economics leggers Economics Letters 56 ~i 997) 121- 127
ELSEVIER
Can public sector employment spur human capital acquisition? Mukti P. Upadhyay* Department of Economics, University of Connecticut, Storrs, CT 06269-1063, USA Received 6 November 1996; accepted 19 March 1997
Abstract Ill a general equilibrium model oI' a product and an education sector, we add government employment of educated labor for public goods provision and lbr political economy reasons. Education subsidy may cause fewer public goods and retard the product sector. © 1997 Elsevier Science S.A.
Keywords: Public employment: Human capital; Education subsidy: Educated unemployment JEL classification: O41; J24; J68
1. Introduction This paper answers two questions: (l) How does a government decision to employ educated labor affect the acquisition of human capital? and (2) If an expansion of human capital is a goal of social policy, is an education subsidy better than direct public sector employment of educated labor and, if yes, how much better? We model the public sector as an employer of educated labor to produce public goods. But the employment policy also serves as a mechanism to grant political favor to certain sections in. the society) Education and employment policies determine the growth of human and physical capital, private sector output, and the unemployment rate.
2. The model We extend the two-sector human capital models of Findlay, Rodriguez (1981); Chaudhuri, Khan *Tel.: 860-486-4762; Tel. (mess.): 860-486-3022; fax: 860-486-4463; e-maih
[email protected] ~See Heller, Tait (1984), Table I, p. 7, that shows thai the public sector employs a large share of the non-agricultural labor force (39% in 31 developing countries and 24% in 16 OECD countries, in the early 1980s). Large scale employment of temporary or "ghost" workers in Uganda, Ghana, Gambia, Kenya and many other countries illustrate the point. Despite public sector reform supported by the World Bank durirg 1980s, "only a handful of countries have cut the number of civil service employees by more than 5 percent since they began structural adjustment..." The democratic transition in Africa has also led to reversals of wage containments and personnel reductions in some countries (such as Congo in 1991 and Ghana in 1992). (World Bank, 1994, pp. 123-4). 0165-1765/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PI! SOl 65-1765(97)001 22-5
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(1984), and Upadhyay (1994) to incorporate government output and employment decisions. The economy produces three kinds of goods: a composite good, Q, satisfies both consumption and capital accumulation. The output in ~his sector exhibits constant returns to scale (CRS) in physical capital K, the human capital E,2 and uneducated labor U. In addition, the firms produce Q with the assistance of public goods, G. The firms consider the stock of public goods as fixed while making production plans. Output Q, however, follows increasing returns to scale whenever public goods increase along with other inputs. Thus we have Q = Q(K ~, E e, U; G).
(I)
The function Q satisfies all the properties of a neoclassical production function with positive first and negative second partial derivatives in each of its arguments. Furthermore, Q ~ o if any of the arguments in (l) equals zero. The production function for education displays CRS in physical and human capital: X = E, = X(K x, E x ),
,,2)
where X is the output of the education sector or the change per period in the stock of human capital. Finally, there is a public sector (PS) that employs labor and produces public goods.~ Government policy also follows political economy considerations where the objective is not to maximize social welfare but, rather, to dispense political favor.4 Here, this favor takes the form of PS employment~a most transp~ent form of political favor in Africa (Gelb et al., 1991), India (Bardhan, 1984; Jha, 1980), and other parts of the developing world. We assume that the PS produces public goods using only educated labor: G = G ( E c;~ E")= G(EI), G' >0, and
(3)
E ~ ~ Et(*~',G)+ E", E,I,0, E ° > 0 ,
(4)
where G is the amount of public goods produced per period, E a is the total employment in the PS, and E ° is the part of PS employment that results from political pressure and is assumed exogenous to Ihe model. A limiting case arises if political pressure is absent, i.e., E ° =0. Let Eq. (4) determine employment in the PS. The partial derivative E~ is not observable, but is only an equilibrium relationship that holds if private production of public goods were possible so that a rise in the educated wage lowers the profit-maximizing employment. The other partial derivative, E shows the responsiveness of productive employment in the PS to a change in public goods production. Finally, E ° is a purely political component of employment and does not contribute to the output G. Eq. (4) implies that, in general, ~->MPE l. The PS operates under a balanced budget constraint each period. The government raises revenue :Human capital is symmymuus with educated labor in this paper. ~Pure public goods, such as the maintenance of law and order, and basic physical infrastructure, are necessary to create an environn~nt tbr private sector activity, Because of the features of huge externalities and nonexcludability in public goods, we assun~ that their production takes place in the government sector. ~See Bardhan (1984): Becker (1983), and Olson (1982).
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through a proportional income tax (and non-tax sources, A, that include foreign aid) and pays educated labor the predetermined wage rPt[rK + w~(E ° + E x) + ff~E~ + wuU] + A = ~ E C,
(5)
where t = tax rate, w~ = educated wage in the private sector, r = rate of return to physical capital, and wU=uneducated wage. Eq. (5) shows that the government revenue equals the PS payment to the educated employees. The tax rate t, varies to balance the public sector budget each period. Factor allocations are as follows: E ° + E x + E G = (I - Ix)E,
(6)
K ° + K x = K,
(7)
E+U=N,
(8)
where IX is the rate of unemployment of educated labor;~ K and E are the total stocks of physical and human capital respectively, and N is the size of the labor force (or total population). The first order conditions for profit-maximization yield: Qk = PXk = r;
(9)
Q~ = pX~ = w~; and
(10)
Qu = wu,
(I 1)
where p is the price of education relative to the numeraire good Q. These equations reflect the marginal productivity pricing of factors. To complete the model, we need two more equations. One follows the approach in Chaudhuri, Khan (1984)--the investment equilibrium condition suitably modiiied to i~aclude expected returns from PS employment. A second condition equates the expected educated wage in the private and public sectors. The model thus incorporates wage dualism since the "minimum" wage for educated workers is above the market-clearing level in one (the public) sector, but not in the other. Algebraically, these conditions are V ( W e) -- W u
(12)
P where V(w ~) is the expected educated wage (see below) while the actual wage of the educated in the private sector, w~, has a close relationship with the PS wage:
We = ~
1 - E~ + Eu
SThe ratio of unemployed educated to total educated.
(13)
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where E t~ is the number of educated unemployed and the expression in parentheses shows the proportion of workers employed in PS to the PS labor force,6 and
V(we) = pPwe + pGvp,
(14)
with the restriction that 0 < p P < l , 0 < p G < l , and 0 < p P + p G < I , where pP and pG are the probabilities of employment in private and public sectors respectively, for an educated individual. Specifically,
p l,
=
E° + EX E
, and pt~ _-
E~ E"
(15)
The sum of these two p ' s is the total probability of securing an educated job and hence equals l - / x
of F-Xl. (6). What is the nature of unemployment in this model'? Since the PS wage exceeds the private educated wage, it pays for an educated worker to search for a job in the PS. We assume that an individual must stay unemployed to look for a PS job.7 As a result, a part of the labor force waits in a queue to obtain a job in the PS, causing unemployment to emerge. The search process reaches equilibrium when the expected PS wage equals the actual private wage, as shown in Eq. (13). An uneducated worker deciding whether to invest in human capital not only evaluates the rate of return on physical capital as an alternative to investment in education, but also weighs the relative probabilities of employment in the public versus private sector to determine the expected return from education,x
3. Discussion of the model and results
The model can be divided into two parts, one for the government and one for the private sector. Eqs. (3) and (4) provide a solution for PS employment and output in a short run equilibrium, given exogenous E ° and if,. The main results are summarized in-a series of propositions stated below?
Proposition L Education expands with pG, the probability of a government job, which is a direct function of political pressure in the short run and employment for public goods production in the long rl,~n .
An increase in political pressure is reflected in a higher E °, the employment in the "pit", which raises p~. in the short run, when the government finances increased wage payments either through a higher non-tax revenue or a higher aid inflow, the probability of a government job improves, raising the "The PS labor force comprises those actually employed in this sector and the educated unemployed who are waiting for the PS employment, ~(Layard et ai. {1991 ), p. 42) note that some workers may not be willing to work in the secondary sector "because it is harder to find a primary sector job while already employed in the secondary sector than while unemployed." SRewriting (12), using (14) and (15), and then substituting from (13) implies after a little algebra that in equilibrium the investment efficiency condition reduces to r = ( w c - w u ) l p. "Proofs arc sketched in an Appendix which is available from the author.
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expected educated wage. Since there is no immediate repercussion in the private sector, ~° there is a greater demand for education. If new employment is, however, financed by raising the tax rate, the total educated employment will change according to two kinds of labor movements. First, a rise in public employment will attract more labor in the queue. Hence the probability of a PS job, defined as the fraction of total PS labor force actually employed, may or may not change, and if it does, may go up or down. A greater wage differential between public and private sectors and a higher elasticity of marginal productivity of E p which equals E ° + E x will generate a disproportionately larger movement toward PS, increase educated unemployment and depress the probability of a PS job. Second, as in conventional trade theory, the supply of the factors of production is inelastic, hence unaffected by a higher income tax. The factor owners thus bear the full incidence of the tax. Since all incomes are taxed equiproportionately, the relative rates of return between human and physical capital and between educated and uneducated labor remain constant. Thus in the short run the expansion of education depends directly on the fraction of PS labor force actually employed in the PS.
Proposition ,.9. A rise in the public sector wage rate tends, under certain circumstances, to reduce the tax rate on factor incomes, given A, unless the wage increase is accompanied by employment in the "sink." E G, the total PS employment, consists of productive employment E ~ and the political component E °. Thus if a decision to raise ~ is taken independently of employment E °, there will be a fall in the optimal level of E ~ and hence in E C. From Eq. (5) the effect of a change in if, on tax rate comes from its effect on the private sector factor rewards. The rise in the PS wage increases the labor supply for this sector and pushes the expected educated wage up. As more uneducated workers choose to go to schools, the education sector expands. If education is relatively more intensive in E, then the educated wage rises further. Assuming K and E are gross substitutes in Q and U and E are gross complements, r tends to rise and w u tends to fall in the short run. Thus, under proportional income tax, the tax rate will fall if the share of uneducated wage in total tax revenue has been relatively low It and rise if this share has been high. In the last two paragraphs we have assumed that a rise in if, inevitably reduces E ~ and hence E C. If, as is more likely, E ~ is kept stable through a partial shift of E from E ~ to E °, the higher wage and steady public employment raise the expected educated wage and cause a greater flow of E into the PS. This keeps the output of public goods constant and induces lesser adjustment in the Q sector. If the 12 budget balance is maintained, however, the tax rate must rise to finance increased wage payments. This last case results when the government pay decisions are made independently of the employment decisions and better resembles the case of PS employment analyzed by Gelb et al. (1991).
Proposition 3. A rise in education subsidy may expand the production of composite good as well as education if the subsidy is paid out from an exogenous rise in government revenue. A tax financed subsidy, on the other hand, depresses the composite good production, especially if education is relatively intensive in human capital and composite good in physical capital. ~C'Taxpayments do not change and therefore neither does the employment. I~So that higher revenue requirements can still be met with a lower fi'action of the increased income o1"E and K. ~2An alternative would be to try to secure fresh inflows of foreign aid to support wage growth and employment expansion.
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A subsidy to education modifies Eq. (12) as follows: W(w e)
r=
--
Wu
p(I - 7") '
(16)
where V(w~) is the expected educated wage that includes the probabilities of employment in different sectors. The subsidy also modifies Eq. (5) so that the government expenditure, ~E C, now includes a second term: rpx, the amount of subsidy. Since 0 < r < I, the subsidy immediately increases the private expected return per unit cost of schooling. The profitability of the education sector improves with greater demand for schooling and attracts more resources. We can divide the effect of a change in education subsidy into three parts. The first relates to the factor price changes that leave the cost of education unaffected in a general equilibrium. A second part indicates the effect on the relative price of education. And, finally, the third addresses if it matters how the subsidy is linanced as between foreign resource inflow and the income tax on domestic residents) ~
Prolu~sition 4. A joint govermnent decision to raise educational subsidy and public employment has implications for the Q sector depending on whether or not the employment growth increases the supply of public goods. In many instances we observe educational subsidy go hand in hand with higher employment of school and college graduates in government. When the subsidy is combined with a growth of educated employment for public goods production, the decline in Q is oft~et partly by greater availability of public goods. Since Q displays increasing returns to scale in all inputs including G (but constant returns without G), the net effect on Q depends on the exact degree of returns to scale (Helpman, 1984) together with the elasticity of substitution between K and E and the elasticity of complementarity between E and U (Jones, Easton, 1983). A higher returns to scale, greater substitutability between K and E and weaker complementarity between E and U tend to increase the production of Q. In contrast, when the rise in employment results from political pressure and leads to no change in the amount of public goods produced, the Q sector contracts unambiguously.
4. Conclusion A political economy with public employment may create job opportunities for newly educated workers but the model shows that this would neither be a lasting solution to the unemployment problem nor provide an automatic rationale tbr more rapid human capital accumulation.
Acknowledgements I thank Ali Khan, Louis Maccini, Stephen Miller, Susan Randolph and seminar participants at the University of Connecticut for helpful comments. ~'The.~ ett~cts are derived in an Appendix available from the author.
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