Experimental school education multifactor productivity estimates

This paper contains new experimental indexes of multifactor productivity for Australian schools.

Released
24/09/2021

Introduction

Productivity measures are useful to assess performance and efficiency of resource use. The ABS currently compiles multifactor productivity (MFP) estimates for market sector industries but not for non-market sector industries¹. Non-market sector industries have a large portion of output which are provided at prices that are not economically significant. That is, goods and services are provided at prices below the cost of provision, such as public school education.

For non-market industries there are conceptual and practical difficulties in measuring and interpreting productivity. Given the importance of non-market industries to the Australian economy, the ABS has a research agenda to address this gap in productivity statistics.

This paper describes experimental productivity indexes developed for Australian schools. It builds upon recently published experimental indexes, expanding the scope for the volume of output of school education services². This paper also introduces experimental measures of input volumes used in the production of school services.

The experimental estimates indicate that school MFP fell on average 1.2% each year over the period 2008-09 to 2018-19, and labour productivity fell on average 1.1% each year over the same period. When interpreting these productivity measures it is important to remember that they don’t capture quality changes in the delivery of education services, such as changes to class size, individual learning plans, or other labour-intensive educational settings such as special learning units.  It is estimated that around 60% of the fall in productivity could potentially be attributed to changes in the ratio of students to staff. If this is taken into account MFP would have fallen on average 0.5% each year.

These estimates do not reflect the impacts of COVID-19 as the analytical timespan ends at 2018-19. However, the methodology used in this paper will reveal medium to long term impacts of COVID-19 on school output and productivity when data becomes available.

Footnotes

1. Industries considered to be non-market for the purposes of productivity statistics are Divisions O (Public Administration and Safety), P (Education and Training), and Q (Health Care and Social Assistance).
2. School output measures in the Australian National Accounts: experimental estimates, 2007-08 to 2017-18 | Australian Bureau of Statistics (abs.gov.au)

Overview of school education services in Australia

School education plays an important role in the Australian economy. Government recurrent expenditure on school education was $66b in 2018-19 (in 2018-19 dollars), an increase of 32% over the past decade (from$50b in 2018-19 dollars) in 2009-10³. Schools contributed 2% of total Australian output in 2017-18⁴.

In Australia, school education (ANZSIC group 802) covers the activities of primary schools, secondary schools, ‘combined’ primary and secondary schools, and special schools⁵. School education represented 50% of education industry output and 63% of its filled jobs in 2017-18⁶ ⁷.

Regulation and funding for Australian schools is primarily the responsibility of States and Territories. However, the Commonwealth government also plays a role in funding school education. Fees, charges, and other parental and private contributions provide an additional component of school funding⁸.

In Australia, school enrolment is compulsory for children until the completion of year 10⁹. Changes in the number of students enrolled in school each year is primarily driven by demographic changes in each state and territory.

Services are provided through government (public) and non-government (private) schools¹⁰ ¹¹. Primary and secondary school services represented 93% of total school output in 2017-18, with special needs schools contributing the remaining 7%. Both sub-industries are dominated by public schools. Public schools accounted for 76% of total government recurrent funding for primary-secondary school education, while 80% of funding for special schools went to public schools in 2017-18¹² ¹³.

Fees, charges, and revenue from private sources constituted less than 20% of total net recurrent income for primary-secondary education and less than 2% for special schools in the 2018 calendar year¹⁴ ¹⁵ ¹⁶. The majority of funding from private sources goes to private schools.

Footnotes

1. 4 School education - Report on Government Services Productivity Commission (pc.gov.au), Table 4A.10
2. Australian National Accounts: Input-Output Tables (Product Details), 2017-18 financial year | Australian Bureau of Statistics (abs.gov.au) (latest release); Table 1.
3. Australia and New Zealand Standard Industry Classification (ANZSIC) 2006
4. Labour Account Australia, Annual Balanced: Subdivision, Division and Total All Industries (abs.gov.au)
5. Australian National Accounts: Input-Output Tables (Product Details), 2017-18 financial year | Australian Bureau of Statistics (abs.gov.au) (latest release); Table 1.
6. National report on schooling in Australia-2018
7. Report on Government Services 2021, Part B section 4
8. Government schools are owned and managed by State and Territory governments. Non‑government schools, including Catholic and Independent schools, are owned and managed by non‑government establishments-Report on Government Services 2021, Part B section 4
9. As per Standard Economic Sector Classifications of Australia (SESCA), 2008
10. Based on special school education data acquired from Department of Education, Skills and Employment
11. Section 4 School Education - Report on Government Services 2020 (pc.gov.au), page reference 4.
12. national-report-on-schooling-in-australia-2019.pdf (windows.net) table 1.25
13. Based on data provided by Department of Education, Skills and Employment (DESE)
14. Net recurrent income is defined as the amount of income received by a school from the Australian Government, and state or territory government, plus fees, charges, parent contributions and other private sources, which is available for expenditure relating to the ongoing costs of schools

Output measures

The experimental output volume index was constructed as an annually reweighted chain linked Laspeyres index. The annual growth rates in primary-secondary and special schools student Full-Time Equivalent (FTE) enrolments were combined using expenditure (cost) shares as aggregation weights. The index was expanded from the previously published series to include special school education¹⁷.

Figure 1 shows the previous and current index series. The current index grew faster than the previously published index, driven by relatively faster growth in special school enrolments and increases in the cost share of special schools over time. The current index grew steadily at an average annual rate of 1.3%.

Data for compiling the output volume index was sourced from the ABS and the Australian Department of Education, Skills and Employment (DESE).

• Primary-secondary student FTE enrolment data came from the ABS Schools Australia collection¹⁸. These estimates were adjusted to exclude special school education student FTE.
• The aggregation weights for primary-secondary education for public schools were calculated as the sum of operating expenditures. Weights for private schools were calculated as the sum of enrolment fees received and recurrent government grants. These were sourced from the ABS Government Finance Statistics (GFS) and Economic Activity Survey (EAS) collections.
• The student FTE enrolments data and aggregation weights for special school education were derived from data acquired from DESE for the calendar years 2010 to 2019. The derivation involved converting the calendar year data to financial year by averaging the estimates for each ‘pair’ of successive calendar years, and back casting them to cover 2008-09 and 2009-10 using extrapolation techniques.
• Many attributes of quality improvement that are intrinsic to improved outcomes of school education sit outside the 2008 SNA production boundary. These include factors such as changes in class size and the impact of individual learning plans and special learning units on improvements in academic performance over time. While the additional inputs consumed in delivering more tailored and individualised education services are captured, their impact on the quality of outputs are not. This limitation needs to be considered when interpreting the results presented in this paper.

Footnotes

1. Technical details are available in the Appendix
2. Schools Australia publication, table 43a

Labour input

In line with the current approach used in compiling ABS productivity estimates, hours worked were used as the labour input measure.

Estimates of the total number of hours worked were sourced from the Labour Accounts for ANZSIC Subdivision level 80¹⁹. The index for hours worked in schools is shown in Figure 2²⁰.

Footnotes

1. Labour Account Australia, Annual Balanced: Subdivision, Division and Total All Industries, available in ABS.Stat
2. Quality adjusted labour inputs have not been calculated for this analysis. Developing a quality-adjusted labour input measure may be the focus for future development.

Capital services

The ABS currently measures capital services (for purposes of compiling multifactor productivity statistics) only for market sector industries²¹. Divisions O (Public administration and safety), P (Education and training) and Q (Health care and social assistance) are excluded.

Experimental capital services indexes have been constructed for the education industry as a whole (Division P). The methodology for the new indexes is described in a separate paper²², and the results used in this paper as a proxy for growth in capital services for school education. The index for capital services is shown in figure 3.

A limitation of using the Division P capital services index for school education is that the composition of assets providing capital services for the division may differ from that for school education. However, the impact of this on productivity measures are expected to be immaterial, due to the small capital share.

Footnotes

1. The market sector industries include Divisions A to N, plus Divisions R and S (see Chapter 19, ABS 2015).
2. Experimental capital service indexes for non-market industries, 2021

Intermediate inputs

Intermediate inputs are goods and services consumed in the production process and can be broadly grouped into energy, materials, and services. While estimates for intermediate inputs are available from the National Accounts, they also include intermediate inputs consumed by other educational providers, which are outside the scope of this paper. Therefore, intermediate inputs for public schools were calculated using the ABS GFS collection. For private schools, intermediate inputs were calculated from the ABS EAS collection. A total volume measure was then derived using the price deflation method (headline CPI - all groups). The resulting intermediate input estimates for school education is shown in Figure 4²³.

Combined input of labour, capital and intermediate use

The combined input index was calculated as a weighted average of the growth rates of labour, intermediate, and capital services indexes, where the aggregation weights vary for each time period and are defined as the mean of the relative expenditure shares of the components in two adjacent years. Expenditure shares from the GFS and EAS were used as weights. On average, the ratio between labour inputs, intermediate inputs and capital inputs were 74:20:06 over the analysis time span.

The combined index along with the individual input indexes are shown in Figure 5. The fact that schools are highly labour-intensive means that both composite indexes reflect the labour input index growth. While the capital services and intermediate input indexes grew faster than the labour input index, their influence on the composite indexes was small due to their low cost shares.

Productivity

Productivity is a measure of economic performance that compares the change in the volume of goods and services produced (output) with the change in the volume of inputs used to produce those goods and services. Two experimental productivity indexes have been produced for school education - a labour productivity index, and a multifactor productivity index.

Labour productivity

Labour productivity compares the change in the volume of goods and services produced (output) with the change in the volume of labour (input) used to produce that output.

Over the period 2008-09 to 2018-19, the average annual output growth rate of 1.3% was outpaced by the labour input index which grew on average 2.6% per year. Labour productivity for school education in Australia declined on average by 1.1 % per annum. The interpretation of this result is covered later in the paper.

Multifactor productivity

Multifactor productivity compares the volume of goods and services produced (output) to the volume of combined inputs used to produce that output²⁴.  It is calculated as a measure of output per unit of combined inputs. The inputs include some or all of labour, capital and intermediate inputs (energy, materials and purchased services). All inputs have been included in this analysis.

As school education service delivery is labour intensive, the multifactor productivity index exhibits a similar pattern to the labour productivity index, with a slightly higher annual average rate of decline (1.2%).

The decline in MFP is a result of average annual growth rate of the volume of output index of 1.3% outpaced by the stronger growth in the combined input index of 2.7% per year on average.

Figure 8 shows the contributions to output growth. Labour and intermediate inputs were two key drivers to output growth contributing 1.9 and 0.6 percentage points per year on average, while multifactor productivity contributed -1.3 percentage points per year on average.

In the growth accounting framework, growth in labour productivity can be decomposed into growth in capital deepening (which refers to an increase in the capital to labour ratio), intermediate intensity (which refers to an increase in the intermediate input to labour ratio), labour quality and MFP²⁵. Changes in labour quality have not been incorporated in this analysis due to data limitations.

Figure 9 shows that the main contributors to labour productivity growth were changes in MFP and intermediate intensity, averaging -1.3 and 0.1 percentage points per year respectively²⁶.

Figure 10 shows the contribution of each component to output growth over time, on a cumulative basis. Labour input and intermediate inputs were the key contributors to cumulative output growth each year. These positive contributions were partly offset by MFP decline on a cumulative basis each year.

Footnotes

2. Australian System of National Accounts: Concepts, Sources and Methods, 2020-21, chapter 19
3. Changes in intermediate input intensity could change once that input is nominalised using a deflator better fit for purpose

Interpreting school education experimental productivity estimates

Conventional methods may not be sufficient to measure productivity for service industries like education where there is a significant amount of non-market activity. One of the recommendations in the 2010 Parliamentary Inquiry into the productivity slowdown was to present the results in a more customised way, perhaps to complement dashboard approaches²⁷.

In this analysis, gross output (cost weighted student FTE enrolments) was used as the output measure. Productivity declined because the growth in the volume of inputs (mainly teaching staff) outpaced the growth in output (students)²⁸ ²⁹. However, the decline may not reflect technological regress or less efficient service delivery.

The Australian school education policies aim to provide access to education to all school aged children, while ensuring the delivery of services is adaptable to cater to varying learning abilities. This takes the form of capping student to teacher ratios, and the use of specialist support staff and learning support units to help students with specific learning requirements³⁰ ³¹.

Over the 10 years to 2018-19:

• The student to teacher FTE ratio dropped by about 2.6% (teaching staff make up about 71% of staff FTE), and
• The student to non-teaching staff FTE ratio dropped by about 19%³².

While specialist support staff represent a small proportion of the school staff workforce (about 3% on average), it grew  by 44% over the 10 years to 2018-19, much faster than teaching or administrative staff.

As an indication of how the change in student to teacher ratios may impact productivity estimates, we held constant the  student to staff ratio, as at 2008-09, then recalculated the student FTE and the resulting volume of output and productivity indexes. This provides an approximate measure of the impact of falling teacher to staff ratios on productivity estimates.

Figures 12 and 13 show the effect of holding the student to staff ratio constant on the labour and multifactor productivity indexes as shown in figures 6 and 7.

Around 65% of the cumulative decline in labour productivity over the period from 2008-09 to 2018-19 may be attributed to the change in the student to staff ratio. If the ratio was held constant labour productivity would have declined on average 0.3% annually.

Again, about 60% of the cumulative decline in MFP could be attributed to the change in the student to staff ratio. If the ratio was held constant labour productivity would have declined on average 0.5% annually.

Further investigation is needed to identify opportunities to record other quality metrics such as attendance, academic performance and the adoption of technology to understand the productivity story in more detail.

Footnotes

1. Inquiry into raising the productivity growth rate in the Australian economy (2010)
2. Schools, 2020 | Australian Bureau of Statistics (abs.gov.au),Tables 51a and 43a
3. Staff FTE data from table 51a does not include cleaners. Other exclusions and inclusions are available in the National School Statistics Collection (NSSC) manual, 2019.
4. 1 teacher to 8 students in ACT for example; ACT class size policy
5. Specialist support staff are those who perform functions that are of special benefit to students or teaching staff in the development of the school curriculum. While these staff may spend the majority of their time in contact with students, they are not employed or engaged to impart the school curriculum.
6. Non-teaching staff is comprised of the following functional categories as per Schools Australia collection: Specialist support staff, administrative & clerical staff (incl. Teacher aides & assistants) and building operations, general maintenance and other staff

Limitations

In addition to the limitations described in the previous section, other limitations that need to be taken into consideration while interpreting the results include:

• The annual labour accounts data, used to construct the labour index in this paper, will be revised in December 2021. The impact in terms of the analysis presented in this paper over the 2008-09 to 2018-19 timespan is expected to be small³³.
• The CPI all-groups index was used to deflate schools’ intermediate input current price data. Its purpose is to provide a level of economy-wide price pressure, which schools would face when acquiring intermediate inputs. Using a deflator more suited to the mix of intermediate inputs consumed by schools may improve the accuracy of MFP estimates.
• The labour input has not been quality adjusted in this paper.
• The labour input is calculated for ANZSIC subdivision level (80) of the education industry which is comprised of preschool and school education, whereas the output volume index is at ANZSIC group level (802) and includes school education only. This is due to source data limitations for the labour input. The impact of the scope mismatch on labour productivity is expected to be immaterial because the output of preschools is small compared to the output of schools (preschools contributed about 4% of ANZSIC subdivision 80 output in 2017-18)³⁴.
• The experimental capital services index used in this analysis is compiled at education industry division level, whereas the labour and intermediate inputs are compiled at subdivision level. As the weight attached to capital services index in the combined input index is small, the impact of this limitation on the experimental estimates is expected to be immaterial.

Conclusions and next steps

Experimental measures of school education labour productivity index show a decline of 1.1% on average per year over the period 2008-09 to 2018-19. Experimental multifactor productivity measures show a similar decline, about 1.2% on average per year over the same period. Faster growth in the labour input index relative to output growth was the biggest contributing factor to each of these declines. About 60% of the MFP decline was attributable to falling student to staff ratios over the timespan.

This analysis could be further extended or enhanced in a number of ways, some of which are discussed below. The ABS welcomes comments on future directions for this work.

• Inclusion of preschools in the output index would complete the coverage of the preschool and school education sub-industry (ANZSIC subdivision 80).
• Development of quality-adjusted labour productivity estimates would allow for analysis of productivity adjusting for changing labour input quality.
• Compilation of school-specific capital services indexes could be contemplated.
• Compilation of a school specific TIU deflator may enhance the accuracy of intermediate input growth and intensity.
• This analysis concludes in 2018-19, but it has the potential to highlight longer term impacts of the COVID-19 pandemic on school education output and productivity in future years, possibly reflecting changes in the ways in which school output is delivered.
• The ABS has compiled a similar experimental productivity analysis for higher education (ANZSIC class 8102). This class includes higher education services provided by universities, as well as non-university providers of higher education. If the same approach is taken for technical and vocational education and training (ANZSIC class 8101) and adult, community and other education (ANZSIC subdivision 82), it would be feasible to construct experimental multifactor productivity estimates covering the entire education industry.
• Estimates of school output presented in this paper are compiled within the national accounts framework. Some other National Statistics Offices adjust estimates of school output growth, outside the national accounts framework, to account for changes in quality over time. While there is no consensus on which quality indicators should be used or how to weight them together, possible quality metrics could include changes in standardised test scores, changes in attendance records, and changes in school retention rates.

Acknowledgements

The principal author of the paper is Nirmala Narayan.

The author gratefully acknowledges the support received from Jason Annabel, Katherine Keenan, Derek Burnell and Kristen Stone in finalising this paper. The author also thanks her ABS colleagues in the Methodology, Education and Training, Annual Industry Statistics, Government Finance Statistics, National Accounts, Labour Accounts and Labour Employer surveys sections for their ready cooperation and support.

The author further wishes to thank the Australian Curriculum and Reporting Authority, the Department of Education Skills and Employment, and the Report of Government Services section within the Productivity Commission for timely provision of data and advice.

References

Martin J (2019), “Improved methods for total public service productivity: total, UK, 2017”.

Cornell-Farrow S (2019), “Improving Measures of School Education Output and Productivity in Queensland”, Queensland Productivity Commission.

Gonski D (2018), “Through Growth to Achievement”, Report of the Review to Achieve Educational Excellence in Australian Schools.

Productivity Commission 2017, Shifting the Dial: 5 Year Productivity Review, Report No. 84, Canberra

Statistics New Zealand (2013). Education and health industry productivity 1996–2011

Atkinson, T., 2005, “Atkinson Review: Final Report – Measurement of Government Output and Productivity for the National Accounts”, United Kingdom.

Measuring Productivity, OECD Manual (2001)

Technical appendix – Equations

Appendix A - Volume indexes

This analysis uses Laspeyres and Törnqvist volume aggregation methods to develop the volume of output and composite input indexes.  Information relating to these indexes are available in 2008 SNA, chapter 15.

• Output index -This is compiled as a chain linked Laspeyres volume index across two school levels (primary-secondary schools and special schools), using their relative "cost" shares as aggregation weights³⁵.

$${L^t} = {L^{t - 1}}*\sum\limits_{s = 1}^2 {\left[ {\frac{{f_s^t}}{{f_s^{t - 1}}}*\frac{{e_s^{t - 1}}}{{\sum\limits_{s = 1}^2 {e_s^{t - 1}} }}} \right]}$$

Where $$L^t$$ is Laspeyres volume index for time t>1,

s =1,2 represent school levels primary-secondary education and special school education

$$f_s^t$$ represents student full time equivalent for school level s at time t

$$e_s^t$$ represents cost share (the aggregation weight) for school level s at time t, and

t=1 represents the index reference year (2008-09) when $$L^1$$ =100.

• Composite input index – This is compiled as a chain linked Törnqvist volume index by aggregating the three input indexes (labour, intermediate input and capital) using their relative (two point average) expenditure shares as aggregation weights.

$${T^t} = {T^{t - 1}}*\prod\limits_{k = 1}^3 {{{\left[ {\frac{{q_k^t}}{{q_k^{t - 1}}}} \right]}^{\left( {\frac{{w_k^t + w_k^{t - 1}}}{2}} \right)}}}$$

Where $$T^t$$ is Törnqvist volume index for time t>1

k=1,2,3 represent labour input, intermediate input and capital input

$$q_k^t$$ represents input index for class k at time t

$$w_k^t$$ the weight attached to $$q_k^t$$ at time t, such that $$\Sigma_k (\omega_k^t)=1$$for each time period t, and

t=1 represents the index reference year (2008-09) when $$T^1$$ =100.

Footnotes

1. The "cost" refers to a) sum of operating expenditures (for public schools) + enrolment fees received together with recurrent government grants (for private schools), for primary-secondary education, and b) Total net recurrent income for special schools. They are each equivalent to the "cost" involved in the provision of those services, i.e., primary-secondary and special school education.

Appendix B - Labour and multifactor productivity related indexes, formulae

Productivity – This is measured as growth in units of output relative to growth per unit of input.

$$P_t=\frac{O_t}{I_t}$$where $$P_t,\ O_t\ and\ I_t$$ represent productivity, output and input at time t.

Labour and multifactor productivity indexes – These are compiled by chain linking the ratios of output to input for each time period t

$$P_{index}^t=P_{index}^{t-1} * P_t$$

Where $$P_t$$ represents productivity estimate at time t

$$P_{index}^t$$  represents the productivity index at time t, and

t=1 represents the index reference period (2008-09)  when $$P_{index}^1$$= 100.

Growth in labour productivity equation - In the growth accounting framework, growth in labour productivity can be decomposed into growth in capital deepening, intermediate intensity, labour quality and MFP.

The derivation is as follows:

$$\delta(O_G) =\omega_k*\delta\kappa+\omega_l*\delta L +\omega_i*\delta\iota+\delta (MFP)$$

Where,

$$O_G , \kappa, L,\iota\ and\ MFP$$ represent Gross output, capital input, labour input, intermediate input and multifator productivity respectively

$$\delta O_G , \delta \kappa, \delta L\ and\ \delta \iota$$ represent their respective natural log changes, and

$$\omega_k, \omega_l \ and\ \omega_i$$ represent their respective weights (two point average of cost shares) such that $$\omega_k + \omega_l + \omega_i = 1$$

$$\delta(O_G) - \delta(L)=\omega_k*\delta \kappa +\omega_l*\delta L+\omega_i*\delta \iota+\delta (MFP) - (\omega_k + \omega_l + \omega_i) * \delta (L)$$

$$=\omega_k* (\delta \kappa - \delta L)+\omega_i*(\delta \iota - \delta L)+\delta (MFP)$$

i.e.,  $$\delta\left(\frac{O_G}{L}\right)$$  $$=\omega_k*\delta\left(\frac{\kappa}{L}\right) + \omega_i*\delta\left(\frac{\iota}{L}\right) + \delta(MFP)$$

Thus,

$$\delta (lab.\ productivity)_{gross\ output\ basis}=\omega_k*\delta(capital\ deepening)+\omega_i*\delta(intermediate\ intensity)+\delta(MFP)$$

It is calculated as the total of a) the weighted sum of (log) change in capital deepening and (log) change in intermediate intensity where the weights are allowed to vary for each time period and are calculated as the two-point average of the relative cost shares in two adjacent years for intermediate and capital input respectively, and b) the (log) change in multifactor productivity index.

$$\Delta P_L^t=log\left(\frac{K_{index}^t}{K _{index}^{t-1}}\right)*\omega_k^t+log\left(\frac{I_{index}^t}{I_{index}^{t-1}}\right)*\omega_i^t +log\left(\frac{P_{index}^t}{P_{index}^{t-1}}\right)$$

Where

$$\Delta P_L^t$$ represents change in labour productivity for t > 1

$$K_{index}^t,\ I_{index}^t\ and\ P_{index}^t$$  represent the capital deepening, Intermediate intensity and multifactor productivity indexes at time t, and

t=1 represents the reference year (2008-09) when $$K_{index}^1,\ I_{index}^1\ and\ P_{index}^1$$ are each equal to 100.