W1,.59I
POLICY RESEARCH WORKING PAPER 2541
Household Schooling An analysis of a field survey to
investigate household
Decisions in Rural Pakistan decisions about schooling in
rural Pakistan suggests that
Yasayuki Sawada hiring more female teachers
Michael Loksbin and providing more primary
schools for girls closer to
villages will improve the
chances of rural Pakistani girls
entering school and staying
enrolled.
The World Bank
Development Research Group
Poverty and Human Resources H
February 2001
PoLicy RESEARCH WORKiNG PAPE. 2541
Summary findings
Human capital investments in Pakistan are performing There is a high educational retention rate,
poorly: school enrollment is low, the high school conditional on school entry, and that male and female
dropout rate is high, and there is a definite gender gap in schooling progression rates become comparable at higher
education. Sawada and Lokshin conducted field surveys levels of education.
in 25 Pakistani villages and integrated their field * A household's human and physical assets and
observations, economic theory, and econometric analysis changes in its income significantly affect children's
to investigate the sequential nature of education education patterns. Birth order affects siblings'
decisions-because current outcomes depend not only on competition for resources.
current decisions but also on past decisions. * Serious supply-side constraints on village girls'
Their full-information maximum likelihood estimate of primary education suggest the importance of supply-side
the sequential schooling decision model reveals policy interventions in Pakistan's rural primary
important dynamics affecting the gender gap in education-for example, providing more girls' primary
education, the effects of transitory income and wealth, schools close to villages and employing more female
and intrahousehold resource allocation patterns. They teachers.
find, among other things, that in rural Pakistan:
This paper-a product of Poverty and Human Resources, Development Research Group-is part of a larger effort in tie
group to study the role of gender in the context of the household, institutions, and society. Copies of the paper are available
free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Patricia Sader, room MC3-632,
telephone 202-473-3902, fax 202-522-1153, email address psader@worldbank.org. Policy Research Working Papers are
also posted on the Web at http://econ.worldbank.org. The authors may be contacted at sawada@'stanfordalumni.org or
mlokshin@tworldbank.org. February 2001. (31 pages)
The Policy Research Working Paper Series dissensinates the findings of work in progress to encourage the exchange of ideas about
development issues. An objectiveof theseries is toget thefindings outquickly, even if the presentationsare less thanfully polished. The
papers carry the naoses of the authors and should be cited accordingly. The findings, interpretations, and conclusionls expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
HOUSEHOLD SCHOOLING DECISIONS
IN RURAL PAKISTAN*
by
Yasuyuki Sawadaa b ** and Michael Lokshinb
a Department of Advanced Social and International Studies, University of Tokyo, Komaba
b Development Research Group, World Bank
Keywords: sequential schooling decisions; income shocks; birth-order effects; supply-side constraints
* This research is financially supported by the Scientific Research Fund of the Japanese Ministry of
Education, the Foundation for Advanced Studies on International Development, and the Matsushita
International Foundation. We would like to thank Sarfraz Khan Qureshi and Ghaffar Chaudhry, the
former director and the joint director, respectively, of the Pakistan Institute of Development Economics;
Punjab village enumerators Azkar Ahmed, Muhammad Azhar, Anis Hamudani, and Ali Muhammad; and
NWFP village enumerators Aziz Ahmed, Abdul Azim, Asad Daud, and Lal Muhammad for support of
field surveys. Suggestions and guidance from Harold Alderman, Takeshi Amemiya, Jere Behrman,
Marcel Fafchamps, Nobu Fuwa, Anjini Kocher, Sohail Malik, Jonathan Morduch, Pan Yotopoulos, and
seminar participants at Stanford University are gratefully acknowledged.
** Corresponding author, email: sawada@stanfordalumni.org.
I
1 Introduction
The recent revival of economic growth theory has renewed interest in the nexus of human capital
investment and growth (Barro and Sala-i-Martin 1995). Studies across countries show that human capital
investments in Pakistan are performing poorly: the school enrollment rate is low, school dropouts are
widespread, and there is a distinct gender gap in education (Behrman and Schneider 1993; Sawada 1997).
Theory suggests that the low level of education in Pakistan may have a strong negative effect on the
country's long-term macroeconomic growth. The microeconomic behavior of Pakistani households
should underlie such a macroeconomic movement, involving the interplay of parental objectives and
constraints faced by the households.
However, human capital is accumulated through a complicated decision-making process. The
educational outcome is typically represented by years of completed schooling, which is a stock rather
than flow,variable. In this case, the current outcome depends not only on the current decision but also on
past decisions. Therefore, general reduced form solutions will include the entire history of exogenous
influences (Strauss and Thomas 1995, 1974-75). Yet, such historical data on individual and household
characteristics are rarely available. Because appropriate data are typically missing, the dynamic aspects
of education are ignored in most of the reduced form empirical literature. However, even if we have the
data that theory requires, introducing dynamics by having the current period's outcome depend on past
outcomes'complicates the estimation procedure.
This paper attempts to overcome these two issues in the existing literature on education by
making two important contributions. First, to examine explicitly the dynamic and sequential aspects of
schooling decisions, we use a unique data set on the whole retrospective history of child education and
household background, which was collected exclusively for this analysis through field surveys in rural
Pakistan. This data collection itself contributes to the literature, shedding light on dynamic aspects of
education. Second, in addition to the data contribution, this paper uses the full-information maximum
likelihood (FIML) method to cope with the complicated estimation procedure of multiple integration of
conditional schooling probability. This method, combined with the unique data set, enables us to estimate
the full sequential model.
The estimation results of sequential schooling probabilities provide new and important insights
on demand for education. In sum, five important findings emerge from our estimation. First, the most
striking feature discovered is the high educational retention rate, conditional on school entry. Second, the
schooling progression rates become comparable between male and female students at a high level of
education. These observations indicate that parents might pick the "winners" for educational
2
specialization and allocate more resources to them, regardless of their gender. Third, we found that this
schooling pattern can be explained partly by physical and human asset ownership and parental income
and health shocks. Fourth, we found gender-specific birth-order effects that suggest resource competition
among siblings. These third and fourth findings are consistent with the theoretical implications of the
optimal educational investment behavior under binding credit constraints. Hence, this paper gives
important new insights for understanding the dynamics of household risk-coping strategies and
educational decisions in developing countries. Finally, we found that the supply side constraints of
education in the village significantly restrict education, especially for females. The last finding suggests
the importance of future research on the supply side management of education.
This paper proceeds as follows: Section 2 describes the key features of human capital
investments in rural Pakistan, which were identified from the field research. Based on initial observations
from the field, Section 3 applies the standard theory of dynamic schooling investment decisions. Based
on the theoretical framework, we derive an econometric model with which we can estimate the
conditional schooling probabilities in Section 4. Section 4 then shows estimation results of the empirical
model. The final section offers conclusions and policy implications.
2 The Key Features Identified in the Field
Our approach follows an iterative process of (1) initial hypothesis, (2) field survey, (3) theory, and (4)
empirical analysis, which is suggested by Townsend (1995). Instead of directly implementing
econometric tests based on an existing well-defined data set, this paper starts with key features of
household behaviors discovered in the field. Modification of data collection was undertaken in the initial
stage, and the standard theory is augmented afterward according to the field observations.
Field surveys were conducted twice to gather information exclusively for this paper. In the first
round of the survey in February through April 1997, the survey team carried out interviews in fourteen
villages of the Fisalabad and Attock districts of Punjab province. Then the second-round surveys were
conducted in eleven villages of the Dir districts of the North-West Frontier Province (NWFP) in
December 1997 through January 1998. Our field surveys covered 203 households in Punjab and 164
households in NWFP. Hence, 367 households were interviewed, and information on a total of 2,365
children was collected.' The combined data give a complete set of retrospective histories of child
' The selection of our survey sites was predetermined, since we basically resurveyed the panel households that had
been interviewed by the International Food Policy Research Institute (IFPRI) through the Food Security Management
Project (Alderman and Garcia 1993; Alderman 1996). The initial IFPRI data collection was based on a stratified
random sampling scheme. A detailed description of the procedure of our field surveys is summarized in the
3
schooling, together with household and village level information.
The most striking feature uncovered in the field is the high educational retention rate, conditional
on school entry. According to our survey data, years of schooling averaged 1.6 years for all female
children in the overall sample, whereas they were 6.6 years for male children. On the other hand,for
children who had entered primary school, the average years of schooling become 6.0 years for girls and
8.8.years for boys. These numbers indicate that after entering school, children's years of schooling
dramatically increase.
To examine the school progression rates in detail at different educational stages, we utilize the
framework of estimating the conditional survival function. The Pakistani education system is composed
of five years of primary education, five years of secondary education, and postsecondary education.2
Educational outcomes can be understood as a result of five sequential schooling decisions. The first
decision is whether to enter primary school (S*i), where S*, represents schooling time of a child at T-th
educational stage. For those who attended primary school, the second decision is whether to finish
primary school (S*2). Then the third decision for primary school graduates is whether to continue to
secondary school or stop education at grade five (S*3). For those who entered secondary school, the
fourth decision is whether to stop before grade ten or to graduate from secondary school (S*4). The final
decision is whether to continue beyond secondary school-that is, to enter college, technical, or teaching
school (S*5).3
Let nk denote the number of students whose have completed education of the stage of S*k ,. We
simply used data where S*k-I is not right-censored at the education level k- 1. The set of individuals whose
school attainment is at least S*k.l is called the risk set at the k-th stage of education, S*k, and thus nk
represents the size of the risk set at the level k. Among nk students, let hk denote the number of children
who have completed education level k, and therefore hk = nk+1. Then, an empirical estimate of the
conditional survival probability at education level k would be hk/nk. This number represents the fraction
of studenis who go on to a higher stage of education, conditional on the completion of the education level
k- 1. Also, this can be interpreted as the sample conditional probability of school continuation to the
education level k.
The estimated conditional survival or school continuation probabilities are summarized in Table
2. As we can see in Table 2, the survival rate at the first entry-that is, the probability of ever entering
appendix.
2 Strictly speaking, secondary education in Pakistan is composed of three years of middle education and two years of
high school education.
3 We assume that for those who did not enter a primary school, the decision was made when the child was at the age
of six, which is the median age of primary school entry (Table 1). We impose similar assumptions for secondary and
postsecondary education.
4
school-is low both for boys (64 percent) and girls (24 percent). We can also note that the female
conditional schooling probability is less than half of the male conditional probability at primary school
entry. After entering primary school, however, conditional primary school graduation rates become 82
percent and 69 percent for male and female students, respectively. These statistics indicate that after
entering school, the majority of children remain at school. Another interesting finding is that while the
conditional schooling probability is lower for girls than that for boys at primary school entry and
graduation and at secondary school entry, the conditional schooling probabilities after secondary school
entry are consistently higher for females in Punjab province. The gender gap in education eventually
seems to disappear at the higher stages of education.4 This finding indicates an important dynamics of the
gender gap in education, which has not been pointed in the literature.
These basic statistics also suggest substantial differences in the degree of the educational gender
gap among districts. According to Table 2, in the Dir district of NWFP, the conditional survival rates are
consistently lower for females at all stages of the schooling decision. The district differences seem to be
largely due to sociocultural factors. For example, the custom of seclusion of women, purdah, is strictly
maintained in the Dir district. These regional divergences in gender gap in rural Pakistan raise an
important policy issue. Alderman et al. (1995) pointed out that when the government allocates education
expenditures, disadvantaged groups such as girls and children in lagging regions should be targeted to
assure more equitable gains from schooling.
3 The Standard Theory of Educational Investments
Having discussed the key observations in the field, the next step is to formulate a formal model of the
household's optimal schooling behavior, integrating the key features. A possible interpretation of the
above findings is that parents might pick the "winners" for educational specialization and allocate more
resources to them. As an initial theoretical framework to account for this household behavior, we employ
the two sqts of optimal behavioral rules. First, parents decide the intertemporal allocation of resources so
as to maximize the expected total lifetime utility of the family. Second, parents also make a decision on
the allocation of educational resources among children, given the overall resource constraint of the
household.
4 We also estimated the Kaplan-Meier product limit estimator, and the results are available upon request from the
corresponding author. The Kaplan-Meier estimator of survival beyond stage k is the product of survival probabilities
at k and the preceding periods. Graphing survival probability against sequence k produces a Kaplan-Meier survival
curve. Again, at the primary school entry level, the school survival rate is much higher for males than for females.
The slope of survival function, however, is flatter for females, indicating that gender gap in education becomes
smaller at the higher levels of education.
5
We use a standard investment model of education as the benchmark and apply it to the context of
rural Pakistan. The basic setup of our model is based on the seminal works by Levhari and Weiss (1974)
and Jacoby and Skoufias (1997) on human capital investment under uncertainty. In particular, we extend
the Jacoby and Skoufias (1997) model to a generalized form with multiple children. Essentially, risk,
uncertainty, and constraints on insurance and credit influence poor Pakistani households' investment and
consumption decisions. Therefore, we formalize human capital accumulation in rural Pakistan as
households' sequential schooling investment decisions under uncertainty and credit constraints.
Suppose a household with n children decides household consumption, C, and schooling for child
i, Si, so as to maximize the household's aggregated expected utility with concave instantaneous utility
function, U(*), given the information set at the beginning of time t, Q. The infornation set, Q, includes
initial asset ownership and the whole history of household variables. Such a household's problem can be
represented as follows:
T-t
Mar E E P U (Ct,k ) + W (AT+I Hc T+I X H2 +I> HnT+l )I | Q
S.t A(+1 = LAt + Y, (HP ) + Wi w;(-Q i -3 Ct ](I + rt )
n
Hc,,+ =H,c + E[(St, q,t ) +ejt i=l, 2, *., n
i=l
At + Y,(HP) + 1W,(1SE,)+B 2C,
1=1
B >2O, HP, AO and B0 are given, AT 2 0.
In this problem, the objective function includes a concave function, W(.), of financial bequest and salvage
value of the final stock of the child's human capital. The parameter ,B represents a discount factor. The
first constraint is the household's intertemporal budget constraint. This household's consumable
resources in each period are composed of assets, A; stochastic parental income, YX which is a function of
parents' human capital, HM; and total child income, Elw,(I-Si,), with w; being the child-specific wage rate.'
Note that a child's total time endowment is normalized to 1. The second constraint is the human capital
accumulation equation. The human capital production function,fte), includes the variable q, which
represents the school supply side-effect, the gender gap, and subjective factors. Among others, the
variable q is a function of a time-invariant gender indicator variable that takes 1 if the child is female and
5 We assume that a child's schooling does not change the child wage rate immediately, and accumulated human
capital, He; is reflected in income after the child becomes an adult. In rural Pakistan, the child labor market does not
seem to be segmented by level of education, since it is well known that the wage rate is not sensitive to education in
rural agricultural areas (Fafchamps and Quisumbing 1999).
6
0 if the child is male. Also, there is an additive stochastic element e, which incorporates possibilities such
as risk of job-mismatching after schooling. We assume that e is independently distributed with E(ei, In,) =
0 for all i. The third constraint represents the potentially binding credit constraint where B is a maximum
amount of credit available to a household.
This stochastic programming model has n+1 state variables: physical assets, A, and child human
assets, Hic., i = 1, 2, ..., n. When income is stochastic, analytical solutions to this problem, even without
human capital, cannot be derived in general (Zeldes 1989). However, we can derive a set of first-order
conditions that is necessary for an optimum solution, applying the Kuhn-Tucker conditions to the
standard Bellman equation. In the arguments below, we will use the first-order conditions of the above
problem.6
Now let us specify the functional forms of utility and human capital production functions. For
the utility function, we assume the constant absolute risk aversion (CARA) specification.
(1) U(C,) = a --exp(C,),
a
Note that a represents the coefficient of absolute risk aversion. For the human capital production
function, we also select the exponential function:7
(2) f(Si, ,qit ) = qit [O -y y exp(-S, )S]t
where yo > 0 and y, > 0 and it is easily verified thatfs > 0 andfss < 0.
Noting that parental human capital affects permanent income, let Ytp(HP) and Y,T represent
permanent and transitory components, respectively, of parents' income, YXHf). Then, by definition, we
have Y,(If) = Y/P(if) + Y/ with E(Yn,S) =YP(Hf) and E(Y,TIQ,) = 0. Our further assumption is
represented by Y, - N(Y/P(HI), cr/)-that is, parental income follows an augmented i. i.d. normal
stationary process. Moreover, we select that following particular specification for the permanent income
function: YtP(Hp) = p Hpt + g(H), where the first term in the right hand side represents that human capital
adjusted time-trend of income with parameter p. The second term, g(.), is a general nonlinear function
that defines the form of parents' human capital specific wage profile.
There are two different solutions for this problem. First, when a household can borrow and save
money freely at an exogenously given interest rate, the credit constraint is not binding. In this case, the
household determines the evolution of optimal schooling so as to equalize the net marginal rate of
transformation of human capital production and the nonstochastic market interest rate, that is,
6 For the full derivation of the first-order conditions, see Sawada (1999).
7 For an alternative specification of the human capital production function, see Sawada (1999).
7
af/asS, =1 + r, V i.
af /as1,-
Using the functional form of equation (2), the optimal schooling decision rule then approximately
becomes
(3) S; = X,, P + Sl1 , V i,
where XPN is defined as
X,jt 3 git r, i
Gender Gap
Subjective Factor
School Accessibility
where g represents the growth rate of q, which includes effects of school accessibility, gender gap, and
subjective factors, and Xis a matrix of proxy variables for g and r. Equation (3) is a linear difference
equation for the optimal schooling decision, S*. This equation indicates that the optimal level of
schooling is a function of school availability and quality, gender-specific elements, and the market
interest rate. Hence, if the credit constraint is not binding, parental income or schooling decisions of
other children do not affect the schooling decision for a child. In this case, two separabilities hold: one
for consumption and schooling decisions and the other for intrahousehold schooling allocation.
Alternatively, if the household is constrained from borrowing more, the household effectively
faces an endogenous shadow interest rate, which is given by the marginal rate of substitution of
consumption over time. Under credit market imperfections, the separability between consumption and
schooling investment decisions breaks down. The optimal condition becomes the following equalization
of the marginal rate of transformation to the marginal rate of substitution:
aflasi, au/ac, 1
= PE,_1 8U/C I,
Also, note that the separability among different children's schooling decisions does not hold. Under these
nonseparability properties, the reduced form schooling decision can be represented by the following
linear difference equation:
(4) S,; = Xi, C + S,;, +6i., V i,
where XI3C is defined as
_ _In_ _ _ _ 1+a a a 2_ _ 2 _
) " -( I+a )I+ (pP + )+ a A 2(1+a) 2 a j*)
(I)~~~~~~~~~~~~~~~~~~~~~~~~(V
Gender Gap Olwnership and Accumulation Esx Post Ex Ante Opportunity Costs of
Subjective Factor of Assets Transitory Income Income Instability Siblings'Schooling
School Accessibility (Precautionary Saving)
8
Note that ej, indicates a mean zero expectation error of parental income Y,. We allow a possibility of
serial correlation of this expectation error. In our estimation, we use various proxy variables for X, which
includes the following five components (equation 4'). First, X includes the gender indicator variable, the
school accessibility variable, and household-specific subjective factors of educational investments. The
second component of X is the ownership and accumulation of human and physical assets. The third term
(III) shows that an ex post realization of transitory income of parents, AY,T, has a positive impact on child
schooling. In contrast to a household with perfect credit availability, where parental income variable does
not affect child schooling, a credit-constrained household faces a high marginal cost of schooling if there
is a negative income shock. This reflects that consumption and schooling decisions are not separable
under a binding credit constraint. The fourth term (Ill') shows the negative effect of income instability.
This term basically indicates that, given a positive third derivative of utility function, there is a motive for
precautionary saving as an ex ante optimal behavior against income instabilities. The positive
precautionary saving negatively affects child education since there is resource competition between asset
accumulation and investment in education. The final term indicates educational resource competition
among siblings. For example, an increase in other children's schooling time, AS* , Vj # i, or its
opportunity cost, wAS;.j, decreases child P's optimal level of schooling.8 Alternatively, the wage earnings
of older siblings will enhance the optimal time allocation to schooling by decreasing WjAS;j.
Testable Restrictions
The important testable hypothesis can be derived by comparing equation (4) with equation (3). We can
easily note that the four terms of the right-hand side of equation (4)-terms (II), (III), (III'), and (V}-
should be 0 under perfect credit availability. On the other hand, under the binding credit constraint,
proxy variables for asset ownership and accumulation, transitory income, income stability, and sibling
variables should affect a child's schooling behavior. Hence, our theoretical framework offers testable
restrictions that characterize two different credit regimes.
The economic intuition of these results should be clear. The two terms (II) and (III) in equation
(4') indicate that a household's overall resource constraint and life-cycle considerations will determine
the total amount of expenditure devoted to education. Credit and insurance availability become
8 According to equation (4), the optimization behavior of a household for the ith child is conditional on that for all
other children. The optimal choice of child i's schooling, S*¶, depends on S*.i, the optimal schooling decision made
for a child other than i. We therefore derived a Nash equilibrium of child educational decisions implicitly. Strategies
that comprise a Nash equilibrium at each date are referred to as Markov perfect. The equilibrium represented by
equation (4) can thus be interpreted as the Markov perfect equilibrium (Maskin and Tirole 1988; Pakes and McGuire
9
especially important at this stage. If borrowing is allowed under an exogenously given interest rate, a
household can maximize the total wealth simply by investing in the human capital of each child so that
the marginal rate of return from educating each child is equal to the interest rate. However, if credit
availability is limited and thus household's consumption and investment decisions are not separable, the
household resource availability such as parental income and assets affect the cut-off shadow interest rate
for educational investments. For example, when there is an unexpected income shock, credit-constrained
poor households have relatively high marginal utility of current consumption. This leads to an increase in
the cut-off shadow interest rate and a decrease in child education. In this case, implicit or explicit child
labor income can act as insurance that compensates for unexpected income shortfalls of parents.9
4 The Econometric Framework
There are two empirical approaches for investigating the schooling decision-making process, based on the
basic investment model of equation (4).10 First, the traditional approach employs a simple linear
regression model for years of schooling with various household background variables as explanatory
variables (Taubman 1989). However, the problem of this approach is that the linear regression model
combines the sequential schooling decision process into an estimation of time-invariant parameters and
therefore parameters in the model cannot be interpreted well as structural parameters.
The second approach fornalized the process of schooling as a stochastic decision-making model
(Mare 1980; Lillard and Willis 1994, Behrmnan et. al., 2000). The model explicitly investigates the
determinants of sequence of grade transition probabilities. In other words, the probability of schooling at
?h grade conditional on completing schooling at T- 1 th grade is empirically estimated. The model has a
substantial advantage over the linear regression approach since it gives estimates of structural parameters.
The statistical foundation of estimating such a sequential decision-making model was first provided by
Amemiya (1975). The model framework was then applied to estimation of schooling grade probabilities
1994; Besley and Case 1993).
9 In fact, many estimates of schooling fimction using household data sets from developing countries report positive
coefficients of current household income variables, which imply the existence of credit market imperfections
(Behrman and Knowles 1999; King and Lillard 1987; Sawada 1997).
'O In fact, a third approach consists of applying the structural estimation framework for a dynamic stochastic discrete
choice model. For a literature survey, see Amemiya (1996) and Eckstein and Wolpin (1989). Yet, given a household
having n children, the household's schooling choice set is composed of 2" mutually exclusive, discrete dependent
variables. Since n takes about seven on average in our households from Pakistan, the structural estimation of such a
model will be computationally intractable. Applications of this framework to development issues include estimates
of the gender and age specific values of Korean children (Ahn 1995), an analysis of sequential farrn labor decisions
using Burkina Faso's data (Fafchamps 1993), well investment decisions in India (Fafchamps and Pender 1997),
bullock accumulation decisions of Indian farmers (Rosenzweig and Wolping 1993), and an analysis of fertility
10
with family background characteristics as determinants of these probabilities. For example, using a
Malaysian data set, Lillard and Willis (1994) estimated the sequential schooling decision model,
controlling for individual unobserved heterogeneity. Cameron and Heckman (1998) constructed an
alternative choice-theoretic model to examine how household background affects the school transition
probabilities. Other papers focus on only one transition out of the many sequences of schooling process,
such as the transition probability of high school graduates (Willis and Rosen 1979).
We will follow the second econometric approach and estimate the sequential schooling decision
model jointly. To estimate probabilities of the sequential decisions with an assumption of serial
correlation, we employ the full-information maximum likelihood method. Recall that there are the three
levels of education in Pakistan: primary, secondary, and postsecondary. Educational outcomes are
assumed to result from the five sequential decisions, as discussed in Section 2.
To formalize the sequential schooling process, we can define an indicator variable of schooling:
(5) Si, = 1 if S*it > O
= 0 otherwise,
where r indicates the Tth stage of education and S' is a latent variable and corresponds to the schooling
time variable, S*, in equation (4). Note that 3,i, = 1 if child i goes to school at the re' stage of education.
We discretize the years of schooling into five categories, and thus r takes on five values. With this new
discrete variable, the sequential process of schooling decision is described as follows: children are born
with zero years of schooling. If children become the age of six or so, some children enter primary school,
while other children stay uneducated. The uneducated children with no primary school entry, S*', = 0, is
represented by the indicator variable 6i, = 0. Having entered primary school (S*il > 0 and 8i, = 1), some
children finish primary school (6,2 = I or S*¶2 > 0) while other children drop out from primary school (5,2
= 0 or S*'2 < 0). Then, of those children who have finished primary school, some enter secondary school
(58 = 1 or S*63 > 0), while others do not (d3 = 0 or S*a3 S 0). Given entered secondary school, some
children finish secondary school (°i4 = 1 or S*j4 > 0), while other children do not (3i4 = 0 or S*j4 < 0).
Finally, after finishing secondary school, some children enter postsecondary school (3I5 = 1 or S*,5 > 0),
although others do not (3i5 = 0 or S*j5 < 0).
By rewriting equation (4), the estimation equation for child i can be represented by
(6) SIT, = Xi Pr 3 Ui +
where r =i 1, 2, ..., 5, and ui, -- S*i,,I + gKr. X is assumed to include the gender indicator variable, the
school supply variables, determinants of the household preference, household shock variables, and the
decisions using Malaysian data (Wolpin 1984).
11
sibling composition variables. Note that S*io = 0 by construction.
Under an assumption that the decision making is independent across stages, or equivalently, ui, is
independent across T, the sequential model of equation (5) and (6) can be estimated by maximizing the
likelihood functions of dichotomous models repeatedly (independent error term specification) (Amemiya,
1975). However, our theoretical result indicates that schooling decisions are not independent across
stages by construction. It is straightforward to show that Cov(S*it, S*i,r) 0, since UiT S*j.T + El,.
These correlations can be explained, for example, by some unobserved propensity for schooling that is
stronger among the children who graduated from a certain grade than among the children who did not
finish this grade.
Suppose that the joint probability density function of the error terms UIT is represented byAtu,1, u,2,
uM3, uA4, uM5). Then, for example, the probability of entering postsecondary education, that is, Pr(8,5 = 1),
can be represented by
(7) Pr (S*i5 > 0, S*4 > 0, S*g > 0, S*,2 > 0, S*ii > 0)
f= f f f f f(u1,u2,u3,u4,u5)dU5du4dU3du2duI
Xa1 -XI2j -X3 -X,33 -X4j4 -X,iP5
The direct calculation of such a high-dimensional integral is computationally involved and maybe
infeasible, as the integral must be evaluated at each step of the likelihood maximization. There are two
possible ways to deal with the problem. Both ways rely on the fact that the unconditional joint
distribution (7) can be presented as a weighted sum of products of univariate distributions. If no
assumptions are made about the form of the joint distribution of the error terms of (6), u,,T then, assuming
the common-factor error structure, the joint distribution can be approximated nonparametrically by a step
function (Heckman and Singer 1984; Mroz 1999). Alternatively, under an assumption of joint normality,
the distribution of the error terms of (6) can be approximated using Gauss-Hermite quadrature (see Judd
1998). The first method imposes fewer restrictions on the error structure in the system of equation (6),
but it is less stable computationally. The likelihood function that results from nonparametric estimation
of the error distribution (7) is highly nonlinear, and our maximization algorithm fails to find a global
optimum. An approach based on Gauss-Hermite quadrature demonstrated much better convergence
properties in our case, and this is the method we use for our estimations (we will refer to this method as
FIML further in the text). The log-likelihood function 3 for the system of equations (6) is then:
N / U 2 U3 U4 R \
-1= J£ Log( E WZ fi W2 fi W3 E W4 PR| P7 (XiT |T I Vm. i VM2 5 VM3 MVm4
n=1 m=1 m2sl m3=1 m4=1 T=L
where N is total number of observations in the sample, PR'(*) are the cumulative distribution functions
12
for every equation in system (6) conditional on the common factors, v's and w's are one-dimentional
quadrature points (nodes) and weights from a Gauss-Hermite rule (Stroud and Secrest 1966), M's are the
numbers of quadrature points. As before, Xs represent the equation specific sets of explanatory variables
and P's are the vectors of unknown parameters to be estimated.
The estimations presented in the paper are based on the approximation of the probability integral
by Gauss-Hermite quadrature with four nodes." Further increase in the number of nodes fails to improve
the value of log-likelihood function. Identification is achieved through inclusion of the set of stage-
specific variables such as school supply variables, household human and physical assets, and household
income and health shock variables, as will be discussed in the next subsection. According to the
likelihood-ratio test criterion, the independent error specification is rejected in favor of the FIML
specification that assumes a joint normality of the error distribution. 12
5.1 Variables
As we estimate the above sequential schooling model, we start by inspecting the basic data
characteristics. According to the median age of school entry, children enter primary schools at the age of
six, secondary schools at the age of eleven, and postsecondary schools at the age of seventeen (Table 1).
Moreover, our survey data show that primary and secondary education last an average of five and six
years, respectively. Since the formal length of the secondary-level schooling is five years in Pakistan, an
extra year in secondary education in our sample indicates that grade repetition or a delay of secondary
school entry, which is quite common in Pakistani villages.
Table 3 summarizes descriptive statistics of variables used in the sequential model of equation (6)
as the discrete dependent variable, S*i,, and covariates of conditional probabilities, X. According to our
theoretical model (4), X is assumed to include gender gap indicator variables, school supply variables,
subjective discount factor, physical and human assets, transitory income change, and sibling composition
variables.
The gender gap indicator variables are divided into two subgroups according to province. The
first gender variable is for Punjab province and is a dummy variable taking I for females in Punjab
I I Parameters of the model are estimated by maximum likelihood using DFP algorithm (Powell 1977) with analytical
derivatives. The variance-covariance matrix of the estimated coefficients is estimated by approximating the
asymptotic covariance matrix by the so-called "sandwich" estimator (see, for example, Davidson and MacKinnon
1993, 263).
12 Results of the independent error term specification are available from authors upon request. While the independent
error term model is thought to provide biased coefficients owing to correlations of sequential decisions, qualitative
results of the independent error model and the FIML estimates are comparable.
13
province and 0 otherwise. Similarly, the second gender dummy variable for NWFP takes 1 for females in
NWFP and 0 otherwise. These female dummy variables indicate that the share of female students
declined at the primary school entry level (Table 3).
The second block of independent variables contains the gender-specific school supply variables.
The first supply variable takes 1 only if the child is male and there is a male school within the village of
the child's residence. Otherwise, this variable takes 0. The second supply dummy variable takes 1 only if
the child is female and there is a female school within the village. We can see that for primary school
entry level, 37 percent of male children do not face supply constraints, whereas only 18 percent of girls
have access to female schools in their village (Table 3).3
Third, we assume that a household's subjective preference depends on the household's social
class or caste status. Traditionally, the caste status, called biraderi in Punjab and quom in NWFP, is
identified with an occupational position (Eglar 1960; Ahmad 1977; Barth 1981; Ahmed 1980). For
example, agricultural landless laborers are strictly distinguished from landowners. Nonagricultural
laborers such as casual laborers and artisans are also differentiated from landowners. This system of
caste has prevailed in the form of social norms, and members of each class are expected to act according
to their social and economic status. Hence, the caste system indirectly constrains the educational
opportunities of low-caste children. In order to capture these sociocultural effects, we include parents'
occupation dummy variables-farmers with land, landless farmers or nonfarm casual laborers, and
business and government officials. The default variable is those who are unemployed and/or at home
because of sickness or unemployment. According to Table 3, more than 30 percent of our sample is
composed of farmers with land for all schooling processes. It is notable that, at higher schooling stages,
the fraction of children from landless farmers or casual laborers declines significantly. On the other hand,
the share of children of farmers with land ownership increases after secondary school entry. These casual
findings are consistent with the sociocultural background of Pakistani society.
The fourth set of variables is composed of household human and physical asset variables.14 The
first two variables are time-invariant dummy variables for father and mother's education, which take I if
the father,or mother has completed at least primary school and take 0 otherwise. Household physical
asset variables include the amount of land ownership and a dummy variable for tractor ownership. We
can easily see that all four of these household asset variables increase as the child education level
increases (Table 3). Children who are studying at higher levels of education are basically from relatively
13 No village in our sample has upper-secondary and/or postsecondary education. This implies that supply constraints
such as the accessibility of schools are severe at higher levels of education.
14 Although our theory requires us to include asset accumulation as independent variables, we utilize a total asset
variable instead of its first difference. This is simply because markets for land and agricultural machinery are thin in
1a
rich households of educated parents.
With respect to the transitory income shock variables, the model includes good- or bad-year
dummy variables based on household's subjective and retrospective assessment of agricultural
production, wage earnings, and livestock income. The health shock effects are also considered by
including dummy variables for the health of the household head and the wife, which take I if they are
physically inactive and take 0 otherwise. As Jacoby and Skoufias (1997) pointed out, a distinction
between unanticipated and anticipated components of transitory income movements might be important.
The health shocks might be interpreted as the unanticipated components since these shocks are largely
unexpected. On the other hand, income movements include both anticipated and unanticipated
components.
As sibling variables, we take the number of older brothers and sisters. Alternatively, we can
incorporate more detailed sibling composition variables, separated by current schooling status. Yet, our
older sibling variables are predetermined, and thus we may be allowed to regard these variables as being
exogenous. The descriptive statistics show that there is a negative relationship between education level
and the number of older brothers and sisters (Table 3). This finding suggests that those students who
could obtain higher education are from households with a small number of children. This can be a
reflection of intrahousehold resource competition or birth-order effect.
Finally, according to the age distribution of sampled children of the household head, the average
age of children is 20.5 in 1998. However, there is a large variation in age. Some members are older than
50. The age distribution indicates that there will be a potentially large cohort effect, and thus the
empirical model needs to control for it. Hence, we include age cohort dummy variables.
5.2 Estimation Results of the Sequential Schooling Decision Model
Columns in Table 5 summarize a set of estimated coefficients of the full sequential schooling decision
model for each school level. These results are a derived FIML estimation of conditional probabilities
represented by equations (7) and (8). Detailed descriptions and interpretations of our FIML estimation
results are presented below.
Gender Gap
First, coefficients on gender dummy variables indicate that daughters have lower conditional schooling
rural Pakistan and thus we do not observe change in assets frequently.
15
probabilities at the primary entry and exit levels than sons have. The female coefficients in Punjab
province are smaller than those in NWFP at the primary school entry, indicating a smaller gender gap in
Punjab. This regional difference seems to be largely due to the different degree of sociocultural
constraints. Yet the coefficients on the female dummy variable are not statistically significant after
secondary school entry. The gender gap in education seems to disappear among the students who are
studying at seconrdary and postsecondary level schools. Therefore, schooling progression rates become
comparable between male and female students at higher levels of education. Table 6 summarizes the
discrete marginal change of schooling probabilities with respect to gender dummy variables, evaluated at
mean dependent variables.'5 We can easily verify that the marginal effects are different between girls and
boys at the primary school entry level, while the difference disappears at the secondary school exit level.
These marginal effects confirm the above interpretation of the estimation results in Table 5.
Development researchers and practitioners have argued that women are significantly less
educated than men in Pakistan (Khan 1993; Shah 1986; Chaudhary and Chaudhary 1989; Behrman and
Schnieder 1993). There are several possible explanations for the distinct gender gap in education. For
example, the high opportunity costs of daughters' education in rural Pakistan may lead to apparent
intrahousehold discrimination against women in terms of education. Because of the custom of seclusion
of women, purdah, parents might have a strongly negative perception of female education. However, our
estimation results represent that evidence is not so simple or monotonic. Although there is a distinct
gender gap in primary-level education, the gap is likely to disappear among those who have entered
secondary education.
School Supply
The school availability coefficients are positive and significant for female schools, while the coefficient is
not statistically significant for male schools. This result suggests that the lack of primary and secondary
schools in the village clearly impedes female education, while supply-side constraints are not severe for
male students. The marginal effect of primary school availability within the village is represented in
Table 7.'6, According to Table 7, accessibility to a primary school within the village seems to contribute
15 To calculate the marginal effects in a given simulation, the certain value of the variable of interest is assigned to all
the households in the sample in a particular state. The simulated probabilities are generated for each household by
integrating over the estimated distribution and averaging the probabilities across the sample. Next, the value of the
variable of interest is changed, and this changed value is assigned to the whole sample of the households. Then the
new set of simulated probabilities is generated. The marginal effect-that is, the effect of the changes in the particular
parameter on the probabilities of school participation-is calculated as a difference in these simulated probabilities.
16 See footnote 15 for explanations of our methodology to calculate the marginal effects.
16
to a 18 percent increase in a girl's primary school entry probability. Moreover, female primary school
drop out will decline by 16%. In fact, our qualitative survey data show that, in 32.5 percent of school
termination decisions, households listed the supply side as the main reason for their decision problems,
including inaccessibility to school and the low teacher quality (Table 4). A significant portion of the
gender gap in Pakistani education may be explained by supply-side quantity and quality constraints
(Alderman et al. 1995, 1996). Although traditional Pakistani culture requires single-sex schools, the lack
of school availability affects female education more seriously than male education (Shah 1986). Parents
are unwilling to send daughters to school if a female school is not available nearby. Since allowing girls
to cross a major road or a river on the way to school often involves the risk that daughters will break
purdah, parents will choose not to let daughters go to school. Moreover, sociocultural forces also create
the needs for women teachers to teach female students in the village. It has been pointed that irrespective
of the monetary or nonmonetary incentives in the form of scholarships, girls will come only if schools are
opened with female teachers in each village (Chaudhary and Chaudhary 1989).7 Even if a girl's school is
available in the village, a chronic shortage of women teachers imposes serious constraints on female
education.
Social Class Effects
The overall estimated coefficients of the social class variable indicate that, at primary and postsecondary
entry levels, children of business or government official households have the highest schooling
probability among the social classes considered. The second finding is that the farmers with land
ownership have higher level of educational investments at the primary school entry level than landless
farmers or casual labor households. These results suggest that the occupation, which is traditionally
related to social status, affects educational investment decisions at the initial entry decision to schools and
at higher levels of education.
'7 Although the supply of teachers is constrained in part by the shortage of women candidates, the village
environment also prevents expansion of female teachers in rural areas. Attracting and retaining high-quality female
teachers from outside villages poses a different set of problems, since they must relocate, gain local acceptance, and
clear the difficult hurdle of finding suitable accommodations. Even locally recruited teachers could be chronically
absent from school because of responsibilities for their household chores (Khan 1993). Nevertheless, there is not
enough monetary compensation to attract women to be teachers. Provincial governments, for instance, provide
teachers in villages with lower allowances for house rent than teachers in urban areas. Moreover, there might be a
17
Parental Human Assets
Father and mother's education variables have consistently positive and significant coefficients in all
levels of schooling except at the secondary school exit level. These estimation results indicate important
complementarity between the education of the parents and the child schooling investments. This
complementarity is generated possibly by educated parents' positive incentive of educating children,
improved technical or allocative efficiency, and/or superior home teaching environments, as pointed out
by the preceding studies (Schultz 1964; Welch 1970; Behrman and others 2000). Subjective factors
might be important as well. According Table 4, in 13.4 percent of cases, households listed "the
accomplishment of the desired education level" as the primary reason of a child's school dropout. This is
a purely subjective reason, implying that schooling choice may differ depending on ethnicity, network,
and social status (Psacharopoulos and Woodhall 1985). The more educated mother and father seem to be
better able to perceive the benefit of education than uneducated parents, since they can estimate returns to
education more precisely.
Household Physical Assets
At the primary school entry decision, while the tractor ownership variable has a positive and significant
coefficient, land ownership has a negative significant coefficient. This asymmetry in two physical assets
might be attributable to the difference in complementarity with education. In poor Pakistani villages,
tractor ownership is an obvious measure of a household's wealth. Hence, our results suggest that the
primary school entry probability of children is systematically higher for households with wealth.
Moreover, it has been argued that technology and education have complementarity (Psacharopoulos and
Woodhall 1985; Foster and Rosenzweig 1996). It is likely that tractor operation requires at least a basic
level of education. On the other hand, the negative coefficient of land ownership at the primary school
entry level might suggest that there is a complementarity between land ownership and on-farm child
work, which results in less education of children.
At the postsecondary education entry level, both tractor and land ownership have positive and
statistically significant coefficients on the conditional schooling probability. At this level, household
ownership of physical assets seems to play an important role in education decisions. In general,
households' resource availability extends their self-insurance ability and thus encourages high-risk and
high-return investment opportunities. Risk-taking and precautionary saving behaviors may be closely
school quality problem originating from the teacher's low level of education (Warwick and Jatoi 1994).
18
related to physical asset ownership (Morduch 1990). The negative effect of accumulating precautionary
saving on educational investment will be less severe for those households that have assets.
Household Shock Variables
Negative income shocks discourage schooling continuation significantly at the primary school exit and
the secondary school entry and exit levels. Moreover, negative health shocks increase dropouts from
secondary school. These estimation results are favorable to our theoretical model under binding credit
constraints (Equation 4). In general, Pakistani households face considerable income instabilities. Risks
of disaster such as large income shortfalls, sickness, and sudden death of an adult member impose serious
constraints on a household's resources, since there is a severe limitation on formal and/or informal
insurance and credit availability in rural areas. Accordingly, exogenous negative shocks have non-
negligible effects on the household's educational investment decisions. Pakistani households might adopt
perverse informal self-insurance devices by using child labor income as parental income insurance,
sacrificing the accumulation of human capital.18
Sibling Competition
According to the estimated coefficients in the sibling variables block, the number of older sisters seems to
be associated with more primary education for younger siblings. This finding is consistent with
Greenhalgh (1985) and Parish and Willis (1993) using Taiwanese data. Older sisters may extend the
household's resource availability, either by marrying early or by providing domestic labor. This suggests
that households are not discriminating against all daughters, although the older daughters might bear a
large portion of burden under binding resource constraints (Strauss and Thomas 1995).
On the other hand, at the secondary school exit and postsecondary entry levels, the number of
older brothers, instead of the number of older sisters, increases schooling probabilities. These results
suggest that once a child is picked as a "winner" of educational investment within the family, his or her
education at the secondary and postsecondary level is supported partly by the older brother's resource
contributions. At these higher levels of education, an older brother's farm or nonfarm monetary income
contributions to household resources might be more important and significant than a daughter's
nonmarket domestic labor contribution to the household.
1 Sawada (1997) and Aldermnan et. al. (2000) also found the imnportant impact of shocks on school enrollments in
rural Pakistan.
19
Existing empirical studies indicate mixed results for birth-order effects-that is, the sibling
resource competition effects over time.19 There is no consensus in the literature about whether birth-order
effects really exist, and if they exist, whether they are positive, negative, or nonlinear in form (Parish and
Willis 1993). Our estimation results suggest that, under credit constraints, birth-order effects exist, and,
more important, the effects are specific to gender and education level.
6 Concluding Remarks
This paper investigated the sequential educational investment process of Pakistani households by
integrating observations from the field, economic theory, and econometric analysis. The paper makes two
contributions to the literature. First, we use the unique data set on the whole retrospective history of child
education and household background, which was collected exclusively for this analysis through field
surveys in rural Pakistan. Second, in addition to the data contribution, this paper employed full-
information maximum likelihood method to cope with the complicated estimation procedure of multiple
integration of conditional schooling probability. This method, combined with the unique data set,
enabled us to estimate the full sequential model of schooling decisions.
The most striking feature revealed by the data is the high educational retention rate, conditional
on school entry. Moreover, we found important dynamics of the gender gap in education, the significance
of shock variables, wealth effects, and intrahousehold resource allocation with our full sequential
schooling model. These findings are consistent with a household's optimal education investment under a
binding credit constraint.
Although the demand for education cannot be controlled directly by the government, supply-side
interventions will be effective. Our estimation results suggest that, in addition to household demand
considerations, raising the quantity of female primary schools has a substantial effect in improving
'1 There are two possible cases (Behrman and Taubman 1986). The first possibility is a negative birth-order effect.
As more children are born, the household resources constramint becomes severe and fewer resources are available per
child. If this per child resource shrinkage effect is dominant, the younger (higher-order) siblings will receive less
education than older siblings. Alternatively, the resource competition effects might decline over time, since
households can accumulate assets and increase income over time. Moreover, the older children may enter the labor
market, contributing to household resources. Therefore younger (higher-order) siblings could spend more years at
school. This is the case of positive birth-order effects. Also, an economy of scale due to household-level public
goods might exist, since siblings can share various educational inputs and materials. Positive knowledge externalities
might be important as well, since younger children can learn easily from the experience of their older siblings through
home teaching. In sum, having older siblings might promote the education of a younger child, rather than impede the
education of that child, if the resource extension effects, scale economies, and externalities are larger than the
competition effects.
20
education in Pakistan. Indeed, the push to expand access to schooling by increasing the supply of schools
has dominated the agenda for education in developing countries since the 1960s (Lockeed et al. 1991).
Yet remote and inappropriate female school locations and resultant high schooling costs are still serious
problems in rural Pakistan. Hence, the cost-effectiveness of providing primary education can be
significantly improved, if the allocation of funds is shifted toward recurring expenditures for construction
of female schools and employment of more female teachers. These supply-side policy interventions have
significant potential for reducing gender biases in human capital investment. We should also note that
closing the gender difference in education creates long-lasting positive effects on economic development,
since education of mothers relates to fertility and population over time. Many empirical studies show a
highly educated mother has lower infant mortality rate, fewer children, and more educated and healthier
children (King and Hill 1993).
21
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24
Appendix: A Summary of the Field Survey
Field surveys were conducted twice to gather information exclusively for this paper. In the first round of
the survey in February through April 1997, the survey team carried out interviews in fourteen villages of
the Fisalabad and Attock districts of Punjab province (Sawada, 1999). The selection of our survey sites
was predetermined, since we basically resurveyed the panel households that had previously been
interviewed by the International Food Policy Research Institute (IFPRI) through the Food Security
Management Project, based on a stratified random sampling scheme (Alderman and Garcia 1993). The
first district in our sample, Faisalabad, is a well-developed irrigated wheat and livestock production area.
The second district, Attock, is a rainfed wheat production region near the industrial city of Taxila. In this
district earnings from nonfarm activities are the major component of household income: Then the second
round surveys were carried out in eleven villages of the Dir district of the North-West Frontier Province
(NWFP) in December 1997 through January 1998. Dir is also a rainfed wheat production area with some
cash crop production such as citrus. There is a limited set of nonfarm income-earning opportunities
within and around the district. However, temporary emigration to the Persian Gulf countries is common
in Dir. As a result, nonfarm income and remittances account for more than 60 percent of average
household income, according to the IFPRI data files (Sawada 1999).
In our retrospective surveys, we used three different sets of questionnaires. The first
questionnaire is composed of questions on basic child information and retrospective schooling progress.
The second questionnaire collects basic household background information, such as household size,
permanent components of household resources, and fluctuations in household assets and income over
time. With the third questionnaire, village-level retrospective information was gathered by interviewing
local government officials and/or educated village dwellers such as schoolteachers. In particular, we
collected information about the year when male and female primary schools were built in the village.
These questionnaires seemed to work well in the field. Farmers remembered incidents related to
child education and enjoyed talking about their children. Each household interview lasted approximately
one and a half to two hours, largely depending on the number of children. We visited the villages without
prior notification, and the availability of respondents was uncertain in advance. Therefore, we may
plausibly assume that our attrition of panel households is determined by a random process.
Our field surveys covered 203 households in Punjab and 164 households in NWFP. Hence, 367
households were interviewed, and information on a total of 2,365 children was collected. The combined
data set gives a complete set of retrospective histories of child schooling, together with household- and
village-level information, which make the estimation of a full sequential schooling decision model
feasible. Moreover, the field survey data set is matched with the IFPRI data files. Since our purpose is an
estimation of the full sequential schooling decision model, we use part of the IFPRI data files that
contains long-term retrospective information on household and village characteristics.
25
Table 1
Distribution of Age at School Entry
Percentile [OK Primary school Middle school Secondary Postsecondary
as edited?] school school
Youngest 10% 5 10 13 16
25% 6 11 14 16
Median 6 11 14 17
75% 7 12 15 18
90% 8 13 16 20
Mean age 6.43 11.64 14.69 17.23
(standard (1.74) (1.73) (2.11) (2.54)
deviation)
Coefficient of 0.2706 0.1486 0.1436 0.1474
variation
Number of 1,150 685 451 177
observations
26
Table 2
Sample Probability of School Continuation
Total Faisalabad Attock Dir
Male Female Male Female Male Female Male Female
Primary school hl/n1 0.64 0.24 0.65 0.33 0.69 0.34 0.62 0.17
entry
Primary school h2/n2 0.82 0.69 0.74 0.72 0.87 0.69 0.84 0.67
graduate
Secondary school h31n3 0.93 0.53 0.97 0.34 0.89 0.59 0.94 0.64
entry
Secondary school h4Sn4 0.59 0.71 0.47 0.87 0.53 0.75 0.68 0.62
graduate
Postsecondary h5/ns 0.57 0.57 0.55 0.77 0.39 0.56 0.64 0.48
school entry
Totalnumberin n1 978 872 232 185 221 176 525 511
sample
27
Table 3
Descriptive Statistics
Primary Primary Secondary Secondary Postsce.
entry exit entry exit entry
Code S1* 52* S3* S4* S5*
Dependent variable
Dummy variable takes 1 if S,* = 1; takes 0 if S* S.*+ 0.45 0.79 0.85 0.61 0.57
=0, where = 1,2,.
Gender variable
Dummyvariable= I if female in Punjab pu_g.en+ 0.20 0.14 0.13 0.07 0.09
Dummy variable= I if female inNWFP nw_gen+ 0.28 0.10 0.09 0.07 0.07
School supply variable
Dummy variable = 1 if male and there is a male p_sup_m+ 0.37 0.64 0.23
school within the village
Dummy variable = 1 if female and there is a psup f+ 0.18 0.19 0.03
female school within the village
Social class variable
Dummy variable = 1 if household head is farmer farm_wl+ 0.30 0.37 0.37 0.42 0.37
with land
Dummy variable = I if household head is landless casual+ 0.44 0.33 0.32 0.27 0.27
farmer or casual laborer
Dummy variable = I if household head runs bus_gov+ 0.17 0.23 0.24 0.23 0.26
business or is officer
Household human and physical assets
Dummy variable = I if father has finished fed+ 0.19 0.29 0.31 0.31 0.36
primary
Dummy variable = I if mother has finished med+ 0.02 0.05 0.05 0.06 0.08
primary
Amountof land ownership p land 13.39 16.85 17.35 21.31 22.31
(37.51) (45.27) (43.83) (48.85) (53.85)
Dummy variable = I if owns tractor ptrac+ 0.01 0.03 0.03 0.04 0.06
Household's shock variables
Dummy variable = 1 if good year p_good+ 0.07 0.05 0.02 0.33 0.06
Dummy variable = I if bad year p_bad+ 0.06 0.06 0.02 0.33 0.06
Dummy variable = 1 if household head is inactive p_hinact+ 0.05 0.06 0.002 0.31 0.02
Dummy variable = I if wife of household head is p winact+ 0.06 0.05 0.01 0.32 0.04
inactive
Sibling variables
Number of older brothers m_old 1.83 1.77 1.69 1.69 1.67
(1.87) (1.82) (1.63) (1.63) (1.56)
Number of older sisters f old 1.56 1.57 1.52 1.53 1.50
(1.68) (1.64) (1.57) (1.56) (1.55)
Cohort variables
Dummyvariable= I if aboveageof40 age40+ 0.11 0.08 0.09 0.09 0.10
Dummy variable= I if age between 35 and 40 age3540+ 0.09 0.10 0.10 0.11 0.12
Dummyvariable= 1 if age between 30 and 35 age3O35+ 0.12 0.14 0.15 0.15 0.16
Dummy variable = 1 if age between 25 and 30 age2530+ 0.16 0.2.1 0.22 0.23 0.21
Dummy variable = I if age between 20 and 25 age2025+ 0.17 0.23 0.24 0.23 0.26
Dummy variable = I if age between 15 and 20 agel520+ 0.13 0.17 0.16
Dummy variable = I if age between 10 and 15 agelO15+ 0.07
Number of observations N 1,850 833 658 557 340
+ indicates dummy variable. Numbers in parentheses are standard deviation
28
Table 4
The Most Important Reason for a Child's School Termination
Reason given Frequency Percent
Subjective reason
Accomplished the desired level 97 13.4
Economic reasons
Education costs too high (tuition) 128 17.7
Needed on farm or at home 72 9.9
Got ajob 55 7.6
Child-specific reasons
Child is ill 23 3.2
Marriage 21 2.9
Child failed in exarn 55 7.6
Supply-side reasons
School is too far 44 6.1
Child does not want to go to school 191 26.4
(Mainly, teacher's punishments)
Other 38 5.2
Total 724 100
Source: Author's interview.
29
Table 5
FIML Estimation Results of the Sequential Schooling Decision Model
Primary entry Primary exit Secondary entry Secondary exit Postsecondary
entry
Si2* S3* 4* S5*
Coeff. Std. error Coeff. Std. error Coeff. Std. error Coeff. Std. error Coeff. Std. error
Gender variable
Dummy variable = I iffemale living in Punjab -1.455 (0.152)*** -1.516 (0.569)*** -3.306 (0.359)*** 0.165 (0.454) 0.443 (0.447)
Dummyvariable= I iffemalelivingintheNWFP -1.716 (0.134)*** -1.111 (0.571)** -2.759 (0.453)*** -0.062 (0.466) -0.475 (0.523)
School supply variable
Dummy variable = I if male and there is amale 0.163 (0.140) 0.320 (0.423) -0.304 (0.285)
school within the village
Dummy variable = I if female and there is a female 0.748 (0.129)*** 1.190 (0.414)*** 1.463 (0.640)**
school within the village
Social class variable
Dummy variable = 1 if household head is farmer 0.436 (0.143)*** -0.359 (0.424) -1.582 (0.645)** -0.549 (0.374) 0.391 (0.450)
with land
Dummy variable= I if household head is landless 0.178 (0.136) -0.593 (0.419) -1.331 (0.641)** -0.022 (0.394) 0.835 (0.439)*
farmer or casual laborer
Dummy variable = I if household head runs 0.719 (0.164)*** -0.262 (0.471) -1.088 (0.670)* 0.256 (0.433) 1.600 (0.500)***
business or is officer
Household human and physical assets
Dummy variable= I if father has finished primary 0.868 (0.112)*** 0.543 (0.268)** 0.734 (0.310)** 0.221 (0.258) 0.555 (0.329)*
Dummyvariable= I if motherhasfinishedprimary 0.818 (0.320)** 1.046 (0.571)* 2.438 (0.748)*** 0.644 (0.478) 1.140 (0.549)**
Amount of land ownership -1.971 (1.116)* -0.673 (2.136) 5.504 (4.793) 1.465 (2.508) 9.201 (4.692)*
Dummy variable= I if owns tractor 1.199 (0.451)*** -0.416 (0.541) 0.377 (0.653) # 1.246 (0.593)**
Household's shock variables
Dummy variable = I if good year -0.074 (0.270) -0.361 (0.539) -0.653 (0.890) -0.236 (0.360) 0.047 (0.531)
Dummy variable =' if bad year 0.095 (0.291) -1.031 (0.510)** -1.202 (0.635)* -1.075 (0.341)*** 0.105 (0.533)
Dummy variable = I if household head is inactive 0.034 (0.337) -0.781 (0.521) -1.795 (0.447)***
Dummyvariable= I if wife of household head is -0.021 (0.300) -0.191 (0.564) -1.017 (0.418)** -0.793 (0.600)
inactive
Sibling variables
Numberofolderbrothers 1.321 (2.199) -0.801 (5.514) 5.186 (7.622) 20.098 (6.634)*** 25.433 (8.588)***
Number of older sisters 4.934 (2.406)** -1.259 (5.998) 12.774 (8.752) 4.393 (6.834) 6.596 (9.210)
Cohort variables
Dummy variable= I if above age of 40 2.164 (0.216)*** 1.679 (0.600)*** 2.539 (0.605)*** 0.340 (0.422) 1.181 (0.594)**
Dummyvariable= I if agebetween35 and40 2.532 (0.218)*** 1.330 (0.488)*** 2.522 (0.601)*** 0.445 (0.411) 0.537 (0.528)
Dummyvariable= I if age between 30 and 35 2.376 (0.196)*** 1.447 (0.443)*** 2.321 (0.548)*** 0.171 (0.349) 0.140 (0.491)
Dummyvariab]e= 1 if age between 25 and 30 2.505 (0.191)*** 1.612 (0.426)*** 2.830 (0.533)*** 0.066 (0.309) 0.597 (0.460)
Dummyvariable= I if age between 20 and 25 2.554 (0.189)*** 1.475 (0.414)*** 2.212 (0.505)*** 0.080 (0.312) -0.166 (0.425)
Dummy variable= I if age between 15 and 20 2.463 (0.194)*** 1.077 (0.422)** 2.567 (0.544)***
Dummy variable= I if age between 1O and 15 1.843 (0.210)***
Constant -2.354 (0.243)*** 0.474 (0.762) 0.625 (0.821) 1.005 (0.509)** -1.760 (0.704)**
Number of observations 1,850 833 658 557 340
Note: * = significant at 10%; ** = significant at 5%; *** = significant at 10%.
# indicates that it is infeasible to estimate coefficients due to colinearity and thus dropped from estimation.
30
Table 6
Marginal Effects of Gender Dummy Variables
SI* S2 S3* S4s55
aP(8 1)/1&' aP(82=1 )/aC2 ap(83=l)/at3 aP(64=1)/1&4 aP(65= 1)/&
x
Male 0.6558 0.8314 0.8887 0.5987 0.5713
Female in Punjab 0.2485 0.5149 0.3281 0.6206 0.6563
Female in NWFP 0.1908 0.6539 0.43095 0.5900 0.4770
Note: See footnote 15 for the calculation formula of the marginal effects. The variable xX stands for the r-th
education stage variable of our interest.
Table 7
Marginal Effects of School Availability
'SI* Sz* S3*
aP(8 =l)/az' aP(o =1)/8z2 aP(&,=l)/az3
Male/school available 0.039 0.050 -0.037
Female/school available 0.177 0.157 0.126
Note: See footnote 15 for the calculation formula of the marginal effects. The variable zt stands
for the r-th education stage variable of our interest.
31
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