Wage Determination of Child Labor and Effect of Trade Reform
Saibal Kar1
and
Basudeb Guha-Khasnobis2
September 2003
Abstract
This study examines the interaction of a small open economy engaged in trade in
goods and services with the process of household decision-making, where
individuals are characterized by a degree of relative risk aversion. In particular,
we determine the demand for child labor originating in the small open economy
and compare that against child labor supply determined by household decisions.
In the process, we determine the equilibrium child wage endogenously, as a
fraction of the equilibrium adult wage. Trade reform policies affect both demand
and supply of child labor and the equilibrium child wage through its effects
simultaneously on the production pattern and on household labor market
decisions. Based on these demand and supply movements generated through
various parametric shifts, we offer our propositions on the incidence of child labor.
1
Address for Correspondence: Dr. Saibal Kar, Research Officer, Reserve Bank Of India Endowment,
Centre For Studies In Social Sciences, Calcutta. R 1, B.P. Township, Calcutta 700 094, India.
PH. 91-33-2462 5794/ 5795/7252. EXT. 230. FAX. 91-33-2462 6183. E-mail: skar<econcsss@giascl01.vsnl.net.in> /
skar1801@yahoo.com
2
UNU-WIDER, Katajanokanlaituri 6 B, Helsinki 00160, Finland. E-mail: basudeb@wider.unu.edu.
1.
Introduction
In almost all the recent studies on the existence of child labor in developing
countries, its alarming extent and magnitude has been carefully documented and
highlighted. The entrenchment of the practice of child labor in developing societies3has
unanimously been declared problematic and upsetting.4 Various policy propositions in
favor of eradicating child labor has at best produced inconclusive results, which in turn
has made implementation of any or all of these policies rather difficult.
As the extensive literature suggests, the issue of the prevalence of child labor
has been approached from many angles. Grootaert and Kanbur (1995) provides an
elegant compendium of how the economics of child labor may be approached, and in
later studies we find a number of points mentioned here being taken up for further
investigation. Apparently, such studies have been successful in creating a large number
of explanations behind incidence of child labor, whether demand determined or supply
determined. Demand for child labor is generated by several factors. Segmentation of
the economy between formal and informal sectors and the degree of informalization is
an important factor in generating such demand. Formal sector of an economy, which
adheres more closely to labor laws prevailing in the country cannot for understandable
3
Although child labor is a much more visible phenomenon for developing nations, a decade or so ago
even the United States had more than 4 million children in the working class (Corbin, 1988). Child labor
by definition of ILO pertains to children below the age of 15 years. We also include children working for
the household at the expense of school time.
4
Child labor is not necessarily considered ‘bad’ in every society. Work instead of education is believed
to instill survival skills in the children (Bekombo, 1981; Agiobu-Kemmer, 1992). A related question may
be: does every child need formal education? On the job training or apprenticeship and skill acquisition
from an early age can provide them with an adequate means of living. Quoting Agiobu-Kemmer, (1992,
p.7), “ Education broadens your mind but it does not teach you how to survive”. There is no doubt a
problem with such arguments. Every child does not have to excel in educational attainments and neither
is that practically feasible. However, every child must have at least primary education to take advantage
of possible socio-economic developments around him/her. This not only enables the child to
communicate with the outside domain but also acts as insurance against future shocks when such skills
may be in considerable need. Moreover, education generates self-esteem and capacity of bargaining in
the face of hostile socio-economic situations.
reasons engage in child labor employment. 5 Demand for child labor mostly originate in
the informal sector which itself bypasses legal regulations for various interests of its
own. This moreover has much to do with the technology used in production under the
behest of the informal economy. Children in developing countries are largely engaged
in production of goods and services where adult labor are imperfect substitutes. This
can range from employment of boys in quarries (where adult labor finds it difficult to
do mining in the narrow tunnels) to chimney sweeps or of children for weaving carpets
with their ‘nimble’ fingers (Grootaert and Kanbur, 1995, p. 195, also see GuhaKhasnobis et al, 1999). Apart from that there is high demand for children workers in
the agriculture and allied sector, involving delicate plantations and harvesting or cattle
herding. Use of children as domestic helps/servants is also a common feature in these
countries. However, despite such widespread evidence on child labor, the problem
remains in estimating the demand for child labor properly, simply because once child
labor is prohibited by law, it does not exist legally and thus obtaining a positive demand
for child workers becomes rather impossible.
On the other hand, there are many supply-side determinants of the occurrences
of child labor, ranging from cultural factors to poverty-related causes. In this
connection Grootaert and Kanbur (1995) raise the issue of household responses towards
risk. If households face income risk, they might send their children to work to better
manage such risks, especially at income levels where any negative fluctuations could
mean disaster. We pursue this point further. While the objective of this study is laid
out shortly, we can elaborate a little bit more on this ground presently.
In the absence of savings, liquid assets or ability to borrow (Mendelievich,
5
Exceptions are plantation farms (eg. Bonnet, 1993, for Africa; Goonesekere, 1993, for Sri Lanka).
1979) most individuals seem to be distributed on the higher scale of relative risk
aversion and decide to engage their children in work for supporting an unstable
household income. In the later part of the study, we obtain a critical degree of such
relative risk aversion, such that, all individuals distributed with a relative risk aversion
above the critical level would spontaneously trigger the decision to send their children
to work with or without possibilities of adverse shocks. It may be argued that if
individuals are characterized by varying degrees of relative risk aversion, then for
highly risk-averse decision-makers, such reactions are obvious; the reverse being true
for low risk-averse individuals. We show that attainment of the critical degree of
relative risk aversion will automatically classify individuals falling into groups of high
risk-averse individuals and low risk-averse individuals even if one begins with an
assumption of equally risk-averse individuals distributed uniformly over a scale of
measurement.
Grootaert and Kanbur (1995, p. 194) carefully distinguish between strategies to
insure against adverse income shocks and that between ensuring old-age care. In the
first case, parents decide to send their children to work, while in the second case they
would want to send their children to school so that old-age transfers are higher.
Although demand for having children would be high in both cases, there is a potential
conflict between short-run and long-run gains as realized by the parents. This should be
reflected in the expected utility facing the parents and as our analysis would show,
parents face a trade-off between high-risk and long run gains. Supply of child labor is
accordingly affected by distribution of parents between high-risk and low-risk choices,
or rather between short run income smoothing choice and long run income transfer.6
There are a number of other models of household decision to send children to
work. Basu and Van (1998) assume child labor to be bad in parental preference, such
that, as household income exceeds some threshold, children are withdrawn from the
labor force. They identify several factors such as price and returns to education, the
price of the goods that households consume and produces, adult wage, child wage as a
fraction of adult wage etc.7 Here as also in Basu (2000), child wage is an arbitrary
fraction of adult wage. Basu (1998) obtains equilibrium employment of child labor
through a demand-supply interaction, but it is based on exogenously given child and
adult wages. Empirically, child and adult labor are shown to be substitutes or
complementary depending on gender, age and country type (see for example, Ray,
2000). One of the contributions we make in this paper is providing a definitive method
of calculating the equilibrium child wage as a fraction of adult wage and obtaining the
nature of relationship between child and adult workers, that can be interpreted suitably
in accordance with the empirical results. Ray (2000) test for the luxury axiom in Basu
and Van (1998), which essentially says that as the family falls into poverty, children are
withdrawn from school. For Peru and Pakistan, the two countries with similar rates of
children living in poverty (approximately 30%), that Ray (2000) tests for, it is observed
that while the axiom is true for Pakistan (although with a gender discrimination against
girls) it is contradicted for Peru.8
6
Note that, this is not a dynamic model. Here all gains are static and can at best be viewed as pesent
discounted value of all future earnings.
7
Also see Baland and Robinson (2000). Brown (2000), Dixit (2000) consider the effect of raising foreign
country price of goods using child labor on the incidence of child labor in developing countries in a
simplified Basu and Van (1998) framework.
8
A possible explanation for contradictory evidence in Peru may be found in Patrinos and Psacharopoulos
(1997, p. 398), “working actually makes it possible for the children to go to school.”
Credit constraints may also play a significant role in influencing supply of child
labor in a household model. Ranjan (2001, also see Dehejia and Gatti, 2002) builds up
a connection between trade policy and child labor in a household model with credit
constraints. This paper shows that trade sanctions might not reduce the incidence of
child labor in a long-run model of trade based on differences in relative endowments
across countries.
Previously, Maskus (1997) shows that imposition of foreign tariff on the
exported good has ambiguous effect on the incidence of child labor. On the other hand,
if child labor serves as a specific factor to the export sector (Melchior, 1996), imposing
tariff on export price of the good lowers returns to child labor and therefore the supply
of child labor. These results seem to differ on the basis of peculiarities in the specific
model building and the study by Edmonds and Pavcnik (2002) takes up an empirical
connection between globalization of the rice price in Vietnam and reduction of the
extent of child labor in the country. The results display a positive causation such that, a
30% increase in relative price of rice helps reducing child labor by an average of 9
percentage points. In rural Vietnam especially, it accounted for 45% reduction in child
labor (about 1 million less child labor between 1993-98), with households having larger
land holdings experiencing larger reductions.
A brief encounter with the economics of child labor thus provides various
paradigms one can look further into. This study is an attempt to bring together the
interaction of a small open economy engaged in trade in goods and services with the
process of household decision-making, where individuals are characterized by a degree
of relative risk aversion. The importance of the study lies in the fact that here we
determine the demand for child labor originating in the small open economy and
compare that against child labor supply determined by household decisions. In the
process, we determine the equilibrium child wage endogenously as a fraction of the
equilibrium adult wage. Trade reform policies affect both demand and supply of child
labor and the equilibrium child wage through its effects simultaneously on the
production pattern and on household labor market decisions, channeled through the
wage movements. Based on these demand and supply movements generated through
various parametric shifts, we offer our propositions on the incidence of child labor. It
should, however, be noted that we are not trying to provide yet another theory of
determination of child wage and extent of child employment. Instead, we emphasize
the importance of observing the link between economic restructuring, wage and labor
mobility and labor market decisions by individuals characterized by relative risk
aversion, in order to focus on the incidence of child labor.
The plan of the paper is as follows. In section 2 we present the model. In
section 3 we provide an overview of the results and conclude.
2.
The Model
Let there be a three-sector small open economy producing three goods X, Y and
Z. X is an import-competing industrial good and is protected by a proportional tariff t.
It requires the use of Y as an intermediate good, which is produced and traded at world
prices, PY * . Z is an export good. Other than Y, X also requires the use of capital, K
(interest rate, R) and adult labor, L (formal and unionized, at an administered wage w ).
One can assume Y to be agricultural output, which is produced with adult labor
(informal, at market-determined wage, w), child labor, C (at a wage γ L w , 0 < γ L < 1 )
and land (T, at rental rate τ ).9 On the other hand, production of Z requires the use of
adult labor, child labor and capital at per unit prices given above.10 Production is based
on fixed endowments of L, K and T and on the basis of given production technologies.
Demand for child labor (C), on the other hand is determined endogenously, such that it
is less than or equal to the stock of children ( C ) in the economy, C ≤ C . We define
child labor wage as,
wC = γ L w ,
0 < γ L <1
(1)
In standard literature (for example, Basu, 2000), γ , a general discounting factor,
is treated as an exogenous constant and thus wC is readily determined once w is known.
We propose that, γ instead is an endogenous variable, which2 may be interpreted as the
equilibrium level of effort exerted by a child labor. A child may exert varying levels of
effort at work and at school. At the point, where such efforts are same, the child is
indifferent between going to school or to work. For sake of simplicity we assume that
the total level of effort exerted by the child in going to school ( γ S ) and to work ( γ L )
cannot exceed 1. In other words,
γ L = 1−γ S
(2)
It directly follows that when the child is full-time in school and not spending any time
9
One can assume X to be food processing industry, using agricultural, dairy, poultry and marine inputs
traded at world prices. Y is a direct example of agricultural product ranging from fruits or cereals to fish
and meat production. Z is an industrial/ handicraft export, using child labor. In case of India, for
example, a famous example is in the carpet industry.
10
Viewed alternatively, the economy consists of a formal (and urban, X) sector and an informal (rural and
urban/semi-urban, Y and Z respectively) sector. Formal sector follows legal procedures and labor laws,
while similar enforcements are not suitably applicable for production of Y and Z. We conceptualize the
general equilibrium structure of the economy in this form that covers main sectors using the essential
in the labor market, γ S = 1 and γ L = 0. The reverse occurs when the child is employed
full-time and has zero school attendance. Any combination of both school time and
work time is possible under this structure.11
In our model, γ L is endogenously determined by the interaction of demand and
supply for child labor. Demand originates from the general equilibrium structure of the
small open economy and supply from the household comparison of parental utilities
from sending the child to work or to school. While the intricacies of such determination
will be presented below, we first offer the general equilibrium system of the small open
economy under perfect competition following other neo-classical assumptions of fullemployment, diminishing marginal returns and so on.
Let
PX* (1 + t ) = Tariff included price of X
PZ* = Price of export good Z
aij = Amount of ith factor for producing one unit of jth commodity.
The following equations display the zero-profit and full-employment
conditions for our economy:
a LX w + a KX R + aYX PY * = PX* (1 + t )
(3)
a LY w + aCY wC + aTY τ = PY*
(4)
a LZ w + aCZ wC + a KZ R = PZ*
(5)
a LX X + a LY Y + a LZ Z = L
(6)
factors of production. One can further introduce capital specificity across formal and informal sectors,
but we believe that it does not change the main results of our model.
11
It is also possible to begin with a total effort level < 1 or > 1, as a function of the inherent capability of
the child, since individuals across ethnicities or country types may have different total effort levels. This
in turn is a function of the existing conditions (including infrastructure, access to public goods, average
aCY Y + aCZ Z = C
(7)
a KX X + a KZ Z = K
(8)
aTY Y = T
(9)
Given world prices of traded goods and w , from (3) we determine, R*. Substituting
R* in equation (5) we obtain w* = w(γ L ) and substituting w* in (4) we determine
τ * = τ (γ L ) , given international prices and the aij ’s. Clearly, determinate solutions of
the above variables require determination of equilibrium γ L . The physical equations, on
the other hand, solve in the following manner. From (9), we determine, Y, given total
land resources, T . Substituting Y in (6), we solve simultaneously for X and Z from (6)
and (8), given exogenous adult labor and capital stocks in the economy. We plough
back Y and Z in equation (7) to obtain the demand for child labor in the economy, C as a
function of γ L . Also, it displays the normal demand function. Intuitively, as γ L rises
child wage rises, and demand for child labor falls. Thus,
DC = C (γ L )
DC′ < 0
(10)
We further assume that (1 − k ) L share of the total labor force is in the
unorganized sector and would therefore be the source of child labor supply. This is
explained next. k varies from country to country, but given the world average
percentage of labor union affiliation one can safely assume k to be around 10% in most
countries.
Now in order to determine the equilibrium value of γ , we need to obtain the
extent of supply of child labor in the economy. Let the economy, and thus all
nutrition levels and health situations, dependence on climatic factors, etc) within the country. However,
individuals face two states of nature, good sate with probability α and bad state with
probability β , such that, α + β = 1 . Note that, organized workers keep earning w under
all states of nature, while unorganized workers are susceptible to wage fluctuations
depending on the state of nature prevailing in the economy. The level of unorganized
wage in the economy is the prime determinant of the supply of child labor in our study.
It is assumed that, w* = w(γ L ) as determined from equation (5) also represents the
critical wage facing an unorganized worker. The reason for invoking this assumption
will be made clear as we lay out the details of the supply-side of the model. However,
we first comment on the potential size of the child labor supply. Since organized
workers always earn more than the critical wage, children belonging to these families
would not be a potential child labor subject to the state of nature. However, if labor
from the organized sector is relocated to the unorganized sector due to effects of
structural reform, children belonging to these parents would also add to the potential
child labor supply. Before such reallocating effects of reform sets in, the actual number
of children who could be potential child labor is obtained in the following manner. The
average number of children (from a stock of C ) per adult worker is C / L , of which,
(1 − k )C / L would be readily affected by swing in the state of nature.
In our model the supply of child labor is determined by parental decision.12 We
assume all parents to be equally risk averse distributed uniformly over a range of
relative risk aversion and individuals are characterized by a von-Neumann-Morgenstern
utility function. The parent (an individual decision-maker representing a household)
we restrict our attention to the case of total effort level equal to 1.
12
Children self-selecting themselves either to school or to work is a possibility we bypass. Orphans, for
example, if not supported by bequests or by social institutions must engage in labor work for survival.
receives utility from sending the child to work and/or to school. The possibility of both
school and work for a child is kept alive because there may be a situation when an
individual would be indifferent between sending the child either to school or to work or
both. More specifically, the individual compares separate utilities from sending the
child to school or to work and at the intersection point of the two utility functions we
obtain the critical relative risk aversion for the group of individuals. Individuals are so
distributed that, those displaying a relative risk aversion greater than the critical level
send the children to work, while those falling in the range where individual relative risk
aversion is less than the critical level decide to send their children to school. The idea
behind such decision-making is simple. It is well documented in the literature that
parents send their children to work for smoothing out risk associated with income
variability. We offer a point of departure in this context. The ultimate decision to send
children to school or work would depend on the level of critical relative risk aversion
and the distribution of individuals around that critical point. Put simply, we propose
that the decision to send children to work for smoothing out income fluctuations is not
universal among all individuals who are subject to wage uncertainties. Instead, it is a
function of the distribution of individuals on the scale of relative risk aversion with
reference to the critical point. This critical level of relative risk aversion defined in the
range [0,1) is obtained next.13
w is the critical wage under steady state general equilibrium facing an
unorganized worker (see appendix for an alternative approach for determining supply of
13
However, Kanbur (1982, p. 18) comments that value of relative risk aversion between 1 and 2 seems to
be reasonable one to take. We use the measure of relative risk aversion as an analytical tool here and
such specifications as r belongs to [0,2) can easily be introduced to check the validity of the model and
results.
child labor). This is obtained from equation (5) above. wα be the wage, such an worker
earns in good state, while he earns wβ in bad state. The two states of nature are results
of economic shifts, engendered through economic reforms in the country. It is a
simplification that in good state, w jumps to wα and in bad state it falls to wβ . In fact,
there can be an infinite number of wage levels between w and wα , and that between w
and wβ . At w, an individual is indifferent between sending the child to work or to
school.14 The idea is that, as w increases above the critical level, parents decide in favor
of sending the children to school. On the other hand, if wage falls below w, children are
withdrawn from school and sent to work.
Based on this behavior, we conceive of two separate utility functions: one for
supporting the household by sending the children to work (USH), and the other for
increasing the educational attainment of the household by sending the children to school
(UHK). For each case there are two possible outcomes.
First, let us consider the case of supporting the household. In good state, which
comes with a probability α , the individual does not send the children to work and the
household does not gather an extra income from child work. Thus in good state, utility
is a function of the difference in wα and w alone. In bad state on the other hand, as adult
wage falls below the critical level, children are sent to work and they earn a fraction of
14
In other words, under steady state equilibrium when adult workers earn w, the economy still may have
a positive supply of child labor as well as positive number of school goers. However, we are more
interested in tracking the changes in the supply of child labor and school attendance that results from
introduction of economic reform.
the prevailing adult wage, γ L wβ . This is added to the household income in bad state.15
On the basis of the above discussion, we construct a Stone-Geary utility function of the
following type.
( wα − w)1− r
USH = 
1− r
( w − wβ + γ L wβ )
(11)
From (10), we obtain the expected utility function for supporting the household.
EUSH = α ( wα − w)1− r + β ( w − wβ + γ L wβ )1− r
where,
(12)
δ ( EUSH )
δ 2 ( EUSH )
> 0,
< 0 . In other words, EUSH is a concave and wellδr
δr 2
behaved function.
Second, the flipside of the above situation reveals that, in good state the
individual decides in favor of sending the children to school with a view to increase the
educational attainment of the children and thus of the household. In good state, this
educational attainment enters the utility function of the parent. In bad state, the children
are simply withdrawn from school and thus utility becomes a function of w and wβ only.
All children are endowed with an innate ability b. Administering individual effort at
15
As noted earlier, any wage level between w and wα , or that between w and wβ may well trigger the
decision to send the children to school or work. At precisely what level of income differences such
decisions take-off possibly needs to be addressed in an empirical framework. Here it is assumed that
( wα -w) is large enough, so that parents decide against sending the children to work and subsequently
make schooling facilities available for them. Conversely, for a large ( wβ -w), parents are hard pressed to
withdraw children from school and send them to the labor market. Utility from work and school are,
however, accounted for separately in our model. Finally, such households do not have any other source
of income or capital assets other than market determined wage earnings. Once again, cost of capital
borrowing or returns from land holdings by individuals can be introduced in this framework to provide
the general equilibrium structure. We believe, adding other markets would extend the main results of the
model without altering any basic findings.
school children acquire b(1 + γ S ) level of educational attainment.16 As already
mentioned, in bad state such return from schooling is zero, children being withdrawn
from school as soon as adult wage drops below the critical level.
The Stone-Geary utility function representing these choices is given below.
[ wα − w + b(1 + γ S )]1− r
UHK = 
1− r
( w − wβ )
(13)
We denote the expected utility from sending or not sending the children to school by,
EUHK = α [ wα − w + b(1 + γ S )]1− r + β ( w − wβ )1− r
(14)
δ ( EUHK )
δ 2 ( EUHK )
> 0,
< 0 depicting a continuous and well-behaved utility
Again,
δr
δr 2
curve.
At the point where the curves depicting equations (12) and (14) intersect and
using (2), we obtain the critical relative risk aversion of adult individuals
( r* = r * (γ L ) ).17 Algebraically, this is obtained at the point where,
α ( wα − w)1− r + β ( w − wβ + γ L wβ )1− r = α [ wα − w + b(1 + γ S )]1− r + β ( w − wβ )1− r
One can check for the intercepts of EUSH and EUHK. It can be easily seen that,
EUHK
r =0
> EUSH
 αb


.
<
,
,
iff
γ
L
r =0
 βw − αb 
 β

(15)
Once again, given other parameters, condition (15) sets the upper limit for γ L such that
a equilibrium point exists. Determination of unique equilibrium further requires that,
16
This may be considered equivalent to the net present discounted value of return from schooling. We do
not explicitly consider the market for education, but this static educational attainment has a market value
equivalent at that point in time. Also, schooling is free, so the only cost of schooling is the wage loss and
other expenses incurred for supporting the children when in school. We believe that, even if these
features are explicitly modeled here, it does not change the basic analysis and results.
δ ( EUSH ) δ ( EUHK )
>
.
δr
δr
Diagrammatically this is shown in figure (1). Individuals distributed to the left of the
critical relative risk aversion ( r* = r * (γ L ), r*′ < 0 , point M) point choose to send their
children to school, whereas those distributed to the right send their children to work.
EUSH, EUHK
EUSH
M
0
r*
EUHK
r
Fig (1)
Intuitively, r* = r * (γ L ), r*′ < 0 is explained as follows. As γ L increases, child wage
increases. Subsequently, expected utility from household support increases and EUSH
curve shifts out. This leads to a drop in the level of critical relative risk aversion among
individuals. Looked at alternatively, as γ L increases, γ S falls and expected utility from
human capital formation falls, such that, EUHK shifts in. As a result, critical relative
risk aversion falls with an increase in labor market work effort of the children.
The attainment of the critical relative risk aversion, therefore, demarcates
individuals distributed with higher relative risk aversion from those distributed with
17
At this stage, we do not rule out possibilities of multiple equilibria.
lower relative risk aversion. This further influences the decision to send the children to
school or to work. At the critical level, individuals are indifferent between sending the
children to school or to work.
This determines the number of individuals who send their children to work. For
those who are distributed with higher relative risk aversion than the critical level, the
decision is to send the children to work for smoothing out risk associated with variance
in income. All individuals with relative risk aversion in the range [r*, 1) belong to this
decision group. The actual number of such individuals is given by
S = (1 − r*)(1 − k ) L
(16)
Now, as noted earlier, the number of children belonging to the unorganized workers
is (1 − k )C / L . Thus, using (16) the number of children who are sent to work is given
by,
S C = (1 − k ) 2 [1 − r * (γ L )]C , S C′ (γ L ) > 0 as r *′ (γ L ) < 0
(17)
S C (γ L ) in equation (17) represents the supply of child labor in the economy.
Now, one can straightaway determine the equilibrium value of γ L (= γ L *) by equating
(10) and (17),
C (γ L ) = (1 − k ) 2 [1 − r * (γ L )]C
(18)
Once γ L * is known, equilibrium values of other variables are also
determined w* = w(γ L *) , τ * = τ (γ L *) . Using these values we obtain the equilibrium
child labor wage in the economy,
wC * = γ L * w *
(19)
Comparative static
a.
Reduction in tariff rate on commodity X, i.e. dt<0.
We show that a reduction in the price of X may change the incidence and
magnitude of child labor in the economy, through its effects on both demand for and
supply of child labor. The effect on demand for child labor is propagated primarily
through factor price adjustments in the economy and subsequently through the impact
of changing factor-prices on the production of goods and services. The supply effect,
on the other hand, operates through shifts in household decisions on labor supply owing
to factor-price movements - essentially, wage movements in the economy.
Proposition I: Demand for child labor rises while supply of child labor falls with a
tariff-cut on of X, if the respective conditions are satisfied :
a.
Demand condition:
λ LX
b.
λ
σ λ λ θ θ
σX
[θ LX − θ KX (θ LZ + θ CZ )] + Z ( LX KZ LZ KZ − CZ ) < 1
σ Y λ KX λ LY θ TY
λ LY
σY
Supply conditions:
For EUSH:
− wβ
For EUHK:
b
δγ L
δγ
> 1 , where, wβ . > w > 0 and L < 0
δw
δw
δγ S
δγ
> 1 , where, b>0 and S > 0
δw
δw
Proof: The detailed mathematical proof of Proposition I is provided in the appendix.
Here, we explore intuitively if a tariff cut on the import of X leads to an increased
demand for and a decreased supply of child labor. A reduction in tariff lowers R in
sector X, along with a reduction in output and employment in sector X. Capital takes a
flight to sector Z increasing production, employment and return to adult labor in the
economy. If γ L is high in equilibrium, child labor is a close substitute for adult labor
and employment of child labor rises. Again, even for a low equilibrium γ L and based
on the structure of the industry and technique in production, there may be
complementarity between adult and child labor.18 Thus, increasing adult employment
also leads to an increase in demand for child labor. However, this does not portray the
complete picture of the economy. A reduction in the output in sector X is associated
with a drop in production and employment in sector Y, the agricultural commodity,
which serves as an intermediate good to the import-competing sector. Thus the overall
impact of trade liberalization on employment of child labor becomes a function of
condition (a) shown above. One may argue that, with a large agricultural sector and
high involvement of child labor in this sector, impact of a downsized food processing
industry on negative demand for child labor may not be very deeply entrenched.
Increased industrial demand for child labor dominates in the case of a tariff-cut,
resulting in a higher overall demand for child labor.
The supply of child labor on the other hand changes in the following manner.
Note that, change in children’s supply of effort at school or at work is a supply-side
phenomenon. We accommodate this feature here, while considering a constant effort
level for earlier determination of shifts in demand. As adult wage unambiguously rises,
parents prefer to withdraw children from the labor market. Consequently, children’s
supply of effort in the labor market falls. In other words
δγ L
< 0 . Also, as rise in adult
δw
wage lowers children’s work effort, expected utility of household support through child
18
In fact, we assume fixed technological proportionality or correspondence between adult and child labor
in sector Y and Z, whether the factors are substitutes or complements in production.
income falls. The curve depicting EUSH shifts in with a rise in adult wage subject to
condition (b) stated above. Similarly, as adult wage rises children are sent to school by
parental decision. Children’s effort at school rises and households’ expected utility
from educational attainment/human capital formation increase. There is an outward
shift of EUHK. The adjusted critical relative risk aversion point (where new EUSP and
EUHK intersect) locates higher up in the scale of relative risk aversion. Thus, more
individuals compared to pre-trade reform situation are now distributed with a lower
relative risk aversion than the critical level. This leads to a drop in the supply of child
labor from the households. We display this supply-side shock with the help of the
following diagram.
EUSH, EUHK
N
M
0
r*
r*’
EUSH
EUSH’
EUHK’
EUHK
r
Fig (2)
Subject to satisfaction of the conditions as in (b) above, EUSH curve shifts inward to
EUSH’, while EUHK shifts outward to EUHK’. Consequently, the critical relative risk
aversion point shifts from point M rightward to point N. This is indicative of an
increase in the proportion of individuals distributed with a relative risk aversion lower
than the critical level. Conversely, the proportion of individuals distributed with a
relative risk aversion higher than the critical level falls with these adjustments.
Therefore, the supply of child labor decreases as a direct consequence of these
movements.
Finally, we address the ultimate question that forms an important, if not the sole
motivation behind this paper. Whether the size of the child labor force declines in
equilibrium depends on the wage elasticity of demand for and supply of child labor. In
this particular example, we observe a conditional increase in the demand for child labor.
On the other hand, subject to fulfillment of conditions as under proposition I there may
be a decrease in the supply of child labor in the economy. Thus the extent and
magnitude of child labor in the post-reform economy would depend upon the relative
strength of these shifts.
b.
Imposition of Import Ban on exports that use child labor
Suppose the rest of the world imposes an import ban on products made with the
use of child labor. In our model commodity Z is such an exportable. This sector is
therefore directly affected by the imposition of import ban. If the technology of this
sector is such that child labor is an indispensable factor input, then export of Z
completely stops. If instead child labor could be substituted by adult labor or some
other form of factor input, then the production and export of Z continues. However,
sector Z can operate at the world prices due to presence of cost advantage generated
from use of child labor. If child labor is replaced by an imperfect substitute, then the
cost advantage disappears and the export sector may cease to exist. This is referred to
as ‘jump’ and in models of international trade this feature can be quite clearly
displayed. The phenomenon of ‘jump’ provides interesting examples of discontinuity in
structures of production and exchange equilibrium. Essentially, jumps here show that
some sectors may completely cease to exist in the face of structural adjustments.19
Alternatively, in the absence of child labor laws stringently enforced within the
domestic economy, the sector may be producing non-traded instead. However, it must
produce at the world prices and thus may face insufficient demand within the country to
sustain previous production level. Thus in any case, output and employment in sector Z
must fall (continuous and interior solution) due to imposition of import ban. In the
extreme case (jump and corner solution), sector Z may cease to exist.
Therefore, capital must take a flight to sector X, where return to capital R falls.
Adult and child labor moves to sector Y. w* = w(γ L ) must also fall, although return to
land τ * = τ (γ L ) increases.
Let us now check the new demand situation for child labor. As capital moves to
sector X, output increases there. Also, since both adult and child labor moves to sector
Y, output increases in Y. Thus there are two cross-effects working on the aggregate
demand for child labor. There is lower demand as production of Z falls, while an
increased demand as production of Y rises. So the net effect on aggregate requirement
of child labor C d = C (γ L ) may go either way depending on the relative strength of the
production shifts in sectors Y and Z.
Next, we investigate the effect of import ban on the supply of child labor. As
19
A similar example can be obtained in Marjit, Kar and Beladi (2003), mimeo, CSSSC, India.
modeled above, parental decision to send child to work or school depends on the
equilibrium wage rate. A fall in wage shifts the EUSH curve outward. This implies
that when adult wage rate falls, at every level of relative risk aversion expected utility of
supporting the household is higher than before. On the same note, this shifts the EUHK
curve inward. Therefore the critical relative risk aversion point shifts to the left of the
previous equilibrium. This increases the supply of child labor in the economy.
This brings us to the determination of γ L as in (18). Successive determinations
of other variables follow once γ L is obtained in equilibrium. Once again, the size of the
child labor force employed in equilibrium depends on the adjusted demand and supply
levels in the economy.
4.
Conclusions
Certain activities of children, usually those of the “helping-hand” variety confined
within the immediate family may be normal, but the excessive involvement of children
in hired labor segments is long-recognized as a social malaise and generally defined as
child labor. It has co-habited with adult labor in nearly all human societies for ages.
Globalization, still a relatively recent phenomenon, has added new and complicated,
chiefly trade-related economic dimensions, to child labor calling for intervention by
national governments and international institutions in this highly informal market.
Policies which are the best for the children themselves may be hard to come by, because
policymakers are influenced by two completely distinct groups of individuals, voicing
from the same platform their concerns about child labor. Admittedly, one of the groups
comprises genuine well-wishers of children who do not seem to have any vested
interests. The welfare of children, especially of those in other countries, may or may not
be of any real concern for the other group, but they certainly have a business interest in
talking about child labor. In dealing with child labor, the task of the policymaker is thus
not an enviable one.
In this paper, we brought together two distinct classes of economic models to
understand both the demand as well as the supply forces of child labor, operating in a
stylized “globalizing” economy. Changes in the demand for child labor are caused by
factor substitution, their reallocation between production sectors and concomitant
changes in output levels of each good triggered by trade policies that are commonly
associated with globalization. One such policy is tariff-reduction, its positive impact on
efficiency well-known and firmly grounded in the theory of international trade. The
distributional impact of tariff reduction, that is, its differential effect on various factor
prices using child wage, is context specific, depending mainly on factor intensities. In
our model, tariff reduction will increase the demand for child labor. The supply of child
labor is based on decisions taken by parents characterized by different degrees of riskaversion in an uncertain world. We show that tariff reduction reduces the supply of
child labor in our model. These two effects on demand and supply determine both the
wage rate as well as the incidence of child labor in the new equilibrium. Whether wages
and incidence rise or fall in the new equilibrium, depend on the relative strengths of the
two distinct changes.
We also discuss another important development associated with globalization, which is
the growing use of trade measures to achieve non-trade objectives such as core labor
standards, elimination of child labor or the protection of environment. Some countries
have decided to impose an import ban on goods that are produced with child labor. We
argue that such a policy can actually increase the supply for child workers in the
exporting country, which is not what the aforesaid group genuinely concerned with
child welfare would want.
References
Agiobu-Kemmer, I (1992), Child survival and child development in Africa, Bernard van
Leer Foundation Studies and Evaluation Papers # 6. The Hague.
Baland, J and Robinson, J (2000), Is child labor inefficient, Journal of Political
Economy, 108, 663-79.
Basu, Kaushik (2000), An intriguing relation between adult minimum wage and child
labour, The Economic Journal, C-50, 110, 462.
Basu, K and P.H. Van (1998), The economics of child labor, American Economic
Review, 88, 412-427.
Bekombo, M (1981), The child in Africa: Socialization, education and work, in G
Rodgers and G. Standing (eds.) Child work, poverty and underdevelopment,
Geneva, ILO.
Bonnet, M (1993), Child labour in Africa, International Labour Review, 132, 3.
Brown, D.K. (2000), A transaction cost politics analysis of international child labor
standards, in A.V. Deardorff and Robert Stern (eds.) Social dimensions of U.S.
Trade policies. Ann Arbor: U Michigan Press.
Corbin, T (1988), Current trends in youth employment, NY State Department of Labor.
Dehejia, R and Gatti, R (2002), Child Labor: The role of income variability and access
to credit across countries, NBER Working Paper # 9018.
Dixit, A (2000), Comment on “A transaction cost politics analysis of international child
labor standards”, in A.V. Deardorff and Robert Stern (eds.) Social dimensions of
U.S. Trade policies. Ann Arbor: U Michigan Press.
Edmonds, Eric & Pavcnik, Nina (2002), Does globalization increase child labor?
Evidence from Vietnam, NBER Working Paper # 8760.
Goonesekere, S (1993), Child labour in Sri Lanka: Learning from the past, Geneva,
ILO.
Grootaert, C and Kanbur, R (1995), Child Labour: An economic perspective,
International Labour Review, 134,2, 187-203.
Guha-Khasnobis, Basudeb et al (1999), Seen but not heard? Dealing with child labor,
Consumer Policy Review, 9, 4.
Kanbur, Ravi (1982), Entrepreneurial risk taking, inequality and public policy: An
application of inequality decomposition analysis to the general equilibrium
effects of progressive taxation, Journal of Political Economy, 90,1, 1-21.
Maskus, Keith (1997), Core labor standards: Trade impacts and implications of
international trade policy, mimeo, World Bank International Trade Division.
Melchior, A (1996), Child labor and trade policy, in Bjorne Grimsrud and A. Melchior
(eds.) Child labor and international trade policy, Paris.
Mendelievich, Elias (1979), Children at work, Geneva, ILO.
Patrinos, H and Psacharopoulos, G (1997), Family size, schooling and child labor in
Peru: An empirical Analysis, Journal of Population Economics, 10, 387-405.
Ray, Ranjan (2000), Child labor, child schooling and their interaction with adult labor:
Empirical evidence from Peru and Pakistan, World Bank Economic Review, 14,
2, 347-67.
Ranjan, Priya (1999), An economic analysis of child labor, Economics Letters, 64,1,
99-105.
Appendix
Proof of Demand-side condition:
dt
From equation (3) as dt < 0, Rˆ =
< 0 . From (5), using equilibrium γ L as given,
θ KX
such that, wˆ C = wˆ , we substitute R̂ to get (also see fn. 16 and the assumption that sector
X requires relatively more capital per unit of labor, compared to commodity Z),
wˆ = −
θ + θ CY θ KZ
θ KZ
dt
dt
> 0 while from (4) τˆ = LY
< 0.
θ KX (θ LZ + θ CZ )
θ TY
θ KX θ LZ + θ CZ
Now, we obtain the changes in the output and employment in various sectors. From (9)
Yˆ = −aˆ TY = −σ Y θ LY ( wˆ − τˆ) < 0 and LˆY = aˆ LY + Yˆ = aˆ LY − aˆ TY = −σ Y θ LY ( wˆ − τˆ) < 0 .
On the other hand from (6) and (8), we get the respective changes,
λ LX Xˆ + λ LZ Zˆ = −λ LX aˆ LX − λ LZ aˆ LZ − λ LY LˆY = M > 0 ,
(A.1)
λ KX Xˆ + λ KZ Zˆ = −λ KX aˆ KX − λ KZ aˆ KZ = N < 0
(A.2)
Substituting for aˆ ij , LˆY in (A.1) and (A.2), we get M >0 and N <0. We use Cramer’s
rule to solve for Xˆ , Yˆ .
 λ LX
λ
 KX
λ LZ   Xˆ   M 
 =
λ KZ   Zˆ   N 
(A.3)
We define ∆ = λ LX λ KZ − λ LZ λ KX < 0 , such that,
λ M − λ LZ N
λ N − λ KX M
< 0 and Zˆ = LX
> 0.
Xˆ = KZ
∆
∆
Also, equation (7) is rewritten as
λCY (aˆ CY + Yˆ ) + λCZ (aˆ CZ + Zˆ ) = Cˆ
(A.4)
Substituting Yˆ , Zˆ in (A.4), and using the assumption that use of child labor in sector Y
and Z do not undergo any technological change following factor-price changes, we
obtain the change in the requirement of child labor in the economy.
λ N − λ KX M
.
Thus with aˆ CY = 0 = aˆ CZ , Cˆ = −λCY σ Y θ LY ( wˆ − τˆ) + λCZ LX
∆
This with suitable manipulations is reduced to the form of
λ LX
λ
σX
σ λ λ θ θ
[θ LX − θ KX (θ LZ + θ CZ )] + Z ( LX KZ LZ KZ − CZ ) < 1
σY
σ Y λ KX λ LY θ TY
λ LY
(A.5) QED.
Proof of supply-side conditions:
From (12)
δγ L
δ ( EUSH )
= −α (1 − r )( wα − w) − r + β (1 − r )( wβ − w + γ L wβ ) − r (1 + wβ
)
δw
δw
(A.6)
such that for
δγ
δ ( EUSH )
< 0, it suffices to have (− wβ L > 1) , where,
δw
δw
wβ . > w > 0 and
δγ L
< 0.
δw
Similarly from (14)
δγ
δ ( EUHK )
= α (1 − r )[ wα − w + b(1 + γ S )]− r (−1 + b S ) + β (1 − r )( w − wβ ) − r
δw
δw
Once again, for
QED.
(A.7).
δγ
δγ
δ ( EUHK )
> 0 , it suffices to have (b S > 1) , where, b>0 and S > 0 .
δw
δw
δw