Gender differentials in the cost of primary education: a study of Pakistan.

Ismail, Zafar H.

The paper examines the differences in the cost of primary education by gender and by province. It shows that the growth in enrolment outstrips the growth in the relevant population cohort, except in Sindh, and that this is faster in the case of girls than boys: that the school construction programme for girls in Sindh, unlike other provinces, outstrips the growth in female teacher employment. This is also seen in the boys' school in Pakistan. Cost of providing education are a function of the availability of teachers and schools, opportunity cost of employment, urbanisation and female literacy. The growth in both recurring and capital outlays and in output costs per student are higher for girls and boys except in Balochistan.

Using a pooled time series and analysis the paper concludes that there is an optimal level for the availability of schools per 1000 population [6.02 and 5.67 respectively for girls and boys in the Punjab and 3.88 for boys in NWFP and Balochistan] and for the number of teachers per 1000 students [7.69 for girls and 3.36 for boys]. It suggests the policy prescription to reallocate resources to employing more teachers for boys for greater cost effectiveness.

1. INTRODUCTION

The Government of Pakistan prepared the second Perspective Plan in 1987-88 for the fifteen years ending in 2002-2003. The Plan recognised that the long-term objectives could be achieved only if the human capital stock in Pakistan was improved. The Plan, therefore, developed a strategy for improving the education, skills, nutrition and health of the people. These objectives have become the cornerstone of the donor supported Social Action Programme (SAP). However, there is general recognition of the resources constraint within which these objectives are to achieved. The low priority that has been attached traditionally to allocations to the social sectors, particularly directed for the female part of the population, has led to increasing the shortfalls in allocation with respect to need. SAP envisages the expansion of primary infrastructure, particularly for female education, through an accelerated school construction programme using cost effective approaches to delivery including need-based criteria for school location and changes in the pattern of allocation of funds among sector inputs. It is in this context that this paper examines the issue of cost effectiveness of the primary education sector in Pakistan and attempts to establish implications for a possible future strategy. Section 2 presents the historical profile of the sector from 1977 to 1991. Section 3 sets out the theoretical framework for analysis. Sections 4 and 5 first estimate the costs and then identify the determinants of spatial and inter-temporal variation in these costs. Section 6 summarises the key conclusions.

2. TRENDS IN PRIMARY EDUCATION

Estimates of enrolment published by the Central Bureau of Education (CBE) of the Government of Pakistan indicate that it is increasing at a faster pace than the growth in population of the relevant age cohort (5-9 years) for each of the Provinces, except for Sindh, gender notwithstanding (see Table 1). As may be seen, the differential in the two growth rates is higher for girls than it is for boys. In the largest province, Punjab, primary enrolment by girls has increased at more than two and a half times the growth rate in the relevant population cohort between 1973 and 1991. In the same period the enrolment of boys has increased by slightly less than twice the growth in the cohort population.

Table 2 gives the corresponding growth rates in the number of schools and teachers. This differential in growth rates between enrolments and education inputs indicates that the average number of students per teacher has been increasing with the passage of time for both boys and girls generally, except in NWFP for both and in Sindh for the girls. However, the number of boys per teacher has seen a worsening of the situation more than for girls. Also the average school size, measured as students per school, has been increasing for the boys school in each province. In the case of the girls school this is seen only in the case of schools in Punjab and Balochistan.

A higher growth rate in the number of schools than in the number of teachers tends to imply that the quality of education is declining with the passage of time. This may be the direct result of the decline in the number of teachers available per school. This would tend to suggest that the teacher:student ratios have worsened. Moreover, this also indicates that the share of capital costs in the provision of education at the primary stage will be increasing over the period. This phenomenon is observed in the case of Punjab and Sindh. Gender differential growth rates indicate that this trend in the decline of the quality of education is observed in the case of female primary education in Sindh and male primary education in Punjab.

3. THEORETICAL FRAMEWORK

Different approaches can be adopted for deriving the cost function for primary education of provincial governments. One approach is to view the provincial governments as engaging in a cost minimisation behaviour, given knowledge of the production function of enrolments with respect to inputs like schools, teachers, etc. In this view unit costs are the minimum average costs for achieving a target enrolment ratio. However, this approach assumes rational behaviour with full knowledge of the production function, and no resource constraints such that targets can be fully met. These assumptions are generally not satisfied in practice.

A more realistic view of how provincial governments behave is that they generally operate in an overall resource constrained framework, both for recurring and development expenditures, and that given the overall quantum of resources available in the recurring budget and the ADP, funds are allocated to primary education on the basis of inter-sectoral priorities. According to this view then the actual choice of level of inputs need not correspond to the cost minimising combination. As such some inputs are likely to be overused while others remain at sub-optimal levels. For example, if development allocations for primary education are high, especially in recent years following the launching of SAP, then too many schools may be built relative to teachers whose numbers may be constrained by lack of revenues to finance recurring expenditures.

We set up the theoretical framework which is consistent with the latter view. Accordingly if the development and recurring allocations for primary education are [bar.[I.sub.t]] and [bar.[E.sub.t]] respectively in year t than the incremental number of schools, [DELTA][S.sub.t], is given by

===== append qc=====

[bar.[DELTA][S.sub.t]] = [C.sub.t] * [[bar.[I.sub.t]] ... ... ... ... ... (1)

where [C.sub.t] is the unit capital cost (at constant prices) per school.

The total number of schools, [S.sub.t], in year is

[bar.[S.sub.t]] = [bar.[S.sub.t-1]] + [bar.[DELTA][S.sub.t]] ... ... ... ... ... (2)

The capital stock embodied in these schools is evaluated at historic cost and represented by [K.sub.t] in year t. We have that

[K.sub.t] = [K.sub.t] ([bar.[S.sub.t]]) ... ... ... ... ...(3)

The number of teachers, [T.sub.t], is given by

[T.sub.t] = [bar.[E.sub.t]]/[W.sub.t] ... ... ... ... ... (4)

where [W.sub.t] is the average wage rate (at constant prices) of teachers. This wage rate includes overhead costs and costs of inputs (books, etc.) which are complementary to teaching.

The total cost of primary education to provincial governments is given by where [[upsilon].sub.t] is the rental price of capital and includes a depreciation component and a component for the opportunity cost of capital.

[C.sub.t] = [W.sub.t] [bar.[T.sub.t]] + [[upsilon].sub.t], [bar.[K.sub.t]]([S.sub.t]) ... ... ... ... (5)

The production function of primary education is represented as

[E.sub.t] = [f.sub.t] ([bar.[T.sub.t]], [bar.[S.sub.t]], [Z.sub.t]) ... ... ... ... (6)

where [E.sub.t] = enrolments and [Z.sub.t] a vector of variables on the demand side determining the rate of utilisation of education facilities.

Therefore, we have that the average cost, A[c.sub.t], in year t per enrolment as

A[C.sub.t] = [C.sub.t]/[E.sub.t] = [W.sub.t][bar.[T.sub.t]] + [[upsilon].sub.t][K.sub.t]([bar.[s.sub.t]])/[f.sub.t] ([bar.[T.sub.t]], [bar.[S.sub.t]], [Z.sub.t]) ... ... ... (7)

Differentiation of the average cost function yields

[delta]A [C.sub.t]/[delta][bar.[S.sub.t]] = 1/[f.sup.2.sub.t] [[f.sub.t] [[upsilon].sub.t] [delta][K.sub.t]([bar.S])/[delta][bar.[S.sub.t]] - [C.sub.t] [delta][f.sub.t]/[delta][bar.[T.sub.t]]] >/< 0 ... ... (8)

[delta]A [C.sub.t]/[delta][bar.[T.sub.t]] = 1/[f.sup.2.sub.t] [[f.sub.t][W.sub.t] - [C.sub.t] [delta][f.sub.t]/[delta][bar.[T.sub.t]] >/< 0 ... ... ... (9)

If provincial governments engaged in cost minimisation behaviour then both derivatives would be zero at the optimal levels of [S.sub.t] and [T.sub.t]. But since these magnitudes are given exogenously at [bar.[S.sub.t]] and [bar.[T.sub.t]] respectively it is likely that both derivatives diverge from zero. Different possibilities can be identified as follows:

[delta]A [C.sub.t]/[delta][bar.[S.sub.t]] < 0, [delta]A [C.sub.t]/[delta][bar.[T.sub.t]] < 0 ... ... ... ... (i)

This implies that both inputs are being underused from the view point of cost minimisation. This case highlights the likelihood of under expenditure generally on primary education.

[delta]A [C.sub.t]/[delta][bar.[S.sub.t]] > 0, [delta]A [C.sub.t]/[delta][bar.[T.sub.t]] > 0 ... ... ... ... (ii)

In this case, both inputs are being overused.

[delta]A [C.sub.t]/[delta][bar.[S.sub.t]] < 0, [delta]A [C.sub.t]/[delta][bar.[T.sub.t]] > 0 ... ... ... ... (iii)

In this case, there exists a case for reallocation of funds from teacher s salaries to building more schools if cost effectiveness of the sector is to be enhanced.

[delta]A [C.sub.t]/[delta][bar.[S.sub.t]] > 0, [delta]A [C.sub.t]/[delta][bar.[T.sub.t]] < 0 ... ... ... ... (iv)

Here, there is a case for more teachers and fewer schools.

Therefore, our approach enables determination of the future expansion path of inputs into primary education which maximises cost effectiveness of expenditures.

We also have from Equation (7) that

[delta]A [C.sub.t]/[delta][W.sub.t] = [bar.[T.sub.t]]/[f.sub.t] > 0 ... ... ... ... ... (10)

[delta]A [C.sub.t]/[delta][[upsilon].sub.t] = [K.sub.t]/[F.sub.t] > 0 ... ... ... ... ... (11)

[delta]A [C.sub.t]/[delta][Z.sub.t] = - [C.sub.t]/[f.sup.2.sub.t] * [delta][f.sub.t]/[delta][Z.sub.t] < 0 ... ... ... ... (12)

Therefore, determinants of average cost are given by

A [C.sub.t] = A [C.sub.t] [[bar.[S.sub.t]], [bar.[T.sub.t]], [W.sub.t], [[upsilon].sub.t], [Z.sub.t] ... ... ... (13)

4. ESTIMATION OF COSTS

Information on public sector costs of providing education are contained in the annual budget documents of the provincial governments. (1) A more meaningful analysis is by gender of school (boys/girls) and by location (urban/rural). Unfortunately, disaggregation of the data in this manner is not available. Information on the numbers of schools constructed for boys and girls separately is contained in the Federal and Provincial Annual Development Plans and the profile of completions is available from the statistics published by the CBE. In addition, the number of male and female teachers employed is also available in the CBE data base. The annual "Demand for Grants: Recurring Expenditure" provides the budgeted costs for the ensuing year, the revised costs for the current year and actuals of the preceding year for the province as a whole aggregated for both the categories of schools and teachers. Costs have been allocated by gender on the basis of teachers (establishment charges) and schools (other costs).

Information on the development expenditure is provided in the Annual Development Plan in considerable detail and is summarised in the "Demand for Grants: Development Expenditure". As the construction of schools is spread over a number of years, the data on development outlay would need to be lagged. Moreover, given inter-provincial differences in construction speeds, this lag should ideally reflect this. Unfortunately, data for this is not available, thus a constant two-year lag for each of the Provinces has been used.

The sum of these represent the effective annual outlay of resources on primary education. The cost of providing primary education to a particular student is the aggregate expenditure incurred over the five years he/she spends in school. Further, as these costs are incurred at different periods of time one needs to convert these into real terms. In arriving at the costs of providing education to students the enrolment at the end of the fifth year has been equated to be the output from the schooling system. The PIHS from 1990-91 also shows the rate of attrition within the first four years of schooling to be exponential in character. Our data which is intertemporal also indicate this at the macro level.

The recurring expenditure series of each of the four provinces has been converted to real terms (at constant prices of 1990-91) by inflating the nominal values by the implicit deflator for the Public Administration and Defence sector of the economy. Development expenditures largely represent the construction of schools. Therefore, the nominal expenditures have been adjusted to real terms using the implicit deflator for the Construction sector. The trend growth rate in these implicit deflators indicates that the former has been rising by 8.1 percent annually and the latter by 8.8 percent annually. This would imply that the construction of more schools in preference to the provision of more factor inputs may be less cost efficient.

In real terms N.W.F.P. has been increasing its recurring expenditure much more rapidly than the other Provinces, and much more so in the case of female primary schools. Sindh, however, outstrips the others in its annual increase in development expenditure, particularly for girls' schools. Inter-provincial differences in growth rates may be seen in Table 3. These clearly highlight the priority in the mix of expenditure for each of the provinces.

An important conclusion by comparison of the growth rates in Tables 2 and 3 respectively is the fast increase in expenditure relative to the growth in physical inputs. This indicates that the unit cost, [C.sub.t], of constructing a school has been rising in real terms while the real recurring cost per teacher has also demonstrated some increase. The growth rate in these magnitudes is given in Table 4.

The output of the primary stage of education is the number of students completing the fifty year. As information on completions, successful or otherwise, is not available, the output at this stage has been equated to the enrolment in class 5. To estimate the recurring costs spent on a student produced by the system we have aggregated the cost per enrolment over the five year span.

The value of the base stock of schools in 1973 has been derived by first estimating the average per school cost in real terms and then applying this to the base quantum. This however, underestimates the value of the base stock as it does not include the value of those primary level classrooms available in the higher category of schools (middle and high). Information for the marginal capital cost of such classes is not available. To this base year estimate each year's addition to the capital stock is added. This is then converted into an annualised stream by aggregating the opportunity cost of the stock of schools each year and the current year's depreciation. The opportunity cost has been assumed to be 12.5 percent (the long term return on government bonds) of the value of the stock. The life-span of a primary school has been assumed to be 40 years. These have then been translated to the per student cost.

These province-wise estimates on a per student basis of primary education are presented in Table 5, and Table 6 summarises the growth rates in enrolment and output costs.

It is also of some interest to note the inter-provincial and inter-gender variation in costs. In the Punjab and NWFP which started with output costs for both boys and girls at about the same level, the output costs of girls have outstripped that for boys by 1990-91. Sindh started with higher output costs for girls and this differential has only increased with time. Balochistan, however, has seen no change in the relative costs. Costs in the NWFP and Balochistan are higher because of the high component of capital costs due largely to higher costs of construction.

5. DETERMINANTS OF COSTS

The general specification of the average cost function (with respect to enrolment) of primary education for provincial governments is given by Equation (14). For econometric estimation we scale the number of schools by the school going age population in age group of five to nine years. The latter variable reflects potential demand. Similarly, the number of teachers is scaled by the number of schools, to yield the input mix. Also, since the impact on unit cost of [bar.S] and [bar.T] is ambiguous, these variables enter in a polynomial form in the cost function.

The resulting equation to be estimated is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

where

[bar.[A.sub.t]] = school going age population in year t,

[Y.sub.t] = real per capita income,

[U.sub.t] = extent of urbanisation, and

[I.sub.t] = relative price index for wages to construction cost.

[Y.sub.t] is included to capture the real wage effect (inclusive of labour into school construction) and a possible demand effect. [U.sub.t] is a demand related variable. [I.sub.t] derives the cost implications of a divergence between inflation in wages and construction costs.

The magnitudes of [[beta].sub.2] to [[beta].sub.6], are of special significance. These will help in identifying the presence of economies or diseconomies in the use of inputs.

Equation (14) is estimated separately for genders on a pooled time series data for the four provinces for the period, 1972-73 to 1990-91. The results are given in Table 7. The cubic term with respect to the availability of schools skews the results substantially by reducing the importance of the availability of teachers. In fact its inclusion leads to a result where the impact of a teacher become insignificant. As this is counter intuitive, the term has been dropped. Intercept and slope dummies for the provinces have been used wherever significant. The intercept term was insignificant and was, therefore, neglected in the subsequent analysis. Only the provincial dummy for Balochistan was significant. The results inclusive of all provincial dummies is shown as a footnote so that the reader may be able to draw conclusions independently of the author. The estimated equation demonstrates that there are some significant inter-regional differences in these coefficients, with Punjab and Sindh falling into one group and NWFP and Balochistan into another group. (2)

For all provinces the equation indicates that the average cost falls initially and then rises subsequently with increase in ([bar.[S.sub.t]] / [[??].sub.t]), the ratio of schools to school-going age population. Therefore, there exists for each province and within provinces for each gender an optimal ([bar.S]/[??]) which minimises unit costs. Any expansion in schools beyond this level raises the unit cost. With regard to teachers per school, we observe a rise in costs initially and then a fall with increase in ([bar.T]/[bar.S]) upto a level beyond which costs rise once again.

The estimated optimal cost minimising magnitudes of inputs by gender for each province are given in Table 8. The optimal number of schools per 1000 school-going age population in Punjab and Sindh is 6.02 for girls and 5.67 for boys. Sindh was close to this level by 1990-91, and Punjab had substantially more than the optimal for boys. For NWFP and Balochistan the corresponding optimal magnitude is 3.88 for boys. In the context of girls, the optimal level of 0.27 schools per 000 population appears to be unrealistic. This may possibly be due to the very low level of enrolment which exists in both NWFP and Balochistan. The result, therefore, needs to be considered with caution. However, it would appear that given the very low levels of enrolment, the optimal for these two provinces cannot be readily determined for the girls' schools. Therefore, in at least two provinces of the country, Punjab and Sindh, the priority in allocation of resources has to shift from school building for the boys. This activity can perhaps only be justified on regional equity considerations in areas which are backward and have low levels of coverage.

Table 8 also indicates there is underprovision generally of teachers for both boys and girls. It appears that their role in raising quality and demand for primary education has not been fully recognised. Actually inputs of teachers per school are above cost minimising levels only in the context of girls in the Punjab. Overall we have the conclusion that the composition of expenditure budgets (with the possible exception of Balochistan and, perhaps, also NWFP) has to be dramatically altered. The recurring allocations for employing more teachers need to be raised and simultaneously development allocations scaled down in the case of boys. The same strategy is recommended for the Social Action Programme. However, expansion in number of primary school teachers raises issues of adequate training facilities, remuneration levels and decentralisation of management down to community level to increase accountability of teaching inputs. In addition, the availability of female teachers for the rural areas poses some problems which need to be tackled within a social development/awareness framework.

6. CONCLUSIONS

This paper has examined the degree of cost effectiveness of the primary education sector of Pakistan. Annual enrolment and output costs have been estimated by gender for each province for the period, 1972-73 to 1990-91. These have shown a rising trend generally because of the increase in real recurring costs per teacher, in costs of school construction and because of the divergence in the physical level of use of education inputs, schools and teachers, from the cost minimising levels. In particular, the number of teachers and of schools is substantially below optimal levels in the context of girls. There also appears to be an over supply of schools for boys. In this instance some improvement is needed in the number of teachers per school to attain optimal levels. This indicates that cost effectiveness of provision of primary education can be significantly enhanced if the allocation of funds is shifted towards recurring expenditures for employment of more teachers away from development allocations for construction of new schools in the context of boys' education at the primary level.

Author's Note: I wish to acknowledge the help provided by Dr Hafiz A. Pasha, Dr Aynul Hasan, Dr Aisha Ghaus, A. Rauf Khan, and Rao Asif Iqbal. Any errors are the sole responsibility of the author.

REFERENCES

Coombs, Philip H., and Jacques Hallak (1972) Managing Educational Costs. London: Oxford University Press.

Coombs, Philip H., and Jacques Hallak (1987) Cost Analysis in Education: A Tool for Policy and Planning. Washington, D. C.: The World Bank.

Ismail, Zafar H., Hafiz A. Pasha and Rauf A. Khan (1994) Cost Effectiveness of Primary Education: A Case Study of Pakistan. The Pakistan Development Review 33:4.

Jimenez, Emmanuel, and Jee-Peng Tan (1985) Educational Development in Pakistan: The Role of User Charges and Private Education. Washington, D. C.: The World Bank.

Khan, Shahrukh R., Naushin Mahmood and Fazal Hussain (1985) An Appraisal of School Level Enrolment and Facilities in Pakistan: 1970-71-1982-83. (Mimeograph.)

Khan, Shahrukh R., Naushin Mahmood and Rehana Siddiqui (1985) Strategy, Subsidies and User Charges in Pakistan's Public Sector Education: 1970-71--1982-83. (Mimeograph.)

Levin, H. M. (1983) Cost Effectiveness: A Primer. California: Sage Publications; Beverley Hills.

Mingat, Alain, and Jee-Peng Tan (1988) Analytical Tools for Sector Work in Education. Washington, D. C.: The World Bank.

Pakistan, Government of (1988) 7th Five-Year Plan 1988-93 and Perspective Plan 1988-2003. 1: Islamabad: Planning Commission.

Psacharopoulos, George, and Maureen Woodhall (1985) Education for Development: An Analysis of Investment Choices. Washington, D. C.: The World Bank.

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World Bank (1993) Aide Memoire: Social Action Programme Project Mission: September. Washington, D. C.: The World Bank.

(1) Indicates the share of provincial governments in provision

(2)

Variable Coefficient Std. Error t-Statistic Prob.

FSPOP -5633.686 2753.216 -2.046220 0.0462
FSPOP2 3225.714 733.675 4.396656 0.0001
FSADPS -2824.831 499.148 -5.659300 0.0000
FTCHS 2544.277 2777.290 0.916101 0.3642
FTCHS2 -416.9571 935.0591 -0.445915 0.6577
FTCHS3 18.80473 69.86479 0.269159 0.7890
PCINC 0.547088 0.372830 1.467393 0.1488
URBAN 698.7680 239.8615 2.913214 0.0054
IND -3994.553 1855.635 -2.152661 0.0364
BAL 2347.518 2819.734 0.832532 0.4092
SIND -19237.87 8264.563 -2.327754 0.0242
NWF -4106.616 3103.411 -1.323259 0.1920

Variable Coefficient Std. Error t-Statistic Prob.

MSPOP -6913.986 1824.217 -3.790111 0.0004
MSPOP2 755.0930 210.1301 3.593455 0.0008
MSADPS -183.7410 72.13917 -2.547035 0.0141
MTCHS 11170.93 6502.811 1.717862 0.0923
MTCHS2 -1919.994 2478.339 -0.774710 0.4423
MTCHS3 53.68137 307.8388 0.174381 0.8623
PCINC 0.103565 0.121893 0.849637 0.3997
URBAN 408.6920 60.18213 6.790920 0.0000
IND -2411.989 732.2949 -3.293741 0.0019
BAL 11060.06 1901.702 5.815872 0.0000
SIND -7318.895 868.6464 -8.425631 0.0000
NWF 4326.896 1929.039 2.243032 0.0295

Zafar H. Ismail is Senior Principal Specialist at the Social Policy and Development Centre, Karachi.

Table 1
Growth Rates in Enrolment and School Going Age
Population, 1972-73 to 1990-91

(Percent)

 Pakistan Punjab Sindh N.W.F.P. Balochistan

Cohort Population 2.98 2.15 3.42 3.46 7.22
 Girls 3.05 2.16 3.79 3.30 7.16
 Boys 2.92 2.14 3.16 3.60 7.28

Total Enrolment 4.23 4.53 2.61 4.34 9.52
 Girls 4.95 5.42 3.04 4.41 8.24
 Boys 3.90 4.01 2.44 4.33 9.80

Table 2
Growth Rates in Inputs to Primary Education
1972-73 to 1990-91

(Percent)

 Pakistan Punjab Sindh N.W.F.P. Balochistan

Schools 4.16 3.97 4.73 3.91 4.19
Teachers 3.87 3.49 2.92 6.71 8.45
Girls' Schools 5.92 3.97 11.19 6.97 2.25
Girls' Teachers 4.76 4.39 4.84 7.38 5.91
Boys' Schools 3.19 3.96 1.44 2.35 4.57
Boys' Teachers 3.39 2.92 1.99 6.47 8.88

Table 3
Real Growth in Expenditures on Primary Education
(1972-73 to 1990-91)

(Percent)

 Pakistan Punjab Sindh N.W.F.P. Balochistan

Recurring 4.96 4.03 5.76 8.61 2.00
 Girls 5.48 4.07 6.59 9.12 1.10
 Boys 4.46 3.98 4.59 7.86 2.71

Development 2.95 2.35 5.08 3.41 1.97
 Girls 4.18 2.52 8.29 5.21 1.70
 Boys 172 2.20 1.10 1.23 2.18

Table 4
Growth in Costs of Primary Education Inputs
1972-73 to 1990-91
(1990-91 = 100)

(Percent)

 Recurring Cost Construction
 per Teacher Cost per School

Pakistan 5.21 2.08
Punjab 5.21 2.01
Sindh 5.07 5.13
NWFP 5.60 2.50
Balochistan 3.46 2.22

Table 5
Enrolment and Output Costs Per Student in Primary Education.
(At 1990-91 Prices)

 Punjab

 Enrolment Costs Output Costs

Year Girls Boys Girls Boys

1973 782 810
1974 815 850
1975 858 852
1976 857 853
1977 833 842 4,145 4,208
1978 910 916 4,274 4,314
1979 883 906 4,342 4,370
1980 908 920 4,391 4,438
1981 929 942 4,464 4,527
1982 928 946 4,558 4,631
1983 1,038 1,052 4,686 4,766
1984 1,094 1,172 4,896 5,032
1985 1,108 1,130 5,097 5,241
1986 1,293 1,293 5,461 5,592
1987 1,339 1,330 5,872 5,976
1988 1,363 1,346 6,197 6,270
1989 1,359 1,341 6,462 6,440
1990 1,299 1,243 6,653 6,553
1991 1,348 1,309 6,707 6,569

 NWFP

1973 1,927 1,838
1974 1,988 1,924
1975 1,884 1,923
1976 1,935 1,911
1977 1,905 1,898 9,638 9,495
1978 2,004 1,962 9,715 9,618
1979 1,992 2,002 9,719 9,696
1980 2,079 2,096 9,913 9,869
1981 2,307 2,157 10,286 10,115
1982 2,591 2,231 10,972 10,448
1983 3,249 2,384 12,217 10,871
1984 3,456 2,427 13,682 11,296
1985 3,851 2,493 15,454 11,693
1986 3,903 2,620 17,050 12,155
1987 4,373 2,780 18,832 12,703
1988 4,325 2,945 19,907 13,264
1989 4,518 2,909 20,970 13,746
1990 4,767 2,883 21,887 14,136
1991 4,700 2,803 22,684 14,319

 Sindh

 Enrolment Costs Output Costs

Year Girls Boys Girls Boys

1973 690 795
1974 751 856
1975 925 788
1976 928 799
1977 874 730 4,169 3,967
1978 991 830 4,470 4,003
1979 948 790 4,667 3,937
1980 1,006 821 4,748 3,970
1981 1,030 843 4,849 4,014
1982 1,068 850 5,043 4,134
1983 1,217 943 5,269 4,247
1984 1,192 929 5,513 4,386
1985 1,320 1,014 5,826 4,579
1986 1,766 1,274 6,562 5,010
1987 2,127 1,391 7,622 5,551
1988 2,266 1,442 8,671 6,050
1989 2,416 1,228 9,894 6,349
1990 2,484 1,210 11,059 6,545
1991 2,387 1,092 11,680 6,362

 Balochistan

1973 1,952 2,530
1974 1,836 2,446
1975 2,069 2,430
1976 1,950 2,501
1977 1,941 2,371 9,748 12,278
1978 2,050 2,393 9,846 12,141
1979 2,105 2,494 10,114 12,190
1980 2,278 2,520 10,323 12,280
1981 2,265 2,650 10,638 12,428
1982 2,355 2,852 11,052 12,909
1983 2,254 3,036 11,257 13,552
1984 2,171 3,143 11,323 14,201
1985 2,190 3,128 11,235 14,809
1986 2,632 3,299 11,603 15,458
1987 2,482 3,560 11,729 16,166
1988 2,692 3,570 12,167 16,700
1989 2,392 3,403 12,388 16,959
1990 2,382 3,297 12,580 17,128
1991 2,259 3,172 12,208 17,001

Table 6
Real Growth in Enrolment and Output Costs of Primary Education
1972-73 to 1990-91
(At 1990-91 Prices)

(Percent)

 Pakistan Punjab Sindh

Annual Cost per Student 3.76 3.31 5.52
 Girls 4.24 3.43 7.20
 Boys 3.43 3.19 3.21
Output Cost 4.31 3.73 6.06
 Girls 5.21 3.81 7.43
 Boys 3.36 3.66 4.20

 N.W.F.P. Balochistan

Annual Cost per Student 4.83 1.99
 Girls 6.34 1.51
 Boys 2.92 2.37
Output Cost 5.50 2.50
 Girls 7.30 1.82
 Boys 3.28 3.02

Table 7
Results Of Regressions
Average Cost per Enrolment is the Dependent Variable

 Girls
Variable *** Coefficient t-ratio

([[bar.S].sub.t], / [[??].sub.t]) -1231.099 -1.035 **
[([[bar.S].sub.t], /
 [[??].sub.t]).sup.2] 2293.720 7.368 *
[([[bar.S].sub.t], /
 [[??].sub.t]).sup.2] . DPS -2191.407 -11.951 *
([[bar.T].sub.t], /
 [[bar.S].sub.t]) 5742.642 5.079 *
[([[bar.T].sub.t], /
 [[bar.S].sub.t]).sup.2] -1407.147 -3.476 *
[([[bar.T].sub.t], /
 [[bar.S].sub.t]).sup.3] 89.609 2.634 *
[U.sub.t] -21518.984 -1.932 **
[Y.sub.t] 0.603 1.571 **
[I.sub.t] -6209.950 -4.317 *
DUMBAL 5857.647 7.889 *
[R.sup.2] 0.956
F 121.325
Degrees of Freedom 49

 Boys
Variable *** Coefficient t-ratio

([[bar.S].sub.t], / [[??].sub.t]) -5430.697 -5.638 *
[([[bar.S].sub.t], /
 [[??].sub.t]).sup.2] 700.412 8.163 *
[([[bar.S].sub.t], /
 [[??].sub.t]).sup.2] . DPS -221.149 -14.168
([[bar.T].sub.t], /
 [[bar.S].sub.t]) 25887.877 7.853 *
[([[bar.T].sub.t], /
 [[bar.S].sub.t]).sup.2] -7784.920 -5.063 *
[([[bar.T].sub.t], /
 [[bar.S].sub.t]).sup.3] 780.281 3.465 *
[U.sub.t] -8172.684 -3.826 *
[Y.sub.t] 0.369 2.036 **
[I.sub.t] -6049.055 -6.750 *
DUMBAL 4605.334 19.003 *
[R.sup.2] 0.987
F 429.087
Degrees of Freedom 49

DUMBAL = 1 for Balochistan; zero otherwise.

DPS = 1 for Punjab and Sindh; zero otherwise.

* Significant at 1 percent level.

** Significant at 5 percent level.

*** Significant at 10 percent level.

Table 8
Actual (1990-91) And Optimal * Number of Schools per 1000 School-going
Age Population and Teachers per School by Province

 Actual Optimal Difference
Girls (1) (2) (2-1)

 S/A

 Punjab 1.43 6.02 4.59
 Sindh 1.58 6.02 4.44
 NWFP 2.73 0.27 -2.46
 Balochistan 0.69 0.27 -0.42

 US

 Punjab 8.21 7.69 -0.52
 Sindh 6.65 7.69 1.04
 NWFP 2.72 7.69 4.97
 Balochistan 2.32 7.69 5.37

Boys

 S/A

 Punjab 6.95 5.67 -1.28
 Sindh 5.86 5.67 -0.19
 NWFP 5.03 3.88 -1.15
 Balochistan 4.22 3.88 -0.34

 T/S

 Punjab 2.56 3.36 0.80
 Sindh 2.66 3.36 0.70
 NWFP 3.14 3.36 0.22
 Balochistan 2.66 3.36 0.70