Deme, Franck and Naqvi(2005) showed that the increased government expenditure on education, training and skill acquisition leads to lower unemployment rate, expansion of the urban formal sector and the contraction of the urban informal sector. This was observed to be the case in Lesotho. The result is based on the two vital assumptions: public expenditure on education ,training and skill acquisition should be very large; and the skill acquisition function is a rising step function. We present a general equilibrium model with perfect capital mobility to analyse the impact of government expenditure on skill acquisition on urban unemployment, the urban formal sector and the urban informal sector.We find that it is possible to derive the Deme, Frank and Naqvi(2005) result independent of the level of government expenditure and the nature of the skill function.skill acquisition; economic development

Bandopadhyay, Titas Kumar

English

Research Papers in Economics

 
 
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SKILL ACQUISITION AND ECONOMIC DEVELOPMENT—SOME 
COMMENTS 
                                                          BY 
  TITAS KUMAR BANDOPADHYAY 
                       BAGNAN COLLEGE,BAGNAN,HOWRAH, 
                                      WEST BENGAL, INDIA 
                                                                         
 
                                         
 
                                     
ABSTRACT: 
 Deme, Franck and  Naqvi(2005)  showed that the increased government expenditure on 
education, training and skill acquisition leads to lower unemployment rate, expansion of 
the urban formal sector and the contraction of the urban informal sector. This  was 
observed  to be the case in Lesotho. The result is based on the two vital assumptions: 
public expenditure on education ,training and skill acquisition should be very large; and 
the skill acquisition function is a rising step function. We present a general equilibrium 
model with perfect capital mobility to analyse the impact of government expenditure on 
skill acquisition on  urban unemployment, the urban formal sector and the urban informal 
sector.We find that it is possible to derive the Deme, Frank and Naqvi(2005) result 
independent of the level of government expenditure and the nature of the skill function. 
Jel Classification: H52,I28, J24 
Key words:  skill acquisition, economic development. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                                                 
 
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1.INTRODUCTION: 
 
The informal sector is generally characterized by low productivity ,bad working 
conditions, poor technology and an occupational risk to health and safety. It is natural to 
think that these problems would be solved if informal workers were to develop their 
skills.Fretwell and Colombano(2000) have pointed out that skills and education have a 
positive rate of return for the informal sector. Burki and Ubaidullah(1992) showed that 
investment in human capital yields the same return in both the formal and the informal 
sectors. 
In general, informal sector workers have very little access to formal education and most 
of them are unskilled. In Mali, 76% of the informal sectors workers did not receive any 
education at all(Lautier,2000). In Kenya, 85% of the informal sector’s workers have not 
received any training . We find a similar situation in Uganda. 
Workers in the informal sector can acquire skills through formal, non-formal and 
informal training. Formal training is provided by  government organizations. However, 
formal training is not so useful for the informal sector for a number of reasons: often, 
such training programmes are too theoretical and biased towards white collar jobs; the 
fees for training are very high and the method of training is suitable only for the educated 
workers only; and further such training is not designed to satisfy the market demand 
outside the formal sector. 
Non-formal training means training outside the formal education system and is  generally  
provided by voluntary and non-government organizations. Such training programmes are 
flexible and starts from the grassroots levels. One of the most innovative methods of 
providing non-formal training is mobile training. Despite its advantages, non-formal 
training has also some problems. For instance, such training is specific and limited to the 
potential workers. Often, the training staff are inefficient. Further, it is often the case that 
there is a lack of co-ordination among the various programmes conducted by the NGOs 
and duplicated activities are common. 
Informal training is characterized by its lack of structure, the absence of underlying 
curriculum and the absence of a specified time period for learning. The most commonly 
used method of informal training is the apprenticeship training.Such training is flexible , 
dynamic, self-regulating and costs nothing to the government.Entry into such 
programmes require little in the way of prior skills and experience. In West Africa, 60% 
of the informal workers have acquired skills through the apprenticeship. The figure is 
55% in Ghana(WorldBank,1995),67%to76%inKenya(Nelson,1997), and 70% in Africa 
(Mauro,Gerard and Parod,1999).Inspite of its many advantages ,the informal 
apprenticeship training does have limitations.Such training is weak on theory and 
outdated. The quality and extent of training depend on the skill, willingness and ability of 
the master .Further,the range of skills acquired is limited and is difficult to adapt to 
changing situations. 
Apprentices may receive some payments during the training period. However, the low 
apprenticeship fees paid to the master is the main motivator for employers of informal  
 
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workers to recomend apprenticeship training to the workers(Ferej,1996).The 
apprenticeship fees are not a problem for the informal sector workers entering 
training(Nelson,1997). 
We here present a model for skill acquisition in a general equilibrium frame work with 
perfect mobility of capital  within the economy. The model is motivated by Deme,  
Franck, and Naqvi(2005) who showed that if the government expenditure on education, 
training and skill acquisition is very large and the skill acquisition function is a rising step 
function, then  increased government expenditure on education, training and skill 
formation lowers urban unemployment and the urban formal sector expands,where as 
urban informal sector contracts. We show here that the same result can be obtained 
theoretically, independent of the level of such public expenditure and the specific form of 
the skill acquisition function. 
The basic model is developed in Section 2. Section 2 also deals with the comparative 
static effect of rising government expenditure on education, training and skill formation .  
Section 3 concludes. 
2.THE MODEL 
We consider a three-sector model  of a small open economy. The three sectors are: urban 
formal sector(u ), urban informal sector(i) and the rural sector( ) r . The products of the 
three sectors( ) r i u X X X , , are traded internationally.The product prices ( ) r i u P P P , ,  are 
given exogenously by the rest of the world . 
We consider two types of labour:skilled and unskilled labour. The source of skilled 
labour is the urban informal sector, where workers acquire skills(h) through 
apprenticeship training. The apprentices ( a L ) get some amount of pocket money( a W ) 
and at the same time they have to pay fees(e) to their masters. The fees motivates the 
masters  to train the apprentices and the apprentices have no problems in paying them. 
The skill acquired by the apprentices depends on the net payment to them. It is assumed 
that the  apprentices require a fixed wage. The master can not charge high fees, because 
this would lower the rate of skill acquisition in the urban informal sector.Thus, even if 
not all the applicants  for  apprenticeship training  get an opportunity to training at the 
existing net apprentice wage, the masters can not raise the fees because this hurts the 
skills of the apprentice workers. Hence, unemployment exists in the urban sector. 
It is assumed that after completing their training all the apprentice  become skilled 
workers. All of them are absorbed by either  the mother sector or in the urban formal 
sector . There is no unemployment of the skilled workers and the skilled workers are 
mobile between the formal and the informal sectors. Thus, the skill wage rates( s W ) are 
equalized in the two sectors. 
The urban formal sector uses organized labour( u L ), skilled labour( su L ) and capital( u K ) 
as inputs. The variables for production in the urban informal sector are apprentice 
workers( a L ), skilled workers( si L ) and capital( i K ). However, the rural sector uses only 
ordinary labour( r L ) and capital( r K ) in their production activity.  
 
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The endowments of labour(L)and capital(K ) are fixed . Capital is fully employed and 
perfectly mobile among the three sectors, but labour is not fully employed. The perfect 
capital mobility gives a uniform rate of return (r ) to capital in all the three sectors. 
Workers migrate from the rural sector to the urban sector. It is assumed that migration 
takes place over two periods . In the first period, the migrants may obtain employment in 
the urban formal sector or may train as apprentices  in the urban informal sector or may 
remain unemployed. In the second period, the apprentices are employed  as skilled 
workers,either in the urban formal sector or in the urban informal sector. In migration 
equilibrium, the average actual rural wage( r W ) is equalized to the average urban formal 
wage( * u W ) for the unskilled workers, the average net payment to the apprentice workers 
in the urban informal sector and the discounted wage( v Ws / ) of the skilled workers. 
The production structures of the three sectors are as follows: 
). 3 .........( .......... .......... )......... (
); 2 ......( .......... )......... , / (
); 1 ......( .......... )......... , / (
r r r r
i si a i si i
u su u u su u
k f L X
and k L hL f L X
k L L f L X
=
=
=
 
Where  () . ′
j f  >0 and  () . ″
j f   <0 and   r i u k k k , ,  are the factor intensities in the three 
sectors. 
The level of skills acquired by the apprentices depends upon the apprentice wage less the 
apprenticeship fees paid to their masters.Thus, we have: 
) 4 ...( .......... .......... )......... ( e W h h a − =  with h′> 0, h′ ′  < 0. 
The cost of minimization of the apprenticeship training implies: 
( )( ) ). 5 ( .......... .......... .......... 1 / = − ′ e W h h a  
The competitive equilibrium gives the following price equations: 
). 8 ........( .......... .......... )......... , (
); 7 ........( .......... )......... , , (
); 6 ( .......... .......... )......... , *, (
R W C P
and R W e W C P
R W W C P
r r r
s a i i
s u u u
=
− =
=
 
The rural-urban migration equation is: 
). 9 ..( )......... / ( ) ))( /( ( * )) /( ( v W e W L L L W L L L W s a r a u r u r + − − + − =  
The employment functions of the non-trained labour in the urban formal sector is given 
by: 
). 10 ........( .......... .......... *)........ ( u u W L α β + =  
Where β  is a shift parameter and α  is the resonse of non-trained labour in the urban 
formal sector.  
 
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The supply function of the skilled labour( a L ) depends on the net income of the 
apprentices and the government expenditure on education,training and the skill 
acquisition(E ) in the urban informal sector: 
). 11 ...( .......... .......... )......... , ( E e W L L a a a − =  
Where   1 a L  > 0,   2 a L  > 0. 
The endowment equations of the labour force of the entire economy is: 
). 12 .....( .......... .......... L U L L L r a u = + + +  
Where U  is the level of urban unemployment. 
The full employment of the skilled labour is given by 
). 13 .....( .......... .......... .......... a si su L L L = +  
Using Equation (11) into Equation(13) we get, 
 
). 1 . 13 ...( .......... )......... , ( E e W L L L a a si su − = +  
 
The full employment of the capital is given by: 
). 14 ......( .......... .......... K K K K r i u = + +  
Interms of capital intensity equation (14) may be written as: 
). 1 . 14 ........( .......... r r si i su u L k K L k L k − = +  
2.1. WORKING OF THE MODEL 
   
We can solve for fourteen unknowns from fourteen equations. Equation(5) determines e 
and then h is obtained from Equation (4). Given   e and W P W P a i u u   , *, , , Equations (6) and 
(7) determine  s W  and R .  r W   can be obtained from Equation(8),given ,  r P  and R .  u L  is 
obtained from Equation (10),given β , α  and  * u W .  a L  is derived from Equation (11), 
given  e Wa,  and E . Equation(9) yields  r L , given   s a u u r W W e W L W , , *, , ,  and v. 
Equilibrium U  is obtained from Equation(12), given   r a u L L L , ,   and L . Equations 
(13.1)  and (14.1) determine  su L  and  si L . 
 
2.2.EFFECTS OF INCREASED GOVERNMENT EXPENDITURE  
PROPOSITION: 
Increased government expenditure on education, training and skill acquisition may lead  
to expansion of the urban formal sector at the cost of rural and the urban informal 
sector and a fall in  urban unemployment.Empirical  support for this result may be found  
by considering the situation in Lesotho. 
  
 
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PROOF: 
      Suppose government expenditure on education, training and skill acquisition is increased. 
Equation(11) shows that  a L  will rise because this expands the scope of apprenticeship 
training  in the informal sector.Since  a L  does not enter in the determination of  any factor 
prices and fixed employment of urban formal non-trained labour due to the rigid formal 
wage,  r L  must fall with the increase in  a L  to restore the migration equilibrium condition. 
Given  r k , capital will move out of the rural sector to the urban sector. Thus ,in  the urban 
region, the capital-intensive sector expands and the  Labour-intensive sector contracts. 
Capital  and labour thus move to the urban formal sector. Given  u L and  u k ,  su L  must rise 
and  si L  falls. 
 
Using Equations(9) and (12) we get, 
U v W W L e W v W W L v W W W s r a a s r u s r u ) / ( ) / ( ) / * ( − = + − − − + − . Given factor 
prices,  u L , v and ea rise in  a L  due to increased E  implies a fall in U . So, the rise in a L  
exceeds the fall in  r L .Thus, we have the proposition. 
 
3.CONCLUSION 
 
The role of government in education ,training and skill acquisition is very important in 
many developing countries,such as Lesotho. Increasing government expenditure in this 
direction results in there being more skilled workers. Deme, Franck and Naqvi(2005) 
showed that the increased government expenditure on education, training and  
skill acquisition leads to lower unemployment rate, expansion of the urban formal sector  
and the contraction of the urban informal sector. This has been found to be so in Lesotho. 
Their analysis is based on the two vital assumptions: government expenditure  is very 
large and the process of skill acquisition is discontinuous. They showed that small 
infusion has nothing to do with generating highly skilled work force. This is applicable to 
Lesotho. However, this paper shows that, theoretically, the same results can be obtained 
independent of the level of government expenditure on skill acquisition and the specific 
nature of the skill acquisition function.In the present paper, we supplemented simple 
three sector mobile capital model developed by Harris-Todaro(1970) with apprentice 
training in the informal sector.The implication of this paper is that an increased 
government expenditure on education, training and skill formation, no matter whether the 
level is high or low, gives a rising urban formal sector, disappointing urban informal 
sector and lower urban unemployment, irrespective of the nature of the skill acquisition 
function. 
 
 
REFERENCES: 
Burki A. and Ubaidullah A., 1992,Earnings, training and employment in Gujranwala’s 
urban  informal  sector:Evolution  or  Involution,Pakistan  Economic&Social 
Review,30:49-66. 
  
 
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Ferej,A.,1996,The use of traditional apprenticeship in training for self-employment by 
vocational training institutes(VTIs)in Kenya.In Grierson,P. and McKenzie:Training 
for selfemployment through vocational training institutions.ILO. Turin Centre. 
 
Fretwell D.H. and Colombano J.E.,2000. Adult continuing education:An integral part of 
lifelong learning. Emerging policies and programs for the 21st century in upper and 
middle  income  countries.World  Bank.Human  Development  Network,  Education 
Department, Human Development Sector Unit—Europe and Central Asia Region. 
 
Harris,J.R. and Todaro,M.P., 1970. Migration Unemployment and Development: a Two-
sector Analysis. American Economic Review,60.126-142. 
 
Lautier,B.  2000.  Received  and  debatable  ideas  on  the  informal  sector.  Dossier. 
Europa.eu.int/comm./development/publicat/courier/courier-178/en/en-053-ni.pdf. 
 
Mauro Huyghe A.,Gerard E. and Parodi E. 1999.Les apprentissages en milieu urbain. 
Formation  professionnelle  dans  le  secture  informel  en  Afrique.  Analysis  par 
pays:Mali,  Senegal,  Benin  et  Mauritanie.Direction  General  de  la  Cooperation 
Internationale et du Development. Ministere des Affaires Etrangeres. 
 
Mamit Deme, David Franck, And Nadeem Naqvi 2005. A General Equilibrium Skill 
Acquisition  Model  Of  Development  For  Lesotho.  Journal  Of  Economic 
Development.Vol.30,No.1,June 2005. 
 
Nelson,C. 1997. Training goes to market:a comparative study of two Kenyan training 
programs.  U.S.Agency  for  International  Development.  Global  Bureau.  Economic 
Growth Section, Microenterprise Development Office. 
 
World Bank1995. Republic of Ghana,  Vocational Skills  and informal sector support 
project (Report no.13691-GH).Summary.Washington,DC. 

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