

H0 :

{[E(yi|x10, s = s1)−E(yi|x10, s = s2)]− [E(yi|x20, s = s1)−E(yi|x20, s = s2)] = 0

[E(yi|x20, s = s1)−E(yi|x20, s = s2)]− [E(yi|x30, s = s1)−E(yi|x30, s = s2)] = 0,

where, xi, corresponds to i years of experience for i = 10, 20, 30. Thus, the idea of the test is simple:

to verify if the difference in the average salary conditional on the level of education s2 in relation

to s1 is the same for two different levels of experience27,28. According to Heckman et al. (1998),

to test the independence of the average in L different values of x, the values of xi are selected and

separated by at least two times the bandwidth (2hn), such that the estimates are independent and

thus the statistic is asymptotically distributed by χ2(L). Since we use hn = 5, we therefore select

the values of xi spaced 10 by 1029. Therefore, since mxi ,sl is the estimate of E(yi|xi, s = sl), the

statistic for the test for parallelism for the null hypothesis defended above would be, according to

Heckman et al.(1998)::

∆′Φ−1∆d−→ χ2(L), L = 3, (7)

25The quartic kernel is defined as:

K (t) =

{(15/16)(t2 − 1)2 if |t| < 1

0, otherwise

26 Intuitively we are using a local polynomial approximation, through a Taylor expansion in the order p, p = 1,

around x0. In the general case we would have:∑n

i=1

[{yi −m− a1(xi − x0)− a2(xi − x0)

2 − ...− ak(xi − x0)p}2Ki

]

where, a2 is an estimator for f ′′(x0)2 . In the case of p = 0, m it would be the well-known Nadaraya-Watson

estimator.27 In addition to this joint test, we also tested separately for only one difference, in other words for the null

hypothesis:

[E(yi|xj , s = s1)−E(yi|xj , s = s2)]− [E(yi|xl, s = s1)− E(yi|xl, s = s2)] = 0,

for l �= j, (l, j) equal to (10, 20) and (20, 30).28These values for i (10, 20, 30) are valid for comparison of levels of education of over 15 years or more (more

than the SUP), 11 years (EM3) and 8 years (EF8). But those that involve 4 (EF4) and 0 (PRE and NEDUC)

years of education, the grouping of year so experience does not cover 10 years, and therefore the values assumed are:

{20, 30, 40}.29We made estimates for the bandwidths varying from 2 to 10 and there was little change in the smoothing of the

income flow profiles. Thus, we chose, using a subjective criterion, an intermediate bandwidth not unlike to HLT.

15

∆ = M · [mx10 ,s2 , mx10 ,s1 , mx20,s2 , mx20,s1 , mx30 ,s2 , mx30 ,s1 ]′,M =

[1 −1 −1 1 0 0

0 0 1 −1 −1 1

]

and Φ =M ·diag (V ar (mx10 ,s2 ) , V ar (mx10,s1 ) , V ar (mx20 ,s2 ) , V ar (mx20 ,s1 ) , V ar (mx30 ,s2 ) , V ar (mx30,s1 ))·

M ′. To calculate variance we use the estimator proposed by Heckman et al. (1996a):

V ar (mxi ,sl ) =n∑

i=1

Wi (x0, sl)2 ε2i ,

where, εi is the residual of the regression.

4.4.1 Results

The graphs of the experience-income profiles were obtained using a nonparametric estimator for

various levels of education30. Taking Panel I from the Census, which shows relatively stable mea-

sures, as a reference, we see that income flows tend to be a steeper and concave function as the

level of education increases. This point is consistent with the literature (Becker, 1975; Willis, 1986;

Psacharopoulos, 1994), in which the individuals tend to not only earn more with higher levels of

education, but show greater rates of growth, which tend to decline more rapidly over the working

life cycle, for higher levels of education. An initial investigation of these graphs points against

parallelism, given that some salary profiles tend to approach one another. In the case of PNAD

(Panels 2 and 4)31 we see also an approximation for some levels, as well as on Panel 3, where a

crossover of the profiles occurs, behavior similar to that observed by HLT.

Tables 7 — 10 show the tests of the statistic (7) for the joint hypotheses, as well as for only two

pairs for different experiences. In relation to the PNAD, we note that for the majority of years,

for the two specifications, the null hypothesis for the parallelism set is rejected, for some pairs

of different years of education (schooling). It is important to point out that in the results of the

PNAD there is a large variation in the salary differential for a given level of experience, from one

year to the next. One of the reasons for this variation is the lack of a large number of observations

per cell that are necessary for nonparametric estimation methods, which occurred because of the

need to apply filters to the PNAD sample. Thus, a conditional mean estimated for these points

test oscillate more from one year to the next. This oscillation can also be noted in the graphs of

the profiles. Therefore we performed the test for the Census data as well, which, given our sample

limitations, included a larger number of observations per cell and, therefore, less oscillation in the

30The graphs shown are for only two years. The other years may be available from the author by request.31Due to the application of filters to the sample, we see that some education-experience cells have a very low

number of observations of individuals that didn’t graduate from Primary/Middle/High School or College or Mas-

ter’s/Doctorate, principally at the end of the life cycle. This is a recurring problem of these methods, and can be seen

also in the studies by Murphy and Welch (1990, 1992) and HLT, which use the CPS (Current Population Survey)

and the US Census, respectively. For this reason, the graphs from PNAD show only the salary profiles for completed

years of schooling (i.e., completed Primary/Middle/High School or College or Master’s/Doctorate), which have a

greater number of observations per cell.

16

estimates. For all the estimates, with the exception of middle school with regard to primary school

in 1991 and 2000, parallelism is rejected. Thus in the section that follows, we compute the IRRs

to measure the bias of these estimates in relation to the mincerian coefficient.

5 IRR

For the calculation of the IRR we use:

l∑

x=0

Y (x, s+ h)

(1 + r)h+x−

l∑

x=0

Y (x, s)

(1 + r)x= 0, (8)

where, Y (.) are the adjusted values of the parametric (spline and the Taylor expansion32) and

the non-parametric regressions. For the specification of the years of education, h is simply the

difference between the two levels of education. In other words, when we compare the present

value of earnings for those with 8 and 4 years of education, this “h” would be equal to 8 — 4 = 4

years. Nevertheless, when we use the specification for schools, we should take into consideration

the expected average time to finish each level of schooling or degree of education completed. Thus,

when we compare the present value of earnings for those who complete middle school (EF8) with

those who complete primary school (EF4), the h will be the expected average time to complete

middle school less primary school. But because this variable is not available, we use as a proxy

variable the average age of individuals who attend a given grade level33. And we add 0.25 to the

estimate for h, to minimize the measurement error that tends to underestimate the average age

for completing a given educational level, because the PNAD and census are taken in the middle of

August-September, in other words, at a point where one quarter of the school year remains to be

completed34. Below we present the results, after which we will discuss other hypotheses raised in

the calculation of the IRRs.32Relaxing the parallelism assumption, we estimate the IRRs using the non-parametric spacification that has always

presetned and by a parametric specification, i.e., by a 2nd degree Taylor expansion, as defined below::

lnY = α+ β1 exp+β2 exp2+β3S + β4S

2+β5 (S · x) .

This estimate was done to compare to non-parametric estimates and verify the potential discrepancy.33Thus, for example, for the year 1992, the average age for the individual who attended middle school was 16.33

years, and for individual who attended primary school was 11.67 years. The difference between these two averages

4.66, greater than 4 years, which would be the time needed to complete a four-year program without repeating. This

occurs because the proxy for the specification of the series takes into account students who repeat the school year.34 It happens that the INEP provides an estimate of the average time for completion of school, but this was

available only for 1995 through 2001. Thus, for us to have more homogeneous estimates for comparative purposes we

constructed this measure faced on the age of the individual, which differs somewhat from the average of the INEP.

17

5.1 Results

Tables 11-12 show the estimates for the IRRs. The first two lines for each year (Mincer I and II)

refer to the mincerian coefficient35 from the first two original models. They are taken in points of

reference, in order to measure the bias in relation to the estimates of the IRRs. The other lines refer

to the estimates of discount rates, first relaxing the linearity assumption (the spline function) (IRR-

nonlinear, third line) and then parallelism. For the latter, parametric models (Taylor expansions)

and (IRR-nonparallel parametric fourth line) and nonparametric (IRR-nonparallel n-param., fifth

line) were estimated. These estimates are divided in three sets of columns for the PNAD: regressions

estimated without any correction of all; including the sample design and incorporating a sample

design and correcting the bias in the sample selection using heckit. And for the Census: without

correction and estimated using heckit.

We note, both for the Census as well as for the PNADs, that the bias36 tends to be positive

for all levels of education, specifications and types of corrections excepting when it is compared to

a greater number of years of education, when the negative bias shown for the returns to greater

levels of education, becomes positive when we change the focus of the specification of the grade

level, for all types of corrections. The last specification tends to measure the returns to higher

levels of education more accurately, while those for years of education could be combining returns

to an undergraduate education, an undergraduate degree and graduate studies. For this, note

that returns a relatively higher for the highest level of education in the specification of years of

education (S15-S11 in the PNAD and the Census). In terms of magnitude, when we incorporate

only the sample design of the PNAD, the bias reaches a difference of more than 12 percentage

points (p.p.) when compared to the nonparametric IRRs and Mincer II for the EF4-PRE, for the

year 2003 (16.42% - 3.98%). When we incorporate the sample design, and correct the problem of

sample selection (heckit) we also obtained biases that reach more than 12 p.p. when compared to

the nonlinear IRRs and Mincer II for EF4-PRE for the year 2003 (15.71% - 3.53%). The bias for

the higher levels of education are smaller, but nevertheless significant, and can reach a magnitude

of almost 7 p.p., for example, for the year 1993, for this same specification for SUP-EM3. For

the Census the biases are also high and could reach a difference of more than 14 p.p. when the

mincerian return in 2000 went from 17.29% to 3.03% for the MD-SUP group (non-linear IRR) in

the model using heckit.

It is worth noting that there is little difference between the non-linear IRRs (third line) and the

non-parametric (last line). , when the sample design is incorporated, this bias reaches a maximum

of 2.08 p.p. and the comparisons of S4-S0 (9.18% - 7.11%) for 2001, and 1.08 p.p. (7.07% - 5.98%)

when comparing EF8-EF4 de 2003.

35The mincerian coefficient was adjusted for continuous time, as: eβs − 1 = mincerian return.36The bias to be discussed in this subsection is always based in relation to the model in Mincer II, the most widely

used in the literature, unless another IRR is mentioned as a reference base. Thus, it is understood as a positive bias

of the difference between the mincerian return and a given IRR, which is positive.

18

With regard to the Census, the bias when comparing that to the highest levels of education

(S17+-S15) in the year 2000 is almost 2.4 p.p. and for different levels of schooling, with the exception

of 1970, the bias does not reach 1.5 p.p., in absolute terms. This leads us to believe that, despite

our rejection of parallelism, the spline function is a good approximation when estimating IRRs.

Nevertheless, when the last line is compared with the fourth line (IRR non-parallel parametric)

a large bias is observed. Thus, when parallelism is relaxed, it is best to opt for a nonparametric

approach where the biases occasioned by the poor specification of the parametric model are not

incurred.

We will also point out to IRRs 42 levels of education that appear to be relatively low. The IRR

for the MD-SUP (Census) is low, which goes against the common sense reasoning that graduate

coursework elevates the returns by a substantial amount. But what makes these returns low is the

average length of time it takes to complete the course, varying between 5 and up to 10 years. An-

other IRR is one that compares preschool education with zero levels of instruction (PRE-NEDUC,

PNAD). This suggests that the individual who never went to school or only attended preschool

shows an income differential that is insignificant37. It should be pointed out that this should not

be taken as a parameter for public policy, given the vast evidence that investment in preschool

education increases skills, the time that students spent in school and reduces repetition in years,

and consequently increases the productivity of the individuals in the labor market (Heckman and

Carneiro, 2003). Barbosa and Pessoa (2006) estimate IRRs for preschool education, developing an

interesting methodology, which indicates that those with preschool education increase the proba-

bility of remaining in school and the income stream of those who do. Thus, they obtain rates of

the magnitude of 17% that have remained stable over the last 10 years.

In a horizontal analysis of the table, we can infer gains from incorporating the sample design

and using heckit. With regard to the specification of the years of education, note that for the

nonlinear IRRs it is possible to have a negative bias of almost -1.68 p.p. (12.58% - 14.26%) when

comparing S4 and S0 in 1993, and a positive bias of 1.84 p.p. (13.73% - 11.9% for S11-S8 in 1996

if the sample design is not incorporated. In general, the IRR tends to be underestimated for lower

levels of education and overestimated for higher levels of education. With regard to the use of the

sample selection to correct the bias, the gains from estimating using heckit occur at all levels of

education, reaching a positive bias almost 2.56 p.p. (8.78% - 6.21% in 2002) when comparing S4-S0

for PNAD and almost 14.4 p.p. (26.26% - 12.82%, in 2000) for the Census comparing S17+-S15.

In addition, in the majority of cases, the bias is positive, which implies that the returns are lower

yet when correctly estimated. Plus it is highly recommended when estimating a model, to include

37 In general this return is quite low — and can even be negative — which is to be expected because the market does

not tend to pay much more for someone who has attended a preschool than for someone who has no education at

all. For a part of the decision by individuals to complete only the pre-school, one possible explanation could be due

to the quality of the parents (because it is parents who invest in the education of their children when little), which

could have as a proxy the educational level of the parents, which would be low for this group. This is an interesting

issue that could serve as the basis for future research.

19

the sample design of the PNAD and correct for the bias in the sample selection for the PNAD and

the Census.

Thus, these factors point clearly to the conclusion that mincerian returns are biased, differing

widely from the true returns to education measured by the IRR. Therefore, this bias has particular

consequences since the returns are overestimated and therefore do not adequately explain the

changes in demand for education. For Brazil, returns are much less when correctly measured. This

occurs principally due to the specification for the years of schooling (primary, middle, high school

and college) that not been considered in the literature, and, as can be seen on table 11, provide

returns that are much less than the years of education approach, because it considers the average

time expected for conclusion, in other words the term h is greater for the first approach than for

the latter.

We would further point out that the IRRs for the years of education approach are close to

those obtained by Barbosa and Pessoa (2006), with the exception of high school and college were

differences or of a greater magnitude. In addition, they show some similarities with studies based

on the Mincer model such as Blom et al. (2001), because these authors obtained returns for years

of schooling that were much lower in relation to middle school and high school. Logically they are

biased by the evidence shown in our study. Our returns (IRRs) are higher for primary and middle

school, and lower for a high school and college. This same result occurs in the studies Fernandes

and Menezes (2000), Leal and Werlang (1991) and in Ueda and Hoffman (2002).

This difference could be the result of the use of different methods and samples among the

articles. Given the very large range of estimated returns, the question emerges of what is the IRR

for each level of schooling? With regard to the specifications, the specification for schooling is more

and accurate because it incorporates the average time spent, the importance of which has already

been pointed out. However, for comparison with the work of others, we present also a specification

for years of education. With regard to the corrections, we take as a reference, the models with the

largest number of corrections, for example: (i) nonparametric and (ii) the parametric heckit. The

former with no problems and functional form and the latter corrected for the bias of the sample

selection. Thus, we showed two models with corrections in different dimensions, and, therefore,

measuring the difference between them is not a trivial matter38. Nevertheless, we stress that for

both models we noticed that these estimates for reference are not particularly sensitive to the choice

of models. Therefore, we take as references the nonparametric IRR and the parametric (Heckit)

IRR for an analysis of the changes over time. Various studies, as we have already indicated (Blom

et al, 2001), show a decline in mincerian returns for Brazil, with the exception of the college level,

vis a vis an increase in the enrollment at all educational levels. In Panel 5 we see more easily the

38We would need a model that corrects simultaneously the problem in two dimensions and incorporates the sample

design for the survey. The article by Das, Newey and Vella (2003), as mentioned in Note 5, suggests a nonparametric

heckit, but that does not permit the incorporation of the sample design. In other words, this is still an open question in

the literature. Later developments along this line of research may permit an analysis of the gains from the correction

of the problems cited in the future.

20

changes over time.

With regard to the Census (graphs 5.3 and 5.4), the levels of education EF4-NEDUC, EM3-EF8

and MD-SUP increase or remain stable in 1991 when compared to 1970 and/or 1980 and decline

in the last decade. EF8-EF4 declined over the decades and SUP-EM3 increased during the last

decade. With regard to the PNAD data (graphs 5.1 and 5.2), that looks at recent changes, we note

for both the references a behavior that is close to the Census over the last decade.

5.2 Discussion

Some points should be made with regard to the hypotheses and the estimates considered in the

calculation of the IRR. One assumption made by Mincer is that individuals first get an education

and later enter the labor force. Two points should be raised: (i) according to table 1, few individuals

work while they are going to school, but this percentage has increased over time, which has increased

the quality of night school courses in Brazil and; (ii) Mincer assumes that the direct costs of

education are compensated for while studying, or that these are negligible. With regard to the

latter element of the cost of education, Becker points out that the investments in education are

concentrated in the early ages because: (i) over time the individual has a smaller period of time

to recover his investment in human capital and (ii) the opportunity cost increases as the level of

human capital rises. Thus, the cost of time is an important source of the total cost calculation of

the IRR. Becker assumes that in the literature this cost is often overlooked and that it should be

treated in the same way as direct costs. Schultz extends the costs beyond monthly expenditures,

annuities and others ones, where the salary forgone makes up in a significant part of the total cost.

In addition, Schultz raises the question of leaving out the salaries of student workers, for whom

the estimates for opportunity cost tend to be overestimated. Thus, given the evidence noted above

of the increase in student workers, we analyze an additional specification that includes those who

attend school based on additional nonparametric specifications including those who attend school

based on nonparametric and nonlinear specifications. We also incorporate part-time workers (more

than 20 hours per week) because many times this group were only half time in order to be able to

study. In the appendix, the line IRR — additional 1 is compared with the nonparametric estimate,

always incorporating the sample plan or sample weight (tables 13 and 15), and also based on the

nonlinear estimates with the sample plan and the correction of the bias of the sample selection

(tables 14 and 16). There is not a large difference between the rates for all the specifications. This

is because the percentage of working students is still small although growing.

Another hypothesis is l′(s) = 1, assuming that the length of time on the job might not depend

on years of education, and could vary between individuals with the same level of education. Thus,

we relax this hypothesis as well. It should be noted that the length of time working adopted here

is 32 years, because of the limits on the age of the individual39, there being no difference between

39 In other words, since x = i−s−6, then ∆sx = 56−24 = 32 years, for a fixed level s of education. As we consider

the minimum age to be 24 years, therefore, for this age there are already people with degrees from the highest level

21

this hypothesis and one where l′(s) = 0. Thus, on line additional 2, which maintain the hypothesis

that l′(s) = 1, but where the age range includes individuals from 10-65 years of age and with a

working life of the first 40 years: and on line additional 3, we allow individuals to work up to 65

years of age, when they retire (l′(s) = 0)40. We note also a large difference when we use a wider age

range, which shows us that the cost borne at an early age are significant; and their exclusion tends

to bias downward the returns for higher levels of education and biased upward the IRRs for S4-S0

and PRE-NEDUC/EF4-PRE for PNAD. For the Census the same logic applies. Now, comparing

additional 2 with additional 3, we note that the differences in the estimates are small. This is due

to the fact that the earnings at the end of the life cycle are more heavily discounted, therefore

having little effect on the present value of earnings and therefore little impact on the IRR (HLT).

Finally, we include private direct costs (tuition) in the calculation of the IRR41. These costs

were obtained through the Family Budget Survey (POF) for 1995/199642, from which we estimate

an average level of education and adjusted for a standard 40 hours workweek, for the purposes

of comparison of standard income for the individual’s hours of work. Since the private expenses

on education are available only from the POF for this year, we performed a simulation of these

expenses for other years for the purposes of comparison. We estimated total average income for

families that had members in preschool, then we did the same for families that had members in

primary school and so on in succession. And we calculated the percentage of expenditures on

monthly tuition costs in relation to average income, obtained from the POF, and assume this to be

constant for all years. Based on this percentage, we estimated spending using the average income

from PNAD in the same fashion. Table 17 shows these estimates. Thus, according to tables 13 and

14, for the year 1996, based on the original expenses from the POF, (line additional 4 IRR (POF))

we see much lower rates, reaching a drop of more than 3 p.p. (S15-S11) in relation to specification

three. In the same fashion, for the simulated expenditures, we observed relatively large declines for

all years, principally for the higher educational levels.

We should stress that the additional 2-4 IRRs (tables 13-15) are more sensitive between the non-

parametric and parametric models, principally in relation to the returns to middle school education

of education.40We want to stress that the additional 2 and 3 IRRs include a modification to additional 1 IRR, and that additional

4 IRR, that will be presented below includes the changes to additional 3 IRR. In other words, we are relaxing these

assumptions gradually and successively. The note to table 13 reinforces this point.41More precisely, we estimate the IRR using the:

l∑

i=0

Y (i, s+ h)

(1 + r)h+i−

l∑

i=0

Y (i, s)

(1 + r)i−

h∑

i=0

c

(1 + r)i= 0,

where, c are the average direct costs for monthly tuition.42 It should be pointed out that INEP provides data on public spending on education on its webpage on the

Internet. These expenditures could be included in the analysis of the IRRs end a macroeconomic context, which

compares investment in education with other investments, such as capital, as has already been done by Langoni

(1974).

22

compared to primary education (EF8-EF4 e S8-S4, PNAD)43.

Analyzing the data over the years of the Census, we note on graph 6.4, Panel 6, a downward

trend for all levels during the most recent decade and an increase in undergraduate and graduate

education over immediately preceding high school during the last decade. Estimated using heckit,

(graph 6.3), we know a slight difference with respect to EF4-NEDUC, which increased and MD-

SUP which declined in the last decade. With regard to the PNAD, we note that the nonlinear IRR

(graph 6.1) shows similar behavior with regard to the previous section. The nonparametric IRR

(graph 6.2) also shows the same behavior, with the exception of EF8-EF4, which shows a decline up

to 1999 and an increase beginning in that year, and the high school level that remained relatively

stable during this decade.

6 Conclusions

Since the publication of the seminal work by Mincer in 1958, later extended in a 1974 version, various

empirical articles have used the mincerian regression to estimate the “rate of return” for education.

However, some of the assumptions of line behind the original model, to allow the coefficient for

years of education to be understood as a rate of return, have been rejected in this article (linearity

and parallelism). Thus for Brazil, we corroborate the evidence presented in international studies

for the USA. Therefore, we relax various assumptions in order to measure the bias that stems from

the poor estimation of the rate of return. We note that the bias tends to be positive for all levels

of education. Thus, the IRRs tend to be smaller when the assumptions are relaxed; among these,

linearity, parallelism and the inclusion of private cost tend to generate the largest impact on the

estimation of the IRRs. Another significant change in the IRRs was the expansion of the age group

from 24-56 years to 10-65 years. This shows that the costs incurred an early age are significant.

In relation to the specifications of years of education and years of schooling, the latter series adds

an important additional aspect to the estimation of IRRs in relation to the former: individuals

considered the average time to finish levels of schooling. This carries with it a significant reduction

in the IRRs, principally for higher levels of education.

The incorporation of the sample design from the PNAD is an additional benefit for the empirical

literature in Brazil, one that had not been considered in the estimation of various economic models.

This correction not only confirms the tests that had been done, but also has a considerable influence

on the correct measurement of the returns. The correction for the sample selection bias also can be

considered an additional gain, given that even recent studies, such as HLT, do not estimate using

the two-stage estimation procedure developed by Heckman (1979), which alters the magnitude of

the IRRs as well.

Finally, the majority of the IRRs estimated tend to corroborate the evidence in the literature

43A return to middle school diverges from other studies, as mentioned in the previous section. Taking as a reference,

the additional 2-4 IRRs, we note that this return is greater for the nonparametric in comparison with the nonlinear.

23

that returns to education have been declining in recent years, with the exception of higher-level

education (University and postgraduate education) that indicates a growth in this last decade, but

at a lower level of magnitude than those obtained in various recent studies. The correct estimation

of rates of return makes it possible for future research to prepare a detailed analysis of the reasons

for the increase in the IRR for undergraduate and graduate education, given the evidence of a

substantial increase in the rates of enrollment during the recent decade. And it is a key indicator

to serve as a guide to public policy and in the evaluation of social programs.

References

[1] Barbosa Filho, F. H. e Samuel Pessoa (2006). Retornos da educação no Brasil. mimeo.

[2] Becker, G. S. (1975). Human Capital: A Theoretical and Empirical Analysis, with Special

Reference to Education. New York: Columbia Uinversity Press, 2a edição.

[3] Belman, D. e J. Heywood (1991). Sheepskin effects in the return to education: An Examination

of Women and Minorities. Review of Economics and Statistics : 73(4): 720-724.

[4] Binelli, C., C. Meghir e N. Menezes Filho (2006). Education and Wages in Brazil. mimeo.

Apresentado no XXVIII Econtro Brasileiro de Econometria.

[5] Blom, A., L. Holm-Nielsen e D. Verner (2001). Education, Earnings, and Inequality in Brazil,

1982-98. Peabody Journal of Education, 76(3&4): 180-221.

[6] Cameron, S. V. e J. J. Heckman (2001). The dynamics of educational attainment for black,

hispanic and white males. Journal of Political Economy, 109(3): 455-99.

[7] Card, D. (1999). The causal effect of education on earnings. In: Ashenfelter, O. e D. Card

(ed.), Handbook of Labor Economics. Amsterdam: Elsevier. v.3A, chap. 30: 1801-1863.

[8] ––––– (2001). Estimating the Return to Schooling: Progress on Some Persistent Econo-

metric Problems. Econometrica, 69(5): 1127-1160.

[9] Chromy, J. R. e S. Abeyasekara (2005). Statistical analysis of survey data. In: Department

of Economic and Social Affairs of United Nations (ed.), Household Sample Surveys in

Developing and Transition Countries. New York: United Nations. chap. 19: 389-417.

[10] Das, M., W. K. Newey e F. Vella (2003). Nonparametric Estimation of Sample Selection

Models. Review of Economic Studies, 70: 33—58.

[11] Fernandes, R. e N. A. Menezes Filho (2000). A Evolução da Desigualdade no Brasil Metropol-

itano entre 1983 e 1997. Pesquisa e Planejamento Econômico, 30(4): 549-569.

[12] Härdle, W.(1990). Applied nonparametric regression. Cambridge:Cambridge University Press.

[13] Heckman, J. J. (1979). Sample Selection Bias as a Specification Error. Econometrica, 47(1):

153-162.

24

[14] ––––– (2005). Education Policy. Apresentado no Econometric Society 9thWorld Congress,

IFS Lecture.

[15] Heckman, J. J e P. Carneiro (2003). Human Capital Policy. IZA, Discussion Paper n.821.

[16] Heckman, J. J., H. Ichimura, J. Smith e P.E. Todd (1996a). Making the Asymptotic Theory

of Semiparametric Estimation Empirically Relevant. Mimeo, University of Chicago.

[17] ––––– (1998). Characterizing selection bias using experimental data. Econometrica, 66(4):

1017-1098.

[18] Heckman, J. J., A. Layne-Farrar e P.E. Todd (1996b). Human Capital Pricing Equations

with an Application to Estimating The Effect of Schooling Quality on Earnings. Review of

Economics and Statistics, 78(4): 562-610.

[19] Heckman, J. J., L. J. Lochner e P. E. Todd (2006). Earnings Functions, Rates of Return and

Treatment Effects: The Mincer Equation and Beyond. In: Hanushek, E. e F. Welch (ed.),

Handbook of the Economics of Education, v1, chap. 7: 307-458.

[20] Hungerford, T. e G. Solon. (1987). Sheepskin Effects in The Returns to Education. Review of

Economics and Statistics, 69(1): 175-177.

[21] IBGE (2004). Pesquisa Nacional por Amostra e Domicílios (2004) - Notas Metodológicas. Rio

de Janeiro: IBGE.

[22] Jaeger, D. A. e M. E. Page (1996). Degrees Matter: New Evidence on Sheepskin Effects in

The Returns to Education. Review of Economics and Statistics, 78(4): 733-740.

[23] Langoni, C. G. (1974). As Causas do Crescimento Econômico do Brasil. Apec Editora S.A.

[24] Leal, C. I. S. e S. R. C. Werlang (1991). Retornos em educação no Brasil: 1976/89. Pesquisa

e Planejamento Econômico, 21(3): 559-574.

[25] Loureiro, P. R. A. e F. G. Carneiro (2001). Discriminação no mercado de trabalho: Uma

análise dos setores rural e urbano no Brasil. Economia Aplicada, 5(3): 519-545.

[26] Lumley, T (2004). Analysis of complex survey samples. Journal of Statistical Software, 9(8):

1-19.

[27] Mincer, J. (1958). Investment in Human Capital and Personal Income Distribution. Journal

of Political Economy, 66: 281-302.

[28] ––––– (1974).Schooling, Experience, and Earnings. New York:Columbia University Press.

[29] Murphy, K. M. e F. Welch (1990). Empirical Age-Earnings Profiles. Journal of Labor Eco-

nomics, 8(2): 202-229.

[30] ––––– (1992). The structure of wages. Quarterly Journal of Economics, 107(1):285–326.

[31] Park, J. H. (1994). Returns to schooling: a peculiar deviation from linearity. mimeo.

25

[32] Pessoa, D. G. C. e P. L. N. Silva (1998). Análise de Dados Amostrais. 13o Simpósio Nacional

de Probabilidade e Estatística.

[33] Psacharopoulos, G. e H. A. Patrinos (2004). Returns to investment in education: a further

update. Education Economics, 12(4): 111-134.

[34] Psacharopoulos, G. (1994). Returns to investment in education: a global update. World De-

velopment, 22: 1325-1343.

[35] Psacharopoulos, G. (1985). Returns to education: a further international update and implica-

tions. Journal of Human Resources, 20: 583-604.

[36] Resende, M. e R. Wyllie (2006). Retornos para Educação no Brasil: Evidências Empíricas

Adicionais. Economia Aplicada, 10(3): 349-365.

[37] Sachsida, A., P. R. A. Loureiro e M. J. C. de Mendonça (2004). Um estudo sobre retorno em

escolaridade no Brasil. Revista Brasileira de Economia, 58(2): 249-265.

[38] Schultz, T. W. (1963).The Economic Value of Education. New York:Columbia University Press.

[39] Silva, N. D. V. e A. L. Kassouf (2000). Mercados de trabalho formal e informal: Uma análise

da discriminação e da segmentação. Nova Economia, 10(1): 41-77.

[40] Silva, P. L. N., D. G. C. Pessoa e M. F. Lila (2002). Análise estatística de dados da PNAD:

incorporando a estrutura do plano amostral. Ciência & Saúde Coletiva, 7(4): 659-670.

[41] Soares, R. R. e G. Gonzaga (1999). Determinação de Salários no Brasil: Dualidade ou Não-

Linearidade no Retorno à Educação? Revista de Econometria, 19(2): 367-404.

[42] Ueda, E. M. e R. Hoffmann (2002). Estimando o retorno da educação no Brasil. Economia

Aplicada, 6(2): 209-238.

[43] Willis, R. J. (1986). Wage Determinants: A survey and reinterpretation of Human Capital

Earnings Functions. In: Ashenfelter, O. e R. Layard (ed.), Handbook of Labor Economics.

Amsterdam: Elsevier. v1, chap. 10: 525-602.

[44] Yansaneh, I. S. (2005). Overview of sample design issues for household surveys in developing

and transition countries. In: Department of Economic and Social Affairs of United Na-

tions (ed.). Household Sample Surveys in Developing and Transition Countries. New York:

United Nations. chap. 2: 11-34.

26

7 Appendix

Table 1. Percentages in relation to the universe of employed and retired persons - PNADs

Total White Black 10<=i<15 15<=i<18 18<=i<24 24<=i i<50 50<=i<=55 i>=561992 62.96% 60.90% 5.41% 9.24% 53.92% 63.85% 4.21% 0.77% 3.96% 14.63% 80.65% 10.26% 10.98% 78.75%1993 62.69% 61.18% 5.38% 9.45% 54.04% 62.87% 4.67% 0.83% 3.64% 14.55% 80.99% 8.97% 12.27% 78.75%1995 60.25% 60.23% 5.10% 10.48% 53.91% 61.63% 4.61% 1.02% 4.33% 14.35% 80.30% 9.24% 12.84% 77.92%1996 59.91% 61.14% 6.13% 10.66% 54.67% 63.28% 5.55% 0.75% 3.96% 14.95% 80.34% 10.90% 12.14% 76.96%1997 60.07% 59.93% 5.71% 11.19% 54.90% 63.55% 5.16% 0.71% 3.79% 14.75% 80.75% 11.61% 12.96% 75.43%1998 59.79% 59.47% 5.94% 11.58% 54.13% 60.96% 5.03% 0.52% 3.30% 14.79% 81.39% 13.06% 13.72% 73.22%1999 59.39% 59.74% 5.42% 12.13% 52.41% 59.28% 5.11% 0.49% 3.09% 14.60% 81.82% 11.84% 13.84% 74.32%2001 58.35% 58.44% 6.15% 12.81% 51.14% 59.75% 5.49% 0.42% 2.45% 15.29% 81.84% 11.18% 12.95% 75.87%2002 57.85% 58.01% 6.35% 12.74% 50.97% 58.42% 5.64% 0.37% 2.49% 15.04% 82.10% 9.76% 13.19% 77.05%2003 57.58% 57.48% 6.37% 12.82% 50.37% 58.82% 5.67% 0.26% 2.29% 14.86% 82.59% 9.65% 12.14% 78.21%2004 56.77% 56.76% 6.38% 12.51% 50.30% 57.50% 5.94% 0.35% 2.54% 14.53% 82.58% 7.81% 11.49% 80.70%

Universe of retired persons

YearMales attend school

Universe of employed persons

MalesTotalTotal White Black

White and Black Males (Age Ranges), i=years old

White and Black Males (Age Ranges), i=years old

Table 2. Percentages in relation to the universe of employed and retired persons - Census

Total White Black 10<=i<15 15<=i<18 18<=i<24 24<=i i<50 50<=i<=55 i>=561970 76.14% - - 10.11% 69.67% - - 0.92% 4.69% 19.24% 75.15% 19.68% 14.72% 65.60%1980 71.14% 62.06% 5.88% 11.80% 61.75% 66.34% 4.46% 0.94% 5.33% 19.94% 73.79% 13.64% 11.30% 75.05%1991 66.24% 59.97% 4.72% 8.12% 56.50% 64.21% 4.06% 0.65% 3.19% 15.01% 81.15% 8.44% 10.38% 81.18%2000 59.64% 59.47% 6.36% 12.68% 52.92% 60.59% 5.92% 0.38% 2.73% 15.53% 81.36% 13.80% 12.58% 73.62%

TotalTotal White Black

White and Black Males (Age Ranges), i=years old

White and Black Males (Age Ranges), i=years old

Universe of retired persons

YearMales attend school

Universe of employed persons

Males

Table 3. Tests for Linearity of Specification 1 - PNAD

Corrections Year 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004Nº of Obs. 8826 8824 9587 8957 9345 9064 9381 9833 9982 9870 10522F test 11.85 15.85 22.89 15.64 18.34 23.75 24.15 34.45 46.31 39.4 49.2Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 8826 8811 9567 8942 9325 9044 9361 9833 9958 9814 10462F test 8.11 11.3 17.23 9.47 12.54 16.79 15.04 25.59 32.19 30.4 31.2Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 11711 11700 12636 12365 12932 12973 13234 13826 13980 13940 14340F test 7.76 11.03 18.6 9.49 13.09 16.82 14.33 26.22 32.02 30.53 30.89Prob>F 0 0 0 0 0 0 0 0 0 0 0

No Corrections

Inclusion of Sample DeisgnSample

Design & Heckit

Table 4. Tests for Linearity of Specification 2 - PNAD

Corrections Year 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004Nº of Obs. 8826 8824 9587 8957 9345 9064 9381 9833 9982 9870 10522F test 24.75 32.72 51.02 33.73 40.1 52.61 51.79 75.96 104.32 90.67 111.42Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 8826 8811 9567 8942 9325 9044 9361 9833 9958 9814 10462F test 15.76 21.3 37.09 18.44 26.35 36.64 30.38 55.71 71.35 67.36 70.2Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 11711 11700 12636 12365 12932 12973 13234 13826 13980 13940 14340F test 3.22 6.72 10.15 6.66 11.17 7.77 6.86 16.38 16.58 16.96 14.74Prob>F 0.01 0 0 0 0 0 0 0 0 0 0

No Corrections

Inclusion of Sample DeisgnSample

Design & Heckit

Table 5. Tests for Linearity of Specification 3 - PNAD

Corrections Year 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004Nº of Obs. 8826 8823 9587 8956 9345 9064 9381 9833 9981 9870 10522F test 10.25 14.31 22.31 14.83 17.57 20.88 23.44 32.92 43.57 36.25 46.35Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 8789 8778 9537 8912 9298 9021 9337 9808 9934 9793 10423F test 6.59 9.39 16.04 8.49 12.36 14.61 15.55 25.91 31.77 27.34 27.82Prob>F 0 0 0 0 0 0 0 0 0 0 0Nº of Obs. 11652 11650 12578 12317 12888 12933 13189 13767 13938 13896 14270F test 6.02 8.59 17.03 8.55 12.9 14.72 14.78 25.88 30.91 27.38 27.38Prob>F 0 0 0 0 0 0 0 0 0 0 0

No Corrections

Inclusion of Sample DeisgnSample

Design & Heckit

27

Table 6. Tests for Linearity of Specifications 1 - 3 - Census

Corrections Year 1991 2000 1991 2000 1970 1980 1991 2000Nº of Obs. 514457 486437 514457 486437 1010984 965773 514457 486437F test 346.6 803.9 845.67 1955.98 586.76 762.71 414.73 212.66Prob>F 0 0 0 0 0 0 0 0Nº of Obs. 515213 793276 515213 793276 1244886 1158103 515213 793276F test 343.75 685.13 742.15 1132.51 704.66 531.98 367.13 832.89Prob>F 0 0 0 0 0 0 0 0

Especificação 2 Especificação 3

No Corrections

Heckit

Especificação 1

Table 7. Differences in the conditional mean of the log of earnings in two groups of years of

education by level of experience and P-Values of the tests for parallelism for three null hypotheses

- PNADs

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.95 0.93 1.04 0.94 0.96 1.02 0.99 1.18 1.11 1.04 1.0220 0.73 0.97 0.97 0.82 0.77 0.92 0.84 0.96 1.01 1.03 1.0230 0.79 0.79 0.82 0.86 0.74 0.94 0.88 0.82 1.00 0.88 0.93

P-Value"20-10"* 0.0001 0.7628 0.6419 0.0633 0.0025 0.1205 0.0344 0.0000 0.2932 0.9128 0.9998

"30-20"** 0.8128 0.0913 0.4330 0.9197 0.9599 0.9819 0.8844 0.1118 0.9818 0.8821 0.3760Joint*** 0.0004 0.1880 0.1786 0.1296 0.0009 0.2321 0.0356 0.0000 0.3340 0.9627 0.4688

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.35 0.47 0.39 0.46 0.45 0.34 0.35 0.33 0.36 0.38 0.1920 0.51 0.39 0.49 0.62 0.63 0.46 0.43 0.40 0.42 0.44 0.4230 0.23 0.42 0.53 0.32 0.50 0.50 0.43 0.58 0.55 0.52 0.48

P-Value"20-10"* 0.0463 0.8169 0.4540 0.0202 0.0004 0.1709 0.4896 0.1068 0.4983 0.1578 0.0002

"30-20"** 0.0252 0.9673 0.8753 0.0022 0.5134 0.7652 1.0000 0.0132 0.1162 0.4148 0.6782Joint*** 0.0364 0.9372 0.3680 0.0028 0.0014 0.1571 0.6320 0.0007 0.0780 0.0278 0.0000

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.46 0.58 0.45 0.30 0.37 0.43 0.51 0.48 0.38 0.51 0.3920 0.52 0.34 0.34 0.46 0.43 0.34 0.38 0.37 0.40 0.34 0.3430 0.46 0.64 0.47 0.42 0.77 0.15 0.27 0.35 0.45 0.19 0.33

P-Value"30-20"* 0.8150 0.0447 0.0527 0.1520 0.7883 0.4326 0.1372 0.3212 0.9000 0.0000 0.6956

"40-30"** 0.8710 0.1859 0.6076 0.9215 0.0201 0.1068 0.7454 0.9934 0.9019 0.0933 0.9977Joint*** 0.9269 0.0665 0.1053 0.1998 0.0023 0.0160 0.1675 0.4612 0.8917 0.0000 0.7838

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.49 0.64 0.62 0.45 0.37 0.54 0.57 0.28 0.30 0.16 0.4020 0.74 0.69 0.47 0.59 0.62 0.55 0.46 0.37 0.30 0.35 0.3430 0.66 0.64 0.52 0.63 0.47 0.60 0.51 0.53 0.43 0.53 0.40

P-Value"30-20"* 0.1204 0.9092 0.5271 0.4894 0.0039 0.9994 0.5256 0.4868 0.9999 0.2678 0.9128

"40-30"** 0.8663 0.8883 0.9408 0.9410 0.2612 0.9037 0.9071 0.3189 0.6212 0.4227 0.8821Joint*** 0.1009 0.9596 0.6700 0.5551 0.0091 0.9341 0.7169 0.1154 0.7568 0.0023 0.9627

Difference in the conditional mean of the log of earnings between 15+ and 11 years of education (White Males)

Difference in the conditional mean of the log of earnings between 11 and 8 years of education (White Males)

Difference in the conditional mean of the log of earnings between 8 and 4 years of education (White Males)

Difference in the conditional mean of the log of earnings between 4 and 0 years of education (White Males)

*H0:(m(x20,s15)−m(x20,s12))−(m(x10,s15)−m(x10,s12))=0

**H0:(m(x30,s15)−m(x30,s12))−(m(x20,s15)−m(x20,s12))=0

***H0:(m(x20,s15)−m(x20,s12))−(m(x10,s15)−m(x10,s12))=(m(x30,s15)−m(x30,s12))−(m(x20,s15)−m(x20,s12))=0

These hypotheses are exemplified for the first panel above. These apply to the others panels, altering the values of x and s.The greyish areas refer to p-values of joint hypothesis that are greater than 0.05.

This note apply too to Tables 8-10.

28

Table 8. Differences in the conditional mean of the log of earnings in two groups of years of

education by level of experience and P-Values of the tests for parallelism for three null hypotheses

- Census

experience 1991 2000 1991 2000 1991 2000 1991 200010 0.92 1.07 0.43 0.39 0.45 0.42 0.51 0.4520 0.81 0.98 0.51 0.48 0.45 0.45 0.62 0.5230 0.65 0.88 0.50 0.51 0.43 0.43 0.63 0.58

P-Value"20-10"* 0.0000 0.0000 0.0000 0.0000 0.8269 0.0206 0.0000 0.0000

"30-20"** 0.0000 0.0000 0.6671 0.0126 0.3451 0.2475 0.5734 0.0034Joint*** 0.0000 0.0000 0.0000 0.0000 0.4328 0.0633 0.0000 0.0000

8 and 4 years of education 4 and 0 years of education Difference in the conditional mean of the log of earnings between (White Males):

15 + and 11 years of education 11 and 8 years of education

See the notes of Table 7.

Table 9. Differences in the conditional mean of the log of earnings in two groups of years of

education by level of experience and P-Values of the tests for parallelism for three null hypotheses

- PNAD

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.72 0.71 0.52 0.47 0.52 0.58 0.66 0.80 0.84 0.92 0.9520 0.65 0.72 0.49 0.47 0.43 0.59 0.68 0.81 0.84 0.91 0.9230 0.79 0.74 0.43 0.50 0.46 0.59 0.63 0.65 0.75 0.78 0.86

P-Value"20-10"* 0.1537 0.8085 0.6710 0.9727 0.1432 0.9063 0.6976 0.8293 0.9273 0.8475 0.6237

"30-20"** 0.0565 0.8042 0.4087 0.6682 0.7824 0.9939 0.3565 0.0029 0.2030 0.0410 0.3751Joint*** 0.0899 0.9257 0.5477 0.8982 0.3419 0.9929 0.6370 0.0113 0.4096 0.0929 0.3816

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.39 0.46 0.47 0.45 0.46 0.40 0.37 0.35 0.35 0.36 0.3120 0.52 0.40 0.50 0.63 0.62 0.48 0.43 0.41 0.44 0.46 0.4530 0.25 0.43 0.53 0.34 0.43 0.49 0.42 0.59 0.53 0.51 0.49

P-Value"20-10"* 0.0421 0.4966 0.6870 0.0011 0.0001 0.1441 0.1818 0.1174 0.0614 0.0083 0.0155

"30-20"** 0.0129 0.7904 0.6700 0.0001 0.0582 0.8641 0.7891 0.0118 0.2193 0.3382 0.5758Joint*** 0.0334 0.7903 0.7756 0.0001 0.0004 0.2590 0.3977 0.0033 0.0395 0.0018 0.0090

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.45 0.58 0.45 0.31 0.41 0.42 0.49 0.48 0.35 0.48 0.3920 0.48 0.35 0.35 0.42 0.46 0.36 0.40 0.35 0.38 0.36 0.3630 0.62 0.73 0.50 0.49 0.91 0.20 0.27 0.35 0.39 0.19 0.26

P-Value"30-20"* 0.7321 0.0085 0.0562 0.1575 0.5761 0.3403 0.1070 0.0992 0.6087 0.0000 0.6647

"40-30"** 0.2295 0.0400 0.3029 0.4865 0.0000 0.1170 0.5485 0.9893 0.8643 0.0002 0.4284Joint*** 0.3241 0.0134 0.1260 0.0545 0.0000 0.0761 0.1951 0.2354 0.7987 0.0000 0.4612

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.32 0.45 0.64 0.23 0.18 0.46 0.43 0.34 0.32 0.06 0.3520 0.58 0.70 0.42 0.59 0.51 0.44 0.28 0.29 0.43 0.24 0.4530 0.45 0.47 0.38 0.66 0.46 0.58 0.43 0.55 0.34 0.33 0.30

P-Value"30-20"* 0.1473 0.0409 0.1696 0.0464 0.0078 0.8567 0.2840 0.6760 0.5244 0.1772 0.5857

"40-30"** 0.3930 0.1576 0.8339 0.6607 0.7697 0.4235 0.3435 0.1287 0.6361 0.5791 0.4544Joint*** 0.3499 0.1178 0.1802 0.0264 0.0072 0.6768 0.5322 0.3141 0.7817 0.0650 0.7491

experience 1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 200410 0.42 0.38 0.06 0.41 0.28 0.30 0.22 -0.20 0.38 0.41 0.0020 0.36 0.01 0.07 0.10 0.28 0.16 0.32 0.28 0.04 0.23 -0.1230 0.28 0.36 0.28 -0.10 -0.10 -0.08 0.12 0.00 0.23 0.22 0.10

P-Value"30-20"* 0.7841 0.0628 0.9761 0.1083 0.9865 0.4137 0.5873 0.0002 0.1089 0.3326 0.6537

"40-30"** 0.6580 0.0569 0.3976 0.2364 0.0130 0.2325 0.2841 0.1405 0.4469 0.9757 0.2758Joint*** 0.7156 0.0725 0.5901 0.0186 0.0093 0.0842 0.5625 0.0007 0.2765 0.3986 0.5518

Difference in the conditional mean of the log of earnings between PRE and NEDUC (White Males)

Difference in the conditional mean of the log of earnings between SUP4+ and EM3 (White Males)

Difference in the conditional mean of the log of earnings between EM3 and EF8 (White Males)

Difference in the conditional mean of the log of earnings between EF8 and EF4 (White Males)

Difference in the conditional mean of the log of earnings between EF4 and PRE (White Males)

Note: SUP4+: College Degree or Master’s/Doctorate Degree, EM3: High School, EF8: Middle School,

EF4: Primary School, PRE: Preschool and NEDUC: No Education. This note apply to the next table.

29

Table 10. Differences in the conditional mean of the log of earnings in two groups of years of

education by level of experience and P-Values of the tests for parallelism for three null hypotheses

- Census

experience 1970**** 1980 1991 2000 1970**** 1980 1991 200010 0.95 0.99 0.88 1.03 0.52 0.52 0.43 0.3920 0.74 0.72 0.79 0.93 0.46 0.51 0.51 0.4830 0.53 0.55 0.65 0.85 0.45 0.47 0.50 0.51

P-Value"20-10"* 0.0000 0.0000 0.0000 0.0000 0.0000 0.1532 0.0000 0.0000

"30-20"** 0.0000 0.0000 0.0000 0.0000 0.4774 0.0027 0.6671 0.0733Joint*** 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

experience 1970**** 1980 1991 2000 1970**** 1980 1991 200010 0.76 0.56 0.45 0.42 0.66 0.51 0.51 0.4520 0.82 0.59 0.45 0.44 0.71 0.59 0.62 0.5430 0.78 0.56 0.43 0.41 0.75 0.62 0.63 0.61

P-Value"30-20"* 0.0001 0.0038 0.8269 0.1578 0.0003 0.0000 0.0000 0.0000

"40-30"** 0.0232 0.0025 0.3451 0.2425 0.0870 0.0002 0.5734 0.0004Joint*** 0.0004 0.0017 0.4328 0.2794 0.0000 0.0000 0.0000 0.0000

EF8 e EF4 EF4 e NEDUC

Difference in the conditional mean of the log of earnings between (White Males):SUP4+ and EM3 EM3 and EF8

Diferença da média condicional dos rendimentos em log entre (Homens Brancos):

****In 1970, there isn’t the race variable in data set, so the differences were estimated for all males.See the notes of Table 9.

30

Table 11. IRR’s - PNADs

Year/Method1992 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.08% 13.08% 13.08% 13.08% 12.78% 12.78% 12.78% 12.78% 11.81% 11.81% 11.81% 11.81%Mincer II 16.22% 16.22% 16.22% 16.22% 15.97% 15.97% 15.97% 15.97% 15.39% 15.39% 15.39% 15.39%IRR-Non Linear 12.54% 8.35% 12.53% 16.12% 12.86% 8.70% 11.38% 15.84% 11.22% 8.42% 10.77% 15.02%IRR-Nonparallel Parametric 8.26% 11.21% 13.88% 14.31% 8.62% 11.21% 13.53% 13.70% 7.76% 10.35% 12.68% 13.00%IRR-Nonparallel Non-Param. 11.91% 9.33% 11.19% 15.90% 11.91% 9.33% 11.19% 15.64% - - - -1993 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.89% 13.89% 13.89% 13.89% 13.54% 13.54% 13.54% 13.54% 12.68% 12.68% 12.68% 12.68%Mincer II 17.19% 17.19% 17.19% 17.19% 16.94% 16.94% 16.94% 16.94% 16.35% 16.35% 16.35% 16.35%IRR-Non Linear 12.58% 9.68% 11.97% 17.66% 14.26% 9.94% 10.72% 16.93% 12.18% 9.90% 9.99% 16.46%IRR-Nonparallel Parametric 7.81% 11.48% 14.82% 15.73% 8.75% 11.64% 14.25% 14.59% 7.58% 10.69% 13.52% 14.16%IRR-Nonparallel Non-Param. 13.64% 10.37% 10.79% 16.62% 13.62% 10.34% 10.82% 16.52% - - - -1995 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.99% 13.99% 13.99% 13.99% 13.64% 13.64% 13.64% 13.64% 12.76% 12.76% 12.76% 12.76%Mincer II 17.23% 17.23% 17.23% 17.23% 16.93% 16.93% 16.93% 16.93% 16.24% 16.24% 16.24% 16.24%IRR-Non Linear 10.33% 7.64% 14.64% 18.47% 10.99% 7.51% 13.85% 18.54% 8.89% 6.88% 13.66% 18.29%IRR-Nonparallel Parametric 6.22% 10.73% 14.90% 16.58% 6.26% 10.54% 14.48% 16.03% 4.85% 9.49% 13.80% 15.80%IRR-Nonparallel Non-Param. 11.37% 7.95% 13.25% 19.58% 11.37% 7.94% 13.23% 19.59% - - - -1996 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.42% 13.42% 13.42% 13.42% 12.98% 12.98% 12.98% 12.98% 12.06% 12.06% 12.06% 12.06%Mincer II 16.43% 16.43% 16.43% 16.43% 16.09% 16.09% 16.09% 16.09% 15.34% 15.34% 15.34% 15.34%IRR-Non Linear 10.50% 7.99% 13.73% 16.50% 11.70% 8.08% 11.90% 16.29% 9.54% 7.64% 11.19% 15.88%IRR-Nonparallel Parametric 6.79% 10.61% 14.11% 15.30% 7.34% 10.60% 13.56% 14.34% 6.06% 9.55% 12.74% 13.85%IRR-Nonparallel Non-Param. 10.51% 8.73% 11.83% 16.24% 10.54% 8.71% 11.85% 15.99% - - - -1997 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.89% 13.89% 13.89% 13.89% 13.62% 13.62% 13.62% 13.62% 12.87% 12.87% 12.87% 12.87%Mincer II 16.76% 16.76% 16.76% 16.76% 16.56% 16.56% 16.56% 16.56% 15.91% 15.91% 15.91% 15.91%IRR-Non Linear 11.45% 8.40% 13.92% 17.12% 11.22% 8.55% 13.75% 16.37% 9.07% 8.28% 13.00% 15.99%IRR-Nonparallel Parametric 6.64% 10.75% 14.52% 15.89% 6.77% 10.68% 14.25% 15.47% 5.56% 9.71% 13.52% 15.08%IRR-Nonparallel Non-Param. 9.63% 9.00% 13.16% 17.69% 9.65% 8.94% 13.22% 17.66% - - - -1998 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.88% 13.88% 13.88% 13.88% 13.55% 13.55% 13.55% 13.55% 12.99% 12.99% 12.99% 12.99%Mincer II 16.81% 16.81% 16.81% 16.81% 16.43% 16.43% 16.43% 16.43% 15.84% 15.84% 15.84% 15.84%IRR-Non Linear 11.24% 7.28% 13.46% 19.28% 11.71% 7.29% 12.80% 18.69% 10.20% 6.99% 11.76% 18.49%IRR-Nonparallel Parametric 5.74% 10.51% 14.92% 16.78% 5.99% 10.47% 14.60% 16.24% 5.01% 9.59% 13.81% 15.68%IRR-Nonparallel Non-Param. 11.64% 7.94% 12.06% 19.30% 11.71% 7.99% 12.02% 19.30% - - - -1999 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.61% 13.61% 13.61% 13.61% 13.25% 13.25% 13.25% 13.25% 12.61% 12.61% 12.61% 12.61%Mincer II 16.81% 16.81% 16.81% 16.81% 16.51% 16.51% 16.51% 16.51% 15.87% 15.87% 15.87% 15.87%IRR-Non Linear 11.35% 7.65% 12.47% 18.87% 11.52% 8.34% 11.34% 18.06% 9.56% 8.24% 10.82% 17.25%IRR-Nonparallel Parametric 5.59% 10.30% 14.65% 16.50% 6.19% 10.38% 14.22% 15.67% 5.26% 9.52% 13.43% 15.07%IRR-Nonparallel Non-Param. 12.16% 8.89% 10.81% 18.91% 12.18% 8.90% 10.76% 18.92% - - - -2001 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.57% 13.57% 13.57% 13.57% 13.45% 13.45% 13.45% 13.45% 12.80% 12.80% 12.80% 12.80%Mincer II 16.59% 16.59% 16.59% 16.59% 16.70% 16.70% 16.70% 16.70% 15.99% 15.99% 15.99% 15.99%IRR-Non Linear 8.82% 8.71% 11.23% 20.71% 9.18% 8.35% 11.56% 20.51% 7.45% 7.41% 11.04% 19.94%IRR-Nonparallel Parametric 4.19% 9.79% 15.02% 17.66% 4.43% 9.92% 15.03% 17.53% 3.28% 8.90% 14.15% 16.94%IRR-Nonparallel Non-Param. 7.11% 9.42% 10.72% 21.68% 7.11% 9.42% 10.72% 21.68% - - - -2002 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.69% 13.69% 13.69% 13.69% 13.39% 13.39% 13.39% 13.39% 12.46% 12.46% 12.46% 12.46%Mincer II 16.84% 16.84% 16.84% 16.84% 16.65% 16.65% 16.65% 16.65% 15.85% 15.85% 15.85% 15.85%IRR-Non Linear 8.54% 7.20% 12.21% 21.83% 8.78% 7.28% 12.08% 20.83% 6.21% 7.01% 11.40% 20.20%IRR-Nonparallel Parametric 2.47% 8.91% 15.00% 18.51% 2.88% 8.91% 14.60% 17.78% 1.75% 7.96% 13.82% 17.28%IRR-Nonparallel Non-Param. 8.75% 7.53% 11.20% 21.48% 8.76% 7.52% 11.19% 21.33% - - - -2003 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.38% 13.38% 13.38% 13.38% 13.18% 13.18% 13.18% 13.18% 12.40% 12.40% 12.40% 12.40%Mincer II 16.79% 16.79% 16.79% 16.79% 16.61% 16.61% 16.61% 16.61% 15.88% 15.88% 15.88% 15.88%IRR-Non Linear 8.50% 7.06% 11.74% 20.29% 8.54% 6.76% 11.77% 19.75% 6.91% 6.33% 11.23% 19.05%IRR-Nonparallel Parametric 2.84% 8.85% 14.51% 17.71% 2.79% 8.78% 14.42% 17.57% 1.98% 7.97% 13.60% 16.89%IRR-Nonparallel Non-Param. 7.33% 8.09% 10.91% 20.49% 7.36% 8.02% 10.87% 20.51% - - - -2004 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11 S4-S0 S8-S4 S11-S8 S15-S11Mincer I 13.06% 13.06% 13.06% 13.06% 12.67% 12.67% 12.67% 12.67% 11.79% 11.79% 11.79% 11.79%Mincer II 16.41% 16.41% 16.41% 16.41% 16.08% 16.08% 16.08% 16.08% 15.36% 15.36% 15.36% 15.36%IRR-Non Linear 9.68% 6.85% 11.17% 20.78% 9.00% 6.67% 11.28% 19.58% 6.94% 6.35% 10.77% 19.01%IRR-Nonparallel Parametric 2.52% 8.55% 14.25% 17.53% 2.68% 8.47% 13.91% 17.00% 1.67% 7.57% 13.12% 16.44%IRR-Nonparallel Non-Param. 8.31% 6.81% 10.52% 19.73% 8.27% 6.78% 10.50% 19.66% - - - -

No Corrections Inclusion of Sample Design Inclusion of Sample Design & Heckit

31

Table 11. IRR’s - PNADs (continued . . . )

Year/Method1992 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 12.72% 12.72% 12.72% 12.72% 12.72% 12.51% 12.51% 12.51% 12.51% 12.51% 11.57% 11.57% 11.57% 11.57% 11.57%Mincer II 15.85% 15.85% 15.85% 15.85% 15.85% 15.73% 15.73% 15.73% 15.73% 15.73% 15.18% 15.18% 15.18% 15.18% 15.18%IRR-Non Linear 4.29% 6.58% 7.27% 9.04% 9.72% 4.74% 6.44% 7.71% 8.91% 9.21% 3.87% 5.72% 7.51% 8.43% 8.67%IRR-Nonparallel Parametric 1.17% 6.00% 9.60% 10.45% 8.36% 1.27% 6.29% 9.62% 10.19% 8.00% 1.26% 6.25% 9.60% 10.21% 8.03%IRR-Nonparallel Non-Param. 4.95% 6.22% 8.12% 8.63% 9.14% 4.95% 6.31% 7.86% 8.48% 9.17% - - - - -1993 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.48% 13.48% 13.48% 13.48% 13.48% 13.23% 13.23% 13.23% 13.23% 13.23% 12.39% 12.39% 12.39% 12.39% 12.39%Mincer II 16.79% 16.79% 16.79% 16.79% 16.79% 16.66% 16.66% 16.66% 16.66% 16.66% 16.10% 16.10% 16.10% 16.10% 16.10%IRR-Non Linear 3.15% 7.38% 8.08% 9.31% 10.86% 2.76% 8.57% 8.56% 9.41% 9.79% 1.60% 7.78% 8.60% 8.78% 9.41%IRR-Nonparallel Parametric 1.06% 5.70% 9.98% 11.91% 9.68% 1.30% 6.36% 10.13% 11.46% 8.99% 1.30% 6.46% 10.01% 10.70% 8.47%IRR-Nonparallel Non-Param. 3.35% 7.57% 9.02% 9.28% 9.82% 3.35% 7.65% 8.80% 9.07% 10.19% - - - - -1995 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.62% 13.62% 13.62% 13.62% 13.62% 13.39% 13.39% 13.39% 13.39% 13.39% 12.55% 12.55% 12.55% 12.55% 12.55%Mincer II 16.91% 16.91% 16.91% 16.91% 16.91% 16.75% 16.75% 16.75% 16.75% 16.75% 16.10% 16.10% 16.10% 16.10% 16.10%IRR-Non Linear 1.61% 6.51% 6.78% 10.59% 12.07% 0.22% 8.03% 6.79% 10.92% 11.59% -0.98% 7.36% 6.27% 10.74% 11.36%IRR-Nonparallel Parametric 0.69% 4.49% 9.75% 11.51% 10.44% 0.74% 4.58% 9.61% 11.21% 10.10% 0.74% 4.74% 9.16% 11.04% 9.49%IRR-Nonparallel Non-Param. 0.97% 7.56% 7.19% 10.59% 11.99% 0.95% 7.57% 7.10% 10.41% 12.55% - - - - -1996 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.06% 13.06% 13.06% 13.06% 13.06% 12.70% 12.70% 12.70% 12.70% 12.70% 11.81% 11.81% 11.81% 11.81% 11.81%Mincer II 16.10% 16.10% 16.10% 16.10% 16.10% 15.87% 15.87% 15.87% 15.87% 15.87% 15.14% 15.14% 15.14% 15.14% 15.14%IRR-Non Linear 2.14% 6.51% 6.43% 10.36% 12.41% 1.99% 7.21% 6.71% 9.89% 11.60% 1.36% 6.03% 6.30% 9.32% 11.29%IRR-Nonparallel Parametric 0.82% 4.85% 9.02% 10.84% 11.39% 0.98% 5.25% 9.02% 10.43% 10.69% 0.97% 5.31% 9.12% 10.37% 8.58%IRR-Nonparallel Non-Param. 1.64% 6.75% 7.29% 9.76% 11.63% 1.64% 6.78% 7.14% 10.08% 11.94% - - - - -1997 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.56% 13.56% 13.56% 13.56% 13.56% 13.37% 13.37% 13.37% 13.37% 13.37% 12.66% 12.66% 12.66% 12.66% 12.66%Mincer II 16.49% 16.49% 16.49% 16.49% 16.49% 16.39% 16.39% 16.39% 16.39% 16.39% 15.76% 15.76% 15.76% 15.76% 15.76%IRR-Non Linear 1.95% 6.89% 7.11% 11.43% 11.44% 2.54% 6.06% 7.46% 12.09% 10.42% 2.01% 4.83% 7.25% 11.47% 10.09%IRR-Nonparallel Parametric 0.78% 4.78% 8.99% 12.72% 10.44% 0.82% 4.87% 8.93% 12.49% 10.18% 0.82% 4.97% 9.21% 10.86% 9.19%IRR-Nonparallel Non-Param. 3.06% 5.21% 7.79% 11.61% 11.06% 3.07% 5.27% 7.42% 12.42% 10.64% - - - - -1998 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.53% 13.53% 13.53% 13.53% 13.53% 13.28% 13.28% 13.28% 13.28% 13.28% 12.74% 12.74% 12.74% 12.74% 12.74%Mincer II 16.50% 16.50% 16.50% 16.50% 16.50% 16.22% 16.22% 16.22% 16.22% 16.22% 15.64% 15.64% 15.64% 15.64% 15.64%IRR-Non Linear 2.12% 6.46% 6.36% 10.86% 14.73% 2.08% 6.66% 6.52% 11.14% 13.68% 1.64% 5.83% 6.24% 10.25% 13.48%IRR-Nonparallel Parametric 0.58% 4.31% 8.47% 12.74% 12.50% 0.71% 4.61% 8.36% 12.16% 11.72% 0.66% 4.52% 9.07% 11.04% 9.49%IRR-Nonparallel Non-Param. 2.54% 6.10% 6.73% 10.64% 14.32% 2.59% 6.19% 6.68% 10.28% 14.19% - - - - -1999 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.28% 13.28% 13.28% 13.28% 13.28% 12.99% 12.99% 12.99% 12.99% 12.99% 12.40% 12.40% 12.40% 12.40% 12.40%Mincer II 16.53% 16.53% 16.53% 16.53% 16.53% 16.31% 16.31% 16.31% 16.31% 16.31% 15.70% 15.70% 15.70% 15.70% 15.70%IRR-Non Linear 2.25% 7.16% 5.95% 10.60% 12.47% 2.12% 7.14% 6.57% 10.62% 11.39% 1.33% 6.23% 6.43% 10.19% 10.91%IRR-Nonparallel Parametric 0.56% 4.34% 8.07% 13.30% 10.88% 0.59% 4.36% 7.94% 12.96% 10.58% 0.71% 4.62% 8.97% 10.78% 9.19%IRR-Nonparallel Non-Param. 1.76% 7.36% 6.91% 10.19% 11.92% 1.85% 7.42% 6.68% 10.44% 11.41% - - - - -2001 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.27% 13.27% 13.27% 13.27% 13.27% 13.21% 13.21% 13.21% 13.21% 13.21% 12.61% 12.61% 12.61% 12.61% 12.61%Mincer II 16.32% 16.32% 16.32% 16.32% 16.32% 16.50% 16.50% 16.50% 16.50% 16.50% 15.82% 15.82% 15.82% 15.82% 15.82%IRR-Non Linear 2.68% 5.05% 7.51% 7.57% 14.96% 3.01% 4.94% 7.27% 8.53% 14.78% 2.66% 3.99% 6.46% 8.11% 13.83%IRR-Nonparallel Parametric 0.24% 3.28% 8.44% 11.07% 12.64% 0.30% 3.46% 8.54% 11.05% 12.53% 0.30% 3.44% 8.62% 11.37% 10.21%IRR-Nonparallel Non-Param. 2.47% 4.49% 8.06% 8.26% 15.11% 2.47% 4.55% 7.96% 8.46% 15.13% - - - - -2002 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.39% 13.39% 13.39% 13.39% 13.39% 13.16% 13.16% 13.16% 13.16% 13.16% 12.27% 12.27% 12.27% 12.27% 12.27%Mincer II 16.58% 16.58% 16.58% 16.58% 16.58% 16.48% 16.48% 16.48% 16.48% 16.48% 15.70% 15.70% 15.70% 15.70% 15.70%IRR-Non Linear 0.28% 6.57% 6.01% 8.94% 14.77% -0.58% 6.91% 6.18% 9.64% 13.46% -1.62% 5.72% 5.90% 9.05% 12.99%IRR-Nonparallel Parametric -0.15% 2.10% 7.56% 11.99% 12.51% -0.05% 2.37% 7.55% 11.69% 12.07% -0.04% 2.31% 7.78% 11.13% 10.47%IRR-Nonparallel Non-Param. -1.26% 7.07% 6.31% 9.21% 13.89% -1.34% 7.23% 6.37% 9.04% 13.82% - - - - -2003 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 13.10% 13.10% 13.10% 13.10% 13.10% 12.96% 12.96% 12.96% 12.96% 12.96% 12.21% 12.21% 12.21% 12.21% 12.21%Mincer II 16.53% 16.53% 16.53% 16.53% 16.53% 16.42% 16.42% 16.42% 16.42% 16.42% 15.71% 15.71% 15.71% 15.71% 15.71%IRR-Non Linear 2.88% 4.96% 6.12% 8.10% 13.64% 3.02% 4.40% 5.98% 8.92% 12.69% 2.40% 3.53% 5.56% 8.50% 12.21%IRR-Nonparallel Parametric -0.03% 2.37% 7.96% 10.72% 11.75% -0.03% 2.35% 7.91% 10.62% 11.61% 0.00% 2.39% 7.72% 10.92% 10.21%IRR-Nonparallel Non-Param. 3.50% 3.93% 7.00% 8.56% 13.17% 3.50% 3.98% 7.07% 8.57% 12.67% - - - - -2004 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3Mincer I 12.79% 12.79% 12.79% 12.79% 12.79% 12.50% 12.50% 12.50% 12.50% 12.50% 11.65% 11.65% 11.65% 11.65% 11.65%Mincer II 16.16% 16.16% 16.16% 16.16% 16.16% 15.96% 15.96% 15.96% 15.96% 15.96% 15.26% 15.26% 15.26% 15.26% 15.26%IRR-Non Linear 1.30% 7.00% 5.60% 7.92% 12.65% 1.43% 6.09% 5.73% 8.78% 11.50% 0.95% 4.73% 5.47% 8.34% 11.14%IRR-Nonparallel Parametric -0.11% 2.21% 7.29% 10.72% 10.75% -0.05% 2.34% 7.22% 10.46% 10.42% -0.03% 2.24% 7.44% 10.61% 10.01%IRR-Nonparallel Non-Param. 1.10% 5.97% 5.77% 8.37% 11.61% 0.93% 6.13% 5.70% 8.20% 12.38% - - - - -

No Corrections Inclusion of Sample Design Inclusion of Sample Design & Heckit

32

Table 12. IRR’s - Census

Year/Method1991 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15Mincer I 12.54% 12.54% 12.54% 12.54% 12.54% 12.56% 12.56% 12.56% 12.56% 12.56%Mincer II 16.03% 16.03% 16.03% 16.03% 16.03% 16.05% 16.05% 16.05% 16.05% 16.05%IRR-Non Linear 13.35% 9.07% 13.30% 13.94% 24.78% 13.58% 8.88% 13.38% 14.28% 23.65%IRR-Nonparallel Parametric 9.50% 11.27% 12.85% 14.46% 15.86% 9.30% 11.19% 12.87% 14.59% 16.09%IRR-Nonparallel Non-Param. 12.14% 9.26% 13.06% 14.39% 22.83% - - - - -2000 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15Mincer I 13.78% 13.78% 13.78% 13.78% 13.78% 17.49% 17.49% 17.49% 17.49% 17.49%Mincer II 16.92% 16.92% 16.92% 16.92% 16.92% 17.04% 17.04% 17.04% 17.04% 17.04%IRR-Non Linear 12.19% 8.80% 12.63% 18.91% 26.26% 11.38% 8.91% 12.65% 19.79% 12.82%IRR-Nonparallel Parametric 4.81% 9.37% 13.58% 18.04% 22.04% 4.81% 9.37% 13.58% 18.04% 22.04%IRR-Nonparallel Non-Param. 10.76% 8.94% 11.91% 20.52% 23.87% - - - - -

Year/Method1970 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUP EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPMincer I 16.97% 16.97% 16.97% 16.97% - 16.34% 16.34% 16.34% 16.34% -Mincer II 19.55% 19.55% 19.55% 19.55% - 19.08% 19.08% 19.08% 19.08% -IRR-Non Linear 7.67% 14.22% 10.05% 19.77% - 6.98% 14.25% 9.47% 20.07% -IRR-Nonparallel Parametric 7.49% 13.26% 13.16% 17.98% - 6.62% 12.02% 12.61% 17.69% -IRR-Nonparallel Non-Param. 11.35% 16.20% 6.22% 22.80% - - - - - -1980 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUP EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPMincer I 13.65% 13.65% 13.65% 13.65% 13.65% 13.75% 13.75% 13.75% 13.75% 13.75%Mincer II 17.04% 17.04% 17.04% 17.04% 17.04% 17.08% 17.08% 17.08% 17.08% 17.08%IRR-Non Linear 6.30% 9.10% 10.68% 9.24% 5.07% 7.26% 9.78% 11.69% 10.53% 3.57%IRR-Nonparallel Parametric 6.58% 11.01% 12.86% 9.18% 3.97% 9.12% 10.46% 8.69% 4.57% 1.56%IRR-Nonparallel Non-Param. 7.39% 9.83% 12.00% 10.50% 5.60% - - - - -1991 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUP EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPMincer I 12.74% 12.74% 12.74% 12.74% 12.74% 12.77% 12.77% 12.77% 12.77% 12.77%Mincer II 16.31% 16.31% 16.31% 16.31% 16.31% 16.34% 16.34% 16.34% 16.34% 16.34%IRR-Non Linear 9.03% 7.91% 11.96% 9.97% 5.24% 8.98% 7.74% 12.03% 10.04% 5.07%IRR-Nonparallel Parametric 6.28% 9.84% 11.95% 9.07% 2.72% 5.55% 9.32% 11.87% 9.55% 3.04%IRR-Nonparallel Non-Param. 8.49% 8.02% 11.79% 10.00% 5.49% - - - - -2000 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUP EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPMincer I 13.94% 13.94% 13.94% 13.94% 13.94% 16.70% 16.70% 16.70% 16.70% 16.70%Mincer II 17.21% 17.21% 17.21% 17.21% 17.21% 17.29% 17.29% 17.29% 17.29% 17.29%IRR-Non Linear 8.41% 7.19% 10.33% 12.94% 5.45% 7.70% 7.25% 10.42% 12.79% 3.03%IRR-Nonparallel Parametric 3.94% 8.70% 11.91% 11.55% 2.82% 5.57% 9.70% 12.02% 11.07% 2.74%IRR-Nonparallel Non-Param. 7.55% 7.29% 9.96% 13.39% 5.33% - - - - -

No Corrections Heckit

Specification: Years of EducationNo Corrections Heckit

Specification: Years of Schooling

33

Table 13. Additional IRRs — Non-Parametric - PNAD

Year/Method1992 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 11.91% 9.33% 11.19% 15.64% 4.95% 6.31% 7.86% 8.48% 9.17%IRR – additional 1 11.65% 7.78% 13.47% 16.85% 3.44% 6.23% 6.83% 10.32% 9.55%IRR – additional 2 8.09% 19.52% 14.66% 28.39% 1.23% 5.34% 14.97% 11.36% 15.84%IRR – additional 3 8.32% 19.48% 14.59% 28.39% 1.61% 5.66% 14.89% 11.18% 15.79%IRR – additional 4 7.12% 13.87% 12.88% 21.91% 1.19% 4.83% 11.47% 10.16% 12.01%1993 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 13.62% 10.34% 10.82% 16.52% 3.35% 7.65% 8.80% 9.07% 10.19%IRR – additional 1 12.43% 9.15% 13.38% 17.52% 1.60% 8.49% 7.81% 11.13% 10.65%IRR – additional 2 9.59% 17.14% 21.32% 18.66% 0.81% 6.60% 13.47% 17.21% 12.86%IRR – additional 3 9.88% 17.06% 21.31% 18.65% 0.36% 7.08% 13.30% 17.18% 12.76%IRR – additional 4 8.30% 12.61% 17.85% 15.68% -0.07% 6.02% 10.48% 14.93% 10.29%1995 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 11.37% 7.94% 13.23% 19.59% 0.95% 7.57% 7.10% 10.41% 12.55%IRR – additional 1 12.14% 8.69% 12.32% 19.70% 1.22% 7.95% 7.68% 9.77% 12.23%IRR – additional 2 9.12% 13.90% 16.37% 25.65% 0.82% 6.19% 12.30% 12.56% 16.45%IRR – additional 3 9.42% 13.79% 16.35% 25.64% 1.01% 6.63% 12.14% 12.48% 16.43%IRR – additional 4 7.97% 11.16% 13.92% 20.29% 0.61% 5.71% 10.03% 11.12% 12.61%1996 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 10.54% 8.71% 11.85% 15.99% 1.64% 6.78% 7.14% 10.08% 11.94%IRR – additional 1 10.86% 8.91% 11.80% 16.91% 1.62% 6.79% 7.52% 9.26% 12.70%IRR – additional 2 6.71% 14.35% 15.81% 21.11% 1.24% 4.66% 11.57% 12.06% 14.34%IRR – additional 3 7.14% 14.25% 15.77% 21.11% 1.47% 5.13% 11.38% 11.94% 14.32%IRR – additional 4 6.37% 11.06% 13.46% 16.92% 0.93% 4.59% 9.28% 10.63% 11.33%IRR – additional 4(POF) 5.76% 9.87% 12.21% 17.33% 0.92% 4.14% 8.42% 9.85% 11.62%1997 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 9.65% 8.94% 13.22% 17.66% 3.07% 5.27% 7.42% 12.42% 10.64%IRR – additional 1 9.86% 9.43% 11.77% 17.89% 2.94% 5.79% 7.89% 10.39% 11.57%IRR – additional 2 5.83% 13.92% 18.41% 17.68% 1.60% 3.67% 11.02% 16.12% 13.11%IRR – additional 3 6.46% 13.87% 18.38% 17.67% 2.25% 4.38% 10.93% 16.06% 13.06%IRR – additional 4 5.81% 11.11% 15.68% 14.89% 1.68% 3.93% 9.20% 14.00% 10.69%1998 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 11.71% 7.99% 12.02% 19.30% 2.59% 6.19% 6.68% 10.28% 14.19%IRR – additional 1 9.16% 8.45% 12.33% 18.78% 2.89% 5.04% 6.76% 10.76% 14.58%IRR – additional 2 6.21% 12.91% 17.12% 22.93% 1.17% 3.74% 9.88% 14.18% 16.96%IRR – additional 3 6.86% 12.73% 17.10% 22.93% 1.78% 4.51% 9.55% 14.16% 16.95%IRR – additional 4 6.03% 10.19% 14.45% 18.36% 1.29% 3.97% 7.72% 12.38% 13.15%1999 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 12.18% 8.90% 10.76% 18.92% 1.85% 7.42% 6.68% 10.44% 11.41%IRR – additional 1 9.64% 8.34% 12.03% 19.16% 3.27% 5.63% 6.37% 11.20% 12.73%IRR – additional 2 6.58% 10.01% 20.39% 23.35% 1.04% 3.87% 7.77% 18.67% 15.90%IRR – additional 3 7.28% 9.86% 20.37% 23.34% 1.69% 4.90% 7.49% 18.64% 15.87%IRR – additional 4 6.37% 8.37% 17.25% 18.36% 1.28% 4.32% 6.32% 16.04% 12.34%2001 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 7.11% 9.42% 10.72% 21.68% 2.47% 4.55% 7.96% 8.46% 15.13%IRR – additional 1 7.69% 8.64% 10.95% 21.93% 2.45% 4.88% 7.30% 8.43% 15.50%IRR – additional 2 7.25% 12.32% 13.49% 27.47% 0.83% 4.61% 10.10% 10.08% 17.30%IRR – additional 3 7.58% 12.21% 13.48% 27.47% 1.78% 4.99% 9.92% 10.03% 17.29%IRR – additional 4 6.47% 9.91% 11.93% 21.55% 1.40% 4.28% 8.38% 8.87% 13.43%2002 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 8.76% 7.52% 11.19% 21.33% -1.34% 7.23% 6.37% 9.04% 13.82%IRR – additional 1 8.74% 6.64% 11.72% 22.44% 0.46% 6.51% 5.61% 9.55% 14.99%IRR – additional 2 5.20% 10.13% 17.05% 24.84% -1.10% 4.12% 8.09% 13.29% 16.78%IRR – additional 3 5.81% 9.90% 17.04% 24.83% 1.08% 4.60% 7.77% 13.25% 16.75%IRR – additional 4 5.18% 7.93% 14.59% 19.72% 0.81% 4.06% 6.54% 11.81% 13.08%2003 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 7.36% 8.02% 10.87% 20.51% 3.50% 3.98% 7.07% 8.57% 12.67%IRR – additional 1 7.28% 7.35% 10.93% 20.50% 1.39% 5.05% 6.44% 8.44% 13.72%IRR – additional 2 3.74% 14.33% 19.18% 23.08% 0.71% 2.24% 11.91% 13.12% 16.53%IRR – additional 3 4.69% 14.16% 19.16% 23.08% 1.57% 3.39% 11.64% 13.03% 16.51%IRR – additional 4 4.23% 10.82% 16.32% 18.93% 1.13% 3.06% 9.29% 11.25% 13.31%2004 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 8.27% 6.78% 10.50% 19.66% 0.93% 6.13% 5.70% 8.20% 12.38%IRR – additional 1 8.53% 6.43% 10.81% 20.88% 1.17% 6.41% 5.39% 8.54% 12.56%IRR – additional 2 2.94% 15.63% 13.15% 23.59% 0.49% 2.08% 12.24% 9.92% 14.61%IRR – additional 3 4.44% 15.51% 13.16% 23.59% 1.32% 3.50% 11.93% 9.92% 14.57%IRR – additional 4 4.06% 12.01% 11.78% 19.05% 0.99% 3.14% 9.60% 9.17% 11.45%

Non Parametric- Inclusion of Sample DesignSpecification: Years of Education Specification: Years of Schooling

Additional 1: IRR nonparallel, but it was included those who attend school and work at the same time.

Additional 2: Additional 1 with age group between 10 and 65 years old and l=40 early years (l′(s)=1).

Additional 3: Additional 1 with age group between 10 and 65 years old and retirement age equal to 65 (l′(s)=0).

Additional 4: Additional 3 and it was included the direct costs. This note apply to Tables 13-16..

34

Table 14. Additional IRRs — Non- Linear - PNAD

Year/Method1992 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 11.22% 8.42% 10.77% 15.02% 3.87% 5.72% 7.51% 8.43% 8.67%IRR – additional 1 11.12% 7.68% 13.28% 16.46% 3.05% 5.88% 6.59% 10.03% 9.31%IRR – additional 2 9.31% 8.40% 16.39% 20.02% 1.94% 5.23% 7.12% 12.14% 11.11%IRR – additional 3 9.38% 8.27% 16.37% 20.01% 2.01% 5.38% 6.94% 12.08% 11.03%IRR – additional 4 8.09% 7.28% 14.70% 17.18% 1.55% 4.72% 6.24% 11.17% 9.32%1993 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 12.18% 9.90% 9.99% 16.46% 1.60% 7.78% 8.60% 8.78% 9.41%IRR – additional 1 12.79% 8.74% 12.85% 17.80% 1.80% 7.79% 7.28% 10.66% 10.98%IRR – additional 2 11.70% 9.53% 16.21% 21.21% 1.26% 7.15% 7.93% 13.21% 12.46%IRR – additional 3 11.74% 9.44% 16.20% 21.21% 1.34% 7.25% 7.78% 13.17% 12.42%IRR – additional 4 9.93% 8.29% 14.59% 18.08% 0.89% 6.30% 6.97% 12.14% 10.55%1995 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 8.89% 6.88% 13.66% 18.29% -0.98% 7.36% 6.27% 10.74% 11.36%IRR – additional 1 11.63% 8.02% 12.50% 19.32% 0.56% 7.98% 6.96% 9.77% 12.49%IRR – additional 2 10.04% 8.99% 15.69% 25.38% 0.84% 6.59% 7.89% 12.02% 14.98%IRR – additional 3 10.13% 8.89% 15.67% 23.44% 0.94% 6.73% 7.76% 11.95% 14.95%IRR – additional 4 8.67% 7.78% 13.97% 19.59% 0.57% 5.89% 6.88% 10.98% 12.45%1996 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 9.54% 7.64% 11.19% 15.88% 1.36% 6.03% 6.30% 9.32% 11.29%IRR – additional 1 9.80% 8.34% 11.62% 17.69% 1.37% 6.23% 6.85% 9.46% 13.40%IRR – additional 2 9.02% 8.86% 14.83% 21.58% 1.90% 5.23% 7.20% 11.90% 15.54%IRR – additional 3 9.12% 8.76% 14.80% 21.58% 1.98% 5.41% 7.03% 11.84% 15.52%IRR – additional 4 7.95% 7.61% 13.20% 18.05% 1.48% 4.81% 6.25% 10.83% 13.03%IRR – additional 4(POF) 7.06% 7.07% 12.25% 18.42% 1.47% 4.31% 5.87% 10.20% 13.29%1997 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 9.07% 8.28% 13.00% 15.99% 2.01% 4.83% 7.25% 11.47% 10.09%IRR – additional 1 9.88% 8.68% 12.28% 17.67% 2.92% 5.19% 6.99% 11.64% 10.73%IRR – additional 2 8.77% 9.18% 15.17% 21.44% 2.69% 4.55% 7.36% 14.50% 12.40%IRR – additional 3 8.89% 9.09% 15.15% 21.43% 2.77% 4.77% 7.21% 14.47% 12.36%IRR – additional 4 7.72% 8.02% 13.48% 18.16% 2.15% 4.22% 6.33% 12.97% 10.27%1998 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 10.20% 6.99% 11.76% 18.49% 1.64% 5.83% 6.24% 10.25% 13.48%IRR – additional 1 9.18% 7.85% 11.99% 19.51% 1.39% 5.70% 6.36% 10.16% 14.29%IRR – additional 2 8.14% 8.25% 15.43% 23.40% 1.00% 5.18% 6.66% 12.87% 16.26%IRR – additional 3 8.28% 8.13% 15.40% 23.40% 1.10% 5.38% 6.47% 12.82% 16.25%IRR – additional 4 7.16% 7.14% 13.68% 19.47% 0.71% 4.70% 5.66% 11.64% 13.23%1999 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 9.56% 8.24% 10.82% 17.25% 1.33% 6.23% 6.43% 10.19% 10.91%IRR – additional 1 10.37% 7.79% 12.11% 18.70% 2.27% 6.21% 6.02% 10.38% 13.57%IRR – additional 2 9.24% 8.38% 14.77% 22.82% 2.03% 5.52% 6.18% 14.21% 13.90%IRR – additional 3 9.36% 8.28% 14.75% 22.82% 2.13% 5.73% 5.99% 14.17% 13.86%IRR – additional 4 8.06% 7.24% 13.22% 18.65% 1.57% 5.02% 5.24% 12.79% 11.07%2001 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 7.45% 7.41% 11.04% 19.94% 2.66% 3.99% 6.46% 8.11% 13.83%IRR – additional 1 7.82% 7.65% 11.61% 20.65% 2.13% 4.73% 6.44% 8.90% 14.50%IRR – additional 2 7.36% 8.39% 13.96% 24.45% 1.65% 4.60% 7.03% 10.58% 16.96%IRR – additional 3 7.52% 8.27% 13.92% 24.45% 1.73% 4.81% 6.85% 10.48% 16.95%IRR – additional 4 6.50% 7.26% 12.50% 20.11% 1.29% 4.20% 6.14% 9.67% 13.64%2002 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 6.21% 7.01% 11.40% 20.20% -1.62% 5.72% 5.90% 9.05% 12.99%IRR – additional 1 8.42% 6.02% 12.61% 22.00% -0.25% 6.77% 5.19% 9.87% 14.18%IRR – additional 2 7.96% 6.75% 14.69% 25.61% 0.02% 5.96% 5.82% 11.42% 16.44%IRR – additional 3 8.09% 6.50% 14.66% 25.61% 0.12% 6.11% 5.52% 11.34% 16.43%IRR – additional 4 7.00% 5.67% 13.08% 20.98% -0.16% 5.31% 4.91% 10.39% 13.31%2003 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 6.91% 6.33% 11.23% 19.05% 2.40% 3.53% 5.56% 8.50% 12.21%IRR – additional 1 7.75% 6.17% 11.36% 21.00% 0.53% 5.49% 5.58% 8.63% 13.06%IRR – additional 2 7.56% 6.99% 13.43% 25.02% 0.41% 5.38% 6.39% 9.90% 15.40%IRR – additional 3 7.71% 6.76% 13.38% 25.02% 0.51% 5.55% 6.14% 9.77% 15.38%IRR – additional 4 6.65% 5.98% 12.07% 20.91% 0.20% 4.82% 5.49% 8.78% 12.55%2004 S4-S0 S8-S4 S11-S8 S15-S11 PRE-NEDUC EF4-PRE EF8-EF4 EM3-EF8 SUP-EM3IRR-Nonparallel 6.94% 6.35% 10.77% 19.01% 0.95% 4.73% 5.47% 8.34% 11.14%IRR – additional 1 8.26% 5.30% 11.48% 21.06% 0.89% 5.83% 4.64% 8.58% 13.18%IRR – additional 2 7.74% 6.41% 13.61% 24.76% 1.18% 5.05% 5.48% 9.94% 15.27%IRR – additional 3 7.87% 6.14% 13.56% 24.76% 1.26% 5.24% 5.16% 9.82% 15.25%IRR – additional 4 6.79% 5.38% 12.24% 20.42% 0.90% 4.53% 4.61% 8.83% 12.53%

Non Linear - Inclusion of Sample Design & HeckitSpecification: Years of Education Specification: Years of Schooling

See the notes of Table 13.

35

Table 15. Additional IRRs — Non- Parametric - Census

Year/Method1970 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel - - - - - 11.35% 16.20% 6.22% 22.80% -IRR – additional 1 - - - - - 10.57% 17.12% 7.38% 23.89% -IRR – additional 2 - - - - - 9.18% 23.60% 15.07% 33.01% -IRR – additional 3 - - - - - 9.29% 23.60% 14.97% 33.01% -IRR – additional 4 - - - - - 7.10% 19.49% 13.31% 30.23% -1980 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel - - - - - 7.39% 9.83% 12.00% 10.50% 5.60%IRR – additional 1 - - - - - 6.99% 9.46% 12.00% 10.35% 5.44%IRR – additional 2 - - - - - 5.44% 13.70% 18.86% 13.75% 6.16%IRR – additional 3 - - - - - 5.76% 13.65% 18.83% 13.67% 5.99%IRR – additional 4 - - - - - 5.30% 12.34% 17.26% 12.42% 5.76%1991 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel 12.14% 9.26% 13.06% 14.39% 22.83% 8.49% 8.02% 11.79% 10.00% 5.49%IRR – additional 1 11.14% 9.88% 13.64% 15.41% 18.23% 7.93% 8.53% 12.27% 10.76% 4.38%IRR – additional 2 7.90% 12.83% 18.12% 19.71% 15.62% 5.80% 10.94% 16.09% 12.90% 4.86%IRR – additional 3 8.28% 12.80% 18.11% 19.70% 15.67% 6.22% 10.88% 16.06% 12.82% 4.68%IRR – additional 4 7.53% 11.27% 16.33% 16.84% 12.82% 5.70% 9.78% 14.68% 11.23% 4.08%2000 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel 10.76% 8.94% 11.91% 20.52% 23.87% 7.55% 7.29% 9.96% 13.39% 5.33%IRR – additional 1 10.30% 8.68% 12.59% 20.80% 22.44% 6.16% 7.03% 10.53% 14.39% 5.49%IRR – additional 2 5.71% 12.53% 17.65% 27.96% 18.44% 3.50% 10.01% 14.23% 16.91% 6.37%IRR – additional 3 6.36% 12.42% 17.63% 27.95% 18.46% 4.37% 9.79% 14.19% 16.89% 6.07%IRR – additional 4 6.01% 11.09% 16.19% 23.56% 15.32% 4.09% 8.95% 13.30% 14.65% 5.43%

Non Parametric - Inclusion of Sample WeightSpecification: Years of Education Specification: Years of Schooling

See the notes ot Table 13.

Table 16. Additional IRRs — Non- Linear - Census

Year/Method1970 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel - - - - - 6.98% 14.25% 9.47% 20.07% -IRR – additional 1 - - - - - 6.87% 14.15% 10.22% 19.91% -IRR – additional 2 - - - - - 5.19% 16.14% 13.84% 26.93% -IRR – additional 3 - - - - - 5.33% 16.14% 13.80% 26.93% -IRR – additional 4 4.79% 15.13% 13.28% 25.96% -1980 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel - - - - - 6.30% 9.10% 10.68% 9.24% 5.07%IRR – additional 1 - - - - - 6.94% 9.35% 11.80% 10.24% 5.42%IRR – additional 2 - - - - - 5.03% 12.23% 14.71% 9.16% 3.93%IRR – additional 3 - - - - - 5.38% 12.19% 14.68% 9.06% 3.59%IRR – additional 4 5.00% 11.31% 13.81% 8.43% 3.43%1991 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel 13.58% 8.88% 13.38% 14.28% 23.65% 8.98% 7.74% 12.03% 10.04% 5.07%IRR – additional 1 13.53% 8.87% 13.79% 14.39% 24.86% 8.91% 7.73% 12.40% 10.41% 5.04%IRR – additional 2 10.11% 10.88% 18.04% 19.28% 21.54% 6.75% 9.39% 16.07% 12.80% 5.30%IRR – additional 3 10.28% 10.87% 18.03% 19.26% 21.55% 7.01% 9.37% 16.05% 12.74% 5.14%IRR – additional 4 9.11% 9.73% 16.24% 16.34% 15.91% 6.33% 8.54% 14.66% 11.11% 4.52%2000 S4-S0 S8-S4 S11-S8 S15-S11 S17+-S15 EF4-Neduc EF8-EF4 EM3-EF8 SUP-EM3 MD-SUPIRR-Nonparallel 11.38% 8.91% 12.65% 19.79% 12.82% 7.70% 7.25% 10.42% 12.79% 3.03%IRR – additional 1 8.79% 7.30% 12.87% 19.66% 19.51% 5.12% 6.80% 10.38% 13.41% 5.19%IRR – additional 2 13.18% 8.51% 12.95% 22.54% 15.70% 7.80% 6.62% 10.67% 14.37% 3.65%IRR – additional 3 13.18% 8.30% 12.88% 22.54% 15.70% 7.81% 6.26% 10.53% 14.33% 3.16%IRR – additional 4 12.22% 7.88% 12.31% 20.43% 12.96% 7.28% 5.99% 10.16% 13.10% 2.84%

Non Linear - HeckitSpecification: Years of Education Specification: Years of Schooling

See the notes ot Table 13.

36

Table 17. Annual Costs by Level of Education (POF-PNAD) and % of Income (POF)

POF PRE PRI GIN SEC SUP MD1996 1236.14 2051.73 2051.73 2578.34 3837.34 5226.79% of income 5.68% 7.24% 7.24% 7.88% 13.25% 15.32%PNAD PRE PRI GIN SEC SUP MD1992 858.21 867.87 931.51 1127.13 3092.51 4606.651993 913.33 840.75 908.31 1065.66 3192.33 5087.811995 1073.88 1085.60 1205.78 1455.22 4497.32 7280.471996 1211.30 1012.8 1289.02 1476.46 4390.21 8096.801997 1188.49 1019.1 1108.29 1462.84 3939.46 7288.001998 1101.25 1046.87 1068.51 1356.19 4107.70 7676.791999 1094.67 938.23 1037 1148.24 4112.12 8564.412001 935.36 917.38 925.29 1073.03 3746.03 7861.762002 878.45 871.72 925.25 1063.20 3697.14 7281.242003 810.52 853.05 777.2 888.04 2938.66 6199.652004 800.71 848.14 828.96 879.97 3174.58 5087.52Census PRE PRI GIN SEC SUP MD1970 - 1140.43 1140.43 1433.26 2131.31 -1980 493.38 611.88 668.10 864.44 1797.81 1741.821991 452.18 474.95 530.07 674.73 1798.97 3263.082000 469.68 464.02 488.56 617.61 2050.59 3885.65Note: PRE=Preschool, PRI=Primary School, GIN=Middle School,SEC=High (Secondary) School, SUP=College, MD=Master's/Doctorate

Panel 1. Experience-Earnings Profiles - Census — Specification: Years of Education

Graph 1.1. Title: Experience-Earnings Profile, 1991 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 1.2. Title: Experience-Earnings Profile, 2000 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

37

Panel 2. Experience-Earnings Profiles - PNAD — Specification: Years of Education

Graph 2.1. Title: Experience-Earnings Profile, 1992 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 2.2. Title: Experience-Earnings Profile, 1996 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 2.3. Title: Experience-Earnings Profile, 2001 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 2.4. Title: Experience-Earnings Profile, 2004 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

38

Panel 3. Experience-Earnings Profiles - Census — Specification: Years of Schooling

Graph 3.1. Title: Experience-Earnings Profile, 1970 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 3.2. Title: Experience-Earnings Profile, 1980 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 3.3. Title: Experience-Earnings Profile, 1991 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 3.4. Title: Experience-Earnings Profile, 2000 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Note: MD: Master’s/Doctorate Degree, SUP4: Completed College Degree, SUP1-SUP3: Incomplete College Degree,

EM3: Completed High School, EM1-EM2: Incomplete High School, EF8: Complete Middle School,EF5-EF7: Incomplete Middle School,EF4: Complete Primary School„EF1-EF3: Incomplete Primary School, NEduc: No Education.

39

Panel 4. Experience-Earnings Profiles - PNAD — Specification: Schooling

Graph 4.1. Title: Experience-Earnings Profile, 1992 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 4.2. Title: Experience-Earnings Profile, 1996 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 4.3. Title: Experience-Earnings Profile, 2001 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Graph 4.4. Title: Experience-Earnings Profile, 2004 - White Malesy-axis: mean of the main occupation income log, x-axis: experience

Note: MD: Master’s/Doctorate Degree, SUP4: Completed College Degree, EM3: Completed High School, EF8: Complete Middle School,

EF4: Complete Primary School, NEduc: No Education.

40

Panel5. Changes in IRRs Over Time - PNAD and Census

Graph 5.1

SUP vs EM3

EM3 vs EF8

EF8 vs EF4

EF4 vs PRE

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004

IRR - relax linearity (Sample Design Included & Heckit) - years of schooling - PNAD

Graph 5.2

SUP vs EM3

EM3 vs EF8

EF8 vs EF4

EF4 vs PRE

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004

IRR relax parallelism (Sample Design Included) - years of schooling - PNAD

Graph 5.3

EF4 vs Neduc

EF8 vs EF4

EM3 vs EF8

SUP vs EM3

MD vs SUP

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

1970 1980 1991 2000

IRR - relax linearity (Heckit) - years of schooling - Census

Graph 5.4

EF4 vs Neduc

EF8 vs EF4

EM3 vs EF8

SUP vs EM3

MD vs SUP

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

1970 1980 1991 2000

IRR - relax parallelism - non parametric - years of schooling - Census

Note: SUP: MD: Master’s/Doctorate Degree, Completed College Degree, EM3: Completed High School, EF8: Complete Middle School,

EF4: Complete Primary School, NEduc: No Education.

41

Panel6. Changes Over Time of Additional IRRs - PNAD and Census

Graph 6.1

SUP vs EM3

EM3 vs EF8

EF8 vs EF4

EF4 vs PRE

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004

IRR - relax linearity- additional 4 (Sample Design Included & Heckit) - years of schooling - PNAD

Graph 6.2

SUP vs EM3

EM3 vs EF8

EF8 vs EF4

EF4 vs PRE

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

1992 1993 1995 1996 1997 1998 1999 2001 2002 2003 2004

IRR - relax parallelism -non parametric - additional 4 (Sample Design Included) - years of schooling -PNAD

Graph 6.3

EF4 vs Neduc

EF8 vs EF4

EM3 vs EF8

SUP vs EM3

MD vs SUP

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1970 1980 1991 2000

IRR - relax linearity (Heckit) - years of schooling - Census - additional 4

Graph 6.4

EF4 vs Neduc

EF8 vs EF4

EM3 vs EF8SUP vs EM3

MD vs SUP

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

1970 1980 1991 2000

IRR - relax parallelism - non parametric- years of schooling - Census - additional 4

Note: MD: Master’s/Doctorate Degree, SUP: Completed College Degree, EM3: Completed High School, EF8: Complete Middle School,

EF4: Complete Primary School, NEduc: No Education.

42