I
set up a simple static model of school finance and the demand for edu- cators to confirm intuitions regarding the roles of liquidity constraints, government subsidy, and government coordination in the determination of LERs. Suppose there are a finite number of public schools under a govern- ment, and that each school maximizes the per-learner output from educa- tion, given its budget constraint, without government intervention. Assume that each school can employ educators freely and that the number of learners changes exogenously at each school, for example, owing to migration and population growth.Each school has a target LER in each period that maximizes the efficiency in education production, yit = y* + ξit, where ξit is independent and identically distributed with zero mean and finite variance. We assume that y* is small enough, and we ignore a negative range of yit.1 ξ
it could reflect transitory changes in school environments.
Let ei(Li, Hi) denote an efficienty function, where Li and Hi are learners and educators in school i, respectively. I assume the efficiency function takes
Li
a quadratic loss form: ei(Li, Hi) =
[
1 – (yit – —— )2]
, where LER determines the Hilearning efficiency.2 The total educational outcome is defined as e
i(Li, Hi)Li. Each school has its static budget constraint, qiLi + GiwHi, where qi is the school fee, Gi is a subsidy from the government, w is the wage rate (exogenous) for educators, and Hi = His + H
iu for two types of educators, subsidized and non- subsidized, His and H
iu, respectively. By definition, the budget constraint can be separated into two constraints: a government subsidy constraint, Gi≥ wHi, and a school fee constraint, qiLi ≥ wHiu. Nonsubsidized teachers are paid only from school fees. However, since the quality of subsidized and nonsubsidized
115 1 The optimal level of LER can change as endowment for and technology deployment in educa-
tion production vary across schools, if these factors alter the marginal productivity of educators. When other nonpersonnel inputs and LERs are substitutable, equal LERs are not necessary for equal education output.
2 In the range of LERs below the target, the efficiency is increasing in LER. It is assumed that
with positive externalities among peer learners, an increase in number of learners raises the efficiency. However, if this effect is negligible, the target level can be set arbitrarily small.
educators is the same in this framework, the two budget constraints can be added together. Assume that the government decides the per-learner amount of subsidy, gi, so Gi = giLi and gi≥ 0 for all i (the government does not impose a tax).
The school fee is bounded by some limit, q—— i(f), determined by the socio- economic circumstances, f, of the school. In particular, the fee is determined by income level and distribution.3 In fact, school fees are determined by SGBs consisting of educators and community leaders, such that most parents can afford to pay them. Unless the government subsidy gi offsets qi(f), local con-
L dition f affects ——.H
School maximizes the per-learner education output subject to the budget constraint: Li max Etei(Li, Hi) =
[
1 – (yit – ——)2]
x,q H i s.t. Gi≥ wHis qiLi≥ wHiu.Rearranging the budget constraint, we define φ(qi(f); w, gi): w Li
φ(qi; w, gi) ≡ ——————— ≤ ——. q (A.1) i(f) + gi Hi
The LER is constrained below by the ratio of educator wage (per-educator cost) to the sum of the school fee and the per-learner subsidy (per-learner revenue). When the school decides on the school fee and employs educators, the determination of the school fee is simple: qi*(f) = qi(f), that is, collect the highest school fees.4 In this model I assume that, at least in the short 3 For example, if community members vote for a school fee, we predict that the fee will be
determined by the median community income.
4 Since 1996 school fees for public schools have been determined by the SGB, which consists of
the principal, educators, parents (including community leaders), and sometimes learners at the secondary level. Therefore, the level of the school fee reflects opinions within the community. In community-school governance, the school fee increases as the median of monthly household income increases and as the standard deviation of monthly household income decreases. The former result is consistent with the voting implication, while the latter implies that school fee determination is anti-inequality. In this sense, school governance is altruistic to poor families who have difficulty in paying school fees, but it potentially sacrifices school quality (Yamauchi and Nishiyama 2005).
run, the number of learners does not change immediately in response to an increase in school fees (that is, inelastic enrollment), but also that the fees are determined such that most parents can afford to pay them.5
Suppose now that budget constraints are not binding. Then the optimal solution is
Li
xi* ≡ —— = y* > φ(qH —i(f), gi; w). i*
1
In this case Hi = β*Li, where β* = ——. Next consider the case in which the budget y* constraint is binding: y* < φ(q—i(f), gi; w). In this case:
1 Hi = —————————— Li φq—i(f), gi; w) 1 = β*Li +
[
—————————— – φ(q— β*]
Li (A.2) i(f), gi; w) w = β*Li +[
———————— – q— β*]
Li, i(f) + giwhere w < β*(q—i(f) + gi). The second term is an efficiency loss in terms of the number of educators. The government will allocate the subsidies to those with binding budget constraints. Next consider the government’s allocation of school subsidies. Assume that the government maximizes the total educa- tional output
Σ
ieili subject to its budget constraint but does not allocate any subsidy to those schools that are able to attain optimal ratios:w
max
Σ [
1 – (y* – ——————— )2]
L i{ gi}ii|y*<φ(q—i,0;w) qi(f) + gi
s.t.
Σ
giLi≤ G.i|y*<φ(q—i,0;w)
5 Yamauchi and Nishiyama (2005) show that the proportion of learners who cannot pay school
fees, including both those who postpone payment and those who receive official exemptions, is positively correlated with the level of the school fees. The result, however, does not directly show the school drop-out rate. My interviews with school principals indicate that those parents
Without the government budget constratint, the necessary condition is gi* = wy* – q——i(f). In general we have 2
[
y* – φi(gi)][
–φ′(gi)]
= λ, where λ is the Lagrangian multiplier. From this we also know that when q——i (f) decreases, gi increases to compensate for gaps in the capability of collecting school fees (community endowment). In other words, LERs are equalized under the benevolent government’s unitary decision.So, without government intervention, LERs are determined by school-level liquidity (budget) constraints, provided that the best ratio is identical in all schools no matter to which racial group they belong. However, we expect that with active government interventions, the ratios will be equalized across all schools. In particular, the subsidy is allocated more to those schools in less favorable socioeconomic circumstances, that is, those with larger initial LERs.
The 1998 Norms and Standards for School Funding
Sections that are relevant to this monograph are the following:
45. The SASA [South African School Act] imposes a responsibility on all public school governing bodies to do their utmost to improve the quality of education in their schools by raising additional resources to supplement those which the state provides from public funds (section 36). All parents, but particularly those who are less poor or who have good incomes, are thereby encouraged to increase their own direct financial and other contributions to the quality of their children’s education in public schools. The act does not interfere unreasonably with parents’ discretion under the law as to how to spend their own resources on their children’s education.
46. Ironically, given the emphasis on redress and equity, the funding provisions of the Act appear to have worked thus far to the advantage of public schools patronized by middle-class and wealthy parents. The apartheid regime favored such communities with high-quality facili- ties, equipment and resources. Vigorous fund-raising by parent bod- ies, including commercial sponsorships and fee income, have enabled many such schools to add to their facilities, equipment and learning resources, and expand their range of cultural and sporting activities. Since 1995, when such schools have been required to down-size their
who cannot pay school fees are often required to provide services to the schools, such as clean- ing the school facilities, but there is no systematic evidence suggesting that this is the norm in the country.
In the empirical analysis, since we look only at the relationship between changes in number of learners and educators, we do not directly examine the effect of school fees.
staff establishments, many have been able to recruit additional staff on governing body contracts, paid from the school fund.
47. Poor people, on the other hand, especially in former homeland areas, have contributed a disproportionate share of their incomes over many decades to their building, upkeep and improvement of schools, through school funds and other contributions, including physical labor. All too many schools in poor rural and urban working-class communities still suffer the legacy of large classes, deplorable physical conditions, and absence of learning resources, despite a major RDP National School Build- ing Programme, and many other projects paid directly from provincial budgets. Yet the educators and learners in poor schools are expected to achieve the same levels of learning and teaching as their compatriots. 48. Such contractions within the same public school system reflect past discriminatory investment in schooling, and vast current disparities in the personal income of parents. The present document addresses these inequalities by establishing a sharply progressive state funding policy for ordinary public schools, which favors poor communities.