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THESIS

This is to certify that the

dissertation entitled

TWO ESSAYS IN LABOR AND GENDER ECONOMICS AND ONE
IN THE RETURNS TO EXPERIENCE IN AVIATION SAFETY

presented by

Yuri S. D. Soares

has been accepted towards fulfillment l
of the requirements for l

Ph.D. degree in Economics I

 

 

Date Jade [?fllwaz

MS U is m Aflirmaliw Action Equal Opportunity Institution 0-12771

 

LIBRARY
Michigan State
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PLACE IN RETURN BOX to remove this checkout from your record.
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6/01 c:/ClRC/DateDue.p65-p. 15

TWO ESSAYS IN LABOR AND GENDER ECONOMICS AND ONE
IN THE RETURNS TO EXPERIENCE IN AVIATION SAFETY

By

Yuri S. D. Soares

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2002

ABSTRACT

TWO ESSAYS IN LABOR AND GENDER ECONOMICS AND ONE
IN THE RETURNS TO EXPERIENCE IN AVIATION SAFETY

By

Yuri S. D. Soares

This dissertation contains three essays. The first essay looks at household
consumption and labor supply response to the gender composition of household
children in Brazil. Although we find that consumption is largely unresponsive to
child gender, mother’s labor supply is remarkably responsive. Mothers are more
likely to supply labor the more girls there are in the household relative to boys. This
effect is found for children ages 8-16. We find evidence that girls are substituting for
mother’s labor in home production, thus enabling mothers to work in the labor
market. We find no evidence that the labor supply responses are due to either
investment motives or to parental preferences for boys.

The second chapter looks at the evolution of female labor supply in Brazil,
throughout the 19805 and 19903, from a cohort perspective. We find that married
women’s labor supply accounted for the vast majority of increases in participation.
We also find that although cohorts explain the majority of the change in participation,
increases in schooling and decreases in fertility are also important factors. For both
married and single women, we found that women have increasingly entered informal
and self-employment versus formal wage work. The evidence also suggests that
although women were more likely to work informally, they held a sizeable

qualifications advantage in highly male-concentrated occupations. This advantage

decreased over time, as occupations became less segregated. Lastly, we attempt to
separate cohort, period and age effects in women’s employment. To the extent that it
is possible to identify these effects individually, we find that cohort changes are more
important than period changes in explaining increased female participation and
employment.

In the last chapter we determine the importance of pilot experience and
training in mitigating pernicious aviation safety outcomes. We find that in all
aviation flight categories total flight hours is key in reducing the incidence of pilot
error in accidents. It is also important, in varying degrees, in reducing both the
fatality rate of accidents and the extent of aircraft damage. Other experience-related
variables that are found to mitigate harmful and deadly safety outcomes are the
proportion of flight time as pilot in command and the proportion of flight time in the
make and model of aircraft being flown. In addition, the evidence shows strong non-
linearities in the returns to experience. For general aviation flights almost all gains
are realized after the first thousand hours of flight. For trunk carriers returns are steep

for the first three or four thousand hours of flight.

ACKNOWLEDGMENTS

A number of people have helped, in one way or another, to produce this
dissertation. John Strauss spent numerous hours reading and commenting on all drafts of
all three essays. His contribution can not be overstated. I also thank John for his
encouragement and patience. Without his help I would not have completed this project.
David Neumark had several key insights, particularly in the second and third essays. As
always, his comments are thoughtful and to the point. I also thank Jeff Biddle for his
involvement, particularly his interest in the rather exoteric topic of aviation safety and his
suggestions for further work in this field. I thank all three of my original committee
members, as well as John Giles, for serving on my committee, reading the text and
providing comments. I also thank Sergei Soares for comments on the first two papers, as
well as for help with the PNAD datasets. Other people who provided useful comments
were Ricardo Paes e Barros, the participants of the two seminars at Michigan State
University and Marina Farias.

I must also thank those who provided me with the data. Here I thank Ricardo
Paes e Barros and IPEA for providing access to the PNADs and Stan Smith at the NTSB
for the AIDS database.

lastly, I would like to thank my family and friends for the encouragement and
their love, and for helping me through the rough times. In particular, I thank my wife

Marina for her endless patience, love and dedication.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................. vi
LIST OF FIGURES ............................................................................. viii
CHAPTER 1: Gender bias in consumption and labor supply in Brazil ................. 1
Introduction ......................................................................... 1
Theory and review of previous results ........................................... 2
Data .................................................................................. 12
Model ................................................................................ 15
Results ............................................................................... 31
Conclusion .......................................................................... 37
REFERENCES .................................................................................. 38
CHAPTER 2: Trends in female employment in Brazil .................................... 41
Introduction ......................................................................... 41
Review of literature ................................................................ 44
Changes in cohort employment and the data ................................... 47
Main model, results and analysis ................................................ 60
Occupational changes ............................................................. 79
Conclusion .......................................................................... 86
REFERENCES ................................................................................. 88
CHAPTER 3: The role of pilot training and experience in aviation safety ............ 91
Introduction ......................................................................... 92
Model ................................................................................ 95
Data .................................................................................. 105
Results .............................................................................. 112
Conclusion .......................................................................... 129
REFERENCES ................................................................................. 131
APPENDIX 1 ................................................................................... 133
APPENDIX 2 ................................................................................... 148
APPENDIX 3 ................................................................................... 176

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

LIST OF TABLES

Summary statistics, 1988 PNAD and 1987/88 POF ................................ 134
Men and women's earnings and employment rates, 1988 ......................... 135
Outlay equivalency ratios for selected goods ........................................ 136

OLS regressions for the effect of child gender on expenditure shares,
by expenditure type ................................................................ 137

OLS regression for the effect of child gender on expenditure shares,
mothers with low education ...................................................... 139

Probit of mother's employment, 1988 PNAD and full sample of PNADs ....... 140
Probit of mother's employment using full sample of PNADs, Models 1-4 ..... . 141

Probit of mother’s employment, high versus low child wage areas.
difference-in-differences .......................................................... 143

Probit of mother’s employment, households with and without childcare

availability, difference-in-differences ........................................... 144
Summary statistics, women ages 15 through 70, three years ..................... 149
Work probit, married women ......................................................... 151
Work probit, single women ........................................................... 154
Age, period, and cohort effects for model M4 probit .............................. 156
Change in employment rates of married women, based on

probit models Ml-M4 ............................................................. 157
Sector choice model, multinomial logit ............................................. 158
Sector choice model, multinomial logit, both year and cohort effects .......... 160
Effect of policy change, informal sector probit, by control group ................ 161

vi

2.9

2.10

2.11

2.12

2.13

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

Effect of policy change, informal sector multinomial logit ....................... 162

Change in annual occupational and industry segregation, measured
by Dissimilarity index ............................................................. 164

Changes in the degree of feminization of occupations, three years .............. 165

Probit regression for the probability of an occupation being

highly segregated .................................................................. 166
Husband's wage first stage estimates, married (M) models ....................... 167
Summary statistics, three flight categories .......................................... 177
Probit of pilot error, full sample ...................................................... 178
Accident severity probit and ordered probit, General Aviation .................. 180
Extent of damage probit and ordered probit, General Aviation .................. 181
Accident severity probit and ordered probit, Commuters ......................... 182
Accident severity probit and ordered probit, Commuters ......................... 183
Accident severity probit and ordered probit, Trunk Carriers ..................... 184
Extent of damage probit and ordered probit, Trunk Carriers ..................... 185
Probit of fatality or severe injury ..................................................... 186
Tobit model for proportion killed, all observations ................................ 187
Probit of accident probability, by selection criteria ........... . ..................... 188
Probit of accident probability, Trunk Carriers, incidents not used ............... 190
Description of aviation terms .......................................................... 191
Probit for pilot error, with trends and interactions .................................. 193

vii

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.1

LIST OF FIGURES

Wife’s predicted employment for different child age and gender categories
Model 1 - 4 .......................................................................... 145

Wife’s predicted employment probability for households in high and low
wage regions (top) and 95 percent confidence interval for difference
in predicted employment (bottom) ............................................... 146

Wife’s predicted employment probability for households with and without
availability of child care-takers (top) and 95 percent confidence interval

for difference in predicted employment (bottom) .............................. 147
Employment rates for men and women, secular trend .............................. 168
Female employment rates, select years, three year moving average .............. 168

Employment rates for single (top) and married (bottom) women,
five year cohort groups ............................................................. 169

Predicted employment rates versus years of education, married women,
select cohort groups ................................................................ 170

Predicted employment rates versus number of boys ages 4 and under (left)
and number of boys ages 5-9 (right), select cohort groups .................... 171

Predicted cohort, period and age employment effects for married
women, based on model M4, four identification restrictions ................. 172

Proportion of working women employed informally (left), and by type
of formal informal employment (right) .......................................... 173

Proportion of working women self-employed (top) and proportion
employed as informal wage workers (bottom) .................................. 174

Relative risk ratios for period and cohort dummy coefficients from sector
choice model ........................................................................ 175

Density function for flight hours, general aviation (top),
commuters (middle) and trunk carriers (bottom) ............................... 194

viii

3.2

3.3

3.4

3.5

3.6

Non-parametric estimates of pilot error probability, general aviation (top),
commuters (middle) and trunk carriers (bottom) ............................... 195

Non-parametric estimates of fatality probability, general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8 ...... 196

Non-parametric estimates of probability destroyed, general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8 .. . 197

Non-parametric estimates of accident probability, general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8 198

Predicted probability of pilot error from probit model, general aviation
(top), commuters (middle) and trunk carriers (bottom) ........................ 199

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Chapter 1: Gender bias in consumption and labor supply in Brazil

I. Introduction

Recently there has been increased interest in the issue of intra—household resource
allocation and the role of children in that allocation. More specifically, both theoretic and
empirical work has been done regarding the role that a child’s gender plays in the
allocation of resources within the household—how does a household respond to the
gender of children within the household? This work, to some extent, grew out of
evidence of gender bias in South Asia. Sen (1990, 1992) and later Coale (1991) showed
perhaps the most striking evidence of differential treatment of boys and girls in their
documentation of excess female mortality in South Asia. Work by Rosenzweig and
Schultz (1982) also found evidence of gender bias, through differential survival rates for
females and males. Other evidence of gender bias, in the form of differences in
anthropomeuics and nutrition for boys and girls (almost exclusively from the Indian
Subcontinent), is plentiful, although many studies found no differences between boys and
girls.’

Perhaps another reason for the renewed interest in issues of intra-household
allocation is a greater availability of data on household consumption, income and savings,
and just as importantly, theoretical developments which allow for a more careful analysis
of these data. Two recent developments are prominent in this field. The first is the

development of bargaining theories of household behavior, which present an attractive

 

‘ See Dreze and Sen (1989) and Harris (1990) for a review of the nutrition, health and anthopometric
evidence.

 

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alternative to the unitary (or dictatorial) model of household behavior.2 The second is the
methodology developed for deducing household resource sharing rules from data
containing only household-level information on consumption and savings.3 Both of these
will be discussed in section H, as they are important in interpreting possible gender bias
results.

In this paper we will address two issues. The first is the effect of child gender on
consumption, as well as on labor force participation in Brazil. Is there evidence of
gender bias in Brazil? If bias is found, why do we observe it? In other words, we will
examine which hypotheses of household behavior are consistent with the findings here.
In section II, theory and previous results are discussed. In section III the data is
described. In section IV the empirical model is described. In section V results are

presented. Section VI concludes the paper.

11. Theory and review of previous results

The interpretation of gender bias results depends on which hypothesis of
household behavior is assumed. If one assumes that household preferences are unitary—
that is, that all household members share the same preferences—then a gender bias result
may originate because of different net returns associated with boys and girls, or because
of different household preferences for boys and girls. However, if one fails to find
gender bias under the unitary model, it is not necessarily true that household members do

not prefer boys to girls or vice versa. It may be that, in the context of a bargaining model,

 

2 See Lundberg and Pollak (1993), Manser and Brown (1980), McElroy and Homey (1981), and McElroy
(1990).
3 See Browning et al. (1994), Bourguignon and Chiappori (1992), and Chiappori (1988, 1992).

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mothers attempt to favor girls and fathers attempt to favor boys, but that this effect nets
out when one observes overall consumption.

This paper is not an attempt to discriminate between competing theories of
household behavior. However, it is still instructive to briefly review the competing
theories of household behavior, as later results will refer back to them. The reader who is
already familiar with them may safely skip the remainder of this section.

The first class of models are those based on the so—called “unitary” view of
households.‘ The unitary framework maintains that households behave as though one
agent made all household decisions.5 Thus, the household maximizes a given utility
function, subject to production and budget constraints. One can think of the unitary view
as one in which all household members share the same preferences. This framework has
been the workhorse of microeconomics of household decisions, and it is hard to overstate
its contribution to the field. A number of reasons underlie its popularity. First, the
unitary framework’s simplicity presents an appealing way to model economic behavior
by households, allowing economists to analyze economic phenomenon by treating the
household as the economic unit, without having to worry about how the household’s
utility function came about. Also, since one can typically observe characteristics such as
production, consumption, and savings behavior at the household level, but not at the
individual level, it is easier to directly test hypotheses about household behavior and
evaluate the effects of policy on households by treating the household as the economic
unit. For example, by using the unitary framework it is possible to derive demand and

supply functions for households, and to recover household preferences by using

 

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household level data. Of course this is only possible because the unitary model is
assumed to be true.

Becker’s (1973) pioneering work used this framework to first discuss allocation
of household resources in the context of a marriage model. In his model, allocations are
determined by maximizing the household dictator’s utility function, subject to income
and time constraints, and to an exogenous sharing rule. In a later paper Becker also
introduces interdependent utilities or the ‘caring’ type. That is, the dictator’s utility
depends on the spouse’s utility also. By doing this, allocations are not such that the
wife’s utility is just equal to her reservation utility; instead the wife will be outside her
utility frontier outside the household because the husband cares about her utility.

An alternative and more flexible way to model household behavior is the
bargaining framework. In the bargaining framework households are composed of
heterogeneous agents, who each have their own set of preferences, and who bargain with
each other for control of household resources. Household allocations are the result of this
bargaining process.6 Manser and Brown (1981) apply a Nash-bargained solution to the
bargaining model of a two-member household. In their model individuals may marry
because of shared goods and because of greater utility associated with marriage. They
specify a model in which members face a reservation utility corresponding to the utility
outside the marriage. The resulting allocations of the bargaining model are then given by
a cooperative solution in which the product of the gain function for each member is
maximized, subject to budget and time constraints. The resulting demands are then

functions of husband and wife’s incomes, prices, as well as factors that may shift the

 

5 See Behrman, Pollak and Taubman (1982) for an exposition of a unitary pure investment model.

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reservation (or threat-point) utility levels of each party. Manser and Brown also show
that the unitary model is nested inside this framework. McElroy and Homey (1981) use a
similar framework but derive generalized comparative statics for the Nash-bargained
household solution, for which the unitary model’s comparative statics is a specific case.
McElroy (1992) also discusses the comparative statics of extrahousehold environmental
parameters, such as factors affecting the competitiveness of the marriage markets,
parent’s incomes, and others. These parameters determine the reservation utility outside
the household, and therefore are functions of household demands. Her paper looks at the
changes in household demands due to shifts in these parameters.

The papers above treated as threat points the utility that household members
would receive outside the household, but this is not the only possible threat point. A non-
cooperative Nash solution is a possible threat point. Lundberg and Pollak (1995) discuss
this, and they point out that household members may retreat to non-cooperative strategies
where each member is maximizing his utility subject to the other agent’s strategy. This
solution is not Pareto optimal, and both members would be better off by cooperating.

The shared good, as would be expected, is also underprovided in the non-cooperative
solution.

In papers by Chiappori (1992), and Bourguignon et a1. (1993, 1994), the authors
develop another model of household allocation. Their premise is different from the
previous two models in that they do not explicitly specify a bargaining structure. Instead,
they derive individual demands when all that is assumed is that household members’

allocations are efficient. As it turns out, this framework is equivalent to assuming that

 

6 For a review see Browning (1992).

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maximize their individual utilities subject to the sharing rule in a second stage. In effect
the sharing rule is providing each member’s weight in a household utility function. The
unitary model is, again, nested in this model.

The framework developed by Bourguignon and his colleagues has an additional
advantage: it allows recovery of some information about the sharing rule with only
household-level data on consumption. With only household level information and
income from household members, it is possible to derive the marginal rate of substitution
between members’ sharing rules. It is also possible to recover the ratio of Engle curve
slopes of both members. Furthermore if one can observe individual consumption of just
one good, the sharing rule can be recovered up to a constant.7 The model also lends itself
to testing both the validity of the unitary models and to testing its own validity. For
example, if one can observe mother and father’s incomes separately, one can compute the
ratio of the demand of private goods with respect to each income. If the unitary model is
the true model, this ratio should be unity because the unitary model is equivalent to
assuming that household incomes are pooled—who owns the income should not matter.
The change in demand due to a change in mother’s income should be the same as the
change in demand due to a change in father’s income, up to sampling variability. The
second test that can be performed is that of the pareto-efficient model itself. If household
allocations are indeed efficient, then it must be true that the ratio of the change in demand
due to a change in mother’s income to the change in demand due to a change in father’s

income must be the same for all private goods. The framework described above has

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allowed several tests of both the unitary model, through tests of income pooling, and of
the efficient model.8

In the context of the unitary model, gender bias may originate for a number of
reasons. The first reason is that households may have different preferences for boys than
for girls. It is important to make a distinction here. Under this hypothesis, a household
does not prefer a boy because he may bring the household future benefits (or lower costs)

which a girl would not. The preference here is because of differences in how boys and

 

7 Alternatively, if consumption of two excludable goods (goods that only one individual consumes) is
observed, again, the sharing rule can be recovered up to a constant.

8 Thomas (1992) uses Brazilian household data to test if unearned income of different household members,
which is treated as exogenous, has the same effect on health outcomes. He finds that it does not, and that
income under a mother’s control affect child survival probabilities and weight for height much more than
income under the control of the father. This is evidence against the unitary view of the households, which
predicts that household income be pooled. However, the treatment of unearned income as exogenous may
be problematic, to the extent that it represents past labor supply and human capital investment decisions.
These decisions, in turn, may be driving part of the difference in the paternal and maternal effect.

Thomas and Chen (1994) use data from Taiwan’s Personal Survey of income distribution to test
the validity of the unitary model. They estimate Engle curves and reject the hypothesis that each member’s
share in income does not affect demand (i.e. they reject income pooling). Their results are robust to the
types of income used (both earned and unearned). Furthermore, they cannot reject the hypothesis that the
ratio of the change in the Engle curve due to changes in husband and wife’s incomes is not the same across
consumption groups. This is evidence in favor of the efficient model. Their findings in this respect are
stronger for urban areas than for rural areas.

Bouguignon et al (1992) were the first to outline and test the collective model. They also find
evidence against the unitary model, but reject conditions for their efficient model to hold. They find that
the change in household expenditures on consumption items due to changes in household member's
incomes is not the same for each household member (a necessary condition for the unitary model to hold),
but that these differences are not the same across consumption items (a necessary condition for the efficient
model to hold). This, again, is inconsistent with household members pooling their income. If members did
pool incomes, these elasticities should be the same, regardless of the income's source.

In their article, Thomas, Schoeni and Strauss (1997) look at the effects of mother and father's
education on sons and daughters. They also test for income pooling, and thus homogeneous preferences.
Thomas et a] first test if the difference in the effects of parental education on sons versus daughters is the
same for mothers and fathers. They find that it is not. This is consistent with a rejection of income
pooling, but is not a test of income pooling, as boys and girl's production functions may be parent specific.
They then use a similar approach as above, but use parent's income, not education, since income is not
likely to be in a production function. Here they also find that the difference in the parent's income in the
outcomes of boys versus girls, or "difference-in-differences" is not zero. Income "ownership" is important
in determining the relative effect of income on boys’ and girls’ educational outcomes. They also find that
these differences are more pronounced for younger cohorts and for less educated households.

Udry (1996) uses data from agricultural production in Sub.saharan Africa to test for pareto
efficiency. He finds that plots controlled by women in the household have lower yields than plots
controlled by men. In a Pareto-efficient model plot control should not determine yield.

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girls enter the household’s utility function. If this is the case, households will be expected
to provide greater resources to a boy than to a girl.

If boys are expected to earn higher income than girls do, the birth of a boy will
have two effects on the household. The first is an income effect. The birth of a boy
represents higher future incomes for the household, and the household can be expected to
react by increasing consumption. To the extent that households seek to smooth
consumption over time, as is predicted by the Life-cycle and Permanent Income
hypothesis, they will increase consumption immediately in response to a positive “gender
shock”. Also, to the extent that leisure is a normal good, household members may also
consume more leisure and reduce their labor supply, although this may well depend on
how each parent’s time enters into their sons and daughters’ human capital production
functions.9 It is important to note, however, that even if households cannot appropriate
incomes from their offspring, if they are altruistic they may also decide to allocate
resources according to the gender of a newborn. For example, if households care for
their children’s well being after they leave the household, and if there are indeed higher
market returns to investing in a boy, households may want to make more transfers to
daughters than to sons. This would arise because the higher marginal utility associated
with lower incomes for a daughter would prompt parents to make unequal transfers. In
expectation of these higher transfers they may increase labor supply and decrease

expenditures.

 

9 For example, if mothers are better at transmitting human capital to daughters, perhaps the birth of a
daughter will lead the mother to spend less time working and more investing in her daughter. In this case,
it is possible that the marginal product of her time will compensate for the income effect on her leisure.

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The second effect one can expect if boys face greater earnings in the labor market
is a substitution effect. Boys may represent a productive asset for a household, so
households may substitute from other assets into boys more than they would into girls.
This will typically take the form of more schooling, health care, or in the case of
households near poverty—more food provided to a boy than would be provided to a girl.
It may also involve more time spent with children, to the extent that parent’s time enters
into the child’s human capital production function.

A third way in which gender bias may originate is through differential costs for
boys and girls. This is parallel to the income effect associated with differential market
returns for boys and girls. Recent studies on gender bias and differential costs have been
done in India and have focused on marriage costs, which are higher when daughters are
married off.10 However, since there is no social institution such as a Dowry in Brazil,
there is little reason to believe that girls will represent higher costs to households, apart
from an income effect due to differential returns to girls.

Even if the true model of household behavior is not the unitary model, but, say, a
bargaining model, many of the results described above will still carry through. The key
difference is that in an individualistic model, resource control will have an affect on the
allocation of goods within a household after the birth of a boy or a girl. And if household
members do have different preferences, possibly including different preferences for boys
versus girls, resource control should affect any possible gender bias.

In the context of the Indian ICRISAT data, both Deolalikar and Rose (1995) and

Browning and Subramaniam (1995) have analyzed the effect of a “gender shock” on

 

10 See Browning and Subramaniam (1995).

hou:
as tl
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a de
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on r
imp
and
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betx

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relur

household consumption and production decisions. The “gender shock” can be thought of
as the realization of the sex of a child. In Deolalikar and Rose’s analysis the birth of a
boy, relative to that of a girl, is associated with an increase in household consumption and
a decrease in production income. Since ICRISAT follows rural Indian villages across
time, the authors can model savings, consumption and production income as depending
on present and past fertility decisions. The authors’ results, although estimated
imprecisely, suggest that households increase consumption the year following the birth,
and that they decrease production in the year of the birth, and for subsequent years.

These effects are more significant for large landowners than for the landless or for small
farm owners.

Also using ICRISAT data, Browning and Subramaniam attempt to distinguish
between three possible motivations for the observed relationship between consumption
and income (and thus savings), and the birth of a boy, relative to that of a girl. They
entertain three underlying motivations that explain why households save more when a
girl is born. The first is that rural Indian households prefer boys to girls, the second is
that there are higher net returns associated with having a boy (these two discussed
above), and the third is that there are higher marriage costs associated with having a girl.
They show that if households have preferences for boys, consumption of adult goods
should fall after a boy is born, as households substitute to goods that the boy will
consume. Overall consumption should also increase. Because consumption with adult-
only goods rises with the birth of a boy, the authors conclude that the evidence from the
ICRISAT villages is consistent with both the marriage cost motive and the higher net

returns motive. If boys represent a more productive asset, households would have higher

10

go
Uh
6X1
tha
the
red
a h
Cqu
but

81 gr

Hor

here

Th
“Hint:

permanent income after the birth of a boy, and thus would be expected to increase
consumption of all goods, including adult goods. But this is also true if girls represent
higher costs than boys. Then, if a boy is born, households again will have higher
permanent income because they will not face a Dowry payment in the future. These
results do not hold for households with small land holdings.

Deaton (1989) takes a different approach to the issues of gender bias. Instead of
looking at the birth of the last born, Deaton looks at the relative effects of an additional
boy versus an additional girl on household overall consumption and consumption of adult
goods. Using cross-section data he constructs outlay equivalence ratios, which are just
the ratio of a composition elasticity to an income elasticity.ll Treating children as
exogenous, he shows that an additional child in the household brings in new needs, so
that the additional child acts like a reduction in income. In the absence of gender bias,
the ratio of the reduction in the expenditure on adult goods due to a new child to the
reduction in expenditure due to a change in income should be the same, weather a girl or
a boy is born. He breaks the groups down into age— gender cells and compares the outlay
equivalent ratios using the 1985 living Standards Survey of cote d’Ivoire and Thailand,
but finds that the differences in outlay equivalent ratios for boys and girls are not
significant for any of the age groups.12

One of the frameworks used in this paper follows much of Deaton’s framework.
However, whereas previous work in the area has looked only at consumption and income,

here we also look for labor supply responses to child gender. First, we will test for the

 

11 The composition elasticity is just the percentage change in expenditure due to a percentage change in the
number of individuals in a particular group (boys vs. girls in this case).

11

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part of 11
boys am
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analysis

1999 Pe
surveys.
labor su
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relative effects of an additional boy or girl on household consumption. This will be done
at the aggregate level and by age and education groups. We use Deaton’s methodology
to test for appropriate adult goods and to test for demographic separability. In the second
part of the paper we look at labor supply. In particular, we test for differential effects of
boys and girls on father and mother’s labor supply. Hypotheses that are consistent with
the observed patterns are then discussed. All of the analysis will be done by regression

analysis, the data and methodology being described in detail below.

111. Data

We use the 1987-88 Pesquisa de Orgamentos Familiares (POF) and the 1981-
1999 Pesquisa Nacional por Amostra de Domir’ilios (PNAD), both Brazilian household
surveys, to measure the effect of the gender of a newborn on household consumption and
labor supply decisions.13 Although the PNAD cross sections span nineteen years, there
are only seventeen surveys, since surveys were not conducted in 1991 or 1994. Analysis
is also done with the 1988 PNAD alone, for greater comparability with the 1987-88 POF
results. The POF contains detailed information on household expenditure, income, as
well as some personal and demographic characteristics pertaining to household members,
such as age and education. The survey was conducted between 1987 and 1988, and
covers the 11 largest Brazilian metropolitan areas. It contains observations on 56,569
individuals from 12,959 households (for an average of 4.4 people per household). Every

resident in selected households is interviewed.

 

12 The Engle curve specified is an extension of Working’s (1943) functional form, changed to include
household demographics.
‘3 Note that PNADs were not fielded in 1991 and 1994.

12

Consumption information is available on a number of categories. We use
consumption with three categories: education, health, and adult goods. The first two are
of particular interest because they represent, in part, investments in human capital. The
last is of interest because it may be an assignable good, consumed only by the adults of
the households. We also compute overall household consumption.14 Consumption is
measured by two methods. The first is a “notebook” in which the household annotates
consumption of every-day items. The second is consumption measured by four- and six-
week recall. These are for items purchased less frequently. All monetary values are
deflated to October 1987 Cruzados (Brazil’s currency at the time).

The PNADs are surveys of much larger scale. Whereas the POF only covers the
11 largest metropolitan areas, the PNAD is a representative sample of the entire country,
both rural and urban. The only areas that are not covered are selected rural areas of the
North. Since POF does not have questions about labor supply, we use the PNADs for our
labor supply analysis and the POF for our consumption analysis. In both cases our
interest is in households with both a mother and a father present. All observations with
missing age or education values were discarded, as were all households with single
parents. This leaves a total of 9,314 households in the POF dataset. For the seventeen
cross sections of the PNAD the sample sizes vary, the smallest survey being 1986
(65,446), the largest besing 1989 (119,651). Even though we use “mother” and “father”

throughout, couples without kids are also part of our sample.

 

14 Since some households do not rent (they may own, or perhaps live in a relative’s house), or do not
report any rent, a value is imputed for those households. The rent is predicted by regressing the rent from
those who do rent on the number of rooms in the household, the number of bedrooms, dummy variables for
the type of water supply (no water, well water, water duct, city water), dummy variables for the type of
sewer (no sewer, city sewer, county sewer), as well as a dummy variable for the interviewer’s classification
of the house (rustic, temporary, permanent no floor, permanent cement floor).

13

h'I

H
Ll'o

Que
Eta
Coli-

Table 1.1 presents summary statistics of the variables used in the analysis, using
the 1987 POF and 1988 PNAD. It is important to notice that even though the two
analyses are done using household survey data, these two populations are quite
dissimilar. The urban POF population is more educated: 19 percent of the POF husbands
have at least one year of college (13 percent for the wives), whereas only 12 percent of
the PNAD population do (9 for wives). On the other side of the spectrum we see that 22
percent of the husbands in the PNAD report having completed less than primary school,
whereas this number is 10 percent for the POF.15 The results are similar for mothers.
This is consistent with the POF being a survey that covers only the main urban areas of
the country, which are typically wealthier and more educated.

We can also see in Table 1.1 the breakdown of consumption, by category.
Amounts are given on the lower left column and percentages on the right. Food
consumption accounts for 21 percent of total consumption, healthcare for only six
percent, and education for even less: three percent. We also see that expenditures with
adult-exclusive goods account for roughly 8 1/2 percent of all household consumption.

From the PNAD we see that 93 percent of the husbands in the sample are
employed, as opposed to only 41 percent of the wives. Mothers who work also work on
average eight fewer hours per week than fathers do. Finally, we see that the proportion of

working mothers that is self-employed is similar to that of fathers.

 

15 Some of this difference may be due to different education questionnaires. The POF education
questionnaire asks if the respondent completed or not primary middle, high school, or if he has a college or
graduate degree. The PNAD questionnaire asks the highest grade and school (primary, middle, high,
college) completed for both those in school and those not in school.

14

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ob
en

in.

f.

IV. Model
Labor market differences

One of the strongest arguments for differential gender effects is that a boy is
associated with a higher expected future income. It is thus useful to first describe any
gender differences in the Brazilian labor market. If they do exist and are prominent, then
households may indeed expect to have an “income” effect when a boy is born. On the
other hand, if they do not exist, then the “income” effect argument loses validity.

Table 1.2 describes basic gender differences in Brazilian labor markets for 1988,
by age and education level. In the right panels one finds employment rates for men and
women; in the left, average monthly earnings (in 1987 Cruzados). These figures are
obtained from the same 1988 PNAD that is used later in the analysis. We clearly see that
employment rates are higher for men than for women. The difference tends to slowly
increase, from a low of 30 percentage point difference to a high of about 50 percentage
points for the 55-64 age group, before falling to 25 percentage points for those 65 and
older. If we consider only lesser-schooled individuals—those with less than primary
schooling—this increase is not so pronounced. However, for this same group
employment rate differences are even larger (about 10—15 percentage points larger than
for the full sample). Some of the increase in the difference in male to female
employment rates is because women tend to retire earlier;16 therefore one will have many
more retiring women in the 45-54 and the 55-64 age groups. This effect is then reversed
in the 65 and older group, as the men retire. Another possible explanation is that the

increase in the difference of male to female employment rates is largely capturing cohort

 

16In fact, for purposes of social security, Brazilian law allows women to retire five years earlier than men.

15

effects, women entering the labor force in the seventies and eighties. Since only one year
is shown, one cannot separate the cohort from the age effect.17

Table 1.2 also shows average earnings for men and women. We see that for all
age groups men’s earnings are substantially higher than women’s, ranging from 25 to 60
percent. We also see this difference increasing monotonically with age. Again, the
analysis is replicated for those with less than primary schooling. The gap for the lesser-
educated is larger, except for the oldest groups, and shows a similar increase with age
group. The table suggests that differences in labor market participation and earnings
favor men, and that these differences increase with cohort (or with age), the older cohorts
(older men) having the largest differences. We also see that these differences are largest
among the lesser-educated.

There are two questions of interest here. First, what is the effect of a child’s
gender on household consumption and labor supply decisions, and does this effect vary
with household (and individual) characteristics and previous fertility outcomes? Second,
why do we observe this effect?

Household behavior may be different when faced with the birth of a boy versus a
girl for a number of reasons. In the context of a utility maximization model households
may allocate resources differently because they prefer one gender to the other (say, boys
to girls) or because one gender represents a higher net return. In terms of net returns, a
boy may be associated with a higher expected income, because of differences in labor

force participation rates, differences in hours worked, or differences in wages—this

 

17 With a panel one could separate age and cohort effects (albeit not age, cohort and period effects). With a
single cross-section one can only identify age or cohort effects, as older people will also belong to older
cohorts.

l6

woul
ban
for t
pref

hou

lat

ll‘tt

would be an income effect. Alternatively, households may allocate resources differently
because the returns to education, health, or even nutrition investments may be different
for boys than for girls. Furthermore, as was mentioned previously, different “household”
preferences for boys and for girls may reflect different preferences of individual
household members

If households simply prefer boys to girls, one would expect consumption with
adult goods to decrease after the birth of a boy and consumption with other goods to
increase. We would also expect labor supply to increase, as household members work
more hours to increase the boy’s consumption. However, households may also decrease
labor supply and increase leisure, to the extent that their gender bias may be through
increased enjoyment of leisure when a boy is born.

If households respond to the gender of a child simply through the pure investment
model, one would expect a boy to increase the household’s expected future income.
Households would then be expected to react to the birth by increasing consumption (since
their permanent income is now higher), including consumption with adult goods and
decreasing labor supply (if leisure is a normal good). However, since a boy may
represent a more productive asset, households may also increase expenditures with
education and health care. Health care expenditures may be expected to increase
immediately. However, expenditures with education may only be increased when a child

reaches school age.‘8

 

18 It is important to note that school fees, when present, tend to be minimal in Brazil, and almost all public
urban schools have no fees at all. Similarly, public universities are free, although the entry requirements
can be stringent. Thus, expenditures may be in the form of outlays with private (higher quality) schools
and more and better supplies. However, costs of school attendance which are not tabulated include the
opportunity cost of the child not working, for poor families, as well as the parental costs associated with
schoolwork.

17

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Chat

If husbands and wives bargain for control of household resources, and they have
different preferences for boys and girls, one would expect that some of the gender bias
effect would depend on household members’ individual incomes (in so far as that will
determine their relative bargaining position in the household). Factors such as education
and age could also determine relative bargaining positions. Therefore, more educated
mothers may be able to affect the sharing rule; for example, it might increase her
reservation utility outside the household. If this is true, and if husbands and wives have
different preferences, households with more educated mothers may allocate resources
differently after the birth of a boy and the birth of a girl. This is, however, by no means a
test of the unitary model. It is perfectly possible for husbands with different child gender
preferences to also have different preferences for the education levels of their spouses.
This could explain a correlation between gender bias and education levels (or any other

demographics, for that matter).

Outlay equivalency ratios

In this section we test for the validity of adult goods, which will be used in the
main analysis. We will also test for gender bias using the methodology developed by
Deaton (1989). The approach is to find a group of goods, all of which respond in the
same way to the addition of a child. That is, when a child enters the household that
member will bring about a change in consumption of different types of goods. An
acceptable set of adult goods is one in which expenditures on each good react in the same
way to an additional child as they would to a decrease in income. In this way, the only

Change in consumption of that good brought about by the child is through an income

18

effect—there are no substitution effects. Goods which satisfy this property are said to be
demographically separable from children. Deaton, Ruiz-Castillo and Thomas (1989)
develop preferences which are consistent with demographic separability using a unitary
model framework. Here we will be somewhat more general and, following Deaton
(1997), show demographic separability using the efficient bargaining model developed
by Chiappori, Bourguignon and Browning.19

Bourguignon and his colleagues derive a system of demand equations from a
pareto-efficient bargaining outcome in which each party maximizes his utility subject to a
sharing rule. For example, suppose there are N agents. Agent j will
(1) max U’(x,g) s1. pjx=6’(p,p,,y,nc)
where x is a vector of goods consumed by agent j, g is the optimally provided public
good, and p is the price vector for all goods. Theta is the sharing rule, which allocates
each agent’s share of total outlays. For our purposes, there are two types of groups,
children (j=C) and parents (sz). Let nC represent the number of children. Note that we
can trivially redefine parents as adults, and include the number of adults in the sharing
rule, however, for simplicity we are only allowing the number of children to vary, and
thus the number of parents fixed. We are also assuming that all income accrues to
parents. The solution to this maximization problem yields a set of demand equations for

parents:
(2) xi)=fi(0p(p,p,,y,nc),p,g.nc)
The budget constraint in (1) implies that

(3) 0C(p,pg,y,nc)= y-pgg -qu

 

‘9 See Chiappori (1992) and Bourguignon et a1. (1994).

19

Now define a group of adult goods, qA ,such that these goods satisfy demographic
separability with respect to the number of children. This implies that the number of
children only has an income effect on adult goods (through the sharing rule), and thus is
not an explicit price effect in the demand function. Therefore, omitting the public goods

for simplicity, we have adult goods demands:
(4) x.‘ = f." (9P(p,y,nc),p)

For each adult good demand function we can calculate two partial derivatives, on with

respect to the number of children and the other with respect to income:

ax,‘ ax,A af, a0” ax,A ax; af, aa”
(5) C = P C ’ = P °
an Bfi. 86 an 8y 8f, 86 By

 

 

 

Notice that the ratio of these partial derivatives,

 

 

9e ea:
i=fini.
3y 3y

does not depend on i and therefore is the same for all adult goods. This allows us to test

 

for an appropriate (i.e. demographically separable) set of adult goods: goods in which the
ratio of demographic effects to income effects are the same.

In the preceding discussion we dealt with demand equations, which means they
had prices as their arguments. In a cross-section there is only negligible variability in
prices, so the results above will be applied holding prices fixed. This does not change
any of our results since the ratios in (6) do not depend on prices. In fact, if we estimate

expenditure shares rather than demand functions (which is what we do), the results in (6)

20

still i

C8110

iti is
com

adul

still hold, since the prices will appear in both the denominator and the numerator and will
cancel out.

Redefine x; as expenditures with good i. Now consider a function which relates
expenditures with good i to total expenditures, and household characteristics.
(7) x, = f (x, n, z)
x,- is expenditure with good i, x is total outlays, n denotes a vector of demographic
composition, and z a vector of household characteristics. According to the definition of
adult goods above, the ratio of the change in expenditure in good i due to a change in the
number of members in the demographic group r (here r can index both sex and age
groups combinations), n’ to that good’s marginal propensity to spend should be the same
across all adult goods. That is, a group of goods x1, x2 Myra is a set of adult goods if and
only if:

2x195. ax

a

 

algae: :ae; - .
(8) 8x1 9L2 Bx for all children categories.

— a

3x 8x 8x

 

Deaton defines an outlay equivalency ratio (oer) as

 

3x1
(9) oer”= M n

g x

3x

So that the definition of adult goods can be rewritten in terms of outlay equivalency ratios

(10) oer” = oerz, = = oerg, for all child categories.

In order to estimate an oer, we follow Deaton in our specification of an Engle curve.

This function specifies a linear relationship between the share of expenditure with each

21

good and th

by Working

x,
(n) -:
I

Here n den
Note that c
adults. Th

13-15. Fit

The stand
gOOds fro
The first
these [hfi
EMS. 11'
needs fol
Th5 CStir
ThaJ'lanc
Deaton
Clothing

I0r [he I

good and the logarithm of total expenditures. It is the same type of Engle curve proposed

by Working (1943).
x_ X J—l n_

(11) 4:51,. +,B‘. ln[—)+n, ln(n)+27ij[—’-]+5iz+ui
x n 1 It

Here n denotes total household size and n,- denotes the number of people in category j.
Note that only J-I groups are estimated. The omitted group, group J, is the group of
adults. The six other groups are boys ages 0-5, 6-12, and 13-15; girls ages 05, 6-12, and

13-15. From (11) above one can compute oers as follows

J-l nj
711-1314?" "2711(7)
1

(12) oeri, =
a.- +5-
x

 

The standard errors for (6) are computed using the delta method.20 Three groups of
goods from the POF were tested as possible adult goods: tobacco, beer and adult clothing.
The first part of Table 1.3 presents the estimated outlay equivalency ratios for each of
these three goods and for each of the children categories. The oers are negative for all
goods, which is what one would expect since the additional child would bring in new
needs for the family, and since we do not expect children to consume these adult goods.
The estimated oers are in general larger than those estimated by Deaton using data from
Thailand and Cote d’Ivoire, and present less variation between demographic groups than
Deaton’s. The oers for tobacco and beer are very similar, but not the oer for adult
clothing. Two Wald tests for the equality of the oers are performed. In the first we test

for the equality of all three adult goods, the second we test for the equality of tobacco and

22

beer. We reject the equality of all three oers in all but one of the demographic groups,
but fail to reject the equality of beer and tobacco oers in all but one demographic
category.21 Hence, tobacco and beer are a more suitable group of adult goods than all
three goods combined.

In the absence of gender preferences, an additional child should affect the
consumption of adult goods to the extent that said child acts as a reduction in income.
So, one way to test for gender bias is to test the equality of oers for boys and girls for the
different categories of adult goods. Note however that a rejection of their equality does
not necessarily mean that households have different gender preferences, as boys may
bring different needs than girls.

The bottom part of Table 1.3 presents the difference in oers for boys and girls, as
well as the standard error for this statistic. In all but one case the addition of a boy acts
like a larger income shock than the addition of a girl. That is, households reduce
expenditures with adult goods more when a boy is born than when a boy is girl is born.
However, these differences are never significantly different than zero, even at the 10%
confidence level. Hence, we can conclude that there is no evidence of gender bias in

consumption.

 

20 See Deaton, Ruiz-Castillo and Thomas (1989) for a description of the formulas used to calculate the
standard errors and for those used to calculate the Wald statistic.

21 Note that we cannot disqualify adult clothing as an adult good. It may be that adult clothing is the adult
good and tobacco and beer are not. And in general, strictly speaking this definition of adult goods does not
necessarily imply that an additional child brings only an income effect. It is consistent with goods with
similar substitution effects also.

Model for the main analysis

 

In this section we describe the model for the main analysis. One possible

empirical specification would be the following:

(13) (E(yir+j.boy) - E(yit.nocl1ild )) —(E(yir+j. girl) - E(yir.nochild )) . f0rj=1...T

Were y denotes consumption and labor supply, i denotes the household, and t denotes the
year. This can be thought of as an experiment in which households are chosen to have
children and randomly assigned a boy or a girl. Their consumption and labor supply is
observed before the child is born and then compared 1,2,. . .,J years after the child is born.
However, estimation of this model is not possible. First, we do not have a panel data, and
therefore cannot observe the same household over time. Second, we cannot control a
household’s decision to have a child, much the less how many children to have. This is a
selection problem. The households who do have children may not be a random sample of
our population of candidate households. Lastly, even if the decision to have a child were
exogenous, the decision of when to stop having children may not be. That is, if
households have preferences for boys, their probability of having an additional child may
be closely related to whether or not they already have a boy. The same could hold, for
example, if households prefer a “gender balanced” household, and are more likely to
have another child if it has only boys or only girls. Therefore, we cannot guarantee that
observed gender effects hold for households who did not decide to have a child.
However, if fertility decisions are correlated with observable household characteristics,
such as age and education variables, then it may be possible to match households who
decided to have children with those who did not. That is, we can instead attempt to

estimate

24

(14) 5(1),”)... Ill-E(y,~,.,-,,,., IZ) forj:1...T
In equation (14) we are controlling for the level effects of demographic variables Z. In
addition, we may compare slope and level effects by estimating equation (14) by
education and age groups. That much said, we can never be certain that all covariates
related to fertility decisions have been taken into account—one must still exercise care in
generalizing gender bias results (if found) to the population as a whole.22

The method used to estimate (14) above is to estimate consumption and labor

supply equations:

5 5
(15) y =a+Zfljnb0yj+z5jngirlj+Zy
j=1

j=l
Here nboyj and ngirlj are the number of boys and girls in category j, respectively, where
j={0-5 years old, 6-9 years old, 10—11 years old, or 12-13 years old and 14-15 years old}.
For the labor supply results j={O-9 years old, 10—11 years old, 12—13 years old, or 14-15

years old}.23 Z is a vector of mother’s attributes, including schooling, age, age squared,

 

22 . . . . .

For the consumptron equations, five education categories were created: less than primary school,
completed primary but less than completed middle, completed middle but less than completed high,
completed high, more than high. less than primary was omitted in the estimation. For the labor supply
equations a fully flexible dummy variable specification was used, with “no schooling” omitted. Other
demographic controls include father and mother’s age, father and mother’s age squared, household size,
and a dummy for whether the household is headed by the father (dummy equals 1) or the mother (dummy
equals 0).

23 In earlier estimations the two youngest groups were estimated separately, but results were very similar
(and insignificant). Therefore they were concatenated into one category.

25

and household size.24 Our measure of gender bias is then ,6, — 6,. Their equality is tested

for with either an F-test (for OLS equations) or a Chi-squared test (for probit
regressions). Here we should note that, even if number of boys and number of girls is

endogenous, and therefore ,6, and 6,. may be biased, most of this bias is likely common

to both boys and girls, and will disappear in the difference in the coefficients.

OLS equations are estimated for consumption’s share of total expenditures,
education’s share of consumption, health care’s share of consumption, and adult goods’
share of consumption. That is, consumption divided by total expenditures, education
expenditures divided by total consumption, etc. These equations are also estimated
separately for the entire sample and for the lesser-educated sub-sample, where lesser-
educated is defined as those with less than primary school (21 percent of mothers in our
1999 sample). Results are presented in Tables 1.4 and 1.5.

The employment equations were estimated with a probit regression, and the
marginal effects are reported on Tables 1.6 and 1.7. These estimates are done for the
1988 PNAD, for comparability with the 1987 consumption results, and with the full set of
the PNADs. Since one has reason to believe that households in the poorer regions of
Brazil (north and northeast) may be quite different than households in the richer regions
of Brazil (south, southeast), region dummies were included in the 1988 PNAD results. In

the full sample of the PNADs, we use both region and year dummies, since heterogeneity

 

24 Since the POF has only credential schooling information, we are unable to construct a completed years
of schooling variable. Therefore, for the consumption regressions, we use as schooling categories: less
than elementary (omitted dummy), completed elementary, some middle, completed middle, some high
school, completed high school, more than high school. One should note that the schooling system
gradually changed in Brazil, starting in the late sixties, in which a three-tiered schooling system
(elementary, middle, high), was replaced with a two-tiered system. The first tier absorbed what used to be
first eight years of schooling and became the “1° grau.” The “20 grau” then became roughly equivalent to

26

may arise between households of different survey years. This also accounts for changes
in macroeconomic conditions over years that might also affect labor supply.

Six labor supply models are estimated for mothers, all of them probit models. In
all models the labor supply variable is whether or not the mother reported work as her
main activity during the reference week. In the first labor supply model employment is
regressed on mother’s education variables, mother’s age, age squared, household size,
and child status variables. Since there were no differences in the age categories 0-5 and
69, these were combined into one category. A dummy variable, child, for whether the
household had children was also included.

Our first probit model is simply the probit of equation (15) above, allowing for a

different intercept for households without children.

(16) p(y =1) = <1>[a+24;,6jnboyj +£16jrzgirlj +6child +27]
i=1 i=1

Boys and girls may have different employment rates and different school enrolment rates.

If wages for boys are significantly higher than wages for girls, one can expect boys to

participate in the labor market to a greater extent as they enter into their teens. They may

also enter the labor market earlier than girls. This in itself may affect mother’s labor

supply as household may substitute into child labor and away from mother’s labor, the

more boys there are in the household. Therefore, in the second probit model we include

the proportion of children at work as a control variable.25 In the third model we include

 

the old high school and encompassed the remaining three years (grades 9-11). For the labor supply
regressions we use a flexible functional form or seventeen completed years of schooling dummies.

5 We also use alternative definitions of child work, including children who reported working ten or more
hours per week. In addition, we estimate the model by using only the respondent’s own children in the
proportion. In all cases estimates were similar. All child labor proportions are for children ten years or
older since no labor supply information is asked of young children.

27

the proportion of children who reported to have “worked at home” as their primary
activity in the reference week. If girls help in household chores to a greater extent than
boys do (as they get older), mothers may substitute away from home care, the more girls
there are in the household. In the last model we include both proportions. Thus, Model 2

— Model 4 can be summarized:

4 4
(17) p(y = 1) = <I>[a+ z ,Bjnboyj + Eajngtrzj +60child + 77. p, + a, pkxchild + Z7],
j=l

j=1
where k=1 for proportion of children at work (Model 2), and k=2 for the proportion of
children doing housework (Model 3). These proportions are endogenous, since boys and
girls are not randomly assigned to work. However, since there are no good instruments
to deal with this endogeneity, we will present the results and interpret them with this in

mind. In any case, even if r], and 6,. are biased (and therefore ,6, and 6,. will probably be

biased also) there is no a priori reason to believe that this bias will be present in the

difference in boy— girl coefficients, ,6, — 6,. . In Tables 1.6 and 1.7 child status variables are

reported, together with the child activities proportion variables discussed above. Note
that Models 1-4 are estimated with regional dummies.

A second issue concerns expected future employment of boys and girls.
Households may react not to the current higher labor force participation of boys relative
to girls, but to expected future labor participation and earnings. We will not postulate
that households make rational expectations about future employment and earnings levels.
Instead, a more likely expectations mechanism is that households make expectations
about the next five or ten years based on current observed levels of employment and

wages. To account for this in Model 5 we computed the average ratio of boy to girl

28

wages for children 10-15, and for young adults, ages 18-24, by region (north, northeast,
central east, south, southeast), urbanization (major urban, minor urban, rural) and year.
The hypothesis is that if households do react to expected future labor force differences,
we may expect to see larger labor force reactions for households in cells whose current
differences are large. In effect, we are comparing the reaction of households in high
difference cells to those in low difference cells. We do this by defining a high difference
cell dummy variable, equal to one if a household is in a high difference cell and zero
otherwise. We then interact this dummy variable with the child composition-gender
variables. Three thresholds are used for the high-difference dummy variable, both based
on the percentile distribution of the ratio of boy to girl wage. The first threshold
corresponds to the 50Lh percentile (i.e., household is in high difference cell if that cell’s
percentile is at or above the 50’“), the second to the 70‘“, the third to the 90'h percentile.
Results presented in Table 1.8 correspond to the first threshold, but were similar for all

three.

7 4 4 \
a+ 2 fljnboyj + 2 (Sjngirlj + Gochild + nhidif
j=l

i=1

(18) P(y=l)=<b

 

 

4 4
+2 K'jnboyjhidif + zljngirljhidif + Zy l

\ j=1 j=1

From this model we can compute a few statistics of interest. The first is the gender bias

statistic, controlling for current labor market differentials,

 

Eiaq) am

a b -3 . l]=((flj—6j)—(Kj—/11)xhidif) x (D(.,) where the high difference
n 0y ngzr

dummy can be evaluated at the sample mean (either 0.5, 0.7 or 0.9, depending on the

29

threshold used). ¢(.) is the density function evaluated at the sample mean. The second is

the difference in this statistic between high and low differences cells,

3(1) _ 3(1)
dnboy angirl

 

 

E 3(1) __ 8(1)
8nboy Bngirl

,highdif =l]—E[ ,highdif =0)=(1cj —aj)x¢(.).

The last model to be estimated, labeled Model 6 in Table 1.9, is an attempt to
identify the role of child care availability in gender bias results. In particular, if girls do
substitute for mother’s household activities, including child-rearing, one would expect
gender bias results to particularly strong in households where there are no older relatives
to take care of children, and attenuated in households where older relatives can take care
of children. In Model 6 we compare gender bias results for both households using a

difference-in-differences estimator similar to the one in Model 5.

K 4 4
a + 2 ,Irjnboyj + 2 ajngirlj + Bochild + nchildcare l
j=l j=1

(19) P(y=l)=<l> 4 4
+ z anboyjchildcare + Z lingirljchildcare + Z7

t i=1 i=1 1

 

 

Here childcare is a dummy variable for the presence of older female relatives, ages 20-
65, in the household.26 The first difference and the difference-in-difference statistics are
computed in the same way as (18).

In addition to the tabular results discussed at length below, we present predicted
employment rates from a probit model for different child age categories—and for boys

and girls separately. The specifications used for Figures 1.1 — 1.4 closely follow Model

 

26 We also used as controls in alternative specifications (a) the presence of older female relatives 55-65
years old and (b) older unemployed females ages 20-65. The magnitudes of the bias effects in (b) were
similar and more significant. The magnitudes of the bias effects for (a) were smaller, but still present.

30

anze:

hous

IVK

Fast

ICSU

CXpt
bent
338C

COD

That
boy
film
the

1 - Model 6.27 However, for the difference-in-difference models separate regressions
are estimated for each of the differences sub-samples (high and low wage areas and

households with and without available childcare).

IV. Results

Results are highlighted in this section, and presented in full in the appendix tables.
First consumption results, found in Tables 1.4 and 1.5, will be discussed. Labor supply
results (Tables 1.6, 1.7 and 1.8, 1.9) will follow.

In Table 1.4 we find that controlling for household size, consumption’s share of
expenditures decreases with both the number of boys and the number of girls, this result
being larger for younger children. Higher father and mother’s education tend to be
associated with higher overall consumption shares. This result holds for the share of
consumption categories also. This suggests that children consume less than adults, which
one would expect. Older households (measured by the age of the father) also consume
larger shares than younger households do. This result does not hold for women’s age.

What is absent from Table 1.4 is any discemable gender effect. The null
hypothesis for the equality of boy and girl variables is rejected in every single case. The
joint test for significance also rejects gender bias in consumption in all instances. There
is no evidence of any convincing gender effect in the consumption tables. And in

particular, we find no evidence whatsoever of any change in household consumption of

 

27 One should note that the empirical specification used for the graphs is slightly different than the ones for
model I - model 6. In particular, the model is more flexible, as fifteen different age categories are used for
boys and for girls. However, for the graphs, these age categories are actually dummy variables, and not the
number of boys or girls in each category. In most cases this is irrelevant as few households will have more
than one boy or girl of the same age.

31

adult goods. If households prefer boys to girls (or vice versa) there should be a
difference in the adult goods category for boys and for girls. In addition, if boys or girls
represent net wealth gains associated with future incomes, there should be a difference in
the effect of boys and girls on overall consumption category. None of this is evidenced
in Tables 1.4, or Table 1.5.

Looking at Table 1.6 we can compare the labor supply results using both the 1988
PNAD and the full sample of 1981-1999 cross sections. The specification used for this
table was Model I. The results for both time periods are similar, if more precisely
estimated for the full sample (as expected). Although not reported, effects are not present
for fathers, who have inelastic labor supply. For mothers, labor force participation
increases almost monotonically with schooling level, for the first years of schooling.
This holds true for the first two school levels—primary and middle—but not for high
school. Mothers who complete high school (grade 11 in Brazil) are eleven percent more
likely to work. These large returns to higher levels of education are widely documented
in Brazil. The more young children in the household (ages nine and under), the less the
mother’s probability of being in the labor force. Presumably those mothers would more
often than not be needed at home to help with child-rearing activities. For the older age
groups the result reverses itself: mothers now are more likely to be in the labor market in
households with more children ages 10—1 1, 12-13 or 14-15. As we will see below this
reversal is much more significant for girls than for boys. It is plausible that these
children substitute for mother’s labor efforts in the house. Mother’s age also affects

employment in the usual hump-shape. Again, results are similar for both time periods.

32

gender
work (1.
boy ag
boysr
pretic
fighe
M ode
trork
ivork
the’c

three

nhou
than
Iler.
CCXEl
help
t0t)
lElbe

If the first set of labor supply results were somewhat expected, the ones relating to
gender bias were not. In Table 1.7, for Model I, we see that mothers are less likely to
work (1.2 percent for every additional boy ages 10 to 11, 1.9 percent for every additional
boy ages 12 to 13 and 3.1 for every additional boy ages 14-15) in households with more
boys relative to girls. This result is significant at any conventional level. As mentioned
previously, it is sensible to believe that some of this difference could be attributed to
higher labor force participation rates among boys and young teens than among girls.
Model 2 controls for this by adding to the regression the proportion of children who are at
work. If a higher proportion of boys in the labor force drive the gender bias result at
work, we should see the coefficients reduced significantly. This is not the case. In fact,
the coefficient on the difference between boys and girls increases in magnitude for all
three of the older age groups.28 In other words it does not seem that mothers were
reacting to higher earnings from boys by reducing their labor supply. On the contrary,
mothers seem to be employed to a greater extent when boys are working in the household
than when girls are. In Model 3 we include the proportion of children doing housework.
Here we see the exact opposite of what we say in Model 2. The gender difference
coefficients are significantly smaller when we control for the proportion of children
helping in the household. Although we still see gender differences, they are now one half
to two thirds of what they are in Model I . In Model 4 we control for both employment
types, and we see that the difference in gender coefficients due to the inclusion of the

housework variable, conditional on proportion of children at work, is similar to the

 

28 We also use the proportion who work at least 10 hours a week. Results were similar.

33

unconditional difference. This is what we would expect since the housework and market
labor variables are mutually exclusive in the PNAD labor questionnaire.

Lastly, a few comments on the proportion variables are in order. The estimates of
the proportion variables are somewhat puzzling, and difficult to interpret due to their
endogeneity. The more children at work, the more the mother herself will work. If child
labor were endogenous, one would expect an income effect leading to a reduction of
mother’s labor supply. However, households with more children working may in fact be
responding to a negative income shock, and thus may be adjusting by increasing labor
supply of both children and mothers.29 Child labor may also be correlated with other
unobservables which also increase mother’s labor supply. For the proportion of children
reporting housework during the reference week, we expect that the more children help
out in the household and in child-rearing—wthe more mothers will be able to work outside
the home. This seems to the case, although the magnitude is certainly small: a fifty
percentage point increase in the percentage of children doing housework is associated
with a 2.6 percentage point increase in a mother’s work probability.

Tables 1.8 and 1.9 present the difference-in-differences results: Model 5 and
Model 6. For the high versus low relative wage experiment we find little evidence that
differences in child wages—and thus no evidence that child employment among girls and
boys—is driving mother’s labor supply results. For the first differences we see the same
results as in Table 1.7: large and statistically significant gender bias differentials. When
we look at the difference-in-differences estimator, these differences vanish. Mother’s in

high relative wage areas do not exhibit greater labor supply biases.

34

In Table 1.9 the results are markedly different. Here we expected to see lower
bias results for mothers in households who have older female relatives who can engage in
child-rearing and other household activities. This would be consistent with the
hypothesis that older girls substitute for the mother in these activities and therefore allow
the mother engage in market employment. The results support this hypothesis. We see
that when no childcare is available the employment bias is substantially greater for both
the 12-13 age groups and the 14-15 age group. Furthermore, the results are significant at
the five and one percent levels for each group, respectively.

The graphical results closely parallel the tabular results presented above. Figure
1.1 presents predicted mother’s employment for several child age categories, and for boys
and girls. To illustrate, the value for boys age one and under is given by
f

15 15
Ed) a+213jboyj+2251girlj +6child +Z7|boyl =1]
j=l j=l

(20) \f 15 15
= (b CHE—2,6165). +£61.33]. +6child +27]
\ j=2 j=l

 

We see immediately that there is a marked employment bias for the older ages, beginning
in most cases with age 11. In Figures 1.2 and 1.3 results are presented for high and low
relative wage areas (Figure 1.2) and for households with and without childcare
availability (Figure 1.3). In addition, the bottom panels present the 95 percent confidence
interval for the difference in the predicted boy- girl employment for each child age group.
As with Model 6, we see that the gender bias is strong in households “Ii—them the

availability of childcare, and not significant in households with available childcare.

 

29 Lam, Duryea and Levison (2000) find evidence of an “added worker effect” for both children and
mothers.

35

Thee
anyoi
consi

whiel

pape
then
title
inon
nunt
boys
S“Pl
SCCC
doll
that
son]
SUOI
COng
[0 a |

than

The results of this paper are lukewarm in one respect but remarkable in another.
The consumption results were not significant or strong enough for us to be able to say
anything about the nature of the gender bias evidence. No significant results were
consistently found, and in particular we found no gender bias results in adult goods,
which suggests the absence of differences in preferences for boys or girls. Since no
significant bias results were found in overall consumption, we likewise find no evidence
of income effects associated with boys versus girls.

The strong evidence of gender bias in labor supply is the striking result of this
paper. We see that the more boys relative to girls are present in the household, the lower
the mother’s probability of being in the labor force. These results are robust to several
different specifications. The results hold for both the lesser-educated households and the
more educated households, although they are stronger for the former. We hypothesized a
number of explanations for this effect, including that mothers in households with more
boys were reacting to greater present and future household earnings by reducing labor
supply. Both the empirical specifications designed to test this hypothesis rejected it. A
second explanation espoused is that girls enter into the household production function
differently than do boys. In particular, they are more close substitutes for mothers in
child-rearing and other household activities. Although our levels specification did find
some support for this hypothesis (Model 3), the difference-in-differences estimator results
strongly support it. One must keep in mind, however, that there are other hypotheses
consistent with this explanation. In particular, it is possible that this gender effect is due
to a belief that girls can “take care” of themselves better and thus require less supervision

than boys. This would certainly be in line with most of the results found. The common

thread throughout this analysis is that women seem to be responding less to income and
substitution effects generated by child gender, but primarily by different roles that boys

and girls have in the household.

V. Conclusion

Brazil is a country that lacks social institutions that heavily favor the existence of
higher net market returns for male workers. Furthermore, the wage gap between men and
women is not as large as in other countries where gender bias has been found, and has
reduced considerably over the last decade. Differences in educational outcomes between
men and women in Brazil have also narrowed drastically over the past decades. And in
recent cohorts, women’s educational attainment has surpassed that of men. There are
certainly gender differences in labor market outcomes, but all things considered Brazil is
an unlikely setting for one to find gender bias. The evidence presented here finds little
support for the type of income and substitution driven gender effects economists have
found elsewhere. Gender effects on consumption are very subtle or altogether absent.
Nevertheless this same evidence suggests extremely large differences in mother’s labor
supply in response to the number of boys (relative to girls) in the household. This is
important in two ways. First, it is the first gender bias result outside of Asia (indeed,
outside of the Indian subcontinent). But more importantly, it extends gender bias studies
to encompass labor supply effects. And in doing so this study finds evidence that labor
supply bias effects, in Brazil, are due largely to differences in household production and

not to conventional income and substitution effects associated with boys and girls.

Beck

Beck

Beet

Beh

Bro

Brt

Br

Br

REFERENCES

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Behrman, Jere R. Robert Pollak and Paul Taubman. “Parental Preferences and Provision
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Deaton, Angus. “Looking for Boy-Girl Discrimination in Household Expenditure Data.”
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Deaton, Angus, Javier Ruiz-Castillo, and Duncan Thomas. “The Influence of Household

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Ilene

[here

Hani

Lani

Lund

Man:

)leE

lleE

Ros

Sen.

Tho:

Tho:

Thor

Thor

Deaton, Angus. The Analysis of Household Surveys: a Microeconometric Approach to
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Lam, David et al. “Effects of Economic Shocks on Children’s Employment in Brazil”,
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Lundberg, Shelly and Robert Pollak. “Separate Spheres Bargaining and the Marriage
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Manser, Marilyn and Murray Brown. “Marriage and Household Decision-making: A
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McElroy, Marjorie B. and Mary Jean Homey. “Nash-bargained Household Decisions:
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39

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40

Chap

ubiqt
of th
We 1
(yea
othe
sect
of a
hen

legi

his
ear
195
An
pat
the

Pill

Chapter 2: Trends in female employment in Brazil

I. Introduction

One of the most striking changes in recent labor supply trends has been the
ubiquitous increased labor participation and employment of women during the latter part
of the twentieth century. In this paper we explain this increased employment in Brazil.
We focus on the role of life-cycle (age), cohort and—to the extent possible—period
(year) effects. We also focus on the extent to which these effects are in fact proxies for
other covariates, such as education and child status. We will then discuss changes in the
sectoral distribution of female employment over time, and explain these changes in terms
of age and cohort effects. Lastly, we use a 1988 constitutional change in mandated
benefits for working women to determine the effect of more generous women’s labor
legislation on both female employment and sectoral choice.

In the United States the literature on changes in female labor participation is quite
large. This literature shows that female labor force participation started to increase as
early as 1930.1 In 1930 the participation rate for American women was below 0.25; by
1980 over half of all women ages sixteen and above were in the labor force. In Latin
America there is a smaller but growing literature dealing with female labor force
participation. This literature points to significant heterogeneity in women’s entrance into
the labor market. Caribbean countries such as Jamaica, Barbados and Haiti had female
participation rates over 0.5 as early as the 1950. On the other hand, during this same

period countries such as Brazil, Ecuador and Honduras had female participation rates in

 

 

' For a review see Goldin (1990).

41

the to

1970'

put:
empf
men

nine

man
seve
part1
poin
mar.

[her

poir

pres

the

Set
. We

For
M er:
PM.
daUgl
(10 no

the teens and low twenties.2 They only experienced growth in participation rates in the
19703, 803, and 903.

In Brazil female labor force participation increased from 17 percent in 1950 to 41
percent in 1999. Figure 2.1 details the more recent change in male and female
employment rates throughout the 19803 and 19903.3 We see a considerable decrease in
men’s employment, from around 0.80 in the mid eighties to under 0.75 in the late
nineties. For women the change is even more pronounced: a ten percentage point increase
in female employment over the two decades. However, not unlike the American pattern
in the sixties and seventies, Table 2.1 shows that this increase has been mostly from
married women. In the table we see three years of means—1981, 1990, 1999—for
several variables of interest for married and single women, ages 15 to 70.4 The change in
participation rates for single women was of 5.7 percentage points and 2.7 percentage
points for the 19803 and 19903 decade, respectively. Compare that to the change for
married women: a full ten percentage points for each of the two periods. The figures for
the employment for those two decades tell a similar story: a six and three percentage
point gain for the single women group and a ten and six percentage point increase for the
married group. Closely related to Table 2.1 are the patterns we see in Figure 2.2, which
presents the age-employment profile for selected years, from 1981-1999. Here we see

the classic hump shaped life-cycle employment profile, with employment rates increasing

 

2 See Psacharopoulos and Tzannatis (1993) for a compendium on female employment in Latin America.

3 We define the employment rate as the proportion employed, as opposed to proportion in the labor force.

4 For the purposes of this study, “married” is defined as household heads with spouses and their spouses. It
refers to currently married and not to ever-married. There is no information on past marriages in the
PNAD, so ever-married determination is not possible. In a small but significant number of households
daughters and sons of the household head may also be married. These are treated as “single”, since the data
do not allow for their identification.

42

rapid
and 1
large
m

SCCC

mul
eff:
Th1

ine

rapidly as women reach their late teens and early twenties, leveling off though the thirties
and forties, and then dropping off in the late forties and early fifties. We also see that the
largest increases in employment rates occur in the first decade (the eighties), and to a
smaller extent in the first half of the second decade (early nineties). The latter half of the
second decade shows very little increase in employment rates.

Our approach is to model changes in female employment with both probit and
multinomial logit models. The probit model is more appropriate for estimating the
effects of education, child status, and household composition on female employment.
The multinomial logit model allows us to determine which sector cohorts chose as they
increasingly entered the labor market. We also attempt to identify all three time effects
(age, period, cohort), although there are several difficulties with this endeavor, described
below.

Beyond explaining the extent of female participation, we also would like to know
what sectors and occupations these women entered. The multinomial logit model
provides a crude measure of sector choice; however, we also present a mainly descriptive
analysis of changes in occupational structure over the nineteen year period, by using
measures of gender concentration.

The remainder of the paper is structured as follows. Section 11 provides a brief
review of the literature. Section III describes the problem at hand and the data. In section
IV the models are described and results are discussed. In this section, we also discuss the
effect of changes in labor legislation on women’s employment and sector choice. In

section V we describe occupational changes in women and men’s employment. We also

43

dheuss

paper.

qunel.
descnr
forcej)
hmere
theinet
iaetors
loree
incre
stag
inn

\1

We

 

discuss changes in the degree of gender segregation. In section VII we conclude the

paper.

II. Review of literature

The literature dealing with female employment and wages in the United States is
quite large and varied. Goldin (1990) provides the most comprehensive historical
description of American women’s work. She points out that almost all the gains in labor
force participation have come from married women. Participation rates for single women
have remained relatively unchanged since the early nineteen hundreds. Explanations for
the increased participation of women can generally be cast into either supply or demand
factors. Smith and Ward (1984) favor demand-side explanations for the increased labor
force participation. They use Mincer’s (1962) technique and find that 60% of the
increase in female labor force participation from 1900 to 1980 can be explained by rising
wages. Some of this increase is through a direct wage effect, some of it though wage’s
impact on fertility. However, the majority of research on changes in female labor supply
has emphasized supply-type factors. These have more often than not used variants of
methods pioneered by Mincer (1962) and Ben-Porath (1973) to estimate labor supply
functions. They emphasize the role of education and other forms of human capital in
explaining labor supply.

In newly industrialized (or non-industrialized) settings the so-called “U”-
hypothesis is commonly invoked to explain changes in participation rates.5 The “U”-

hypothesis maintains that during the early phases of industrialization female participation

falls.
in pa
jobs
atai
ferti
Psat

31110

size
dynz
de I
moc‘
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She
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llll't
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Are

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falls. This fall occurs, in part, as home production gives way to industrialized goods, and
in part as agricultural employment declines. Women are unable to find compensating
jobs in industry, these jobs going mainly to men. Participation then increases with the
availability of more administrative and secretarial jobs, and as women reduce their
fertility and increase their schooling. This hypothesis has found support in
Psacharopoulos and Taznnatos (1989), Goldin (1995) and Mammen and Paxson (2000),
among others.

The literature concerning female participation and employment in Brazil is
sizeable, but consists mostly of cross-sectional analysis, with little or no mention of a
dynamic component. Tiefenthaler (1992) uses the 1989 Pesquisa Nacional por Amostra
de Domz’cilios (PNAD), a Brazilian household survey, to estimate a multinomial logit
model of female employment. She finds that higher levels of education are strongly
associated with formal employment (versus informal, self-employed or no employment).
She also found that small children had the largest negative effect on formal employment.
This large disemployment effect is also found in Soares (2000). Humphrey (1996)
investigates the cyclical nature of children and female employment in the state of 350
Paulo. He found that the quality of jobs held by women actually increased during
recessions, a trend that did not carry over to men. Men’s jobs became more informal and
lower paying during recessions. This is evidence against the “added worker effect”.
Arends-Keunning (1997) looks at changes in female labor force participation in Brazil,

from 1976-1990. Arends-Keunning, using the PNADs, applies the methodology

¥

5 Note that the U-hypothesis is also applied in industrialized countries to explain their female participation
CXperience. See Goldin (1995).

45

dei'

fen

tilt

det

pet

ad

developed by Heckman and McCurdy (1980) to evaluate the effect of income changes on
female labor force participation. She creates cohort x education cells and uses fixed cell-
effects to distinguish between temporary and permanent income changes. She finds that
decreases in family incomes during the early eighties account for almost fifty percent of
the observed increase in female labor participation among single women and twenty
percent among married women. She argues that this is strong evidence in favor of the
added-worker effect.

Sedlacek and Santos (1991) estimate a labor supply function for women, focusing
on the role of husband’s earnings. They find that a husband’s earnings affect the wife’s
employment in a U- shaped manner. Among the very poor families the wife’s
participation is higher, as it is among wealthy families. Wajnman and Rios-Neto use the
PNADs to make projections about female labor force participation. Based on a stationary
assumption regarding future cohort participation rates, they find that participation rates
will increase simply due to the age composition of present and future cohorts. Although
the focus of their paper is to outline secular changes in the wage gap in Brazil, Barros,
Ramos and Santos (1993) describe changes in female labor participation during the
19803. They find that between 1981 and 1989 the proportion of workers who were
women increased from 29.8 to 35 percent. They find that women are not over-
represented in low-paying occupations or sectors. Rather, they are over-represented in
higher-paying occupations. Also, in their analysis they find that in higher-paying
occupations women have higher levels of schooling than men.

Lam and Duryea find a strong link between increased school attainment and

decreases in fertility in Brazil, using data from the 1984 PNAD. However, they find

46

highly significant, if weak (in magnitude) link between fertility and labor supply. They
discard the explanation that a decrease in fertility led to an increase in women’s labor
force participation. Instead, Lam and Duryea favor the hypothesis, based on work by
Willis (1973) and Becker and Lewis (1973), which maintains that higher levels of
schooling raised the shadow price of children and thus led to a substitution into quality
versus quantity. Lastly, Soares and Izaki (2001) do a multivariate analysis of female
labor force participation in Brazil using five PNAD cross-sections. They find that, as in
the United States, increases in female labor force participation in Brazil came mainly
from married women. In their model education explains 50 percent of the increase in
labor force participation. Fewer children in the household were also associated with an
increase in participation, but these and all other variables accounted for only three percent
of the increase over the 19-year period spanned by their cross sections. Neither cohort

nor year effects were explicitly modeled in their multivariate analysis.

IH. Changes in cohort employment and the data

A number of factors likely contribute to the changes in female labor supply.
Marriage, the decision to have children—and how many children to have—and
retirement are among the major factors that vary over a woman’s lifecycle. These
covariates will lead to different employment rates for women at different ages, creating
an age profile for female labor supply. In addition, the labor supply, income and wages
of other household members will also affect female labor supply through income and

substitution effects. If we look at leisure time as a normal good, if other members of the

47

household face a higher wage, women would be less likely to participate in the labor
market, ceteris paribus.

Secular changes may also be associated with changes in labor supply. In
particular, cyclical factors, such as recessions, will affect the demand and supply of labor.
During recessions the demand for labor will contract, and employment and wages will
fall. Also, during recessions women may delay their entry into the labor market because
of lower wages or high unemployment, deciding instead to invest in more schooling or
training. Women may also change their fertility decisions based on cyclical factors. In
recessionary periods women may delay entry into the labor market (or exit labor markets)
in favor of starting a family. Secular changes also reflect both more progressive attitudes
toward women’s work as well as changes in the degree and nature of discrimination in
labor markets, although these effects may arguably be driven by inter-cohort changes
rather than by inter-year changes.

Changes between cohorts play a key role in determining labor supply. Schooling
levels, and the quality of schooling, will likely vary between birth-year cohorts, with
latter-year cohorts being more schooled and having access to better quality schooling.
Beyond schooling, younger cohorts will also have different attitudes toward work:
current generations may favor careers for their daughters to a greater extent than their
parents did. Closely related to this, social norms may change from cohort to cohort,
increasingly favoring the entry of women, and married women in particular, into the
labor force. Lastly, to the extent that younger cohorts have fewer children (and perhaps
higher quality children), and thus have fewer household commitments, they may be more

likely to enter the labor force, and less likely to exit the labor force for child-bearin g.

48

C0\

ch:

oft

In describing age, period and cohort effects we have described all the major
covariates commonly associated with labor supply: education, child status, marriage,
changes in social perceptions regarding women in the workplace, and wages and income
of other family members (husbands in particular). If we knew for certain that these were
the only factors affecting labor supply—and if we could measure them perfectly—we
would not need age, period or cohort effects. However, most of these measures, when
they are available, may be measured with error, and others may not be measured at all.
For example, although one can obtain a respondent’s completed years of schooling, it is
exceedingly difficult to measure the quality of schooling. Also, a woman’s fertility
history, although not difficult to measure, is not routinely asked in household surveys.
Instead what is usually measured is the age of children currently living in the household.
This may be a poor proxy for children ever born, especially for older households.
Husband’s wage, although easy to obtain, may be endogenous and actually reflect other
covariates. In particular, successful men may marry highly schooled and career-oriented
women, and vice versa. Finally, changes in social attitudes and perceptions are hard to
conceptualize, let alone measure—and any measurement would be ambiguous at best.
Therefore, the use of age, period and cohort effects is justified as a way to take into
account omitted or poorly measured/modeled variables. In this paper we primarily
answer two questions related to time effects and female labor supply (i) what role do
changes in education, child status and other household variables play in the changing
labor supply of Brazilian women and (ii) when these effects are taken into account, how
much do age and cohort (and year) variables shape labor supply. For identification

reasons detailed below we focus on age and cohort effects.

49

efi

CG

CI

lor

C0

ob

C0

110

wt

col

ON

As the discussion above makes clear one can expect, age, period and cohort
effects to be large. However, there are a number of difficulties in using age, period and
cohort effects. First, these correlations are devoid of any causal interpretation, to the
extent that said effects largely measure the degree to which we are unable to account for
or quantify economic and social variables that determine labor supply.6 Second, true
cohorts require that one follow the same households from survey to survey. Due to the
logistical problems of following people over time there are few surveys with this design;
and these suffer from serious attrition problems, as people move, die, or simply are no
longer willing to participate in the survey.7

That much said, there are several advantages to using these effects. First, a
dynamic labor supply picture is necessary to eliminate bias associated with confounding
life-cycle effects with cohort effects. In a growing economy (such as is the casein
Brazil), the life-cycle profile taken from a single cross-section will overstate the
employment at younger ages, and understate the employment at older ages, as older
members of the cross-section will also be those belonging to older cohorts and older
cohorts will tend to have lower labor employment rates. In effect, the life-cycle effects
obtained from a single cross-section will be picking up cohort effects as well. Second, it
is reasonable to proxy omitted and poorly measured covariates with age, period and
cohort effects. In a sense these estimates will tell us the magnitude of what we either do
not know or cannot measure. Also, to the extent that these latent variables are correlated
with the variables we gag measure, such as schooling or child status, omitting age and

cohort effects may engender serious omitted variable bias. Including the age and cohort

 

6 This point is elegantly developed in Heckman and Robb (1985).

50

effe-
deta

will

esti

011C

Wht
cha
dun
proi
e )‘t
efft
om
alst

and

effects can mitigate this bias or, in some instances eliminate it altogether.8 Furthermore,
detailing the life cycle and inter-cohort patterns in employment is a laudable goal in itself
with its own policy-making implications.

The task then becomes one of modeling age, period and cohort effects and
estimating them empirically. The main problem with modeling all three effects is that,
once you know an individual’s birthyear and his age in the survey, you will know the
year of the survey. This presents a serious identification problem. Consider the labor
supply function:

(1) y,=a+X,’,B+f(A,C,T)+e,.,

where y is a measure of labor supply, X is a vector of household and individual
characteristics, A are age dummies, C are cohort dummies and T are period (year)
dummies. The problem then becomes how to specify and estimate f(A, C, T). This is
problematic due to the fact that a person observed at year t, and born on year c, must be t-
c years old. In other words, a=t-c. This makes identification of year, cohort and age
effects simultaneously impossible without ad hoc restrictions. On the other hand,

omitting either of these effects will likely bias the other two effects, and possibly bias ,6

also (to the extent that individual and household covariates are correlated with age, period

and cohort effects). Consider estimation of a simple linear-effects model:

(2) yi=a+X,’,B+na+Kr+/lc+e,,

 

it, In addition, for these surveys to be useful they must follow families for numerous years.
For example, as Deaton (1997) points out cohorts may be used to create fixed-effects estimators.

51

she
estit

sub

We
tha
col

ma

C38

(All

in

cat

ide

du
lin

ad.

where a, t and c are age, period and cohort trends. We know that this model is not
estimable, due to the a=t~c identity. If we omit one of the effects, say time, we obtain by
substituting a+c for t

y, =a+X,. ’fl+na+x(a+c)+2c+c,
Y; =a+Xi ’,B+(n+rr)a+(2+rr)c+e,

(3)
We can see that the coefficient on both age and cohort will be biased; and to the extent
that household and individual covariates increase or decrease with time, conditional on
cohort and age, the coefficient on ,6 may be biased. The same type of argument can be
made if effects are modeled flexibly, with age, cohort and year dummies.

There are a few solutions proposed for this identification problem. Consider the

case were dummies are used. Then (2) becomes

(4) y,=a+X,’,B+Ap+Tg+Cl/I+e,,

where A, T, and C are matrices of rowsize equal to the number of age, period, and cohort
categories and ,u,g,t,1/ are vectors of a ,t and c dummies. In this case we have the
identity Asa = C3,. +Ts, , where 30,30, 3, are trend vectors. For example, so = {1, 2, 3,...,a} ,

where a denotes the number of age categories. Again, this implies that even after one
dummy is omitted in each of the effects matrices, we will still have vectors which are
linear combinations of each other. The only way to estimate the model is to impose
additional restrictions on the parameter values. The most parsimonious restriction would
be to drop an additional dummy category from one of the effects matrices. If this were

done for the first age group we would have the restriction a] = or, in effect restricting the

age effect to be the same for the first two age categories. One could also impose stronger

52

fur

sit

If

his
dur

functional form restrictions. If one believes that year effects increase linearly, one could
impose the restriction that g, — g = g, — g, = = g, — gH . This is equivalent to estimating

a time trend instead of the more flexible dummy configuration.9 Lastly, one could simply
omit one of the effects, most notably the period effects. If period effects are orthogonal

to the ,6 parameters, the only induced bias would be on the age and cohort effects—and

since these coefficients have no economic interpretation, arguably this bias is innocuous.
In all of the identification strategies described, interpretation of the effects parameters is
very tenuous. One cannot know to what extent one is picking up true effects and to what
extent one is picking up an inappropriate identification strategy. For this reason, for the
most part we omit period (year) effects, and are mindful that cohort and age effects will
be biased. We also attempt to identify all three effects based on restrictions placed on the
year effects. In particular, we use both (a) differences in functional form and (b)
restrictions on dummy variables to identify effects. The differences in functional form
are between the treatment of age and the treatment of period and cohort effects. Age is
modeled with a quartic polynomial, while period and cohort effects are treated with a
fully-flexible dummy variable specification. Although the quartic specification is not as
flexible as a semi-parametric dummy variable specification, a preponderance of labor
supply evidence indicate that age-employment profiles are ‘hump-shaped’; therefore we

feel that the specification is flexible enough. Second, we also restrict level year effects to

 

9 Deaton (1997) adds a time trend to the year effects matrix, and subtracts the same time trend from the age
and cohort effect matrices. He then imposes the restriction that the year effects be orthogonal to the time
trend. In our specification we rely both on functional form differences and restrictions on year and cohort
dummies to identify all three effects. In particular, age is modeled with a quartic polynomial, while cohort
and year effects are modeled with dummies. The reason age is modeled with a quartic is that, a priori, we
can be confident that age-employment profiles will follow the hump-shaped pattern found in virtually all
labor supply studies, and therefore their functional form does not require the semi-parametric flexibility of
dummy variables.

53

be the same for a range of years. In both Figure 2.1 (which presents a time trend
progression of female employment) and Figure 2.7 (which presents a time—series picture
of informal employment), we see that there is very little difference in the employment
pictures between 1996 and 1999. Therefore, in our identification strategy we restrict the
year effects to be the same for the last four survey years. We do this by modeling year
effects with dummies and omitting the last four dummies in the estimation. We also
present results for alternative sets of restrictions, in order to better understand how
sensitive age, period and cohort identification is to alternative specifications.

Before proceeding further it is necessary to detail the methodology used to
construct cohorts. The data used, which will be described in detail below, consist of
several cross-sections. That is, we do not have a true panel, since the same households
are not re-interviewed every year. Rather, a new sample is drawn in each successive
year. With this design one cannot follow cohorts, since the households will only be in the
survey on one particular year. Synthetic birth cohorts (which we will refer to simply as
cohorts) are then constructed by matching individuals of age a in year t with individuals
of age a+1 in year t+1, individuals of age a+2 in year t+2, and so on. It is important to
note that this method actually has a number of advantages (and disadvantages) over true
cohorts. The main advantage is that survey attrition is not a problem, since we are not
attempting to match the same individuals from one survey to the next. Second—and
related to the first point—cohorts can be constructed for unlimited number of cross-
sections. In panel data, the longer the panel length, the less representative successive
rotations will be of the original sample. On the other hand, cohorts can tell us nothing

about the dynamics within a cohort, a key advantage of panel data. Also, cohorts

54

implicitly assume that the sample of individuals (and households) of age a+n in sample
year t+n is drawn from the same sample as individuals of age a in sample year t, n years
latter. This may not hold for older cohorts, since many of them will have died, or if there
is migration from populations not sampled in year t (e.g. other countries, areas not
sampled, etc.). A more serious problem can occur if household heads are replaced by
their progeny. In this scenario, the household heads in year I may be reclassified as father
of household head in year t+n.10
The question we would like to answer is exactly what accounts for the increase in
employment rates among women, and among married women in particular. Among the
factors that customarily enter into a labor supply function, education and child status
(fertility) are prominent. More educated women are more likely to work outside the
home than less educated women, an empirical regularity observed in countless settings.
Child status is also important, as couples will, to varying degrees, determine family size
and labor supply jointly. Regional differences are important in Brazil, since there is
substantially observed (and unobserved) heterogeneity between different regions,
particularly between the industrialized Southeast and the economically depressed
Northeast. A likely additional source of heterogeneity arises from deep cultural
differences (which may partly determine attitudes toward female work), which although
we cannot quantify, may vary to a large extent from region to region. Beyond regional
differences, the dichotomy between urban and rural setting is also important—indeed,

one can argue that the urban centers of the more developed Southeast have more in

 

‘0 See Deaton (1997), Deaton and Paxson (1994) and McKenzie (2001) for a detailed discussion of the
potential problems involved in drawing inferences from synthetic-cohorts.

55

common with the urban centers in the Northeast than they do with the sparsely populated
rural settings of the Southeast.

Even when accounting for the covariates above, both observed and unobserved
factors common to birth cohorts are likely explanations for increased employment rates.
Although we may not observe these factors, we can certainly observe their effect, by
analyzing the employment rate of each cohort separately. Figure 2.3 presents a visual age
profile of the employment rate of eight cohorts, for both married and single women. First
notice that although the employment rates for married women have increased, they are
still significantly below that of single women. Single women’s employment rate peaks at
0.75, while the employment rate of the highest employed married cohort barely reaches
0.5 at around 35-40 years of age. Second, one immediately notices that the cohort lines
for single women are close to each other. In fact, there is no discemable trend. This is
characteristic of a stationary state cohort, as the age-employment profile of each
successive cohort basically mirrors the previous cohort’s. The same cannot be said of the
married group. Here we see that each successive cohort of married women has an
employment rate markedly above its predecessor’s. We also see the largest cohort gains
between the 1937-41 and the 1942-46 birth-year cohort, and between the 1942-46 and the
1947—51 birth-year cohort. The gains taper off for younger cohorts, and are modest
(albeit very discemable) between the youngest two cohorts.

Returning to Table 2.1, we would like to know to what extent these cohort
changes are driven by changes in variables of the women’s labor supply function, such as
school attainment, child status, and urbanization. Although the table is ordered by year

and not by cohort, one can still see that all the covariate changes commonly associated

56

with higher employment rates are present in both the top (married) and bottom (single)
panels. The proportion of women in rural areas declined in both periods (1981 to 1990
and 1990 to 1999), consistent with the observed migration to urban centers throughout
the two decades. In fact the increase in urbanization accelerated during the second
period. In both panels we also see a marked increase in educational attainment, mostly
driven by increases at lower levels of education. It bears noting that the increase is not
symmetric with respect to gender. During the 19—year period covered by our analysis
girl’s schooling equaled and eventually surpassed schooling levels for boys. One should
also note that education levels, as measured by completed years of schooling, are biased
downward, to the extent that many of those still in school are also in the sample. The last
set of changes is those with respect to child status. They show that the number of boys
and girls declined dramatically in both periods. This is in line with the observed
concurrent decline in total fertility rate by 50 percent in the first decade.

The data used in Table 2.1 and throughout the analysis are from the 1981-1999
PNADs.ll The PNAD is an annual household survey conducted by the Brazilian
Statistics Ministry (Instituto Brasileiro de Geografia e Estatt’stica, IBGE). It is a
representative sample from the entire country, except for a few rural regions in the north,
which are not surveyed. The PNADs include detailed information on labor supply asked
of all household members at or above the age of ten. This information includes type and
sector of employment, formal employment (employees who work under the auspices of
the government), informal employment (employees who work outside the legislated

employment framework), hours worked, earnings, tenure (later years only), etc. Every

 

11 Since the survey was not conducted in 1991 and 1994, data from those years are not available.

57

household member is surveyed, and information is collected on schooling, age, race (later
years only). All relationships are measured vis a‘ vis the household head. Therefore it is
possible to identify the household head’s spouse and children, but not stepchildren. This
poses a problem since our variable for sons and daughters will include all the household
head’s sons and daughters living in the household (from all marriages), but will exclude
both sons and daughters of the spouse from another union, or children no longer in the
household. Since household heads are predominantly male (80 percent male), this will
potentially affect son and daughter information for 80 percent of the wives in the sample.

We use two samples in our analysis, the married sample and the single sample.
Both samples are limited to women ages 15-70. Girls ages 10-14 were omitted since the
labor supply of children is likely very different than that of teens and women. On the
other hand, since many adolescents enter the labor market after 8 years of schooling
(primary school) and after 11 years of schooling (secondary school), 15 years old would
encompass most of the secondary-schooled and all of the primary-schooled. For the
married women we dropped all observations for which any of the covariates was missing
for either the husband or the wife (43,828 observations), leaving a sample size of 963,102
observations. For the single women sample the total number of observations was
684,514. The husband’s wage was deflated to constant 1999 Reais.12 Note that for all
models data is pooled across years.

The multinomial logit model will try to account for the different employment

choices made by women. The choices were defined as follows: (0) not at work, (1)

 

12 The exchange rate in October of 1999, the month of the survey, was 1.7 Reais to the US. Dollar. Since
all PNADs deflate monetary values to October of the survey year, the October price index is used to deflate
values across years.

58

formal worker ,(2) informal and (3) self-employed.13 Informal wage workers tend to be
in very low-paying, low quality, jobs, characterized by high turnover. Self-employed
workers will be small business owners, usually with no employees, as well as self-
employed professionals. We did not stratify the self—employed by number of employees,
although the data permit us to do so. They were treated as one category, irrespective of
establishment size.

As mentioned previously, defined benefits introduced in 1989 considerably
increased the firing costs of all formal workers and increased the labor costs of women in
child-bearing age, to the extent that these women now had increased maternity leave and
were protected from being fired while pregnant, or immediately following a birth. In
particular, the second legislative innovation allowed women to take unpaid maternity
leave during their pregnancy followed by up to four months of paid maternity leave after
birth. To test the hypothesis that these legislative innovations caused employers to
increasingly hire “hi gh-risk” women informally, or perhaps not hire them at all—we will
compare the employment of women in child-bearing ages (20-35) to that of older women
(40-55). The sample of older women will in effect serve as a control group, to the extent
that their employment is not affected by the legislative change to the same extent as the
employment of younger women is affected. We will also use a second control group,
single women 20-35. We compare this group to the group of married women 20-35, who

are arguably at the highest risk for child bearing. This reflects the fact that the majority of

 

13 Formal workers carry a “worker’s notebook”, which the employer must sign. This entitles the worker to
paid vacation, as well as numerous other worker benefits. It also means both the worker and the firm must
pay income tax on any earnings. Informal workers do not have their notebook signed, and thus the
government does not know of their employment. Although this is technically illegal, in practice there are
few consequences for either the firm or the worker.

59

births are in wedlock, and employers can expect single women to have lower fertility

rates than married women.14

IV. Main model, results and analysis

Four models are estimated. The first is a probit model for employment. This is
the focus of the analysis. The second is a multinomial logit model. We use the
multinorrrial logit to allow coefficients to differ across employment choices. The third
and fourth models are probit and multinomial logit models for informal employment and
employment type, to determine the effect of the changes in labor legislation mentioned
above. In all of our model estimates it is important to keep in mind that education, child
status, and other covariates are not exogenously changed from individual to individual.
These are all variables that are likely correlated with a number of other variables, most of
them unobserved. Education is certainly correlated with ability, and with other forms of
human capital. Child status is likely to be endogenous, as couples by-and-large decide
when to have kids, how many, and the spacing between them. These decisions are jointly
made with labor supply decisions. The husband’s wage may also be endogenous—at
least to a certain extent—due to the fact that career-driven and high ‘ability’ husbands
may chose wives with certain characteristics, such as high schooling levels. However,
since we have information on husband’s schooling and age, two covariates which wives
may also select on, the endogeneity of husband wages will not be as pernicious as the

endogeneity of child status. There are certainly methods to try to deal with labor supply

 

14 This control group strategy also rests on the assumption that employers can observe marital status at time
of employment.

60

endogeneity, however, our attempt to deal with the problem here will be limited to
controlling for most observed sources of possible heterogeneity.”
For the married women four probit models are estimated, to allow for the

incremental inclusion of covariates. They are as follows:

(M1) p(emp)=<l>(2ia,-R, +2514 +2jfljcj)
(M2) p(emp) =¢(Z,04-Rt +2,§1At +2.45. +2j/31C1)
(M3) p(emp) = <I>(Z,.a.-R.— + 2,974, +2.48. + 2.71.11... + 2,419)

(M4) p(emp) = (p(ziafi, +294 +2.35. +2manm +Z,#.F. +2jfljcj)

R,- are six regional dummies and one macroeconomic variable, GDP growth. A, are four
age polynomials (age, age squared, age cubic, age quartic). S), are seventeen education
dummies. Hm are four husband variables (husband’s predicted wage, wage squared, years
of schooling and age). F,, are two sets of six child status dummies and household size.16
Cj are fifty cohort dummies. Note that the husband’s education enters into the husband’s
wage and into the wife’s employment equations. The motivation behind this is that apart
from increasing wages, husband’s schooling may also affect the degree of assortive
mating, child quality, and general attitudes toward work. To the extent that more
educated husbands may prefer women who work (do not work), and to the extent that

professional women may prefer well educated (less educated) husbands, it is appropriate

 

15 There is a vast literature on instrumental variable techniques, fixed effect models, as well as studies of
twins and siblings, among others. Other approaches try to find exogenous sources of variation in
covariates, or “natural experiments”. If there are no good instruments, or no exogenous sources of
variation, one can try to control for all known correlations, in an attempt to capture most of the omitted
variable effects and thus mitigate the bias involved.

61

to control for husband’s schooling beyond its effect on wages. Furthermore, since
schooling and time at home enter into the child quality production function, conditional
on husband’s wage, women with more educated husbands may want to spend less (more)
time with their children. The exact direction of the effect cannot be determined a priori
by economic theory and will depend on how the husband’s education enters into the
production function.

Table 2.2 presents the probit results for the employment of married women.
Marginal effects are reported. Since there are 53 birth year cohorts (1921-73), only every
fifth cohort is reported, starting with the 1925 cohort. All cohort results are relative to the
omitted category, the 1921 cohort. Controlling for age and region only, we see that the
cohort coefficients are very large, the youngest cohort being more than 30 percent more
likely to work than the oldest. However, the marginal change in employment
probabilities is not as strong in the older cohorts as Figure 2.3 suggested. In fact, the
changes between cohorts are small until the 1930 cohort and then distributed evenly. We
also see that even the age quartic is significant at conventional levels. This result
motivated us to keep the four degree polynomial format for age.

Seventeen education dummies are added for model M2. As expected, higher
educational attainment is associated with higher employment probabilities. We also see
that these “returns” are highly non-linear. The returns to the first ten years of schooling
amount to about eleven percent. The return to an addition year adds a full ten percentage

points to the employment probability. This is not unexpected since the 11‘” grade is the

 

16 One daughter 0-4 years old, two daughters 0-4 years old, three or more daughters 0-4 years old, one son
0-4 years old, two sons 0-4 years old, three or more sons 0-4 years old. Same for daughters and sons 5-9
years old.

62

last grade of the Brazilian high school. If labor markets are susceptible to returns to
credentialism, then the high school diploma should affect wages (and thus employment)
beyond the marginal effects on human capital of an additional year of schooling.
Furthermore, to the extent that students who repeat years are more likely to drop out of
school, holding a high school diploma will also be a signal of those characteristics
associated with non-repetition.

Adding the education dummies (M2) reduced the cohort coefficients by about one
third. This indicates that a good portion of the increase in married women’s employment
rates across cohorts was due to more and more educated cohorts. In M3 husband’s
covariates are added in, using a two stage approach. Wages are predicted in a first stage,
based on seventeen husband education dummies, age and age squared, as well as region
dummies. These predicted values are for working husbands only; results are reported in
the Appendix Table 2.13.17 The predicted values are then used in the wife’s employment
probit in the second stage, and standard errors are adjusted. We see that even after
accounting for age and education in the husband’s wage and wage squared, schooling and
age are significant, more schooled husbands decreasing a wife’s employment probability.
Both polynomials of the husband’s wage are significant, with the linear term positive and
the squared term negative.18 There is no obvious interpretation for this result. One

would expect substitution and income effects to move in the opposite direction, to the

 

17 Note that husband’s schooling and age are entered into the woman’s employment probit also. Non-
linearities in returns to one’s own education in Brazil have been widely documented, motivating the
flexible functional form in the first stage estimation. However, we have no reason a priori to expect that
husband’s education will affect wife’s supply in a largely non-linear way, conditional on husband’s wage.
We maintain that the effect of education and age on men’s wages is going to be significantly more non-
linear than the effect of these covariates in the wife’s employment probit (second stage).

extent that leisure is a normal good. It is possible that wages are still capturing omitted
variables associated with assortive mating. In any case, this is contrary to the results
found by Sedlacek and Santos. Also note the inclusion of husband’s covariates had very
little impact on the cohort effects.

The last probit model (M4) introduces child status and household composition
variables. Household size and six child status variables for daughters and six for boys are
included, although the 5-9 year old dummies are not reported in the table. We see that
additional young children are associated with large decreases in employment
probabilities, and these decreases are relatively linear in the number of children. We also
see that larger households will more likely have the wife employed. The inclusion of the
child status and household controls again reduced the magnitude on the cohort
coefficients. Although the reduction was not as large as the one associated with
schooling, it is in the direction expected, and is around two to three percentage points for
all but the oldest cohorts.

So far we have estimated a labor supply function, allowing different level effects
for each cohort. However, it is possible that the underlying supply function may have
changed from one cohort to another. One way to determine this would be to estimate
different supply functions for each cohort. Figure 2.4 presents predicted employment
rates for different levels of schooling, based on cohort-specific supply functions.
Predictions are made at sample means, except for age, which is held constant at 35 years

of age. The model used to make predictions was the one based on the M4 probit model,

 

18 Higher degree polynomials were also modeled for wages, as was a partially linear model. In both cases
the result was similar to the level and quadratic formulation described above. Furthermore, when model
M4 was estimated for each cohort separately, the wage functions were similar to the pooled model.

only with cohort effects omitted, since equations were estimated by cohort. We hold age
constant to net out any age effect associated with cohorts having different average ages in
different cohorts. Although there is some evidence of a more concave education effect
for the older cohorts, this effect is not very pronounced. In general the education effect
seems to be similar across cohorts, with older cohorts having slightly lower returns.

In Figure 2.5 results are presented for the same set of cohort-specific equations
with respect to the child status variables. The estimates are for married women. Here it
bears repeating that fertility and labor supply, at least to some extent, are jointly
determined. Therefore, caution is warranted when interpreting the child status
coefficients as causal. The panel presents predicted employment rates for households
with one, two, and three or more boys ages 0-4. The estimates for ages 5-9, as well as the
estimates for girls are not graphed.19 We clearly see that the effect is not the same across
cohorts. In particular, the effect tends to be greater for younger cohorts than for older
cohorts. For the 1962-66 cohort the effect of one boy 0-4 is associated with a full ten
percentage point reduction in employment rates of the wife. The disemployment effects
are also nonlinear, with the first child being larger than the second, and the marginal
effect of the second larger than the third. The inter-cohort differences are also evident,
with older cohorts seeing smaller effects than younger cohorts. This may be due to the

fact that older cohorts with young children in the household may be unrepresentative of a

 

19 Results for the 5-9 year old group are significantly smaller, and are smaller for older cohorts than for
younger cohorts.

65

typical working family. The same may also be true of the youngest cohort, but to a lesser
extent.20

Although the focus of this paper is on married women, as this is the group that has
experienced the most dramatic increases in employment and participation rates, labor
supply functions are also estimated for single women. In their case, child status variables
are not reported, as they are of small magnitudes and often not significant at conventional
levels. Table 2.3 reports the probit results for single women. As expected, there is little
inter-cohort change in employment rates. This is the same result found in Figure 2.3, and
confirms the absence of cohort effects for single women. It is also interesting to note that
for single women, the association between education and employment is not monotonic.
In fact, in the first ten years of schooling the parameter estimates vary almost randomly
from one year to the next. The strong positive effect for higher education is still present,

and of similar magnitudes.21

Identifying age. period and cohort effects

In this section we present the results from out attempt to identify all three
temporal effects: age, period and cohort. We have already discussed that any attempt at
identifying all three effects necessarily hinges on some identification restriction, and that
the results are typically quite sensitive to that restriction. Our analysis is no exception.

The identification restriction imposed was that the period effects for the 1996-1999 years

 

20 Results for girls, although not reported, were similar to those for boys. The only difference is that for the
older group more boys are associated with larger disemployment effects. This is similar to the result found
by Soares (2000).

66

be the same. Imposing this restriction was trivial: we simply omitted the last four year
dummies from our labor supply equation. We also should point out that since age effects
are modeled with polynomials and not with age dummies, part of the identification rests
on the disparity in functional form, although it is not clear exactly how this would impact
the period and cohort dummy coefficients (if at all). \

Table 2.4 shows age, cohort and period coefficients for model M4, when year
effects are added in. As mentioned before, only dummy variables for 1981-1995 are
included. The last four period dummies being excluded in order to identify the effects
separately. First we see, as expected that the period and cohort coefficients are
imprecisely estimated due to the inherent colinearity between the two effects. In
particular, most of the period effects are not significant when jointly estimated with
cohort effects. The latter cohort effects are still significant at conventional levels. We
also see that when estimated with cohort effects, the year effects bear little resemblance
to their values in the model without cohort effects. This is not true for the cohort effects,
which are now 20-30 percent attenuated vis-a-vis the model without year effects. This
provides some evidence that cohort effects are more robust to inclusion of period effects
than vice-versa—at least with the identification restrictions that we adopted.

In order to determine how sensitive our period and cohort effects are to
identification restrictions, we estimated the model in Table 2.2 with three other
identification strategies. Therefore, the first identification strategy (corresponding to the

last column of Table 2.2, only with year effects added in) was to restrict the last four

 

2‘ Although not reported in the table, female employment is procyclical, even if the small magnitude on the
GDP growth variable indicates small effects. For the married women a ten percent increase in GDP is
associated with a 0.8 percentage point increase in employment probability. For single women the effect is
about twice as big. In both cases the effect is robust to model specification.

67

year effects were restricted to be equal (i.e. dummies for the last four years were
dropped). In the second and third specifications the year effects for 1997, 1998 and 1999
(for the second specification) and 1998 and 1999 (for the third specification) were
omitted. The fourth specification omitted only the 1999 dummy, relying purely on
functional form restrictions to identify all three effects. The inclusion of four
specifications helps to demonstrate the sensitivity of identification to different
identification restrictions.

Figure 2.6 presents predicted age, period and cohort effects based on the model
M4, only with the GDP growth variable omitted and with the year dummies
corresponding to four different specifications added in. The life-cycle profile is as we
would expect, with women entering the labor force in their late teens and early twenties
and exiting in their fifties and sixties. We also see—and this is true for all effects
estimated—that the first and second identification schemes behaved very similarly, while
the last two schemes behaved rather erratically. Looking at the cohort effects, we see that
the specification relying purely on functional form results in nonsensical values: an
employment profile increasing with birthyear. However, for the three other
specifications, ceteris paribus, changes in cohort birthyear account for a seventeen
percentage point (first and second specifications) and a thirty percentage point increase
(third specification) in employment from the oldest to the youngest cohort. These
changes are also concentrated in the older cohorts. For the year effects we see a similar
story: for the first two specifications the change in employment is rather modest, at about

five percentage point, concentrated in the first decade. For the third specification there is

68

no increase and even a modest decrease in over the years. For the last specification we
see a dramatic secular increase, from 24 percent to 37 percent of married women.

At first glance a simpleminded explanation would be that cohorts account for
much more variation in employment than do year effects. One must, however, keep in
mind that in our sample we have over fifty elapsed cohorts and only nineteen elapsed
years. Indeed, the average change per cohort using either of the last two specifications is
0.3 percentage points. For the same specifications, the average year effects are 0.23
percentage points, all of which occur during the first decade. Indeed, although the
average marginal cohort effects are still larger, the difference is not as large as Figure 2.6

suggests.

Counterfactual simulations

In order to obtain an estimate of exactly what percentage of the secular change in
employment is explained by the covariates, what is explained by the cohorts and what is
unexplained, we have simulated employment rates from model M4, using the 1981, 1990
and 1999 cross sections. In effect, we have estimated the employment rate at the sample
mean for each of these years, using the coefficient estimates obtained from M4. We can
obtain different employment estimates for different covariate subgroups by successively
using the mean of each subgroup from period t+1, while holding the other subgroup
means constant at period t. In other words, consider four subgroups, R, S, H and C. R
consists of age, region and urbanization. S consists of the education dummies. H consists

of the husband variables, as well as child status variables, and C represents the fifty-two

69

cohort dummies. The predicted change in women’s employment from 1981 to 1990 is
given by

(5) d9081=<l>(R90 ’a+ S,,,’2.+H90’17+C90’,B)--<I>(Rm ’or+S,,,’/l+H81’n+C81 36).

If we want to know how much of this change is due to a change in region, we would
compute

(6) <I>(R90’a+S,1’/l+ H81 ’n+C81 ’fl)—<I>(R8,’a+581’2+H3,’n+C81’fl).

We can then add in the schooling means from 1990 to obtain the change due to school
attainment improvements, and so forth.22 Table 2.5 summarizes the results from this
simulation. First, we see that our model is actually not very good at predicting changes in
employment over years. The model predicted a 6.1 percentage point increase in the first
decade, while the change was actually 8.2 percent. In the second decade the model
performed somewhat better. The model predicted a 5.9 percentage point change, when
the actual change was 6.6 points. In other words, in the first decade 74 percent of the
change was explained and in the second decade a full 90 percent of the variation was
explained. The breakdown by covariate group confirms what we saw in the probit tables.
Schooling explains 28 and 48 percent of the change between 90-81 and 99-90,
respectively. Our 52 cohort dummies explained most of the change—61 percent for the
first decade and 55 percent for the second. Also, child status, household size, and
husband’s variables explain a large portion of the change in the first decade (11 percent),

but actually contribute to lower the magnitude of the change in the second decade. This

 

22 Note that since the normal cumulative distribution is not linear, the employment of a mean is not equal to
the mean of individual employments. This means that changes do not necessarily add up to the total
change. However, a similar exercise was done with the linear probability model and results were
comparable.

70

is in line with the dramatic decrease in fertility, whose effects were mostly in the 19803
and early nineties.

In the bottom panel of Table 2.5 we see the counterfactual simulation applied to
changes over cohort. Here we are u'ying to explain the change in average employment
for married women between the 1942 and 1952 cohorts and between the 1952 and the
1962 cohorts. We restricted the cohort range to be twenty years—so that we can compare
the magnitudes with those of the counterfactual period simulations. Unfortunately the
results are not very illuminating, mainly due to a small change in average year over the
period, i.e. the median year of the 1942 cohort was 1987 and 1990 for the 1962 cohort—
only three years of difference. In contrast, the change in median age is of a full 18 years.
This is, of course, because most members of early cohorts are old and most members of
late cohorts are young. If we had more period variation in the sample, we would have a
more complete age-employment profile for early (and late) cohorts.

The counterfactual cohort simulations behave completely disparately for the two
periods. In the early cohorts we have increase of employment of 5.8 percentage points.
In the later cohorts we have a decrease of 3.4 percentage points. For purposes of the
table, in the first period a negative value on the ‘percentage explained’ signifies a

percentage decrease, in the second period it signifies a percentage increase. For the early

 

 

cohorts (1952-1942), we see that age accounts for a large share of the increase in
employment (51 percent), while changes in child status do not contribute to an increase in
employment—to the contrary—they actually act to decrease employment. This is likely
due to the fact that fertility declines only started for latter cohorts. The only effect that is

similar to that of the 1990-1981 period change in the top panel is education. Here we see

71

that schooling did act to increase employment of married women from the 1942 to the
1952 cohort. However, this effect mitigated for the later cohorts’ change. For the 1962-

1952 birthyear cohort change, education plays a smaller role in the employment change:

 

it acts to increase employment, its magnitude being 17 percent of the total change. In
fact, due to the larger variation in median age, age is the greatest predictor of the decrease
in employment across cohorts. This is due to the fact that in later cohorts most members

are still on the upward sloping portion of the age-employment profile.

Sectoflhoice results

The last set of results to be discussed is the sectoral choice logit results.
However, before detailing them it is useful to graphically motivate what changes took
place over the period in the distribution of employment between the formal, informal
wage, and informal self-employed sectors. Figure 2.7 presents a time series of the share
of employment in the two sectors dubbed “informal”. The first characteristic worthy of
notice is a dramatic increase in female participation in the informal wage sector starting
in 1990. One possible explanation for this is that the PNAD questionnaire changed in
1992. However, a priori there is no reason to believe that the change would have
significantly affected the quality of the response to the employment sector variables.23

Another explanation may be related to the constitutional change in 1988 (which went into

72

effect in 1989). The new constitution increased firm’s firing costs of formal workers, and
therefore perhaps increased the attractiveness of informal employment. Theoretically,
this change would impact both men and women, and indeed we do see a decrease in
formal employment for both groups during this period. However, because of the
additional benefits accruing to women, it is possible that employers would hire more
women informally, or perhaps be less likely to hire them at all. This hypothesis is tested
and will be discussed in the next section.

Whereas the secular increase in female employment of married women can
largely be attributed to changes between cohorts, the same cannot be said about sector
choice. Figure 2.8 details the proportion of employed women working informally, both
for self-employment and for informal wage work, by cohort. Unlike the clear cohort
pattern visible in the earlier cohort graph, the cohort pattern here appears to be staggered
five years apart. For our graphs the cohorts themselves are defined by a span of five
years. Therefore we would expect period effects to be seen every five years of age. This
is exactly what we see. In other words, the age profile for the 1957-1961 birth year
cohort at 30 years of age is similar to the age profile of the 1962-1966 birth year cohort at
age 25. This is so because at those loci the two cohorts are actually in the same period

(year). This pattern is most clear for the informal wage workers, but is also present in the

 

23 Prior to 1992 military and so-called “statutory” government workers were classified as workers without
a “worker’s notebook”, since working for the government one does not technically hold a notebook, as
government workers have their own social security system. Therefore, these workers were identified based
on industry and occupation codes and reclassified as workers WITH a notebook for the purposes of this
study. Starting with the 1992 PNAD, a separate question was added to explicitly identify government
workers, who were then also reclassified as WITH a notebook. It should be noted that prior to 1992 the
occupation and industry codes were sufficient to identify an estimated 98 percent of “statutory”
government workers. Even if some discrepancies arose from the questionnaire change, it is unclear why
this would affect women and not men.

73

self-employed panel. In the sector choice model below we attempt to identify both
period and cohort effects.

The multinonrial logit model is important because the three types of employment
are very distinct, and are characterized by different types of workers. Self-employed
workers tend to be poorly educated and mostly urban, and tend to be older.24 Informal
workers tend to be urban and rural, also poorly educated, but tend to be younger than
self-employed. Formal workers, on the other hand, would be the group most similar to
labor markets in the United States. They are more educated and span every industry and
most occupations. Informal and self-employed workers tend to be clustered in particular
industries and occupations. With these differences in mind it is important to know which
of these groups the married women’s cohorts were more likely to enter. Did their
employment patterns across the groups reinforce the patterns existing before the increase
in participation and employment or were they different? The multinomial logit will help
us answer these questions. The variables in the multinomial logit are the same as those in
the probit model M4. In Table 2.6 the effect of a one unit change in the explanatory
variable is given by the relative risk ratio. Coefficients smaller than one indicate a
decrease in participation probability vis-a-vis the omitted category (not at work); greater
than one indicate an increase. The first interesting result is that low levels of schooling
tend to decrease a married woman’s probability of being an informal wage worker,
relative to not being at work. Only at higher schooling levels does this trend reverse
itself. A similar trend is seen for the self-employed, although not as dramatic; a middle-

schooled woman being 40 percent more likely to be self-employed relative to not at work

74

than a woman with no schooling. For formal workers the education coefficients are as
expected. A hi gh-schooled woman is 13 times more likely to work as a formal worker
relative to not being at work than is a woman with no schooling. For higher schooling
levels the increases are even more prominent: for college-educated women relative to
high school-educated the odds ratio is 11.

All the child status results in the same direction, as one would expect. However,
the magnitudes vary from category to category. Young boys and girls have the largest
disemployment effect for formal workers, followed closely by informal workers, and
lastly by self-employed. This may be due to a greater flexibility of work schedule for
informal workers and even greater for self-employed individuals. The effects also tend to
be slightly non-linear in the number of children, as they were in the probit model.

The cohort coefficients tell an interesting story. For both formal and self-
employed employees the results are similar, if somewhat larger for the latter group. The
effects are larger for the younger cohorts. The results for informal wage workers are also
positive, but are significantly larger than for the other two categories; and again the
results are larger for younger cohorts. This indicates that (i) as with the probit results,
younger cohorts are more likely to work, and (ii) this work is more likely to be in the
informal wage sector than in either self-employment of in formal employment. However,
Figure 2.8 suggests that we may also be picking up period effects, and not just cohort
effects. In order to address this we also estimate the multinomial probit model with both

year and cohort effects, omitting the last four year effects, in the same manner that was

 

24 Self-employed also includes a small percentage of well-educated professionals such as doctors, dentists
and lawyers. This group is very different from the typical Brazilian self-employed.

75

done with the employment models. Again, we should restate that identification of all
three effects is problematic and, as we have seen, interpretation of the effects is quite
sensitive to identification restrictions. Figure 2.9 presents the relative risk coefficients for
the year and cohort effects—age effects were essentially the same as in the model with
only cohort effects, and are therefore omitted. For period effects, relative risk ratios are
relative to the four omitted years, 1996-1999. For cohort effects, the ratios are relative to
the omitted 1921 birthyear cohort. The results are also presented in tabular form in Table
2.7. Figure 2.9 clearly shows that while there seem to be some period effects over the
two decades, their magnitude is smaller than the cohort effects. Rather, we see that both
informal wage employment and self-employment increased monotonically with cohort,
relative to no employment. The cohort effects on informal wage employment are
particularly large. There are only modest cohort effects on formal employment. We also
see that most of the period effects for informal and self-employment are concentrated
between 1990 and l993——-even if the effects are in opposite directions. For formal
employment, the period effects are present mostly in the first decade, with an increase of
roughly 30 percentage points in the probability of formal employment versus no
employment. Therefore, although Figure 2.8 suggests that a large portion of the increase
in informal employment is due to period effects, we find qualified evidence (qualified
because of the tentative identification strategy) that cohorts may in fact be more

important that period effects.

76

1988fllicy change

The last two results discussed in this section pertain to the effect of the 1988
constitutional change on employment. Since formally employed women had access to
one month’s maternity leave, and had assured job security after the maternity leave, one
could expect shifting from formal to informal employment following the change. This is
so because the law is only binding on formally employed workers. The informal probit
models the probability of informal employment, conditional on employment. The
multinomial logit model extends this analysis to include shifting into other forms of
employment or into no employment. We chose this structure to empirically test the
hypothesis that more generous labor legislation may have led to the increase in the
informal employment of women. To test this we define two control groups. The first is
the group of women no longer likely to bear children, those ages 40-55. The second is
the group of single women ages 20-35. In the first specification the treatment group
would be women ages 20-35 and in the second it would be married women ages 20—35.
The model is then specified as follows:

(7) p(inf) = a + X ’6 + 7control + nyear9099 + Acontrol X year9099 + E

where “control” is the dummy for the control group, “year9099” is the dummy for post-
policy years. The X vector is a vector of labor supply controls, equivalent to those in S3,
but without age or cohort effects. The results of this model are presented in Table 2.8.
The two questions of interest are (i) how did women’s informal employment change after
1989? and (ii) how did this change differ for the control and for the treatment groups.
Formally, we want to know

(i) E(y | year9099 =1)— E(y | year9099 = 0) = ,u + Axcontrol

77

E ( y I year9099 = 1, control = 0) - E ( y | year9099 = 0, control = 0) —
(E(yl year9099 =1,c0ntrol = l)— E(y | year9099 = 0, control =1)) = -77

(ii)

Item (ii) is the difference-in-differences estimator. The parameter on the 1990-99
dummy, multiplied by the control dummy, evaluated at the sample mean (i.e. the
proportion of control observations in the sample, 0.31 for the first control group and 0.60
for the second), answers the first question; and the r_1_e_ga_ti_ve of the parameter on the
interaction of the year dummy and control dummy answers the second.25 In both cases
we see that there is a substantial post-1989 increase in informal employment of five
(0.164 x 0.31) and fifteen (0.2585 x 0.60) percentage points for the first and second
control group, respectively. We also see that the difference-in-differences estimator
suggests a 5.4 percent treatment effect in the first specification and a 4.2 percent
treatment effect in the second. This is comforting, for it suggest that both of our control
groups behaved similarly. It also suggests substantial shifting to informal employment
following the policy change.

The probit, however, does not model shifting away from employment. It only
models shifting to informal versus formal employment. It is possible that women at high
risk for child bearing may have shifted from formal employment into no employment, or
even into self-employment. In order to capture all four employment altematives—no
work, informal wage work, self employed and formal wage work—we also test the
constitutional change with a multinomial logit model. Here the omitted category is
formal employment, since most interesting comparisons will be with respect to this

group. The dependent variables included are the same as in the probit in (7). The results

 

2 . .
5 This 13 because we defined the control group as equal to one, the treatment group equal to zero.

78

are presented in Table 2.9. First note that the “Control x 1990-1999” parameter estimate
measures the relative risk ratio for the control group, not the treatment group. To obtain
the relative risk ratio for the treatment group (i.e. the treatment effect) one must take the
reciprocal of the control group parameter estimate. Therefore, as reported, relative risk
ratios greater than one actually correspond to a decrease in the category’s probability vis-
a-vis the omitted formal employment category. If we look at the treatment effect in the
two identification strategies we see that the probability of informal employment increased
relative to formal employment for both control groups (by 39 and 25 percent
respectively). However, we also see that the probability of self-employment decreased
(by 18 and 12 percent). If women in the treatment group indeed find it difficult to find
formal employment, it is not clear why they would shift away from self-employment. If
any effect were to be found vis-a-vis formal employment, it would be a shifting to self-
employment.26 In closing, both the probit and the multinomial logit results are consistent
with a shifting away from formal employment for women at high risk for child bearing
following the 1988 constitutional change. The only result at odds with this interpretation

is the observed shifting out of self-employment for the treatment group.

 

26 One should also point out a possible problem with the married women control group. The assumption
necessary for this group to act as a true control group is that its employment patterns resemble those of
single women throughout the period, absent the policy change, and that the policy changes not affect the
group’s employment patterns. The l9-year period in question witnessed dramatic changes in married
women’s employment patterns, so using this group as a control for employment patterns of single women

79

V. Occupational changes

The PNADs provide information on three-di git occupation and three-di git
industry. In this paper we focus on the two—digit classification.27 The main reason for
this is that occupational and industry classifications are fraught with reporting error.
Many respondents will not know exactly what occupation they belong to, and many
others will not belong to any of the available occupations, despite the large number of
occupations available. Also, at the three-di git level it becomes difficult to separate
occupation from industry. In addition, respondent’s self-reported occupational and
industry classification is likely to change over time and even between older and younger
generations. These difficulties are mitigated at the two-di git level. In the case of
reporting error, the respondent may likely mistake an “office receptionist” for an “office
assistant”—two different but neighboring tlrree-di git occupations—but will probably not
mistake “administrative assistants” for “managers”—two neighboring two-digit
occupations. Nevertheless, since most of the occupational change studies done use tlrree-
digit occupations, for comparability purposes, we compute statistics for both two and
three digit occupations.

One question we wish to answer in this section is where did women go as they
entered the labor force? Did they reinforce previous patterns of feminization or did they
enter occupations traditionally held by men? One way to address this is to look at some
measure of the distance between the proportion of men in an occupation and the

proportion of women. One such measure is the index of dissimilarity, which is one half

 

may be inappropriate. Nevertheless, we are comforted by the fact that both control groups yielded similar
results.

27 After 1992 the occupational and, to some extent, the industry classifications changed. All years were
translated back to pre-1992 definitions, but in any case, the changes were only at the three-di git level.

80

of the sum of the absolute difference between men’s share in each occupation (share of
total male employment in said occupation) and women’s share in the corresponding

occupation:

-1 LIL; L212.
(8) D'zzlr M 2213’ ml

where f,-(m,-) is the proportion of women (men) employed in group i, f(m) is women’s
share (men’s share) of total employment, and s,- is occupation i’s share of total
employment (occupation size). Higher index numbers correspond to a greater degree of
segregation. The 1/2 is necessary to bind the index between zero and one.28 This index
has the advantage of being neutral to scalar transformations in employment rates.29 It is
also simple to interpret. The index measures the percentage of men and women who
need to be reshuffled into different occupations in order to achieve perfect occupational

parity. The overall change in the index can be written as:

1 m 1 d0
10 d =_ f" _1..-_(_ __ t-l ___ ds=——a'c
( ) c 225" I ZZS‘ mI-l dt

dc is the change due to occupational cell sizes and ds is the change due to the change in

the gender makeup of each occupation.

 

28 Suppose there are two groups, and in one group women hold all jobs and in the second men hold all jobs,
then the index will be Viz x (|1-0|+|O-1 I) = 1. If on the other hand, employment is perfectly equitable, we
have V: x (l%-%|+|V2-‘/z|) = 0.

Watts (1998) argues that the dissimilarity index is not invariant to changes in the relative size of
occupation cells, and disfavors it for this reason. He also reviews a number of other indexes.

81

Table 2.10 presents the time-series evolution of the dissimilarity index. It also
breaks down the index into changes due to changes in the relative size of the occupation
cells (dc) and changes due to the gender composition of members of each occupation
(ds). A cursory look at the table reveals that for three-digit occupations the index varies
from the low 603 to the mid 603 and for two-digit it varies from the mid 503 to the low
603. In both cases we see a clear decrease of five points in the index over the twenty year
period. We also note that most of the change (8090 percent) is from changes in the
composition of cells, not from changes in cell sizes. Although the author knows of no
other time-series of occupational (dis)similarity in Latin America, there are a number of
studies in the United States. Most of the United States evidence (also using three-digit
occupations) points to a stagnant index for the first half of the century (at around 65),
followed by a decline of 5-7 points, with most of the decline concentrated since 1970.
This is actually quite similar to what we see in Table 2.10.

Table 2.11 we seek to answer a different question. Here we have a multi-layered
picture of the distribution of women in two-di git occupations. We attempt to match
women and men’s qualifications—schooling and age (which is a proxy for training) to
deciles of occupations, where the deciles are over the degree of feminization in the base
year of 1981. In other words, the first decile contains the most feminized occupations
and the last decile contains the least ferninized. We would like to know how much
human capital women bring into occupations, and if they need to bring more human
capital to occupations that are most segregated. First note that women tend to have
higher levels of schooling and tend to be younger than men in the workforce. This is a

regularity of Brazilian labor markets pointed out by a number of labor and development

82

economists. The comparisons between deciles reveal what we suspected. In the least
feminized occupations, women tend to have the largest educational advantage, although
no discemable pattern emerges with respect to age. Furthermore, we see that this pattern
is reinforced as women enter the most male dominated occupations (i.e. as the
occupations become more feminized) and, surprisingly, the same is true as men enter
occupations dominated by women. Indeed, the two most feminized occupation deciles
are the only ones in 1999 in which men’s educational attainment surpasses that of
women. And the top three are the ones in which the educational gap between men and
women is the largest. This pattern suggests that women need a qualification premium in
order to enter male-dominated occupations (as do men entering female dominated
occupations). This premium may be due to discrimination on the part of employers, but
more likely reflects either coworker discrimination, possible lower productivity of
women in a male dominated environment, or even latent costs associated with hiring
women in a male dominated environment. The same argument can be made with respect
to men in a female dominated environment.

The last result we consider is in Table 2.12. In Table 2.12 we would like to know
to what extent occupational growth affects the degree of concentration of men and
women in occupations. In the discussion above we saw that the degree of occupational
concentration did decrease over the last two decades. We also saw that women (men)
with relatively higher levels of human capital were the ones who entered male-dominated
(female-dominated) occupations. Anecdotal evidence would suggest that these entrants
would be young workers joining the labor force rather than older workers changing

occupations. Indeed, one would expect initial entrants, from younger cohorts, to be the

driving force behind the reduction in occupational concentration. In order to test this
hypothesis, we define an occupation in a particular year as being highly segregated if at
least 95 percent of its members are men or 95 percent of its members are women. We
then regress this measure of concentration on the change in an occupation’s share of total
employment (a measure of occupational growth) and on the change in the proportion of
young in an occupation, a measure of an occupation’s ability to draw new entrants. Since
our interest is on the effect of growth in occupational employment on occupation
concentration, we also control for the occupation’s initial status as highly segregated in
1981. We estimate this model by using occupational growth and lagged values of
occupation growth, lagged up to four years, to the extent that women and men may
switch occupations in favor of a more unfavorably concentrated occupation, only when
there is some evidence of growth. Included in the regression as a dependent variable is
women’s share of overall employment in each year. Since most of the segregated
occupations are male-dominated, increasing women’s employment will reduce male-
dominated segregation to a greater extent than it will increase female-dominated
segregation, therefore controlling for women’s share of employment across all
occupations is appropriate. We also estimate a model with both current-year growth and
all lagged growth variables. Note that the results in Table 2.12 are weighted by the size
of each occupation, so larger occupations have a larger impact on the results. There were
77 two-digit occupations and 17 years in the analysis, with 1981 being the first year. The

model is, thus

(1 1) p(highseg) = (Nil. ,6, dshareH. + 21.5,. dyoung,_,. +7 highseg81+ n femshare) ,

84

where highseg is the dummy variable for highly segregated occupation; dshare is the
change in women’s share of employment in a particular occupation; highseg81 is the
dummy variable for the initial (1981) values of segregation; femshare is women’s share
of overall employment.

While many results in Table 2.12 are expected, some are not. As expected, fast-
growing occupations are also the ones becoming less segregated. Furthermore,
occupational concentration is more sensitive to recent growth than it is to growth further
back. An increase of 0.01 in an occupation’s share of total employment is associated
with a 4.2 percentage point decrease in the probability of that occupation being highly
segregated. This effect decreased over time: 2.6, 2.3, 2.2 and 2.1 percentage point effects
for lagged growth. Unfortunately, growth rates from year-to-year are highly correlated,
therefore it is not possible to provide a meaningful analysis by including Log current
period growth and lagged growth in the same specification. This is attempted and
reported under the column “all effects”. One can see that the multicolinearity only allows
us to identify growth effects lagged four periods. All others are not significant. In Table
2.12 we also see that, as expected. the best predictor of a highly segregated occupation is
its segregation status in 1981. The unexpected part of the table is the bottom panel,
which presents the results for the growth in the proportion of young (defined as 16-25
years old) in an occupation. Controlling for overall occupational growth, we see that an
increase in the proportion of young in an occupation does decrease the incidence of high
segregation, but not significantly. Furthermore, inclusion of the change in the
occupational size does not appreciably affect the coefficient on the proportion young—

and in both cases it is not significant. This provides evidence against the hypothesis that

85

new entrants, from recent cohorts, are the driving force behind the observed decrease in
the level of occupational gender concentration. In fact, it appears that occupational
growth does a better job at explaining changes in segregation over time. However,
further inspection will reveal that this is consistent with older, gagged women, driving
changes in occupational segregation. In other words, the evidence suggests that as
married women enter the labor market, they are the ones who enter male-dominated
occupations. A final note of caution is in order. We have thus far interpreted
occupational growth as exogenous. It is certainly possible that we are picking up other
factors (beyond growth in proportion young) that affect occupational growth. It is also
possible—albeit improbable—that gender-diverse occupations are actually better able to
attract new members, and therefore the causality in Table 2.12 would be backwards.
Since in this paper we are not attempting to identify occupational growth (although it
may be possible to do so) beyond the inclusion of the change in proportion young, the

reader is duly cautioned about this possible problem.

VI. Conclusion.

Like almost all countries, Brazil has seen a dramatic increase in the participation
and employment of women during the postwar era. As with the United States and other
first-world countries, we have shown that this increase has come, primarily, from married
women. We have also shown that the correlations in the Brazilian women’s labor supply
functions tend to conform to that of other countries. Education is associated with higher
employment, more young children associated with lower employment of the mother. We

saw that in Brazil’s case education has highly non-linear effects on employment, a result

86

in line with cross-sectional studies of Brazilian labor supply, and in line with studies of
other labor outcomes in the Brazilian labor market, which seem to be non-linearly
correlated with education. However, the focus of this paper has been a cohort analysis of
changes in labor supply, with an emphasis on married women. Here we have seen that
improvements in education and reductions in fertility rates have explained much of the
inter-cohorts differences in employment. Notwithstanding, cohorts still explain a large
portion of explained changes in employment. Furthermore, our sector choice analysis
showed that most of the changes in married women’s participation have been from
women entering self-employment and, above all, informal work. We also tested the
hypothesis that increases in the cost of formal employment of women in child-bearing
age would engender a shifting from formal employment to informal employment. By
using two different identification strategies we conclude that there is evidence that this
shift did indeed take place, although we can never be sure that we are not picking up
other macroeconomic effects that may have affected our treatment and control groups
disparately.

Our occupational analysis revealed that Brazilian occupations have become less
segregated over the last two decades, a result in line with patterns observed in the United
States. We also showed that the degree of segregation is highly correlated with the
schooling advantage that women have over men. In male-dominated occupations
women’s schooling advantage over men is the largest, and in highly feminized
occupations men’s schooling deficits are the lowest. These results are consistent with a
number of discrimination hypotheses, but may also be due to different employment costs

or differences in productivity due to gender concentration in the work environment.

87

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90

Chapter 3: The role of pilot training and experience in aviation safety

The purpose of this study is to determine the effect of pilot characteristics, and
pilot training in particular, on aviation safety outcomes, such as pilot error, accident
severity, and accident rates. Although there is an enormous literature detailing the
returns to training and experience in the workplace, very little exists regarding non-
market returns to experience. This is partly due to the fact that training and experience,
even when general, is believed to have few benefits outside the labor market. One
notable exception to this is the role of experience in the determination of accident
outcomes. This paper focuses on the role of experience in aviation safety outcomes.

This work contributes to aviation safety literature in four important ways. First, it
models the probability of pilot error in aviation accident using microdata, by taking
advantage of the richness of the National Transportation Safety Board’s (NTSB) Aviation
Accident/Incident Database System (AIDS). Although aviation outcomes have been
studied using aggregate airline data, this is one of very few attempts at modeling similar
outcomes using pilot-level microdata—and the first attempt for general aviation. Second,
it models accident severity, both in terms of injury severity and in terms of extent of
damage. These estimates are first calculated conditional on accident occurrence, by using
the full sample of accidents. An attempt is then made to calculate severity and extend of
damage estimates by using a sub-sample that more closely matches the universe of pilots.
Although these estimates cannot be considerd unconditional, per se, they may more

closely match a random draw from the population of pilots. Thirdly, we attempt to model

91

accident probability by comparing sub-samples that more closely resemble the population
of both accident and non-accident pilots to the actual sample of accidents in the AIDS.

The fourth contribution of this paper relates to the scope of analysis. In this paper
we model the safety outcomes mentioned above for private flights in addition to
commercial flights. The private or “general aviation” group of flights has long been
ignored in the safety and aviation literature.

The remainder of the paper is organized as follows. In section I the topic is
discussed, and a review of the existing literature is presented. In section II the model is
developed. In section HI the data requirements are outlined and the dataset is described.

Section IV presents the empirical results and section V concluding remarks.

I. Introduction

There is a sizable literature regarding the determinants of aviation accidents—
perhaps too large, considering the relatively small number of fatalities associated with
flying relative to other forms of transportation.1 Nevertheless, economists and accident
analysts have learned much regarding the factors associated with aviation safety
outcomes. This includes analysis of the effect of maintenance, pilot error, equipment
failure, weather, and air traffic on accident rates and fatality rates (Oster and Zorn,
1989).2 Other safety-related factors studied in the literature include the structure of

flight, such as stops per trip and length of flight (Rose, 1990),3 and shifts from one mode

 

l The Department of Transportation reported 693 fatalities associated with all forms of air travel in the US
for 1999. In contrast, there were 41,611 fatalities associated with highway travel for the same year.

2 Oster and Zorn analyze the effects of factors under the airlines’ control, as well as those outside the
airlines’ control, in the context of deregulation.

3 Rose finds that a longer average flight time is associated with a higher accident rate.

92

of transportation to another (Bylow and Savage, 1991).4 Measures of firm financial
performance have also been studied in association with airline accident and fatality rates
(Globe, 1986; Rose, 1990),5 as have measures of airline experience (Barnett and Higgins,
1989; Kanafani and Keeler, 1989; Oster and Zorn, 1989; Rose, 1990).6

One characteristic is shared by all of the studies above: they relied on aggregate
carrier data. That is, in their studies data are at the carrier level, not at the flight or pilot
level. Also, none of the studies used explicit measures of pilot experience, such as
average pilot experience.7 Two studies (Phillips and Talley, 1992; Phillips and Talley,
1996) use accident-level micro data to determine the effect of pilot characteristics on
accident severity and extent of aircraft damage. In both analyses the authors find that
pilot experience has a small but significant impact on severity of accident and extent of
plane damage.8 However, their approach does not model non-linearity in the returns to
experience adequately. Also, their analysis is limited to commercial flights, and makes

no attempt to account for selection bias in the AIDS.

 

4 Bylow and Savage discuss the decline in auto travel resulting from deregulation.

5 Here the evidence is mixed. Earlier studies, such as Globe’s, found no significant correlation between
financial variables and accident rates. Later studies found that lower company profit margins are
associated with slightly higher accident rates.

6 Barnett and Higgins found that the increased number of new entrants after deregulation explained a
significant portion of the variance in fatality rates across time. Kanafani and Keeler, and Oster and Zorn
found no such relationship when looking at the effect of new entrants on accident rates, not fatality rates.
Rose found a large and significant negative relationship between carrier experience and accident rates.

7 Cumulative hours flown by the carrier were used in most analysis involving experience. This is more a
measure of firm experience than pilot experience. Although correlated with pilot experience, to the extent
that pilots acquire experience on the job, carrier experience does not take into account initial pilot
experience or different rates of pilot turnover. Furthermore, different carriers will have different average
pilot tenure, and average hours flown by each pilot.

Phillips and Talley (1992) use an ordered probit to model the extent of aircraft damage, given that an
accident has occurred. They find that every 1,000 hours of additional pilot experience is associated with a
decrease of 4-6 percent of a standard deviation of the probit index. Note, however, that one cannot say
which parts of the distribution shifted. Their analysis focuses on commercial accidents and incidents.
Phillips and Talley (1996) look at accident severity as measured by fatalities and injuries. Using OLS they
find that an increase of 1,000 hours of pilot experience is associated with a decrease of 1.4 percent of the

93

In addition to the Phillips and Talley references, three other studies used accident-
level data. Chance and Ferris (1987), Mitchell and Maloney (1989) and Borenstein and
Zimmerman (1988) looked at the effect of accidents on the equity value of airlines. In
the context of this paper this is important to the extent that firms should be willing to
invest heavily in training and hire experienced pilots if (a) training and experience do
lower accident rates or mitigate the effects of accidents and if (b) firms bear a heavy
financial burden resulting from accidents and fatalities. To the extent that markets are
efficient, a drop in equity value represents the present value of the true cost to the firm—
including costs related to a possible fall in consumer demand. All three studies use
roughly the same data.9 Chance and Ferris find that the one-day average equity loss is
1.18 percent. They do not find a significant effect on industry equity, only on own-firm
equity. Mitchell and Maloney find a similar number, 1.19 percent. However, they do a
separate analysis for accidents in which the firm was found responsible and those which
were out of the firrn’s control. The decline in equity for the at-fault crashes was 2.2
percent, while for the not at-fault it was 1.2 percent. Borenstein and Zimmerman find a
reduction of 0.94 percent, which they say amounts to roughly $4.5 million in equity loss
in 1985 dollars ($6.52 million in 2000 dollars).

Since there are no equity 1033 studies available using data from the 19803 and
19903, a simple tabulation of equity loss was done for accidents using equity data from
four major US carriers (American, Delta, US Airways and United), from 1983 to 1998.

The tabulation consisted of comparing the average stock quote before and after the

 

proportion of fatalities or injured people. Again, the population is that of commercial accidents or
incidents.

9 All studies use data from the 603 to the mid 803. Borenstein and Zimmemlan’s data start in 19603, while
the others start in the mid-603.

94

accident. In all, these carriers had 22 fatal accidents during the period of study. Due in
part to the small sample size that none of the estimates are statistically significant.
Nevertheless, their magnitudes are in line with those of the studies mentioned above. The
one-day equity loss due to the accident was 0.8 percent, slightly lower than the three
preceding studies. If one only considers accidents in which twenty or more fatalities
were involved (12 accidents), the equity loss jumps to 1.8 percent. If one considers the
most serious accidents, involving forty or more fatalities, the estimate increases once
more, to 3.2 percent. These percent losses, if represented as dollar losses associated with
common stock of the four carriers (as of December of 2000), translate to an average loss
of 6.5, 14.7 and 26 million dollars. This suggests that the accident’s magnitude, as
measured by loss of life, may be key in determining loss of equity. However, one must
again bear in mind that these figures are not statistically significant. A more extensive
sample size would likely be required to draw inferences.

The equity 1033 results suggest that although there are costs associated with
accidents, firms are mostly insulated from these costs. Indeed, this is evidence that
demand is not responsive to accidents. From Borenstein and Zimmerman’s estimates, we
saw that the average loss is 6.25 million in 2000 dollars, or a little over $156,000 per
fatality (average number of fatalities per accident is close to 40). Given the infrequency
of air accidents, an average of one every two years for major carriers, this number is quite

small.

11. Model

95

In this paper we address three types of safety outcomes. The first relates to the
incidence of pilot error in flights that resulted in an accident. The second relates to the
severity of accidents. The third relates to the probability of accident occurrence. The
first two outcomes are relatively uncontroversial, and the limitations associated with
modeling them are well known issues, such as endogeneity and selection bias. These
issues will be discussed shortly. However, in order to model accident occurrence one
would need a random sample from the population of all flights.

The AIDS data set is designed to be a record of all accidents. It contains no
information on non-accident flights. Since the dataset does not include observations
from pilots who did not have an accident, it is difficult to compare non-accident
populations with accident populations. For example, if one is to estimate average flight
hours for pilots who had accidents and compare that with average hours of those who did
not have an accident, observations on non-accidents would be needed also. One is then
faced with the daunting task of identifying observations in the accident data set which
would be representative of the population of pilots at large and use these observations as
“non-accidents”, properly weighted. A few candidate sub-samples emerge. The first is
the sub-sample of pilots who had accidents caused by mechanical failures, or the
mechanical failure sub-sample (MF). Since mechanical failures are determined mostly
by random processes, accidents in this category are hypothesized to be a random draw
from the entire pilot population. There are, nevertheless, a few problems involved with
this scheme. First, it is certainly possible that careless pilots may neglect their
maintenance and be prone to mechanical failures. Second, mechanical failures may be

more prevalent in some makes and models of aircraft, and make and model selection may

96

be endogenous, in the sense that risk-averse pilots may to some extent select aircraft
which are inherently safer to fly. This would not hold in the case of commercial aviation,
where pilots likely do not influence the company’s fleet composition. Lastly, a
mechanical failure does not necessarily result in an accident, so that this sub-population
would be composed of pilots who had mechanical failures and were unable to avoid an
accident. Therefore, problems associated with the sample selection of the entire NTSB
data set may still be present, albeit somewhat attenuated, in this sub-sample.

In the discussion above we mentioned that pilots in the accident data set may be
“worse” pilots, in that they may on average be less prudent, less experienced, have fewer
ratings and certificates, etc. A second way to select a sample which may be
representative of the entire population would be to select only those accidents in which
the pilot was not named as a cause of the accident by the FAA investigator. We will call
this sub-sample the no pilot error sub-sample (NPE). In other words, select only those
accidents in which the pilot did nothing wrong. The problem with this scheme is exactly
the opposite of that with the first scheme. Whereas we may still be disproportionately
selecting “bad” pilots with the first scheme, we may well be disproportionately selecting
“good” pilots with this scheme. After all, these are pilots who were able to avoid
mistakes in their management of the accident. A true representation of the underlying
population may well lie “between” these two sub-samples.

The selection scheme above highlights the difficulty inherent in this type of
sample selection problem. It also highlights that results from this selection process need
to be interpreted with caution, since we are unable to guarantee that the sub-population

selected is actually a good representation of the pilot population as a whole. With this in

97

mind, we will proceed with the analysis and present results from both selection schemes.
For the accident severity and extent of damage models we will present full-sample results
in addition to results obtained from the two sub-samples. For the pilot error model we
will present only the full-sample results. We will also use these selection schemes to

attempt to estimate accident occurrence.

The—aviation environment

Before proceeding with the description of the methodology and problems in
modeling the three types of safety outcome, it is instructive to describe the environment
in which pilots fly.

In this study I look at three types of flights, classified by which Code of Federal
Regulation (CFR) chapter they are operated under: part 121 flights (operated under
chapter 121 of the CFR), part 135 flights, and part 91 flights. Part 121 flights are
comprised of larger commuter and all trunk carrier flights, and will be referred to as trunk
carrier flights. Part 135 flights are smaller commuter flights of less than thirty seats and
on-demand air taxi flights; these will be referred to as commuter flights. Part 91 flights
are private flights, mostly recreational and non-commercial flights (although some small
businesses will occasionally operate under this chapter of the CFR). These flights are

referred to as general aviation flights.”

 

10 Up to now, the aviation literature has focused, almost to exclusion, on trunk carrier and commuter
flights, and has largely ignored general aviation. This bias is not without rationale: commercial flights
involve firms engaged in profit maximizing behavior, while general aviation flights, by and large, consist
of flights by private individuals. Nevertheless, since general aviation accounts for the majority of accidents
(89 percent) and fatalities (92 percent) in American aviation, we also look at pilot training and experience
in this setting.

98

In order to operate in each of these flight environments pilots must satisfy a
number of very particular training requirements, culminating in “certificates” and
“ratings” awarded to the pilots. In order to operate a non-commercial flight, a pilot will
need a minimum of a pilot private certificate.ll This certificate allows for operation of
small aircraft in good weather conditions. A private pilot may then train to obtain an
instrument rating, which would allow the pilot to fly in bad weather conditions. These
conditions are referred to as Instrument Meteorological Conditions, or IMC. Without an
instrument rating a pilot is restricted to flying in Visual Meteorological Conditions, or
VMC. All flights conducted in IMC must follow a set of rules called Instrument Flight
Rules, or IFR. Flights conducted in VMC may follow either IFR or Visual Flight Rules,
VFR. However, flights conducted under IFR are accorded greater radar and air traffic
coverage than VFR flights. In fact, IFR flights receive departure-to—landing air traffic
coverage, thus commercial operators will almost always fly under IFR—regardless of the
weather. VFR flights are common among general aviation pilots, but very rare among
commercial flights. See Table 3.13 for a description of the specific requirements that
define the existence of IMC and VMC.

In order to fly commercially, pilots will need a commercial certificate. Generally,
this allows pilots to fly small commuter and air taxi operations, which are conducted
under part 135 of the CFR. In order to fly large commuter or trunk carriers pilots will
need an air transport certificated. An air transport certificate will allow pilots to fly under

part 121 ofthe CFR.

 

1 Pilots may also operate under part 91 With either a recreatlonal certrficate or a student certlficate. Since
these pilots account for a small portion of flights, and are too heterogeneous to compare with other pilots,
we are not considering them in the analysis.

99

The principal models in this paper will be either probit or ordered probit models.
However, since we suspect that there may be significant non-linearities involved, in
particular with respect to the effect of hours flown on accident probability and severity, it
is useful to first analyze these relationships in a non-parametric framework. The non-
parametric technique used is Cleveland’s (1979) Locally Weighted Scatterplot Smoother,
or LOWESS.12 LOWESS estimates will be done for the accident probability model,
using each sub-population described above as randomly selected samples of non-
accidents. These results will be weighted to account for the different sampling
probabilities involved. For the probability of a fatality, conditional on accident
occurrence, LOWESS estimates will be obtained by using the entire sample of accidents.
In addition, estimates of the effect of total hours flown on fatality rates will also be
presented for the two sub—populations.

Several factors are likely to affect accident occurrence, as well as accident
severity. These can be classified into four categories: pilot training characteristics, other
pilot-related characteristics, environment-related characteristics, and aircraft-related
characteristics. Pilot training characteristics include factors such as (i) pilot experience,
measured by hours of flight, composition of those hours, pilot age and (ii) other training,
such as certificates and ratings. Other pilot-related variables include (i) pilot age and
gender, and (ii) behavior variables, such as filing a flight plan, wearing seat belts, and
obtaining an adequate weather briefing. Environment-related characteristics include (i)
weatlrer-related variables, and (ii) the type of flight (VFR/ IFR, commercial, scheduled).

Plane-related characteristics include (i) the airframe age, (ii) plane size and power, and

;

12 In all estimations a bandwith of 0.8 is used. Also, the lower and upper 2.5 percent of the sample are not
shown in the LOWESS graphs.

100

(iii) time since last maintenance. Note that although pilot age can be viewed as a proxy
for experience, it is also critical in another way, since younger men and women are more
likely to survive an accident, and to survive without severe injury. Since pilot fatalities
account for a large portion of fatalities (particularly in general aviation, where it accounts
for 52 percent of fatalities), differences in the pilot’s age may be picking up mostly
differences in human survivorship. To account for this, the fatality dependent variables
are calculated both to include and to exclude pilot fatalities, for the general aviation case.
The probability of pilot error is modeled with a probit regression. The dependent
variable is one if the FAA investigator listed pilot error as a cause of the accident and
zero if he did not so name him. For accident severity and aircraft damage, three separate
models are estimated. The first is a probit for accident fatality, where the dependent
variable is zero if there were no fatalities or one if there were one or more fatalities. The
second is an ordered probit for the severity of an accident, where the categories are:
minor or no injury, severe injury, and fatal injury. I 3 The ordered probit coefficients tell
us by how many standard errors the injury index’s distribution shifts when an explanatory
variable changes by one unit. Since this is not an intuitive way to think about accident
outcomes (or any outcome, for that matter), we have reported both the ordered probit

coefficients and the marginal effects coefficients.14 The third model is a Tobit regression

 

‘3 The NTSB actually codes accident severity with four categories, no injury, minor injury, severe injury.
and fatality. Since we see very little qualitative difference between the first two, they have been combined
into a single category.

14 What we are interested in is by how much the probability of fatality, severe injury, and minor/no injury
change when an explanatory variable changes. For the first category (minor/no injury) the marginal

coefficient is KE%E(R = _¢(}fl)g, for the second it is KELLER = (_¢ (Ep)_¢(fl _}'fl))fl , and for the

last it is flP=¢(fl_}/3)5.Their respective standard errors are ¢o(}’o)V(l’o)" and ¢t(l’t)V(}’t)"
I

Where mitt/mo, «a wot—W)» 70=’—(/3'X)/3X”71=(1-#)1-(/3’X)5X’-

101

of the proportion of fatalities in a given accident, where the truncation is at zero and one.
A set of models for aircraft damage will also be estimated, where categories for the
ordered probit are no damage, minor damage, severe damage, and destroyed. Accident
occurrence is also modeled with a probit regression. Here the dependent variable is a
dummy equal to one if the pilot was involved in an accident, and zero otherwise. This is
the only estimator that needs to be re-weighted to account for the fact that we have no
non-accidents in the sample. The re-weighing procedure is described below.

Previous mention was made of the importance of both estimating models for sub-
samples that are more representative of all pilots. This is so because one cannot, a priori,
observe pilots who are likely to be in an accident. It is reasonable to assume that pilots
involved in accidents are likely to have fewer hours of flight experience and be less
“prudent”. Furthermore, they are also less likely to be flying a commercial flight, and
less likely to be flying a larger power or larger capacity plane. Parameter estimates of the
above variables, based on this sub-sample, may be inconsistent, to the extent that one of
these variables (probably most of them) will be correlated with the probability of having
an accident. On the other hand, one must recognize that sometimes the question of
interest is the probability of fatality, conditional on accident. For example, if one seeks to
implement safety enhancements designed to reduce fatalities, the target population may
well be those who are likely to have accidents. Therefore, we obtain conditional
estimates, by using the full sample of observations. We also obtain estimates more
closely representative of the entire pilot population, by estimating the model for our two

sub-samples: NPE and MF. The equations being estimated are:

102

Pilot error probability

(1) P(error) = (P(fllT + ,BZX + ,B3Y + ,842)

Severity outcome equations

(2) P.- =<I>(7.T+72X +73Y +7.2)

R =1-<l>(6lT+52X +63Y+64Z)
(3) P2 =1—<l>(6‘,T+62X +63Y+54Z-c,)—P1
P3 =<D(61T+52X +63Y+64Z—c2)

(4) pf =n1T+n2X +n3Y+n4Z+e

Accident probability

(5) P(accident) = <1>( fllT + ,62X + ,63Y + 642)

Equation (1) is the probit equation for pilot error; equation (2) is the probit equation for

severity of the extent of aircraft damage; equation (3) is the ordered probit equation for

the same; equation (4) is the tobit equation for proportion of fatalities and proportion of

accidents in which the aircraft was destroyed; the truncation is at 0 and 1. Finally,

equation (5) is the probit for accident probability.

In the above equations we have: P, denotes the probability of outcome i, either a

fatality (in the case of the severity models) or aircraft destroyed (in the case of the extent

of damage models). Pf denotes the proportion of fatalities in a given accident. T is the

vector of pilot training characteristics, X is the vector of other pilot-related characteristics.

Y is the vector of environment-related characteristics and Z is the vector of aircraft-

related characteristics.

103

Parameter estimates for different types of flights (general aviation, trunk carriers
and commuters) are likely to be quite different. To account for this, separate models are

estimated separately for each category.

Weighing procedure

Two different probit models are estimated for accident probability. In the first we
use the MF sub-sample as the sample of non-accidents. In the second we use the NPE
sub-sample as the control group. The weighing procedure then consists of increasing the
weight of the sample we treat as non-accidents, so that they reflect the inverse of the
proportion of non-accident pilots. Weights for accidents are equal to unity since the
AIDS is a record of a_ll accidents. On the other hand, non-accidents have very large
weights, typically in the high hundreds. This reflects (l) the small proportion of pilots
who have accidents in any given year, and (2) the small number of observations in the
non-accident control group (11 percent for the NPE and 13 percent for MF). Both the

NPE sub-sample and the MF sub-sample are re-weighted.15

 

15 In order to obtain adequate weights for these sub-samples, we must rely on the FAA’s estimates of
accidents per flight hour, which are tabulated by year and by CFR classification (trunk carrier, commuter
and general aviation). We then convert the FAA’s estimates of accidents per hour to accidents per pilot, by
multiplying accidents per hour by the average number of hours flown by pilots, again, by year and CFR
category. The estimate of the average number of hours per pilot is obtained from the accident/incident
databases’ question “hours flown last ninety days” and by expanding that value to 365 days. We now have
an estimate of the average number of accidents per pilot, by CFR type and year. Since the
accident/incident is a complete record, we know what the number of accidents is. If we assume that each
pilot has at most one accident per year, we can then compute the number of non-accidents by subtracting
the number of accidents from the number of pilots. We know how many observations are in our two sub-
populations of non-accidents. Therefore we can compute their sample inclusion probability by dividing the
number of observations in the data set by the estimate of the number of non-accidents in the population.
This probability is then sealed to account for missing observations (observations for which some of the
covariates were not recorded or were not validly coded are considered as missing). The scaling is done by
multiplying the inclusion probability by the proportion of valid (non-missing) observations. Note that the
sub-populations are not eliminated from the original accident sample. Rather, the entire accident sample is

104

III. Data

In the introduction the data was briefly described. Here we describe the data in
detail. The data used are aviation accidents from the NTSB’s Accident/Incident Database
System for the years 1983-1998. The dataset includes pilot-related variables such as age,
gender and pilot experience. The most important pilot experience measure is pilot flight
time.16 Pilots with more flight time are less likely to be involved in an accident or
incident. Also, one can postulate that these pilots would also be able to better manage an
accident, mitigating the extent of accident damage or severity. It is reasonable to expect
the effect of flight time to be plane-specific and to expect that proportion of time spent as
pilot-in-command (PIC) may have a separate impact on outcomes than total time. Thus,
four variables for flight time are included: total hours of flight, proportion of time in the
make and model flown, and the proportion of total hours as PIC. For general aviation
equations, total hours are entered in spline form, in order to capture the dramatically
different slopes associated with the first few hundred hours of flight versus higher levels
of flight time.17 In the case of the probability of pilot error, a visual inspection of the top

panel of Figure 3.2 reveals a clear node at approximately 1,800 hours. For the fatality,

 

preserved, and the sub-sample is added back in with the weights as above, in effect replicating the sub-
sample. Finally, the weights in the analysis are then just the inverse of the estimated sample inclusion
probabilities that have just been calculated. In other words, let hr} be the number of hours flown in year i
and flight type j; let up be the number of accidents, and p,-,- the total number of pilots; let q,-,- be the number of
pilots without an accident and let so- be the number of accidents (or pilots) in our non-accident population.
Then the sampling weight for the non-accident population, w”; is obtained by:

(1) aij/pij = aij/hij x hij/pij

(2) Pij a alj/pij xal’j

(3) qr,- . pr). or,- (if we assume at most one accident per pilot)

(4) Wij a qij/Sr'j
Flight time variables available include: total time, total time as pilot in command (PIC), total time in the
last 90 days and in the last 30 days. Furthermore, separate tabulations are available for all aircraft, and for
the make and model flown.

16

105

severity and extent of damage equations—equations (2)-(4)—Figures 3.3 and 3.4 reveal a
node at 800 hours. For the weighted accident probability probits seen in Figure 3.5, the
node is clearly shown at 1,200 hours. In most of the commercial flights a visual
inspection of the non-parametric results suggest that flight hours and hours squared and
cubed will adequately capture non-linearities. The only possible exceptions are for
fatality probability and accident probability for trunk carriers (see bottom panel of
Figures 3.4 and 3.5). However, when the commercial models were estimated with a
spline they did not perform as well as the polynomial specification. Therefore, we kept

the polynomial specification.

Pilot training

Before proceeding with the model, it is useful to explain the training variables we
are using and how they relate to the aviation industry. The main training variable in the
study is total hours flown and, to a lesser extent, the proportion of those hours as pilot-in-
command. As in the conventional labor literature, these variables reflect the sum total of
all pilot training, as well as the effect of on-the-job training. We also have three
certificate variables: private pilot certificate, commercial certificate and air transport

certificate.18 We also know if the pilot is instrument-rated.

 

17 Splines are estimated subject to the restriction that the function be continuous at all points.

18 All certificates require a combination of ground and flight school. They also require passing both a
written and a practical exam. An instrument rating requires approximately 120 hours of flight training. In
addition, there is a minimum number of hours in instrument conditions, a minimum number in cross-
country flight, and a minimum number of landings performed in instrument conditions. A commercial
certificate requires logging 250 hours, which must include a minimum amount of hours of flight
instruction, a minimum number as pilot in command. It also has requirements as to time spent in various
types of flight (cross country, IFR flights, etc.), as well as number of takeoffs and landing. It also requires
hours in different types of planes. Air transport certificates require a minimum number of flight hours
logged in addition to their training requirements, which are the most detailed and stringent.

106

The private pilot certificate is the lowest form of certificate and everyone in our
sample must have at least this certificate. The instrument rating trains pilots how to fly in
adverse weather conditions, or IMC; it is required of all commercial pilots. However,
one must note that pilots who do not have the instrument rating are limited to fly in good
conditions. Therefore the instrument rating has two effects. The first is the training
effect mentioned above; the second is to eliminate the flight conditions restriction, so that
the pilot may now fly in low/no visibility conditions. It is not possible to determine what
the net effect will be. The commercial certificate is required for pilots who fly
commercially, but are not involved in transporting passengers. These certificates are of
limited use because they are required for entry into the different parts of the industry;
however, they are the only measure of direct training available. As mentioned, every
trunk carrier pilot must have an air transport certificate. Therefore, this certificate
measures the lowest possible training level of trunk carrier pilots. Similarly, depending
on what activity the firm is operating (transporting passengers or transporting cargo),
pilots of commuter flights must have either an air transport certificate or a commercial
certificate. Here, there is some variability in the type of certificate, but not much.
Commuter pilots also, by and large, have instrument rating. The only instance in which
we can observe the effects of the training associated with these certificates is in non-
commercial flights, or general aviation flights. The drawback here is that we have no
reason to suspect that training designed for the commercial arena will have the same
effect on the personal and recreational arena, which is characteristic of general aviaiton.

Most training of commercial pilots’ training is not represented by the training

certificates in the NTSB database. In fact, training certificates are usually obtained prior

107

to a pilot’s employment, either as part of a two or four-year undergraduate program, or in
an aviation course designed to award the pilot the particular training certificate. This
training is mostly paid by the pilot, although airlines will often subsidize a pilot’s training
and offer them employment after graduation. Commercial pilots—and trunk carrier
pilots in particular—undergo ongoing training throughout their careers, mostly paid in
full by the firm.19 Pilots are required to pass a “check ride” twice a year, conducted by
the FAA. Furthermore, for commercial flights, every time a pilot is to fly a different
make and model aircraft he is trained and certified in that aircraft. This consists of
ground school, simulator flight hours, as well as real-world hours. All of this training is
not represented in the certificates, although it is represented by the total flight hours and
by the proportion of flight hours as pilot-in-command.

The last pilot-related class of variables is those associated with pilot behavior.
Among these we include the use of seatbelts and shoulder harnesses, the filing of a flight
plan,20 and obtaining of a preflight weather briefing.21 Note that both the weather-
briefing and the seat belt and harness variables are also correlated with pilot “prudence”,
and in this sense may belong in the pilot error, accident severity and extent of aircraft
damage equations. To account for this we include the flight plan dummy variable in all

equations (indicates if a pilot filed a flight plan) to capture pilot prudence. This is only

 

19 Of course we know from the training literature that whether the firm or the employee pays for training is
not relevant.

20 The FAA recommends that pilots always file a flight plan. A flight plan, even when not required, allows
officials to track a flight and provides almost immediate warning of a missing plane. It is, however, of little
use in preventing an accident or mitigating its immediate consequences. Therefore, the flight plan variable
is used only as a proxy for pilot prudence, to the extent that prudent pilots will file more often than less
prudent pilots. This discussion is not relevant for commercial aviation, since virtually all flights are
conducted under IFR rules, and thus require a flight plan be filed.

2‘ It should be noted that often when a fatality is involved the investigator is unable to determine if a
weather briefing was obtained.

108

applicable to general aviation flights, as the vast majority of commercial flights file flight
plans.

Environment-related variables are important factors in determining accident
outcomes. The dataset includes very detailed environment-related information. The first,
and perhaps most important, is weather. To control for weather, a dummy for the
existence of VMC is used. This is expected to be highly correlated with pilot error, to the
extent that pilots are more likely to commit mistakes in poor weather conditions. It is
also certainly important for other outcomes as well as for accident rates. One expects that
flights conducted in VMC will be less prone to accidents, and conditional on an accident,
may be less prone to fatalities or severe injuries. The same is true, to a lesser extent, of
night flying. Flights conducted during daytime enjoy greater visibility and are less
susceptible to spatial disorientation. A dummy for night flying is included in all
equations.

Since scheduled flights may be associated with different accident rates, a dummy
variable for scheduled flight is also included in the selection equation. This is only
available for the commuter and trunk carrier equations, since there are no scheduled
flights conducted in general aviation.

Characteristics associated with the aircraft being flown will also affect accident
rates and outcomes. In particular, larger aircraft tend to be safer than smaller aircraft. On
the other hand, aircraft with more seats, ceteris paribus, are more likely to have at least

one fatality or at least one severe injury. Thus, a continuous variable for the number of

109

aircraft seats is included.22 For pilot error, we postulate that larger aircraft have
safeguards to reduce the incidence of pilot error. A continuous variable for airframe age,
in years, is also included, as these older aircraft may be more susceptible to accidents,
and may be more dangerous than newer aircraft. To capture the effect of aircraft
maintenance on accident probability, a continuous variable for time since last inspection
is also included in the accident equation. We must point out that this does not account for
the fact that some planes will log more hours than others, and a greater time between
inspection is not necessarily evidence of maintenance neglect. Lastly, pilots who fly
more often are more likely to be involved in accidents, therefore the number of landings
performed in the last 90 days is also included in the accident equation. Since this
variable may also be considered to be a measure of recent experience, it is included in all
equations. In summary, the following is a list of variables included in each estimation:

Total hours and spline (general aviation only)

Total hours flown (commercial equations only)

Total hours flown squared (commercial equations only)

Total hours flown cubed (commercial equations only)
Proportion of hours in make and model

Proportion of hours as Pilot in Command (PIC)

Gender

Age

Dummy variable for a seat belt being used (severity only)
Dummy variable for a harness being used (severity only)
Dummy variable for no flight plan filed (general aviation only)
Pilot is instrument rated (general aviation only)

Pilot has Commercial certificate (general avaition only)

Pilot has Air Transport certificate (commuter and general aviation only)
Dummy variable for WC

Aircraft size, as measured by seats

Airframe age

Number of landings in last 90 days

 

22 We could also include aircraft size, as measured by the total pounds of thrust that the aircraft is capable
of. However, since these variables are highly collinear, we opted for inclusion of only the first of these two
variables.

110

The NT SB data set contains 43,279 observations, from 1983 to 1998. However,
we only use observations for which sampling weights can be obtained. Since the FAA
only reports accidents per hour of flight for commuter (part 135), trunk carriers (part 121)
and general aviation (part 91), only these types of records are used.23 In order to reduce
the heterogeneity in pilot characteristics, recreational, student, military and foreign pilots
are excluded from the sample, as were accidents involving homebuilt airplanes. An
additional concern arises because of serious underreporting of aviation incidents.
Although we refer to all observations in this analysis as accidents, a small proportion of
the AIDS observations are what is referred to as an incident. Incidents can be thought of
as mild accidents.24 This is particularly serious because the underreporting may be
systematically related to pilot experience or training, although one cannot be sure in
which way this correlation would go. One option to deal with this problem would be to
do the analysis for aviation accidents only. Unlike incidents, aviation accidents are hard
to conceal, and severe penalties are applicable for those who attempt to do so.
Underreporting of aviation accidents would then seem much less of a problem than
underreporting of aviation incidents. Since there are relatively few incidents in general
aviation (1 percent) or commuters (12 percent) flights, little would be lost in terms of
precision, and thus only accidents are used in these equations. This is not true of trunk
carriers, where incidents account for the majority of events (54 percent). Furthermore,

since aviation accidents are defined as events that either substantial aircraft damage or

 

23 These flights account for 93 percent of all flights. Flights conducted under other chapters of the CFR,
such as agricultural flights, or international carriers, are excluded.

24 The NTSB defines an accident as “an occurrence associated with the operation of an aircraft which takes
place between the time any person boards the aircraft with the intention of flight and all such persons have
disembarked, and in which any person suffers death or serious injury, or in which the aircraft receives

111

severe or fatal injury, the dependent variables in the severity and damage extent equations
would be incidentally truncated. Therefore, for trunk carriers separate estimates are done
for accidents and incidents and only for accidents. It should be noted that for incidents
pilots only report total flight hours, and do not report hours as pilot in command or hours
in make model. The main trunk carrier estimates, done with incidents, will not have
estimates for the proportion of time as pilot in command or the proportion of time in
make and model. The final dataset includes 40,921 observations. However, when only

observations with no missing values are used, the sample size falls to:

General Trunk

Aviation Commuter Carrier
Pilot error/ Fatality/Severity models 12,851 1,083 671
Extent of damage models 15,649 1,253 751

IV. Results

Summary statistics are presented in Table 3.1. We see that characteristics vary
significantly between the three aviation categories. First notice the difference in the
accident rates between the three categories. In this sense, commuters and general
aviation flights are very similar, with an accident rate of 18 1/2 and 19 1/2 accidents per
1,000 pilots per year, respectively. Trunk carriers have a much lower accident rate of 1.7
accidents per 1,000 pilots. One must note that these accident rates are per pilot and not
per hour or per takeoff/landing. Since commercial pilots fly more often than do general

aviation pilots, their accident rates per hour will be substantially lower. Among general

 

substantial damage.” An incident is defined as “an occurrence other than an accident, associated with the

112

aviation pilots we see that half have instrument training, 35 percent hold commercial
certificates and 10 percent hold air transport certificates. Among commuter pilots, 64
percent have commercial certificates and 57 percent have air transport certificates. All of
them hold either of the two certificates, a requirement for Operation under part 135. All
are instrument rated. All of trunk pilots are instrument rated and hold Air Transport
certificates, which are required for operation under part 121. Commercial pilots have
more experience than general aviation pilots do, with an average of almost 5,800 hours
for commuter pilots and almost 13,000 for trunk carriers versus an average of 2,600 hours
for their general aviation counterparts. However, the proportion of hours in make and
model is lower for commercial pilots (0.21 for commuters, 0.27 for trunk carriers) than
for general aviation pilots (0.32). This is to be expected, since general aviation plane
turnover is much lower than commercial plane turnover. The percentage of hours as PIC
is higher for commuters (86 percent) than general aviation (79 percent), but it is much
lower for trunk carriers (59 percent).

A cursory inspection of the fatality and damage means in Table 3.1 shows that
these are much worse for the general aviation Q11 the commuter population than they are
for trunk carriers. Trunk carriers have a very low fatality rate: only four percent of trunk
carrier accidents result in fatalities. Compare this to 20 percent for both general aviation
and commuters. Other safety outcomes mirror this result.

When considering accident rates, one must, nevertheless, keep in mind that these
are accident rates per pilot, not per hour. Therefore, ex ante, one could expect these rates
to be higher for commercial pilots—both commuter and trunk carriers—given that they

have far more flight hours than do general aviation pilots. This is not the case.

 

operation of an aircraft, which affects or could affect the safety of operations.”

113

Non-parametric results

Before reviewing the discrete and OLS models, it is instructive to look at non-
parametric results. N on-parametric results are important, for they capture the non-linear
functional relationship between safety outcomes and explanatory variables. In this case
we are interested in the non-linear relationship between pilot experience, as measured by
total flight hours, and pilot error, fatality rates, and accident rates. For fatality rates we
present both full-sample results and results for the sub-samples, which throughout this
paper have hypothesized to be more representative of all pilots—not just pilots with
accidents. As mentioned previously, the non-parametric technique used is LOWESS.
The main advantage of LOWESS is that it is robust to outliers and “far out” response
variables.25

In Figure 3.1 we can see the estimated distribution of flight hours, for both
general aviation and commercial flights. We should note that all non-parametric results
are obtained by using a LOWESS bandwidth of 0.8. Also, since there is enough
heterogeneity between the three types of flights being studied, separate estimation was
conducted for each. One first sees that average hours are higher for trunk carriers than
for commuter, which in turn are higher than general aviation pilots. The distribution of
the general aviation pilots also seems to be much more concentrated than the other two
categories (at about 800-1000 hours), with the distribution of trunk carriers the most

being spread out. Commuter hours peak at 3,500, but fall slowly thereafter.

 

25 Median smoothing techniques are also resistant to outliers. Results using median smoothing produced
similar results.

114

In Figure 3.2 we see the first bivariate non-parametric result. The top panel
shows the non-parametric relationship between pilot error probability and thousands of
flight hours for general aviation. The middle panel shows the results for commuter
aircraft and the bottom panel for trunk carriers. For general aviation there is a monotonic
relationship, with most of the gains in pilot error coming within the first two thousand
flight hours. The returns decrease markedly after the first 1,800 hours. For commuters
we also see considerable gains concentrated around the first few thousand hours of flight.
However, for commuters the gains not only level out, but actually reverse themselves at
higher levels of flight hours. Thetrunk carrier panel, again, shows marked reductions in
pilot error probability associated with the first few thousand hours of flight. In this case
the decrease is not as dramatic as in, say, the general aviation case, and is not
concentrated along the first couple thousand hours. The gains persist linearly until 6-7
thousand hours of flight, then level off (or even increase slightly).

Figures 3.3 and 3.4 present the results for the probability of a fatality and the
probability of the aircraft being destroyed. In both figures estimates are presented
separately for three categories: (1) all observations, (2) only observations from the MF
sub-sample, and (3) only observations from the NPE sub-sample. For general aviation
we see that both the slopes and the levels are smaller as you progress from (1) to (3).
This is consistent with the hypothesis that the MF strategy may still over-sample “bad”
pilots, but that the NPE strategy may in fact over-sample “good” pilots. However, what
is most remarkable is that flight hours tend to (at least initially) increase both the
probability of fatality and the probability of the aircraft being destroyed. This initial

effect is seen until roughly 1,200 flight hours. There can be several explanations for this.

115

On

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sug

6X1

prt

866

Fig
ide
Sin
gel
IOU

rate

One is that as rookie pilots gain experience they may become overconfident and thus
more prone to be involved in a serious accident. Another is simply that as a pilot gains
experience, he may better able to eliminate minor accidents than major accidents. In
either case one would observe the initial increase in fatality rates. The top panels also
suggest that for the multivariate analysis, pilot experience would be well modeled by a
spline, with a node at 1,200 flight hours.

For commercial flights one observes a myriad of patterns, none of which are very
informative. For trunk carriers fatality rates increase, then decrease slightly, and then
increase again. For commuters we see a slight increase for both the MF and NPE sub-
samples, but a slight decrease for the entire sample. For trunk carriers and—to a lesser
extent commuters—there is a marked non-linearity. However, when one considers the
probability of having the aircraft destroyed, the patterns change. For trunk carriers we
see a monotonic decline in probability. The decline is more pronounced for the MF sub-
sample. For commuters both sub-samples show an initial decline followed by an
increase, and a monotonic decline for the full sample estimate. Again, Figures 3.3 and
3.4 suggest a cubic polynomial for the commercial flights.

Accident probability results are presented in the last non-parametric Figure,
Figure 3.5. Two estimates are presented in each panel, one using the MF population to
identify non-accidents and the other using the NPE population. Both techniques deliver
similar results, with the exception of commuter pilots, for which results are mixed. For
general aviation we see a marked decrease in estimated accident rates, corresponding to
roughly the 1,200 hours of flight. After that there is little or no reduction in accident

rates (NPE), and a slight increase in accident probability (MF). This result motivated

116

modeling accident probabilities for general aviation with a spline function, with a node at
1,200 hours. For commercial pilots we likewise see a large initial reduction in accident
rates, albeit less dramatic. For trunk carriers the effect seems to level off at about 6,000
hours. However, for the MF specification, there is a muted decrease, followed by a slight
increase and another decrease. For commuter flights there is little discemable trend for
the MF specification, although the NPE specification shows a sharp decline, followed by
a dramatic increase. Based on these results both the trunk carrier and the commuter

equations will be modeled with a cubic polynomial.

Multivariate results

The most obvious effect of training and experience on safety is its effect on pilot
error. One could indeed argue that other outcomes are in fact a function of the reduction
in pilot error. Therefore, the first result discussed is the pilot error probit results of Table
3.2. The flight hours results strongly mirror the non-parametric results we saw
previously. For general aviation, for every thousand flight hours we see a corresponding
reduction of 6.2 percentage points in the probability of pilot error. This number
decreases to 0.2 percentage points after the first 1,800 hours. In addition to the
magnitude, the results are very significant, at any conventional level. The other training
variables tell a similar story. We see that it is not only the total flight experience which is
driving the changes in pilot error, but also the proportion of those hours spent as pilot-in-

command, and the proportion spent in the make and model concerned. For the proportion

117

in make and model, we see that a 0.3 increase in the proportion of time in make and
model (say, from 0.5 to 0.8) is associated with a one percentage point decrease in the
probability of pilot error. For the proportion of time as pilot-in-command the magnitude
is twice as big—and in both cases the results are extremely significant (at the 1 percent
level).

General aviation presents an interesting medium in which to evaluate certificates
and ratings. This is because there is very little variability in these measures outside
general aviation: commercial flights require certain certificates and in all cases require an
instrument rating. The first pattern to observe is that all certificates and training variables
are associated with lower incidences of pilot error. These results are significant for both
the instrument rating and the air transport certificate. For the instrument rating, we find
that instrument-rated pilots are 1.7 percent less likely to be at fault in an accident. For the
air transport certificate the magnitude is somewhat larger: pilots with this certificate have
a probability of pilot error 2.2 percentage points smaller than those without it. The last
training-related variable is age. Although older pilots are in fact more likely to be at fault
in an accident, the result is modest: one percentage point less more likely for every 10
years.

The experience and training results for commercial aviation are mixed. For
commuters we see no significant effect of increased pilot experience of pilot error
probability. Furthermore, we also find no evidence that the makeup of these hours affects
pilot error either. The only training variable that is significant for commuters is the air
transport certificate. Pilots with this certificate are almost eight percentage points less

likely to be at fault in an accident. This is a bit puzzling, since we do find significant

118

experience results for trunk carriers, all consistent with what one would expect. It is
certainly possible that experience and training affects pilot error through a censoring
mechanism. For example, more experienced pilots may be able to eliminate less severe
accidents—where pilot error is not at play—then these observations would be censored in
our data. This is, however, at odds with the results from the two other flight groups, and
we have no a priori reason to believe that censoring would occur only for commuter
pilots.

Table 3.2 is the only table in which results for trunk carriers are separated for
accidents and incidents and for accidents alone. In all other estimations we present the
results for accidents + incidents together. This is in part because the small number of
accidents does not allow us to draw significant inferences. However, in the case of pilot
error we see that the results for both accidents + incidents and for accidents alone are
quite similar. They are more significant for accidents + incidents, no doubt because of
the larger number of observations, but are the same sign in both cases. The only
difference is that in the case of accidents alone the results are larger in magnitude—
roughly twice as large across the board. In both cases we see large returns to experience.
In order to better visualize these effects, the predicted probability of pilot error is graphed
for different levels of flight hours in Figure 3.6. In the bottom panel, which corresponds
to trunk carriers, we can see that the first four thousand flight hours cuts the probability
of pilot error in half—from 60 percent to 30 percent. This is encouraging and speaks to
the potentially large effects of experience in reducing pilot error.

It is unclear exactly how filing a flight plan could affect pilot error. Although a

flight plan requires some planning, and thus may reduce the workload on the pilot in-

119

flight, one must be mindful of the endogeneity of this variable. Pilots who file a flight
plan may in fact be more cautious pilots, and therefore the variable may be picking up
prudence. In any case, filing a flight plan certainly reduces the incidence of pilot error:
general aviation pilots who file a plan are almost five percentage points less likely to be
at fault in an accident.

Lastly, although weather is certainly not the focus of this paper, we cannot ignore
the enormous magnitude of the VMC variable. Pilots who fly in VMC are much less
likely to err. This result is extremely significant, and is the only result that is true across
all flight categories: general aviation and commercial flights. The magnitude of this
effect varies from 19 percentage points to 31 percentage points—in all cases a
remarkable and sobering result.

A second aspect of training and aviation safety is the role of training in mitigating
the results of an aviation accident. These results refer to both aircraft damage and to
personal injury. It is reasonable to expect that some facets of pilot training may better
prepare a pilot to deal with an accident, and in so doing reduce the severity of the
accident. In the non-parametric section we saw that in some cases experience tends to
increase the probability of a fatal accident. Nevertheless, one must always keep in mind
that, for our purposes, there are three categories in both the severity of injury and the
extent of damage analysis. This means that an increase in one category may shift
probability into either of the other two categories. We deal with this, to a certain extent,
by using an ordered probit and reporting the marginal effects for each category. Since
there are only three categories, interpretation of the ordered probit is not as complicated

as it is in the case of multiple categories. If two adjacent parameter values are positive

120

(negative) that implies that the net effect of a marginal change is to shift probability mass
out of (into) the remaining category. Lastly, we estimate the pr0portion of fatalities in
each accident. As can be expected, this variable is truncated at 0 and 1, since the most
severe accidents will likely kill all passengers and the milder accidents will not kill
anyone. Therefore a tobit estimator is used for the proportion killed.

Tables 3.3 and 3.4 present the general aviation probit and ordered probit results
for accident fatality and severity, respectively. In both tables flight time is modeled with
a spline. The spline node is at 800 hours, so that the slope coefficient is allowed to differ,
before and after 800 hours. Although the flight time estimates, by and large, confirm the
non-parametric results (a sharp increase, followed by a modest decrease), they are not
significant. In fact, the only significant result is an initial (up to 800 hours) very
significant negative effect of hours on the probability of a fatality in the NPE sub-sample.
This effect is a 0.6 percentage point decrease in the probability of an accident for each
hundred hours up to 800. The only training results that are consistent in sign across all
specifications are the hours makeup variables: proportion of time as pilot-in-command
and the proportion in make and model. For the proportion as pilot in command we see
that a 0.1 increase in the proportion is associated with a half percentage point decrease in
the probability of a fatality, for both the full sample and the MF sub-sample. Lastly, we
see that, as in the pilot error equation, having an air transport certificate is significant, and
is associated with a four percentage point reduction in the probability of a fatality.
However, this last result is not robust to the sample type, and is only present in the full

sample.

121

An inspection of the ordered probit results largely validates the probit results,
with one important exception.26 Hours beyond 800 have a negative and significant affect
on fatality probability, when the analysis is done using the entire sample. Here we see
that an increase in flight hours beyond 800 tends to shift probability mass out of both the
“fatality” and the “severe injury”. In other words, it appears general aviation pilots,
conditional on accident occurrence, are able to transform some fatal and severe accidents
into those with only minor injuries or no injuries. With respect to both the proportion of
time as pilot-in-command and the air transport certificate, again, the shifting is from
fatality and severe injury to the more innocuous “minor/no injury” category. Since the
ordered probit coefficients for both the “fatality” and the “sever injury” categories are
comparable, the severity outcomes may actually be best modeled by a probit of fatality or
severe injury. This is done and the results are reported in Table 3.9. The results are
somewhat different in that in the fatality/severe injury probit, the returns to experience
are much larger and significant. On the other hand the air transport certificate is not as
significant. Otherwise, the results are comparable.

The last interesting result in Table 3.3 is pilot gender. Male pilots are four
percentage points more likely to be in accidents with fatalities. It is possible that this
figure is picking up survivability differences between the male and female pilot. If
women do in fact survive accident trauma more than men do, the parameter estimate may
be picking up this differential. To deal with this, the fatality model is estimated for 1&1;
pilot fatalities only. This way, the only link between the pilot and the fatality would be

through passengers, eliminating the survivability issue. However, for this second model

 

26 Ordered probit results are only reported for the “all observations” category, and not for the NPE and MF
sub-samples.

122

the results are identical—a 4.2 percentage point increase in fatalin rates associated with a
male pilot. This suggests that the mechanism has little to do with survivability, and more
to do with other differences in male and female characteristics.

The extent of damage table (Table 3.4) echoes the previous results, if attenuated.
Here we see that, again, the proportion as pilot in command reduce the probability of an
aircraft being totally destroyed. We also see a negative coefficient on the air transport
certificate variable, and—again—a positive result for the male dummy. The results are
only significant in the full sample. Nevertheless, they are similar across all three samples
(full sample, MF, NPE), and the magnitudes are similar to those in Table 3.3.

At first, the result of the instrument training variable may be somewhat of a
paradox. We see that pilots with that rating, even controlling for weather and other
conditions, seem to be associated with higher probabilities of aircraft being destroyed.
Although this same result was not statistically significant for the fatality equations, it was
of the same sign and similar magnitude. One would expect the opposite: pilots who
receive this training would be better able to manage an accident and mitigate the
nefarious effects of the accident. While this may be true if we randomly assigned
instrument-trained and non-instrument-trained pilots into accident situations, this is
certainly not the case here. An IFR rating not only indicates that the pilot received the
training, it also allows the pilot to legally fly into hazardous conditions which his non-
rated counterpart would not legally be able to fly in. Many of these hazards may not be
properly picked up by the weather and VMC control variables. Therefore, we may in fact

be observing the effect of the removal of a safety restriction on safety outcomes, rather

123

than the effect of pilot training. If this last hypothesis is correct, then the IFR results seen
in Tables 3.3 and 3.4 are perfectly reasonable.

When interpreting the other training variables—commercial and air transport
certificates—one must be weary that these variables are extremely endogenous. Since
these certificates are required by certain aviation occupations, they are highly correlated
with pilot occupation in the airline business.27 And in so being, they will be correlated
with a myriad of other characteristics that professional pilots have and others don’t. To
the extent that these characteristics are, at best, imperfectly measured in the variables
available to us, they will be heavily biased due to an omitted variable problem. That
much said, there is no surprise that their signs are always negative (i.e. those who have
the certificate have lower fatality probabilities and aircraft destroyed probabilities), of
large magnitude, if of varying degrees significant. In both cases, the presence of a
certificate shifts probability mass away from the most severe outcome, and increases
probability mass in the severe injury and minor injury categories.

The commercial equation results (Tables 3.5-3.8) have fewer significant
coefficients than the general aviation equations. Part of this is due to the fact that there
are fewer commercial observations. However, when present, the results tend to be as
expected. Flight hours turns out to have, generally, the correct sign. That is, more hours
are associated with less severe outcomes. In commuter equations this effect is
insignificant. A test for the joint significance of all hours variables shows that they are
only significant for the trunk carriers and only, and only for the the NPE sub-sample. The

exact shape of the hours curve depends on the sample, but tends to follow the non-

 

27 For example, pilots are required to carry an air transport certificate in order to operate under parts 121 of
the CFR.

124

parametric results. The proportion of time as pilot in command and the proportion of
time in make and model have a negative impact on severity outcomes for commuters, but
neither is statistically significant—in both the severity and the extent of damage
equations.

We have omitted both the commercial certificate and the instrument rating
variable from the commercial equations. We included the air transport certificate in the
commuter equation. The coefficient, as expected, is negative (i.e. indicating a reduction
in severity and extent of damage outcomes) but in all specifications is not significant.

The last set of accident severity results presented is those in Table 3.10. Table
3.10 does not model the probability of fatality (or another outcome category). Rather, it
models the proportion of people who were killed with a tobit. The estimates are similar
to the probit estimates. Results for the full sample are reported. For general aviation,
again we see large albeit statistically insignificant flight hours results. These are in line
with both the probit and the ordered probit severity results. Also, again we see a large
and significant effect of proportion of hours as pilot in command, with magnitudes in line
with out probit estimates. The same is true for the proportion of hours in make and
model. In the commercial flights equations we see an absence of any flight hours effects,
a result similar to the full sample probit results. In fact the only significant results are
those for VMC and night flying for the commuter equation—an effect ubiquitous
throughout all of our analysis results. For trunk carriers the only significant result is a
negative coefficient on male dummy. This is at odds with the positive coefficient found
in most of the general aviation equations, and suggests that gender plays very different

roles in outcomes for the two types of flights.

125

Tables 3.1 l and 3.12 present the probit results for the accident probability. We
left these tables for last as the identification strategy used to obtain a sample of “non-
accidents” is contentious. However, with this in mind, we will discuss the results.

For general aviation one can see that all the experience-related variables are
significant at conventional confidence levels. One can also observe that the effects are in
the expected directions. Total hours of experience reduce the chance of an accident by 0.6
percentage points (MF) and 1.0 percentage points (NPE) for every thousand hours of
flight time up to 1,200. Thereafter the reduction is much smaller, at 0.2 percentage points
per thousand flight hours for both NPE and MF. Controlling for total hours, a 0.1
increase in the proportion of time as pilot in command reduces the probability of an
accident by 0.1 percentage points (MF) and 0.11 percentage points (NPE). The same is
not true for proportion of time in make and model; here we see an increase of 0.2
percentage points associated with an increase of 0.1 in the proportion in make and model '
for the MF strategy. For NPE there is no significant effect. Age also has an effect on
accident probability, but not in the expected direction. Older pilots are associated with a
higher accident rate, when one includes flight time and other training variables. This is,
however, consistent with the hypothesis that almost all training is already captured by
other variables, and that age is simply measuring the effect of aging on accident
probability. If this is the case, then the direction of the effect is perfectly understandable.
In any case, the magnitude is modest, with one additional year being associated with an
increase in accident probability of 0.01 percentage points. Also of note is the fact that
the explicit training variables are not significant. For the bottom part of the panel we see

that the remainder of the covariates estimates are of the expected sign. Greater frequency

126

of flight, measured by landings in the last 90 days is associated with an increased
accident probability, as expected. Also as expected, flying in good weather, as measured
by the VMC variable is associated with a remarkable reduction in accident probability (a
1.5 percentage point reduction). Filing a flight plan, one of our “prudence” variables is
also associated with a 0.65 percentage point decrease in accident probability.

The results for commercial flights are not as strong. We see that hours tend to
reduce accident probability. However, this effect is only statistically significant for
commuters, and even so only in the NPE model. As with general aviation, the age,
landings, and weather variables are of the expected sign. However, their magnitudes are
smaller. Surprisingly, night flying only increases the accident probability of general
aviation pilots, and even so only in the NPE identification scheme. Before moving to the
other outcome equations, one should note that the estimates for trunk carriers in Table
3.11 include both accidents and incidents. Separate estimates done for just accidents are
presented in Table 3.12. Although most of the observations are lost, we see a remarkable
increase in the parameter estimates under the MF scheme. Now the effect of hours is
very significant. Furthermore, the magnitude of the effects increased markedly. This
effect is only present in the MF scheme.

The accident probit results are very significant, both statistically and with respect
to the magnitude of the effect. It suggests that more experienced and better trained pilots
are able to substantially decrease their chances of having an accident. This effect is
substantially larger for general aviation pilots than for commercial pilots. We also see
that the proportion of time as pilot in command is a significant training variable in

determining accident rates in general aviation. This suggests that skills acquired while

127

pilot in command are not only crucial to aircraft safety, but apparently not easily
substitutable by other pilot training.

Taken as a whole, the results of the empirical models estimated point to
potentially large effects of training on aviation safety outcomes. These results are not
limited to the general aviation sample, but pervade every flight type. In all outcome
models the results are stronger for general aviation, but we still see flight hour effects
present for trunk carriers. This is particularly true in the pilot error and in the accident
probits. There we see large experience effects in both flight categories. In the
fatality/severity and destroyed/extent of damage equations the results are varied, but in
almost all cases point to better safety outcomes associated with more experience pilots,
pilot with more time in command, and, to a lesser extent, pilots who have more
certificates. In the pilot error and in the fatality or severe injury probit we see largest
experience effects, effects that clearly show that more experienced pilots are better able
to avoid mistakes and better able to mitigate the effects of accidents. These effects are
larger for general aviation, but again, are present for trunk carriers and are of large
magnitudes. The composition of these hours was also found to be important, as pilots
with more time as pilot in command and in the make and model of aircraft being flown
were at lower risk for pilot error, and were—again—better able to mitigate the effects of
an accident, or to avoid accidents altogether. This result was mostly concentrated in the
general aviation models, although there was sporadic evidence of their effect on
commuters also.

We also studied the effect of certificates on safety outcomes, and found general

aviation to be a possible test case for these certificates, since we were able to compare

128

safety outcomes of pilots with certificates with safety outcomes of pilots without them.
We saw training effects associated with certificates in the expected direction, albeit not
always statistically significant at conventional levels. Possession of an air transport
certificate, in particular, is associated with lower pilot error probabilities, as well as lower
fatality probabilities. The only training variable which did not behave in the way
expected is the instrument-rating variable in the general aviation equation which, for
reasons discussed above, may measure the relaxation of a flight restriction more than it
does the effects of training.

Before concluding one should point out that when dealing with processes that
vary over time, it is always possible that some of the dependent variables may be
cointegrated with the explanatory variable. In particular, one must be wary of trending
processes, that are integrated 1(1). If both the dependent variable and the one or more of
the explanatory variables are 1(1), then the two series may be cointegrated, and one can
attribute causality to the explanatory variable when in fact other factors may be affecting
both variables. In a time-series setting one could test for unit roots using test such as
those developed by Dickey and Fuller (1981) in order to rule out cointegration. Since our
data consist of several cross-sections, and not a time-series per se, what can be done is to
include a trend in the various outcome models and interact this trend with the explanatory

variables. In other words, we estimate

(6) DV = f(aTREND+2i ,BiEV, +zniEVixTREND),

where DV is the dependent variable and EV are the explanatory variables.
If the net trend effect is significant and the interactions terms are also significant,

then the two series may be cointegrated and we may be improperly attributing causality.

129

We perform this procedure on all outcomes. However, the net trend term is only
significant for the pilot error equation. And for the pilot error equation, the only
significant interaction is for the proportion of time as pilot in command. These results,
which are presented in the appendix table 3.14, suggest that the safety outcome findings
of this paper are not driven by cointegration between the safety outcomes and the

explanatory variables.

V. Conclusion

The foregoing pages have been an attempt at modeling the effect of pilot training
in accident safety outcomes. We modeled several different safety outcomes, and when
significant results were found, they always highlighted the importance of experience and
training in reducing pilot error, preventing accidents, and ultimately in preserving lives.
Most of the results are concentrated in the general aviation category, a category which
accounts for the vast majority of accidents and fatalities, but which has more often than
not been ignored in the aviation safety literature. This is not to say that significant results
were not found for commercial aviation, and in particular for trunk carriers, the aviation
category that accounts for most aviation travel. In fact, the role of experience in
reducing the incidence of pilot error is just as strong for trunk carriers as it is for general
aviation. Furthermore, both the parametric and the non-parametric results point to
significant non-linearities in these returns, with most of the gains coming from the first
thousand hours of flight (general aviation), or the first three or four thousand hours of
flight (commercial flights). This suggests that policy measures should focus on young

and inexperienced pilots, for this is where the largest opportunity to save lives exists.

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Borenstein, Severin and Martin Zimmerman, “Market incentives for safe commercial
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Bylow, Lance F. and Ian Savage, “The Effect of Airline Deregulation on Automobile
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Chance, Don and Stephen P. Ferris, ”The effect of aviation disasters on the air transport
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Code of Federal Regulations, 1998, online version. National Archives and Records
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Heckman, J ., “Sample Selection Bias as Specification Error.” Econometrica 47 (1979):
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Mitchell, Mark L. and Michael T. Maloney, “Crisis in the cockpit? The role of market
forces in promoting air travel safety,” Journal of Law and Economics 32 (October
1989): 329-55.

Oster, Clinton V. and C. K. Zorn, “Airline Deregulation: Is it Still Safe to Fly?”in Moses,
Leon and Ian Savage, eds. Transportation Safety in an Age of Deregulation. Oxford
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Phillips, R. A. and W. K. Talley, “Determinants of the Severity of Airline Accidents: 3
Passanger Perspective.” International Journal of Transport Economics 23 (June
1996): 141-156.

Phillips, R. A. and W. K. Talley, “Airline Safety Investments and Operating Conditions.”
Southern Economic Journal 59 (October 1992): 157-164.

Rose, Nancy L. “Profitability and Product qaulity: Economic Determinants of Airline
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Rose, Nancy L. “Fear of Flying? Economic Analysis of Airline Safety.” Journal of
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131

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368.

132

APPENDIX 1

Tables and figures for chapter 1

133

Table 1.1: Summary statistics, 1988 PNAD and 1987/88 POF

PNAD
Mother's schooling
Less than elementary 0.210
Elementary 0.263
Some middle school 0.133
Middle 0.106
Some high school 0047
High school 0.148
More than high school 0.093
Father's schooling
Less than elementary 0.218
Elementary 0.270
Some middle school 0.115
Middle 0.102
Some high school 0.040
High school 0.137
More than high school 0.118
Number of children
Boy, ages 9 and under 0.633
Girl, ages 9 and under 0.637
Boy, ages 10 to 11 0.108
Girl, ages 10 to 11 0.108
Boy, ages 12 to 13 0.096
Girl, ages 12 to 13 0.094
Boy, ages 14 to 15 0.089
Girl, ages 14 to 15 0.084
Household size 4.55
Mother's age 34.93
Father’s age 38.62
Proportion of mothers employed 0.41
Proportion of fathers employed 0.93
Mother's hours 36.45
F ather's hours 48.43

POF

Less than elementary
Elementary

Middle

High school

More than high

Less than elementary
Elementary

Middle

High school

More than high

Boy, ages 0-5
Girl, ages 0-5
Boy, ages 6-12
Girl, ages 6- 12
Boy, ages 13-15
Girl, ages 13-15

Monthly household consumption, in 10003 of 1987 $Cz.‘

( 1) Food expenditures

(2) Health care expenditures
(3) Education expenditures

(4) Tobacco expenditures

(5) Adult clothing expenditures
(6) Beer expenditures

(7) Adult goods expenditures

equals (4)+(5)+(6)

134

722.28
210.83
109.71
42.24
240.38
7.55
290.17

0.119
0.242
0.352
0.156
0.131

0.102
0.230
0.331
0.146
0.191

0.324
0.345
0.319
0.344
0.165
0.170

4.44
39.15
42.79

3,402.38

percent of total
(21.23%)
(6.20%)
(3.22%)
(1.24%)
(7.07%)
(0.22%)
(8.53%)

Table 1.2: Men and women's earnings and employment rates, 1988

Average monthly earningsl Employment rate

Age group Men Women Men Women
All schooling levels

16-24 476.27 300.12 0.72 0.42
25-34 1149.07 666.21 0.93 0.55
35-44 1699.25 847.82 0.95 0.58
45-54 1598.51 661.20 0.89 0.47
55-64 1140.86 624.86 0.74 0.25

65+ 765.71 284.24 0.38 0.08

Less than completed primary

16-24 255.34 118.52 0.78 0.40
25-34 475.55 223.11 0.93 0.43
35-44 631.33 249.33 0.94 0.47
45-54 684.90 287.13 0.88 0.40
55-64 663.23 304.18 0.71 0.23

65+ 777.05 282.99 0.35 0.07

I From 1988 PNAD. Values deflated to thousands of 1987 Cruzados.

135

Table 1.3: Outlay equivilancy ratios for selected goodsl

Age Category

Boys, 5 and under
Boys, 6-12

Boys, 15-15

Girls, 5 and under
Girls, 6-12

Girls, 13-15
Boy-girl, 5 and under
Boy-girl, 6-12

Boy-girl, 13-15

Boys, 5 and under
Boys, 6-12

Boys, 13-15
Girls, 5 and under
Girls, 6-12

Girls, 13-15

Tobacco Adult clothing

0.7010
(0.087)
06750
(0.065)
-09140
(0.092)
-07920
(0.085)
-0.6200
(0.067)
-0.8050
(0.105)
0.0910
(0.092)
-0.0560
(0.093)
-01100
(0.140)

6.080
1.476
9.917
10.035
3.563
12.170

(1)

' Results are weighted. Standard errors in parenthesis.
2 (l) is the hypothesis that all adult goods OERs are equal, (2) is the hypothesis that Tobacco and

Beer are equal. Statistics are distributed Chi-squared with three degrees of freedom for (1) and

two degrees of freedom for (2).

136

Beer
-0.4660 -0.8220
(0.054) (0.207)
-0.5420 06140
(0.044) (0.165)
-0.3890 -0.8140
(0.064) (0.207)
-0.4240 -0.6090
(0.055) (0.234)
-0.4510 -0.2880
(0.053) (0.207)
-0.3540 -1. 1420
(0.069) (0.185)
-0.0420 -0.2120
(0.059) (0.295)
-0.0910 -0.3260
(0.075) (0.276)
-0.0350 0.3280
(0.092) (0.272)

Wald Tests 2

(0.048) 2.976
(0.478) 0.132
(0.007) 1.912
(0. 007) 0.795
(0.168) 0.640
(0.002) 6.962

Adult goods

(2)

05040
(0.058)
-O.56OO
(0.055)
-O.4630
(0.087)
04730
(0.058)
04670
(0.057)
04300
(0.084)
00300
(0.078)
-0.0930
(0.085)
-00340
(0.126)

(0.226)
(0. 93 6)
(0.384)
(0.672)
(0. 726)
(0. 031)

Table 1.4: OLS regressions for the effect of child gender on expenditure shares,

by expenditure typel

Mother's education
Completed primary

Completed middle
Completed high school

College +

Mother’s age/10

Mother’s age/10 squared

F ather's education
Completed primary

Completed middle
Completed high school

College +

F ather’s age/10

Father's age/10 squared

Male household
Log of household size
Log of household expenditures

Log of household consumption

Consumption

0.0900"
(2.50)
0.1377"
(3.85)
0.2598"
(4.35)
0.4450"
(6.86)

-0.0026
(-040)
0.0000
(0.47)

0.1106"
(2.86)
0.1959M
(5.91)
0.3406"
(6.06)
0.5605“
(6.79)

0.0342“
(4.95)
00003"
(-429)

0.1337
(1.39)
0.4712M
(7.67)
.0.5714=M
(-1512)

137

Health

0.0012
(0.34)
0.0025
(0.74)
0.0000
(0.00)
0.0020
(0.32)

-00002
(-033)
0.0000
(0.51)

-0.0028
(-0.89)
0.0003
(0.09)
0.0000
(0.00)
0.0027
(0.50)

00017"
(-2.28)
013*
(2.69)

0.0038
(0.42)
-0.0156**
(-370)

0.0110”
(5.41)

0.0031
(1.58)
0.0069"
(3.31)
0.0137M
(4.75)
0.0217"
(5.11)

0.0011"
(3.74)
041*
(-4.31)

0.0013
(0.91)
0.0076"
(4.36)
0.0105”
(4.95)
0.017"
(5.38)

0.0008"
(2.58)
on
(-240)

0.0035
(1.00)
0.0161"
(6.44)

0.0008
(0.64)

Education Adult good

0.0032
(1.00)
0.0019
(0.59)
-0.0012
(-O.28)
0.0008
(0.14)

00010
(-153)
0.0000
(0.87)

0.0022
(0.67)
-0.0016
(-052)
-00055
(-135)
00098"
(-2.08)

0.0027"
(-4.38)
O**
(3.33)

00216"
(-2.08)
0.0459M
(10.29)

0.0012
(0.69)

Table 1.4 (cont)

Number of children
Boys 5 and under

Girls 5 and under
Boys, 6-9
Girls, 6-9
Boys, 10-11
Girls, 10-11
Boys, 12-13
Girls, 12-13
Boys, 14-15
Girls, 14-15
Difference in boy-girl coefficients
Ages 5 and under
Ages 6 to 9
Ages 10 to 11
Ages 12 to 13

Ages 14 to 15

Joint significance of boy-girl coefficients
(F - statisitc)

Consumption

00891"
(-3.82)
01078"
(-530)
00818"
(-325)
01026“
(-400)
0.0720*
(-190)
0.0350
(0.94)
-0.0706**
(-204)
0.0458
(0.99)
0.0727“
(-222)
-0.0964**
(-3. 19)

0.0187
(0. 64)
0.0208
(0.43)
0.0370
(0.54)
0.0248
(0.20)
0.0237
(0.41)

(0. 60)

Health

00053"

(2.77)

0.0071"

(3.06)
0.0015
(0.69)
0.0003
(0.12)
0.0023
(087)
0.0010
(0.34)
0.0003
(0.09)
0.0035
(1.15)
0.0023
(0.78)
0.0014
(0.48)

-0.0018
(0.45)
0.0012
(0.19)

0.0013
(0.12)

-0.0038
(0.85)

0.0037
(0.90)

(0.44)

Education Adult good

0.0054"
(-5.04)
0.0035M
(-312)
0.0008
(0.55)
0.00351M
(2.77)
0.0001
(0.05)
0.0020
(1.00)
0.0021
(1.12)
0.0027
(1.36)
0.0040
(1.35)
-0.0008
(0.48)

0.0019
(2.13)
0.0027
(2.20)
0.0021
(0.61)
0.0006
(0.05)
0.0049
(2.20)

(1.66)

0.0102M
(-4.64)
0.01 17"
(-5.50)
0.0112"
(447)
0.011"
(4.03)
0.0121"
(-3.65)
0007*
(-l.89)
0.0117"
(-353)
0.0105M
(-3.19)
0.0013
(0.35)
0.0006
(0.18)

0.0014
(0.32)
0.0002
(0.00)
0.0051
(1.16)
0.0012
(0.70)
0.0007
(0.20)

(0.32)

' Results are weighted. t-statistics in parenthesis. F-statistics reported for difference in boy-girl

coefficients.‘ indicates 5% significance level; "”" indicates 1%.

138

Table 1.5: OLS regressions for the effect of child gender on expenditure shares,

mothers with low educationl

Number of children
Boys 5 and under

Girls 5 and under
Boys, 6-9

Girls, 6-9

Boys, 10-11
Girls, 10-11
Boys, 12-13
Girls, 12-13
Boys, 14-15

Girls, 14-15

Difference in boy-girl coefficients
Ages 5 and under

Ages6to9
Ages 10to 11
Ages 12to 13

Ages 14to 15

Joint significance of boy-girl coefficients
(F - statisitc)

-0.0987**

(-2.60)

-0.0976**

(-3.28)
0.0442
(-1.27)

-0.139**

(-3.43)
0.0742
(-0.96)
0.0534
(-100)
0091*
(-1.84)
0.0875
(—1.49)
0.0193
(0.35)
0.0530
(—1.21)

0.001 1
(0.01)
0.0948*
(2. 78)
0.0207
(0.04)
0.0035
(0.00)
0.0337
(0.32)

(1.12)

Consumption Health

00007

(0.27)
0.0028
(-100)
0.0003
(0.12)

0.0066”

(1.98)
-0.0028
(0.74)
0.0019
(0.43)
0.0045
(-1.21)
0.0041
(0.91)
0.0022
(0.47)
0.0042
(0.94)

0.0187
(0.41)
0.0062
(2.49)
0.0009
(0.03)
0.0086
(2.15)
0.0021
(0.13)

(1.00)

-0.0033**

(-2.26)

-0.0051**

(-414)
0.0010
(0.37)
0.0025
(1.46)
0.0015
(0.61)
0.0049
(1.40)
0.0030
(1.04)

0.0007
(0.28)
0.0053
(0.98)

0.0002
(0.09)

0.0187
(0.98)
0.0015
(0.21)
0.0034
(0.65)
0.0037
(0.98)
0.0055
(1.02)

(0. 77)

Education Adult good

-0.0067*
(-1.78)
0.0097M
(-2.69)
0.01 1 1"
(-237)
0.0159"
(-319)
0.0124"
(-2.26)
0.0056
(0.87)
0.0087
(-l.58)
0.0129"
(-252)
0.0002
(0.03)
-0.0036
(0.65)

0.0187
(0.39)
0.0048
(0.46)
0.0068
(0. 75)
0.0042
(0.30)
0.2100
(0.41)

(0. 42)

' Low schooling defined as less than primary completed. Results are weighte, t-statistics in parenthesis.
F -statistics reported for difference in coefficients. * indicates 5% significance level; " indicates 1%.

139

Specification is Model I

Table 1.6: Probit of mother's employment, 1988 PNAD and full sample of PNADsl

1988 Full Sample
Mother's years of schooling

One 0.0099 (0.71) 0.0219" (6.08)

Two -0.0267** (-2.35) 0.0180" (6.26)

Three -0.0201* (-l.92) 0.0306“ (11.58)
Four 0.0011 (0.13) 0.0465" (21.20)
Five 0.0043 (0.92) 0.0583" (16.71)
Six 0.0060 (0.36) 0.0534" (14.06)
Seven 0.0136 (0.83) 0.0653" (17.30)
Eight 0.0103 (0.89) 0.0702" (24.70)
Nine 00452" (1.93) 0.1011" (18.78)
Ten 0.0742" (3.66) 0.1227" (25.38)
Eleven 0.1926M (17.98) 0.2305" (89.56)
Twelve 0.2451“ (6.01) 0.2991“ (33.01)
Thirteen 0.3100M (8.83) 0.3063” g (39.17)
Fourteen 0.3078“ (11.35) 0.3756" (61.23)
Fifteen 0.4005” (23.75) 0.4225" (111.13)
Sixteen 0.4319" (14.30) 0.4585“I (76.43)

Seventeenormore 0.5196M (5.36) 0.4961" (26.71)

Mother’s age/10
Mother's age/10 squared

0.04149" (20.88) 0.0443" (96.07)
-0.0006" (-21.72) -0.0006” (-98.31)

Number of adults (i.e. 16 years and older) -0.0009 (-0.38) ~0.0055** (-9.09)
Child status variables (number of children)

Boys, nine and under
Girls, nine and under

0.0246M (-7.65) 00368" (-46.99)
0.0210M (-6.39) 0.0351" (-44.28)

Boys, ten or eleven years old 0.0074 (0.86) -0.0009 (044)
Girls, ten or eleven years old 0.0214M (2.47) 0.0113" (5.28)
Boys, twelve or thirteen years old 0.0067 (0.78) 0.0074" (3.55)
Girls, twelve or thirteen years old 0.0360" (4.13) 0.0262” (12.41)
Boys, fourteen or fifteen years old 0.0033 (0.38) -0.0029 (-l.38)

Girls, fourteen or fifteen years old 0.0390" (4.36) 0.0281" (13.06)

Child dummy(1 iffamily hasachild) 0.0086 (0.87) 0.0153" (6.57)

' Results are weighted. Marginal effects are reported, 2 -statistics in parenthesis.
“ indicates 5% significance level; ** indicates 1%.

140

Table 1.7: Probit of mother's employment using full sample of PNADs,

Models 14‘

Number of adults

Child status variables (number of children)

Boys, nine and under

Girls, nine and under

Boys, ten or eleven years old

Girls, ten or eleven years old

Boys, twelve or thirteen years old
Girls, twelve or thirteen years old
Boys, fourteen or fifieen years old
Girls, fourteen or fifteen years old

Child dummy (1 if family has a child)

Proportion of children at work
Proportion of children doing housework

Difference in boy-girl coefficients3
Ages 9 and under
Ages 10 to 11
Ages 12 to 13
Ages 14 to 15

Joint significance test of all difference in
boy-girl coefficients (Chi-squared )

Model 1
-0.0050** (-9.09)
-0.0368” (-46.99)
-0.0351** (-44.28)

-0.0009 (-0.44)
0.0113" (5.28)
0.0074“ (3.55)
0.0262” (12.41)

-0.0029 (-1 .38)
0.0281" (13.06)
0.0153M (6.57)

-0.0017 (2.45)
-0.0122" (23.61)
-0.0188" (53.64)
-0.0310** (136.87)

(217.90)

141

Model 2 2
(1) + prop. at work

-0.0060* *

~0.0394**
-0.0377**
0.0002
0.0221 ”
-0.0047"
0.0293"
-0.0364**
0.0191"

-0.0069* "‘

0.2006"

-0.0017
-0.0219**

(-9.81)

(-50.03)
(-47.32)
(0.1 l)
(10.37)
(-2.25)
(13.89)
(-l6.62)
(8.85)

(-2.92)

(68.04)

(2. 47)
(76.1 1)

0.0341M (175.58)
0.0555M (426.59)

(673.34)

Table 1.7 (cont.)

Number of adults

Child status variables (number of children)

Boys, nine and under

Girls, nine and under

Boys, ten or eleven years old

Girls, ten or eleven years old

Boys, twelve or thirteen years old
Girls, twelve or thirteen years old
Boys, fourteen or fifteen years old
Girls, fourteen or fifteen years old

Child dummy (1 if family has a child)

Proportion of children at work
Proportion of children doing housework

Difference in boy-girl coefficients3
Ages 9 and under
Ages 10 to 11
Ages 12 to 13
Ages 14 to 15

Joint significance test of all difference in
boy-girl coefficients (Chi-squared )

Model 3 2

(1) + prop. housework

0.0044 (7.22)
00358" (-45.64)
0.0341 ** (-4299)
0.0075" (3.54)
0.0123" (5.77)
0.0141** (6.70)
0.0238" (11.24)

0.003 (1.53)
0.0234** (10.88)

0.011" (-4.66)
0.0775** (33.07)
-0.0016** (2.38)
-0.0048** (3.63)
-0.0096** (14.11)
0.0202M (57.21)

(76.69)

Model 4
(1) + both
proportions

-0.0048

-0.0384**
-0.0367**
0.0094"
0.0235"
0.0022
0.0268"
-0.0305**
0.0139M

-0.0363**

0.2055"
0.0841“

-0.0017**
—0.0140**
-0.0245**

(-7.81)

(—48.68)
(-46.02)
(4.42)
(10.99)
(1.03)
(12.65)
(-13.87)
(6.42)

(-14.58)

(69.60)
(35.83)

(2.40)
(31.20)
(90.34)

-0.0443* * (269.14)

(383.91)

' Regional dummies included but not reported. Results are weighted. Marginal effects are reported,
z-statistics in parenthesis. Sample is married households with household heads 18 to 64 years old.
Mother's schooling, household size and mother's age and age squared variables were included in the
estimation but are also not reported. * indicates 5% significance level; " indicates 1%.

2 Proportion worked variable is defined as the proportion of children who reported working in the
reference week, and is coded 0 for households without children. Alternate prop. worked variables
used: (1) children who worked at least 10 hours per week and (2) proportion of reference person's
sons and daughters who worked (as opposed to children in the household). Results were similar.
Proportion working at home is defined as proportion who reported "helping with household chores"

as main activity for the reference week.

3 Chi-squared for the hypothesis that boy effects equal girl effects are reported in parenthesis and italics.

142

difference-in-differencesl

Table 1.8: Probit of mother's employment, high versus low child wage areas,

Model 5
Child status variables (number of children)
Boys, nine and under 0041]" (-31.39)
Girls, nine and under 00391" (2954)
Boys, ten or eleven years old -0.0068** (-2.10)
Girls, ten or eleven years old 0.0023 (0.71)
Boys, twelve or thirteen years old 0.0020 (0.62)
Girls, twelve or thirteen years old 0.0243" (7.33)
Boys, fourteen or fifteen years old -0.0030 (089)
Girls, fourteen or fifteen years old 0.0279M (8.28)
Child dummy (1 if family has a child) 0.0186" (7.93)

Number of adults -0.0051** (-8.53)

High child wage dummy and interactions

High child wage -0.0204** (-10.48)
High wage x boys, nine and under 0.0105" (6.67)
High wage x girls, nine and under 001" (6.32)
High wage x boys, ten or eleven years old 0.0101" (2.68)
High wage x girls, ten or eleven years old 0015" (3.92)
High wage x boys, twelve or thirteen years old 0.0101 ** (2.60)
High wage x girls, twelve or thirteen years old 0.0040 (1.02)
High wage x goys, fourteen or fifteen years old 0.0012 (0.31)
High wage x girls, fourteen or fifteen years old 0.0017 (0.44)
Difference in boy-girl marginal effects2
Ages 9 and under -0.0019 (2.61)
Ages 10 to 11 -0.0116** (19.72)
Ages 12 to 13 -0.0193** (51.96)
Ages 14 to 15 -0.0311** (128.06)
High vs. low child wage area difference-in-differences3
Ages 9 and under 0.0004 (0.04)
Ages 10 to 11 -0.0049 (0.87)
Ages 12 to 13 0.0061 (1.29)
Ages 14 to 15 -0.0005 (1.01)
Joint significance test of all difference-in-differences (2.21)

(Chi-squared)

l See note 1 in Table 1.7.
2 (dP/dboy - dP/dgirl). Chi-squared for difference in coefficients are reported in italics.
3 High (low) wage cells are defined by the top (bottom) 50th centile of year x region x urban categories.

143

Table 1.9: Probit of mother's employment, households with and without

childcare availability, difl'erence-in-differencesl

Child status variables (number of children)

Boys, nine and under

Girls, nine and under

Boys, ten or eleven years old

Girls, ten or eleven years old

Boys, twelve or thirteen years old
Girls, twelve or thirteen years old
Boys, fourteen or fifteen years old
Girls, fourteen or fifteen years old

Child dummy (1 if family has a child)
Number of adults

Childcare availability dummy and interactions
Childcare available
Childcare x boys, nine and under
Childcare x girls, nine and under
Childcare x boys, ten or eleven years old
Childcare x girls, ten or eleven years old
Childcare x boys, twelve or thirteen years old
Childcare x girls, twelve or thirteen years old
Childcare x goys, fourteen or fifteen years old
Childcare x girls, fourteen or fifteen years old

Difference in boy-girl coefficients2
Ages 9 and under
Ages 10 to 11
Ages 12 to 13
Ages 14 to 15

Childcare availability difference-in-differences3
Ages 9 and under
Ages 10 to 11
Ages 12 to 13
Ages 14 to 15

Joint significance test of all difference-in-differences
(Chi-squared)

1'2 See note 1 in Table 1.8.

Model 6
-0.0462** (-52.34)
-0.0444** (-49.71)

-0.0018 (-0.74)
0.0124“ (5.01)
0.0072” (2.90)
0.0309" (12.23)
-0.0054** (-2.03)
0.0361 ** (13.44)
0.0156" (6.60)
-0.0168** (-21.49)
0.0156" (6.13)
0.0388" (21.61)
0.0388" (21.31)

-0.0036 (-0.88)
-0.0109** (-2.65)
-0.0091 ** (-2.29)
-0.023** (-5.75)

-0.0036 (-0.92)
-0.0286** (-7.20)

-0.0018 (2.37)
—0.01 16’” (20.95)
-0.0187** (53.20)
-0.0326** (148.20)

0.0000 (0.00)
0.0073 (1.75)
0.0139 (6.67)
0.0250 (21.59)
(30.22)

3 Childcare availability is defined as the presence of a female relative, 16 years or older.

144

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147

APPENDIX 2

Tables and figures for chapter 2

148

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153

Table 2.3: Work probit, single women1

Basic model
(81)

Region (Central-west omitted)

Minas Gerais -0.0199** (-7.41)
North -0.0749** (-23.94)
Northeast -0.0680** (-29.07)
Rio -0.0316** (-10.85)
South -0.0087** (-3.20)
Sao Paulo 0.0422" (15.81)
Rural dummy -0.1519** (-74.08)
Age 0.1810" (42.99)
Age squared -0.0052** (-29.09)
Age cubed/10000 0.0648M (20.29)
Age quartic/10000 -0.0003** (-17.11)

+ education controls
(82)

00191" (-7.08)
00709" (-2252)
00594" (-2523)
-0.0466** (45.72)
-00145" (-534)
0.0348" (12.91)
01195" (-56.10)

0.1424" (33.37)
00040" (-2173)
0.0464" (14.39)

Years of completed education

one
two

three
four

five

six

seven
eight
nine

ten
eleven
twelve
thirteen
fourteen
fifieen
sixteen
seventeen +

Household size

154

-0.0002**

0.0364“
0.0441M
0.0494M
0.0600"
0.0591“
0.0408"
0.0371 **
0.0744"
0.0285“
0.0516"
0.2004"
0.1238"
0.1472"
0.2155M
0.3391 **
0.3447"
0.4645"

(-1 1.40)

(8.14)
(12.31)
(15.37)
(22.90)
(15.95)
(10.38)

(9.65)
(23.03)

(6.43)
(11.91)
(66.60)
(17.44)
(20.47)
(31.40)
(67.79)
(42.50)
(19.63)

+ household size
(S3)

00143" (-527)
-0.0584** (-18.38)
-00535" (-22.62)
.00447'M (-14.99)
-00179" (-6.55)
0.0355" (13.10)
-O.1162** (-5441)

0.1651" (38.26)
00049" (-26.71)
0.0623" (19.10)
00003" (-16.00)

0.0364"
0.0470"
0.0531"
0.0649M
0.0657”
0.0467“
0.0422"
0.0792“
0.0341 **
0.0560"
0.2038M
0.1224'Ml
0.1446"
0.2128"
0.3349”
0.3382"
0.4528"

-0.0l64**

(8.14)
(13.08)
(16.49)
(24.70)
(17.64)
(11.83)
(10.92)
(24.34)
(7.64)
(12.83)
(66.97)
(16.91)
(19.98)
(30.88)
(66.57)
(41.49)
(19.12)

(~53.60)

Table 2.3 (cont.)

Selected birthyear cohort dummies (effects relative to 1921 cohort)

Born 1925
Born 1930
Born 1935
Born 1940
Born 1945
Born 1950
Born 1955
Born 1960
Born 1965
Born 1970

-0.01 18
-0.0174*
-0.0010
0.0298"
0.0480M
0.0482"
0.0493"
0.0299“
0.0280"
0.0322"

(-111)
(-190)
(-010)
(3.24)
(5.00)
(5.08)
(5.26)
(3.35)
(3.20)
(3.57)

0.0063
-0.0044
0.0047
0.0284”
0.0290”
0.0206“
0.0069
-0.0250**
-0.0321**
-0.0325**

(0.62)
(-052)
(0.56)
(3.43)
(3.36)
(2.44)
(0.84)
(-3.26)
(-433)
(-422)

0.0067
-0.0026
0.0065
0.0293"
0.0293”
0.0177"
0.0030
-0.0291“
-0.0382**
-0.0404**

(0.63)
(-030)
(0.74)
(3.36)
(3.21)
(1.97)
(0.34)
(-349)
(-471)
(-4.81)

' Marginal effects reported. Z -statistics in parenthesis. Change in GDP also included but not reported.

155

Table 2.4: Age, period and cohort effects for model M4 probit1

No period effects No cohort effects

Age effects
Age 0.0865“ (14.60) 0.0756“ (13.18)
Age squared -0.0019*" (-8.40) 0.0016“ (-7.35)
Age cubed/10000 0.0193” (5.08) 0.0134" (3.67)
Age quartic/10000 -0.0001*" (-3.98) -0.0001** (-2.30)

Selected birthyear cohort dummies (effects relative to 1921 cohort)

Both period and
cohort effects

0.0872M (14.40)
00020" (—8.48)
0.0196" (5.11)
00001“ (-3.98)

-0.0041 (-0.32)
-0.0005 (-0.03)

Born1925 0.0027 (0.23)
Boml930 0.0119 (1.14)
Bornl935 0.0175* (1.70)
Born1940 0.0457M (4.55)
Born1945 0.0711" (7.05)
Born1950 0.0952M (9.50)
Born 1955 0.1170** (11.65)
Born 1960 0.1328" (13.09)
Born 1965 0.1585" (15.28)
Born 1970 0.1889" (17.45)

Period dummies (effects relative to 1996-1999)

Year 1981
Year 1982
Year 1983
Year 1984
Year 1985
Year 1986
Year 1987
Year 1988
Year 1989
Year 1990
Year 1992
Year 1993
Year 1995

I Marginal effects reported. Z -statistics in parenthesis

156

-0.0964** (39.82)
00712" (30.85)
00579" (25.32)
00597" (26.51)
-0.0489** (22.16)
0.0357" (12.94)
00239" (-8.83)
00239" (-8.82)
-0.0l89** (-701)
00133" (-503)
-0.0158** (-6.03)
00117" (-453)
0.0065" (2.57)

-0.0002
0.0231

0.0434
0.0631 *

(-001)
(1 .02)
(1.59)
(1.96)

0.0807M (2.17)
0.0924" (2.19)
0.1143M (2.42)
0.1434" (2.74)

-0.0368** (-2.13)

~0.0150
-0.0051
-0.0103
-0.0029
0.0067
0.0150
0.01 16
0.0129
0.0149“
0.0049
0.0052

(-0.92)
(-033)
(-073)
(-022)
(0.55)
(1.34)
(1.14)
(1.40)
(1.81)
(0.77)
(0.98)

0.0159" (4.37)

Table 2.5: Change in employment rates of married women, based on

probit models Mi—M4‘

Actual change
Predicted change in employment
Percentage explained by
Change in age (and region)
Change in education
Change in husband's wage
Change in household composition
Change in cohort composition

Actual change
Predicted change in employment
Percentage explained by
Change in age (and region)
Change in education
Change in husband’s wage
Change in household composition
Change in cohort composition

Actual change
Predicted change in employment
Percentage explained by
Change in age (and region)
Change in education
Change in husband's wage
Change in household composition
Change in cohort composition

Actual change
Predicted change in employment
Percentage explained by
Change in age (and region)
Change in education
Change in husband's wage
Change in household composition
Change in year composition

' See text for description of methodology. Since there was a fall in employment, 8 positive value correspon

0.094
0.049

2.0

98.0

0.066
0.090

48.9

51.1

0.058
0.047

88.7

11.3

-0.034
-0.035

157.0

-57.0

Secular change: 1990-1981

0.094 0.094
0.050 0.050
-4.1 5.3
34.9 46.9
-21.2
69.2 69.0
Secular change: 1999-1990
0.066 0.066
0.094 0.093
37.8 48.3
26.0 35.4
-20.6
36.2 36.9
Cohort change: 1952-1942
0.058 0.058
0.055 0.056
39.0 -6.8
53.7 73.4
26.5
7.3 6.9
Cohort change: 1962.1952l
-0.034 -0.034
-0.038 -0.036
147.0 201.2
-9.6 -17.9
-45.0
-37.4 -38.3

to a percentage decrease in employment, 8 negative value correspons to an increase.

 

157

0.094
0.053

~1.4

43.5
«22.6
25.6
54.8

0.066
0.092

36.3
35.0
-23.5
20.2
32.2

0.058
0.056

51.0
68.6
32.5
-57.9
5.8

-0.034
-0.034

162.0
-17.1
-61.0
51.5
-35.4

Table 2.6: Sector choice model, multinomial logit1

Wage workers
Informal

Formal
Region (Central-west omitted)
Minas Gerais 1.0037 (0.26)
North 1.2808" (14.91)
Northeast 1.1985" (13.73)
Rio 1 .0099 (0.63)
South 1.2459" (17.11)
Sao Paulo 1.0449M (3.31)
Rural dummy 0.5044“ (-52.04)
Age 2.2685" (16.34)
Age squared 0.9744” (12.88)
Age cubed/ 10000 1.4641 ** (11.03)
Age quartic/10000 0.9977“ (-10.86)
Years of completed education
one 1.3938M (11.23)
two 1.5267" (18.07)
three 1.7520" (26.55)
four 2.2921M (45.33)
five 2.6696" (38.13)
six 2.7799" (37.23)
seven 3.2993“ (42.86)
eight 4.0405" (63.44)
nine 5.0241" (48.18)
ten 6.0047“ (59.73)
eleven 13.3965" (122.74)
twelve 21.8596M (67.33)
thirteen 23.3251M (78.03)
fourteen 38.1036" (106.21)
fifteen 54.8751" (147.47)
sixteen 69.2131M (111.33)

seventeen +

Husband's variables
Wage ($R/hr, predicted) 1.0601 **
Wage squared
Schooling (completed ye 0.9394“
Age

Household size

09959" *

0.9736"

10265“

1428921“ (46.96)

(5.75)
(-1154)
(-1490)
(-32.65)

(9.48)

158

0.9991
0.8930"
0.9034M
1.2438”

10345“
1.1734"
0.6337“

1.3643"
0.9943M
1.0563
0.9997

0.8410"
0.8141"
0.7768"
0.7019“
0.7536"
0.7162"
0.6992"
0.6258”
0.6849”
0.6566”
0.8784"
1.3844“
1.4247"
1.6820"
2.2276“
4.0047"
4.2344"

0.9604"
1.0004
0.9346"
0.9818M

1.0326“

(-005)
(-4.61)
(-5.48)
(10.42)
(1.94)
(9.24)
(-3200)

(6.04)
(-2.80)
(1.59)
(-154)

(-7.08)
(-10.61)
(-1403)
(-2252)
(-1 1.14)
(-1153)
(-1 1.19)
(-1910)
(-799)
(-933)
(-5.20)
(3.74)
(4.59)
(8.14)
(18.79)
(22.80)
(7.47)

(2.45)
(0.66)
(-1105)
(~16.29)

(10.21)

Self-employed

1.1165“
1.3720”
1.7259"
1.2235M
1.0008
0.8963”
0.6049"

1.6147"
0.9884“
1.1412”
0.9993"

1.0464M
0.9883
1.0478"
1.1559”
1.1696"
1.2913”
1.3818"
1.3856“
1.5202"
1.6323M
1.6533"
1.9899"
2.0990"
2.201 I”
3.2666M
7.5660"
6.5122”

1.0380"
0.9984”
0.9767”
0.9942"

1.0119"

(7.08)
(17.06)
(38.42)
(11.86)
(0.05)
(-724)
(-4431)

(10.24)
(-6.57)
(4.58)
(.413)

(2.15)
(-O.69)
(2.97)
(11.22)
(6.71)
(10.33)
(13.26)
(17.58)
(11.67)
(15.38)
(26.69)
(10.18)
(13.12)
(16.13)
(39.32)
(49.15)
(14.17)

(3.26)
(-3.80)
(-534)
(-7.87)

(4.99)

Table 2.6 (cont.)

Wage workers Self-employed

Formal Informal

Child status

Daughters, 0-4, 1 0.6263" (-44.21) 0.6754“ (-29.09) 0.7567" (-24.38)
Daughters, 0-4, 2 0.4140" (-34.99) 0.5129" (-22.71) 0.6655" (-16.70)
Daughters, 0-4, 3+ 0.2756M (-13.85) 0.4070" (-10.32) 0.6220" (-6.86)
Sons, 0-4, 1 0.6276" (-44.23) 0.6681” (-29.95) 0.7823” (-21.67)
Sons, 0-4, 2 0.4049“ (-37.12) 0.5235" (-22.43) 0.6404" (-18.20)
Sons, 0-4, 3 0.3046M (-14.52) 0.3841" (-11.21) 0.5810" (-7.83)
Daughters, 5-9, 1 0.7893M (-23.28) 0.9914 (-0.70) 1.0081 (0.78)
Daughters, 5-9, 2 0.665” (-18.32) 0.9698 (-1.27) 0.9919 (-0.40)
Daughters, 5-9, 3+ 0.6545“ (-6.03) 1.0754 (1.16) 1.0281 (0.50)
Sons, 5-9, 1 0.7756M (-25.l4) 0.9456" (-4.51) 0.9848 (-1.48)
Sons, 5-9, 2 0.6504“ (-19.55) 0.9716 (-l.21) 0.9705 (-1.48)
Sons, 5—9, 3 0.6173" (-7.16) 0.9139 (-1.38) 1.0026 (0.05)
GDP growth 1.0033“ (3.05) 1.0083" (5.87) 1.0012 (1.10)
Selected birthyear cohort dummies (effects relative to 1921 cohort)

Born 1925 1.3077* (1.81) 1.0896 (0.65) 0.9808 (-O.25)
Born 1930 1.4177" (2.63) 1.1728 (1.36) 1.0347 (0.50)
Born 1935 1.3577” (2.35) 1.3956" (2.91) 1.0426 (0.62)
Born 1940 1.6475“ (3.89) 1.9438" (6.00) 1.0530 (0.78)
Born 1945 1.7977M (4.59) 2.3891“ (7.84) 1.1579" (2.22)
Born 1950 1.8285“ (4.73) 3.2666" (10.73) 1.2624“ (3.54)
Born 1955 1.8502" (4.82) 4.6697M (13.97) 1.3024" (3.99)
Born 1960 1.7670M (4.45) 6.7019" (17.20) 1.3288" (4.23)
Born 1965 1.7923M (4.53) 9.8187" (20.49) 1.4111" (4.97)
Born 1970 1.9561" (5.14) 13.8253M (23.14) 1.4446" (4.94)

l Relative risk ratios reported, 2 -statistics in parenthesis, not at work base category.

159

Table 2.7: Sector choice model, multinomial logit, both year and cohort effectsl

Wage workers
Informal

Self-employed
Formal

Selected birthyear cohort dummies (effects relative to 1921 cohort)

Born 1925 1.2474 (1.46) 0.9993 (0.00) 0.9946 (003)
Born 1930 1298* (1.76) 0.9820 (-0.13) 1.0758 (1.20)
Born 1935 1.2025 (1.13) 1.0666 (0.40) 1.1139 (1.10)
Born 1940 1419* (1.89) 1.3549 (1.60) 1.1609 (1.60)
Born 1945 1507* (1.95) 15169" (1.87) 1.3165 (1.20)
Born 1950 1.4977* (1.70) 1.8887” (2.47) 14856" (1.74)
Born 1955 1.4833 (1.48) 2.455” (3.06) 15923" (1.88)
Born 1960 1.3858 (1.10) 3.203" (3.53) 1.69‘ (1.69)
Born 1965 1.3795 (0.98) 4.2628" (3.94) 1.8767“ (2.20)
Born 1970 1.5029 (1.13) 5.4634“ (4.19) 2.0394" (2.89)
Year effects (effects relative to 1996-1999 period)
Year 1981 0.8552 (-1.38) 0.659" (-3.16) 0.9778 (-1.30)
Year 1982 0.9226 (-0.76) 0.7193” (-2.66) 1.1345 (0.70)
Year 1983 0.9159 (-O.88) 0.9141 (-0.78) 1.1099 (0.90)
Year 1984 0.9287 (080) 0816* (-1.88) 1.1023 (0.99)
Year 1985 0.9840 (-0.19) 0.8251 * (-1.92) 1.1309 (0.98)
Year 1986 1.0412 (0.51) 0.8105M (-2.24) 1.2193" (1.99)
Year 1987 1.0944 (1.23) 0.8443” (-1 .97) 1.245” (2.30)
Year 1988 1.0805 (1.16) 0.7878” (-3.04) 1.2598“ (2.10)
Year 1989 1.0911 (1.45) 0.8576" (-2.17) 1.2044M (2.55)
Year 1990 1.0868 (1.55) 0.781 " (-3.90) 1.3011" (2.54)
Year 1992 1.0434 (1.04) 0.9538 (-0.99) 1.0436 (1.56)
Year 1993 1.0231 (0.66) 1.0207 (0.51) 1.0236 (1.35)
Year 1995 1.064“ (2.62) 1.0221 (0.79) 1.1414" (2.90)

 

I Child status variables, household size, mother's schooling variables, region and rural dummies
and husband's controls are also included but are not reported .

160

Table 2.8: Effect of policy change, informal sector probit, by control group1

Control group
All women, ages 40-55 Single women, ages 20-35

Region (Central-west omitted)

Minas Gerais -0.0537** (-7. 15) -0.0436** (5.65)
North 00594" (-6.60) 00592" (640)
Northeast 0.0803" (12.15) 0.0744" (10.89)
Rio -0.1052** (—12.72) 00909" (-10.91)
South 02741" (-37.35) 02594" (-34.31)
Sao Paulo -0.3250** (-44.52) -0.3067** (40.84)
Rural dummy 0.2565” (39.22) 0.2542M (37.55)
Years of completed education
one -0.1320** (-9.57) 02499" (-11.21)
two -0.1876** (-1 7 .58) -0.2922** (-16.08)
three -0.2730** (-29.42) -0.4112** (-25.35)
four -0.4777** (-66.07) -0.6359** (-45.75)
five -0.5074** (-48.14) -0.7072** (-42.89)
six -0.5200** (-86.67) -0.7566** (43.23)
seven -0.6953* * (-70.16) -0.8640* * (-50.56)
eight 08880” (-102.43) -1 .0596" (-71.59)
nine -0.9845** (-71.86) -1.1 162" (-57 .54)
ten -1.0958** (-85.88) -1 .2333” (-67.43)
eleven -1.4152** (-187.69) -1 .5742" (-116.18)
twelve -1.5035** (-69.87) -1.6396** (-62.46)
thirteen -1.4648* * (-74.36) -1 .5794” (-65.37)
fourteen -1.5378** (—103.63) -1 .6740” (-75.75)
fifteen -1.5710* * (-145.46) -1 .6739” (-99.22)
sixteen -1.1790** (-78.81) -1.2653** (-59.77)
seventeen + -1.5340** (-33.43) -1 .6556" (-23.00)
Household size 00077” (8.89) 0.0141 ** (11.64)
GDP growth 0.0091" (15.91) 0.0117" (15.57)
Difference-in-differences
Control dummy -0.0021 (-0.32) 0.2569“ (34.48)
1990-1999 dummy 0.1643" (32.21) 0.2585" (34.56)
Control x 1990-1999 00536” (-5.98) -0.0416** (-3.84)

' Marginal effects reported. Z -statistics in parenthesis. Sample is of working women. Treatment group

is all working women, ages 20-35 for left panel and working married women, ages 20-35 for right panel.

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Table 2.12: Probit regression for the probability of an occupation being

highly seggregated1

Change in occupation's share of employment
Current period -4.196* *
(-2.31)
-2.617
(-1.54)
-2.312**
(-1 .99)

Lagged one year
Lagged two years

Lagged three years
(-2.43)
Lagged four years

Test of joint significance
(Chi-squared)

Change in proportion young in occupation
Current period -12.640
(-0.59)
-11.204
(-0.52)
-7.021
(-O.43)
-6.160
(-0.44)

Lagged one year
Lagged two years
Lagged three years

Lagged four years

Test of joint significance
(Chi-squared)

-0092 -0.089 -0119 0057
(4.45) (4.05) (4.07) (4.04)

Women's share of total
employment

0.593M 0.595** 0.589" 0.592"
(12.62) (11.86) (12.26) (11.55)

Occupation is highly
segregated in 1981

Log likelihood -293.42 -274.10 -255.75 -237.16

-2.25**

All effects

4.297
(-034)
0.852
(0.25)
0.520
(0.21)
1.160
(0.49)
-3.304*
(-1.83)

-2140"
(-2.97)

12.42”

44.428
(-O.S6)
-0.l87
(-010)
1.078
(0.04)
-O.885
(-003)
4.840
(-0.09)

-6.453 -4.185
(-0.72) (-035)

0.62

-0.06S -0.08O
(4.20) (4.01)

-0.065
(-O.99)

0.595" 0.597"
(14.94) (10.28)

0.596'"
(9.60)

-2l8.60 ~218.51 -217.65

1 Highly segregated defined as 95 percent female or male. Marginal effects reported. Z-statistics in
parenthesis. Regression weighted by occupation size and is based on values for two digit occupations,
from 1981-1999. Highly segregated dummy is defined as one if occupation is 95 percent male or female

and zero otherwise. " indicates significant at 10% level; " at 5%.

166

Table 2.13: Husband's wage first stage estimates, for married (M) modelsl

Region (Central-west omitted)
Minas Gerais
North
Northeast
Rio
South
Sao Paulo
Rural dummy

Age
Age squared

Years of completed education
one
two
three
four
five
six
seven
eight
nine
ten
eleven
twelve
thirteen
fourteen
fifteen
sixteen
seventeen +

l t-statistics in parenthesis.

I67

-O.4683**
-0.3775**
-O.7187**
-O.5957**
—O.3384**
0.3959”
-0.4805**

0.1983"
-0.0016**

0.4335"
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0.8411“
1.4182"
1.7284"
2.0881"
2.3201"
2.9343"
3.0414"
3.7798"
5.2904"
7.5071"
7.9891"
9.0205"
12.6260"
16.3736"
19.2229"

(43.61)
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(41.99)
(40.65)
(11.47)
(-4433)

(47.68)
(-33.08)

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(50.57)
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(154.83)
(49.43)
(63.87)
(65.48)
(90.93)
(132.43)
(39.66)

——+- E

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81 83 85 87 89 91 93 95 97 99
Year
Figure 2.1: Employment rates for men and women. secular trend

1993 1996
l 990

 

 

 

115 2'0 2‘5 3'0 35 4’0 4‘5 5'0 5% 60 85 70
Age

Figure 2.2: Female employment rates, select years, three year moving average

168

 
 
 
 

1967-71
(birth year) ,
/

  

 

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Figure 2.3: Employment rates for single (top) and married (bottom) women,
five year cohort groups

169

 

 

 

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”“7" . i T 1 I 1 1T 1 a
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Years of completed education

Figure 2.4: Predicted employment rates versus years of education,
married women, select cohort groups

170

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employed as informal wage workers (bottom)

174

 

 

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‘ l

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1.4 1

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Year

Figure 2.9: Relative risk ratios for period (bottom) and cohort (top) dummy
coefficients from sector choice model

 

175

APPENDIX 3

Tables and figures for chapter 3

176

Table 3.1: Summary Statistics
General Commuters Trunk
Aviation (Part 91) (Part 135) Carriers (Part 121)

Accident ratel

Mechanical failure 0.019 0.019 0.002

No pilot error 0.019 0.019 0.002
Most serious injury ("none" omitted)

Fatal 0.203 0.205 0.049

Serious 0.103 0.088 0.196

Minor 0.239 0.103 0.126
Damage ("none" omitted)

Destroyed 0.270 0.245 0.039

Substantial 0.709 0.587 0. 149

Some 0.014 0.117 0.383
Proportion of all on board who suffered:

Fatal injuries 0.184 0.181 0.022

Serious injuries 0.089 0.062 0.010
Pilot's flight hours (thousands)

Total 2.6 5.8 12.9

Proportion in make/model 0.321 0.209 0.275

Proportion as pilot in command 0.793 0.863 0.580
Other training

Pilot's age 44.0 37.0 46.6

Instrument rated 0.496 1.000 1.000

Commercial certificate 0.353 0.636 0.241

Air transport certificate 0.104 0.573 1.000
Pilot is male 0.967 0.968 0.993
VMC 0.900 0.789 0.840
Hours since last inspection 48.5 56.3 224.3
Thrust (thousands of pounds) 394 922 48154
Number of seats 4.0 7.8 149.3
Airframe (hours of flight) 2523 6431 18744
No seat belt used 0.008 0.006 0.004
No harness used 0.187 0.095 0.056
Scheduled Flight 0.000 0.232 0.937
No Flight Plan Filed 0.888 0.459 0.000

‘ Accident rate, accidents per pilot, is weighted.

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Table 3.9: Probit of fatality or severe injury

Pilot flight hours (thousands)
Spline, first 1,800 hours

Spline, hours beyond 1,800
Total hours (thousands)
Total hours squared/ 100

Total hours cubic/100

Joint significance test (chi-squared)

Proportion in make/model
Proportion as pilot in command
Male pilot

Pilot's age

Landings

Flight plan filed

Certificates/ratings
Instrument rated

Commercial certificate
Air transport certificate
Visual meteorological conditions

Night flying

N. Observations
Log of Likelihood

General

-0.0024**

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(-O.83)

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(6.92)
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Aviation (Part 91) (Part 135)

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5.40

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(1.44)
(0.009)
(0.83)

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Carriers (Part 121)

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(1.03)
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(0.07)

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186

Table 3.10: Tobit model for proportion killed, all observations

General Commuters Trunk
Aviation (Part 91) (Part 135) Carriers (Part 121)

Pilot flight hours (thousands)

Spline, first 1,800 hours -0.0349
(-1.300)
Spline, hours beyond 1,800 -0.3996O
(-0.770)
Total hours (thousands) -O.l 178 -0.2474
(-0.320) (-0.600)
Total hours squared/ 100 0.0008 0.0147
(0.020) (0.500)
Total hours cubic/ 100 -0.0001 -0.0002
(-0. 130) (-0.310)
Joint significance test 1.32 0.58
(Chi-squared)
Proportion in make/model -0.2381 -0.8552
(-0.760) (-0.660)
Proportion as pilot in command -1 .7902" -1.4572
(-3.600) (-1.050)
Male pilot 1.1549” 0.77960 -2.7472*
2.2000 0.5000 -1.7000
Pilot's age (-0.000) 0.0789" (-0.014)
-0.0100 2.4600 -0.3300
Landings (0.097) (0.167) (-0.026)
0.6100 0.7700 -0.0400
Flight plan filed (-0.394)
-1 .2200
Certificates/ratings
Instrument rated 0.3429
(1.250)
Commercial certificate -0.2600
(-1.010)
Air transport certificate -1.3317** 0.1437
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Visual meteorological conditions -6.8281** -3.7468** -1.0204*
(-1 4.960) (-4.660) (-1 .690)
Night flying 1.7594" 1.4208M 0.5008
(6.540) (2.420) (0.960)
N. Observations 12851 1083 671
Log of Likelihood -4836.35 -41 1.52 -102.15

" indicates significant at the 10% level; " at the 5% level. dF/dx reported. z-statistics in parethesis.

187

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Table 3.12: Probit of accident, Trunk carriers, incidents not used

Mechanical failure No pilot error
Pilot flight hours (thousands)

"‘ indicates significant at the 10% level; " at the 5% level. dF/dx reported. z-statistics in parenthesis

190

Total hours (thousands) -0.0027" -0.0005
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(2.370) (0.770)
Total hours cubic/ 100 -0.0003*"' -0.0001
(-2.300) (0670)
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(1.370) (0.650)
Other training
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(2.640) (0.160)
Male 0.0013 0.0009
(0.410) (0.370)
Landings, last 90 days (thousands) -0.0006 (0.0029)
(-0.680) (2.920)
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Visual meteorological conditions -0.0056** -0.0011
(~2.690) (-l .610)
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(-0.510) (0.190)
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192

Table 3.14: Probit for pilot error, with trends and interactions

General Commuters Trunk

Pilot flight hours (thousands) Aviation (Part 91) (Part 135) Carriers (Part 121)

Total hours (thousands) -0.0014 -0.1492** 0.0639“
(-1.11) (-1.94) (1.74)
Spline dummy -0.0726**
(-6.02)
Total hours squared/ 100 0.0094“ -0.0055
(1.75) (-l.47)
Total hours cubic/100 -0.0002 0.0001
(-1.51) (1.32)
Proportion in make/model -0.0277 -0.0351
(-1.39) (-0.29)
Proportion as pilot in command -0.0022 0.0277
(-0.07) (0.20)
Trend 0.0064 -0.0409 0.0157
(1.50) (-1.l3) (0.89)
Trends Interactions
Trend x total hours -0.0001 0.0017 -0.0069
(-0.42) (0.19) (- l .69)
Trend x spline dummy 0.0018
(1.23)
Trend x total hours squared/ 100 0.0002 0.0005
(0.28) (1.24)
Trend x total hours cubic/100 -0.0001 -0.0001
(-0.63) (-0.99)
Trend x proportion make/model -0.0008 0.0067
(-0.31) (0.45)
Trend x proportion pilot in command -0.0101** 0.0010
(-2.37) (0.06)
Marginal trend effect (dP/dTrend) -0.0037 —0.0154 -0.0023
Joint significance for trend interactions (6.12) (4.95) (5.41)

(Chi-squared)

* indicates significant at the 10% level; ** at the 5% level. dF/dx reported. z-statistics in parethesis.

193

.64
.4‘
.2n

 

 

 

 

 

 

 

0 a
1 T l 7 r T
0 5 10 15 20 25
.15 -
.1 -
.05 ~
0 fl l T l l l
0 5 10 5 20 25
.06 ~
.04 -
.02 —
0 -i
6 5 1'0 1‘5 26 2'5
Thousands of flight hours

Figure 3.1: Density function for flight hours, general aviation (top),
commuters (middle) and trunk carriers (bottom)

194

 

.85 ‘

 

.75 *

 

 

._.
_
-
_(
_
_

.84

.75 ‘

.65 “

 

 

 

1'0 1'5 2'0 2'5 3'0
Thousands of flight hours

0—
0|

 

Figure 3.2: Non-parametric estimates of pilot error probability. general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8

195

.25 a

 

 

 

 

 

 

 

 

_2 _ All observations
.15 -
/ Mechanical'f‘a'ilure' h- -__-—"""““’
1 " [I ................................
No pilot error
.05 a
I l l I I I
.3 -
All observations
.2 —
Mechanical failure ,a~«v¥.":‘””' ------------------
1 _‘ "\_,/-~\,/\-’..,’-T
-' "iii; pilot error
1 i i I
0 g 10 15 20
All observations
.05 T \ ._"s
Mechanical failure ‘~~VL\,\ .........................
O -1
.--"‘No pilot error
-.05 -
l I I r f
0 5 10 15 20
Thousands of flight hours

Figure 3.3: Non-parametric estimates of fatality probability, general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8

196

 

 

 

 

 

 

 

 

 

 

 

.3 a W
All observations
.25 -
r/n\~-~~..v‘ _____________
,2 Mechanical failure '—“'”"‘f_jj:tfi
2 _ I ...........................................
----‘---""‘ No pilot error
.15 a
.1 ‘
r l l 1 i I
0 .8 5 10 15 20
.3 -*
All observations
.25 -
‘T\ f‘q'”"\'-\~_
.2 -l \\ /~\/U-~vf"‘ . . “““
\__,~' Mechanical failure “A-“
‘\\\
............................ \.
'15 _ ......
._ No pilot error
.1 -
6 l l l l
5 10 15 20
.15 ‘
\\ Mechanical failure
\
\
.1 a \
\
\\
\
\\‘\
All observations “\
.05 - “\\
\‘l
I‘qu
.................................. ”\‘\’———-—_
""""" No pilot error
O .1
r l l T l
0 5 10 15 20

Thousands of flight hours

Figure 3.4: Non-parametric estimates of probability destroyed, general aviation (top),

commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8

197

.03 “

 

 

 

 

    

  
      
  
 

 

 

   

 

 

.02 - Mechanical failure”
.01 -
T i l I
0 1.2 5 10 15 20
.05 -
.04 -
.03 a
Mechanical failure
.02 A \ /‘\,"""\/
L~.,.-‘\V__,~ -\ ___________________
No pilot error
01 _1 T l l l l
0 5 1O 15 20
.02 -
.015 r
.01 fi No pilot error
.005 - \
0 Mechanical failure ————————————————————
0 5 1'0 1'5 20
Thousands of flight hours

Figure 3.5: Non-parametric estimates of accident probability, general aviation (top),
commuters (middle) and trunk carriers (bottom). LOWESS, bw=0.8

198

 

 

 

 

 

 

 

.8 '1
.75 a
.7 ~
.65 —
(3 T ' 1'5
Thousands of flight hours
.75 a
.7 -
65 _' l j T l l—
0 5 10 15 20
.6 a
.5 -
.4 a
.3 r
0 5 1'0 1'5 50
Thousands of flight hours

Figure 3.6: Predicted probability of pilot error from probit model, general aviation (top),

commuters (middle) and trunk carriers (bottom)

199