# Experimental higher education multifactor productivity estimates

This paper contains new experimental indexes of multifactor productivity growth for Australian higher education

Released
4/08/2021

## Introduction

Productivity measures are useful to assess the performance and efficiency of resource use. The ABS currently compiles multifactor productivity estimates for market sector industries but not for non-market sector industries.¹ Non-market sector industries have a large portion of output 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, or public hospital services.

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 presents experimental estimates of multifactor productivity for higher education, a sub-component of the education and training industry.

The estimates show that between 2008-09 and 2018-19, higher education labour productivity grew on average by 1.2% per annum. This growth is similar to the average growth of market sector industries (around 1.1%). Multifactor productivity grew on average 0.5% per annum, with increased use of intermediate inputs (per hours worked) contributing about 0.6 percentage point to annual growth in labour productivity.

It is important to note that these estimates do not reflect the impact 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 higher education output and productivity when data becomes available.

### Footnote

[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).

## Productivity measurement

Multifactor productivity is calculated as the ratio of output growth (in volume terms) to growth of a combined input volume measure of labour, capital, and intermediate inputs (i.e. goods and services consumed in production).² The output measure is based on the ABS’s recently published output index for public universities, with coverage expanded to include private universities and non-university institutions providing higher education services.³

## Higher education

Higher education plays an important role in the Australian economy. It has been a major exporting industry during the last two decades, contributing around 27% of Australia’s exports of services in 2018-19.⁴

Higher education activities are classified under the Australia New Zealand Standard Industrial Classification (ANZSIC) Class 8102 – Higher Education, which is part of Division P – Education and training. Units providing higher education services include universities and non-university institutions providing higher education services.³

In Australia, the vast majority of higher education output is produced by universities, which accounted for 90% of total enrolled student load (excluding research degrees) in 2019, compared to about 8% for non-university higher education institutions.⁵

The majority of universities are public universities which are  classified as non-market producers in the Australian National Accounts because they provide services to domestic students at prices which are not economically significant.⁶ In addition, they engage in non-market research activity. However, public universities generate a significant part of their revenue from providing services to international students and full-fee paying domestic students at market prices. The proportion of public universities revenue from government grants decreased from 42% in 2004-05 to 37% in 2018-19.⁷

### Footnote

[4] Higher education fees alone accounted for 12.4% of Australia’s exports of services. See International Trade: Supplementary Information, Financial Year, 2018-19.

[6] 2008 System of National Accounts, paragraph 4.18.

[7] Based on ABS GFS data excluding funding for capital.

## Output measures

### Output index for public universities

The ABS recently developed an experimental measure of output for public universities, based on the direct volume index approach (see footnote 3). In this approach, a volume index for output was constructed by combining output quantity indicators and cost weights. Although public universities produce some market output, this approach was chosen because it is not feasible to disaggregate a university’s output into market and non-market activities. Expenditure weights continue to be the method of aggregation for output of public universities.

Output of public universities was modelled as comprising two main streams: teaching output and research output. The table below shows the components of output, and the quantity indicator used. Expenditure weights were used to aggregate output.

Table 1: Output of public universities
Output of public universitiesQuantity indicator
Research output
- Research funded by Govt and industry grantsResearch income (deflated by CPI)
- Research degree completionsNumber of research degree completions

The aggregation weights for teaching and research output for each university were derived based on the proportion of a university’s academic full time equivalent (FTE) spent on research. The model adopted here assumes that the proportion for FTE on research includes research-only academic FTE and 25% of teaching-and-research academic FTE.⁸ Aggregation weights for research funded by grants and research degree completions were assumed to be time invariant and estimated based on relative Government weights on these two elements in the allocation of research support funding in 2017.

### Expanding the university index to include all higher education institutions

The experimental output index has been extended to include private universities and non-university higher education institutions. Private universities are aggregated using expenditure weights (where expenditure is not available, FTE is used). Similar to public universities, their activities were split into teaching and research. Output from non-university institutions was assumed to be teaching only, where the output index was calculated using total student load. As both expenditure and FTE data were not available for non-university institutions, average unit costs of enrolled student load from universities were used for estimating their weights (see Appendix A for details of the method).

The expanded coverage led to noticeably faster growth in total teaching output and therefore, higher growth in total aggregate output in higher education (Figure 1). Total student load from private universities and other higher education institutions grew faster than public universities, though from a relatively lower base.

Between 2008-09 to 2018-19, the total volume of output for higher education grew at 3.9% per year compared to 3.7% for public universities.

Figure 2 shows output indexes for higher education institution cohorts over the period from 2004-05 to 2018-19. There was considerable dispersion in growth across different groups with non-university higher education institutions experiencing the strongest growth, again from a relatively lower base.

Notes: Go8 – Group of Eight Universities, ATN – Australian Technology Network Universities, IRU – Innovative Research Universities, RUN – Regional Universities Network.⁹ Other includes non-aligned universities and non-university higher education institutions.

### Footnote

[8] Splitting academic staff time between teaching versus research can be subjective due to the lack of relevant data on time use. For example, the Grattan Institute assumed a 40% research share in estimating research productivity (calculated as the number of academic publications per FTE) for universities for the period from 1997 to 2014 (Norton and Cherastidtham 2018).

## 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 Account for ANZSIC Subdivision level.¹⁰ Total hours worked in higher education (ANZSIC Class 8102) were estimated as the total number of hours worked for Subdivision 81 (Tertiary education) multiplied by the ratio of total employed persons in Class 8102 (Higher education) to that in Subdivision 81. However, the Class 8102 specific ratio was not available for 2011-12 and earlier periods. The hours worked index from 2008-09 to 2011-12 was estimated based on growth in FTE.

Figure 3 compares the elementary index of hours worked versus FTE.¹¹ The hours worked index grew at an average rate of 2.7% annually, compared to 2.6% for FTE over the period from 2008-09 to 2018-19.¹² The hours worked index from 2008-09 to 2011-12 was identical to the FTE index because growth in FTE was used over this time period. The hours worked index from 2011-12 onwards (based on the Labour Account estimates) trended slightly higher than FTE. This means that hours per FTE generally increased over this period.

### Footnote

[11] It is worth noting that over the same period there is little difference between the ABS’s quality adjusted hours worked index and unadjusted index at the division level for the education industry as a whole. Appendix B shows that net effects of compositional change in labour based on FTE are minor. This reflects that the staffing structure in universities has been relatively stable.

[12] Throughout this paper, annual rates were calculated as compound annual growth rates.

## Capital services

The ABS currently measures capital services (for purposes of compiling multifactor productivity statistics) only for market sector industries. 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 and training industry as a whole (Division P). The methodology for the new indexes is described in a separate paper¹³, and the results have been used in this paper as a proxy for growth in capital services for higher education.

A limitation of using the Division P capital services index for higher education is that the composition of assets providing capital services in higher education may differ from the average of the education industry. However, the impacts on productivity measures are expected to be immaterial, due to the small capital income share.

## Intermediate inputs

Intermediate inputs cover purchased goods and services used up in the production process such as energy, materials and services. While estimates for intermediate inputs are available from the National Accounts, they also include intermediate inputs consumed by technical and vocational education providers which are outside the scope of this paper. Therefore, estimates covering just the university component of higher education have been constructed using the Department of Education financial performance dataset for universities.

The administrative data covers all public universities and one private university. Expenditure on goods and services were split by four broad categories:

• Repairs and maintenance,
• Scholarships, grants and prizes,
• Other expenditure.

A volume measure for each category was derived using the price deflation method. The repair & maintenance implicit price deflator (IPD) was used for repair maintenance; CPI was used for scholarships, grants and prizes; and subdivision 81 IPD was used for the rest. The IPDs were sourced from the National Accounts. The aggregate index was calculated as a chained Laspeyres volume index.¹⁴

The main limitation of the intermediate input index described here is that it does not include all private universities (only one private university was included in the dataset) and has no coverage of non-university institutions. Since the under coverage is very small, the index is considered to be sufficiently representative.

### Footnote

[14] For comparison, a separate index was constructed using the GFS data for public universities. The results from the two data sets gave rise to similar results. In constructing a chained volume index using the GFS data, expenditure on intermediate inputs was disaggregated to broad categories based on the Department of Education financial performance dataset.

## Combined input of labour, capital and intermediate use

To calculate gross output based multifactor productivity, inputs were aggregated as a Törnqvist index using cost shares as weights. The cost shares for labour and capital are their respective primary income shares divided by the current price value of gross output. For higher education, the cost share for labour is compensation of employees (COE) divided by the current price value of gross output. The cost share for capital is gross operating surplus (GOS) divided by the current price value of gross output.¹⁵ The cost share for intermediate inputs is the ratio of expenditures on intermediate inputs to the current price value of gross output.

In Australia, the vast majority of output of higher education services is provided by public universities, which are classified as non-market producers. Under the international standards for national accounts, no return to capital is accounted for beyond capital that is used up in production. This implies a net operating surplus of zero. This is the current approach used in the Australian National Accounts and is used here. This approach is in line with the relevant convention in the System of National Accounts (SNA).¹⁶

Due to the lack of data for estimating cost shares for private universities and non-universities institutions, the cost shares estimated based on public universities are used as approximation for higher education as a sub industry.

Figure 4 compares growth in various input measures, including a combined input of capital and labour, and total aggregate input of labour, capital and intermediate use.

### Footnote

[15] This assumes that higher education institutions are either non-financial corporation or general government units, and that total net taxes (taxes net subsidies) are allocated proportionally using COE versus GOS (Chapter 19, ABS 2015).

[16] To test whether productivity measures are sensitive to the strict adherence to this convention, productivity measures were also calculated using an alternative option, i.e. where GOS is based on revenue and operating expenses. The main rationale for this approach is that universities generate a substantial part of their revenue from international students and fee-paying domestic students where fees reflect market prices. This alternative approach gave rise to a marginally higher capital cost share. However, the total aggregate inputs index was relatively insensitive to the increased cost share, due to the dominating influence of the labour and intermediate input cost shares relative to the capital share.

## Productivity

The results of various measures for higher education productivity are summarised in Figure 5.

Labour productivity based on hours worked grew at an annual rate of 1.2% from 2008-09 to 2018-19 compared to 1.1% for the market sector as a whole.

Capital productivity, calculated as a ratio of output to capital input, grew annually by 0.6%. In earlier period (2008-09 to 2011-12) capital productivity declined due to strong growth in capital services, and then rose from 2012-13 onwards as growth in capital services slowed.

Multifactor productivity (MFP) grew at 0.5% per year on average, trending lower than labour productivity.

Higher education experienced productivity growth similar to the market sector of the economy. The Government implemented the ‘demand driven system’ for universities from 2010 to 2017 as the result of recommendations by the Bradley Review of Higher Education.¹⁷ This led to increased enrolment of domestic students and may have increased competition (PC 2019).

Labour productivity growth can be analysed in terms of growth of capital and intermediate input relative to labour input and growth in multifactor productivity (Figure 6).  The main sources of labour productivity growth were multifactor productivity growth and increased use of intermediate inputs per unit of labour input. In terms of log growth, multifactor productivity contributed an average of 0.5 percentage points annually, while increasing use of intermediate inputs per hours worked contributed an average of 0.6 percentage points annually. By comparison, capital deepening played a relatively minor role in driving labour productivity growth, contributing around just 0.1 percentage points annually on average.

Figure 7 shows contributions to output growth. Labour input and intermediate inputs were two key drivers for output growth, contributing 1.5 and 1.6 percentage point per year on average, while multifactor productivity contributed 0.5 percentage point per year on average. This can also be seen in terms of cumulative growth as shown in Figure 8.

### Footnote

[18] The y-axis in Figures 6, 7, and 8 is natural log growth*100%.

## Limitations

In addition to limitations outlined in an earlier paper on output growth for public universities (see footnote 3), there are some additional limitations which should be taken into account when interpreting these experimental productivity estimates.

The index for capital services used in this paper was constructed for the education industry as a whole. The assumption is that capital services for the higher education subcomponent of the industry grew at the same pace as capital services for the entire industry. The capital services index is, in turn, based on a number of assumptions articulated in an earlier research paper (see footnote 13). The impact of using industry aggregates for the purposes of this analysis is expected to be small, given higher education is heavily labour intensive.

The intermediate inputs index excludes non-university providers of higher education. The impact on this analysis is expected to be small, since universities deliver the vast majority of higher education services.

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 small. Readers are directed to the Labour Accounts page on the ABS website for more details.¹⁹

Volumes of output produced by higher education providers have not been adjusted for quality change over time. There is no consensus in the national accounting community of the best way to do this for non-market output.

## Conclusions

Higher education experienced growth in labour productivity at an annual rate of about 1.2% from 2008-09 to 2018-19. Multifactor productivity grew at around 0.5% over this same period. The main sources of labour productivity growth were growth in multifactor productivity and increased use of intermediate inputs (this contributed to 0.6 percentage points to annual growth in labour productivity).

The effects of labour composition on productivity estimates have been explored using the breakdown of FTE by staff category for universities. There was an overall net shift toward academic staff relative to non-academic staff. However, overall impacts of such compositional change on labour productivity and multifactor productivity were not material.

There are a number of ways in which this research could be extended. Some options are identified below, though some of these are unlikely to result in materially better estimates. The ABS intends to focus on areas where enhancements will provide the most statistical value. The ABS welcomes any comments from readers on the direction of future research, which could include:

• Further enhancement of output measures, such as stratifying teaching output by academic discipline, refining FTE splits between teaching and research activity, and using price information to weight outputs instead of costs;
• Measurement of capital services using the same approach as that used to calculate Division level estimates, that is, using lower levels of detail;
• Expanding the coverage of intermediate input to include all higher education institutions;
• Investigating the possibility of adjusting output volumes to reflect quality change over time;
• Measuring output and productivity growth for ANZSIC Class 8101 Technical and vocational education and training, and aggregating of ANZSIC 8101 and 8102 to the ANZSIC subdivision 81 – Tertiary education; and
• Extending this analysis to examine the impact of COVID-19 on the output and productivity of institutions providing higher education services.

## Acknowledgements

This paper was authored by Qinghuan Luo, Jason Annabel, Derek Burnell and Matthew Xu. The authors are grateful to Katherine Keenan and Jacqui Jones for their ideas and feedback.

## References

Productivity Commission (2019). The Demand Driven University System: A Mixed Report Card - Research Paper (pc.gov.au)

Norton A, Cherastidtham I, (2018). Mapping Australian Higher Education 2018, Grattan Institute. https://grattan.edu.au/report/mapping-australian-higher-education-2018/

Tertiary Education Quality and Standards Agency (TEQSA) (2019). Statistics report on TEQSA registered higher education providers. https://www.teqsa.gov.au/latest-news/publications/statistics-report-teqsa-registered-higher-education-providers-2019

Tipper A, (2013). Output and productivity in the education and health industries. Paper presented at the 54th New Zealand Association of Economists Conference, Wellington, New Zealand.

Universities Australia, (2019), Higher Education: Facts and Figures, July 2019.

## Appendix A: Output index for higher education

In constructing a total output index for higher education services, higher education institutions were categorised into three groups.

Group 1 includes 39 universities (38 public and one private) for which both financial data (including expenditure) and academic full-time equivalent (FTE) data are available.

Group 2 includes three private universities (Bond University, Torrens University Australia, and University of Divinity).²⁰ For these universities, expenditure data is not available, but staff FTE data is available. Expenditure weights for Group 2 were based on FTE where average expenditure per FTE was estimated from Group 1 universities. The weight for each university in this group was calculated as FTE multiplied by the average expenditure per FTE from Group 1.

Group 3 includes all remaining institutions, predominantly non-university higher education institutions.²¹  As both expenditure and FTE data were not available, total weight for Group 3 was estimated as total enrolled student load multiplied by average unit cost of student load in universities (Group 1 and Group 2). As the weight for Group 3 was modelled based on average unit costs of student load, the weight depends on the split of the university’s expenditure between teaching and research.

Indexes for Groups 1 and 2 were calculated using the same method for the experimental index for public universities. Output from Group 3 was assumed to be in teaching only. Since the data was in the calendar year format, the indexes were initially constructed on the calendar year basis and then converted to financial year series by taking simple averages over two consecutive calendar years.

The total output index was calculated as aggregation of these three groups. Groups 1 and 2 contribute about 95% of total output.

### Footnote

[20] Avondale University College has recently been classified as a university by Tertiary Education Quality and Standards Agency (TEQSA). See New university and three University Colleges registered by TEQSA | Tertiary Education Quality and Standards Agency. Although FTE for Avondale University College is available, it is included in Group 3.

[21] It included those providing both higher education services and vocational education and training (VET) services (e.g. TAFE). In this case, only higher education services are included in the output measures.

## Appendix B: Quality adjusted labour input for higher education

This appendix outlines the method for estimating a quality-adjusted hours worked index based on FTE disaggregated by staff categories. The following derivation is based on university FTE for Groups 1 and 2, but the result is used as a proxy for the entire higher education class.

A quality adjusted index of total hours worked for higher education can be written as the product of an elementary index of hours worked, i.e.  $$H^t/H^{t-1}$$, and compositional change, denoted by $$Q^t$$, that is (Chapter 19, ABS 2015)

$$L^t=\displaystyle{H^t \over H^{t-1}} Q^t,\quad\quad\quad\quad\quad (B1)$$

where $$Q^t$$ is given by

$$Q^t=\displaystyle{\prod\limits_{i,a}\left({h^t_{i,a}\over h^{t-1}_{i,a}}\right)}^{w^t_{i,a}+w^{t-1}_{i,a}\over2}. \quad\quad\quad\quad\quad (B2)$$

In Equation (B2), $$h^t_{i,a}$$ is the proportion of aggregate hours worked by staff category $$a$$ for university $$i$$, and $$w^t_{i,a}$$ are weights based on workers’ salaries. FTE for universities can be split into five staff categories: Academic Level A, B, C, D and above, and Non-Academic staff. These are denoted by $$a=A$$ (Level A), $$B$$ (Level B), $$C$$ (Level C),  $$D$$ (Level D and above)  and $$NAC$$ (non-academic staff).²² The reported FTE data for non-academic staff have no breakdown to different levels.

Because Equation (B2) is aggregation from the level of individual universities, even for the same staff category, compositional change (B2) captures differences among different universities. For example, professors in different universities are treated as having different qualities which are differentiated by their salaries.

As hours worked per FTE are not known, total hours are disaggregated by staff category according to the proportion of their FTE in each category:

$$h^t_{i,a}=\displaystyle{{FTE^t_{i,a}\over \sum_{i,a}FTE^t_{i,a}}}. \quad\quad\quad\quad\quad (B3)$$

Equation (B3) means that average hours worked per FTE are the same across all staff categories. Although this assumption can be restrictive, compositional change in FTE can provide a reasonable proxy measure for capturing change in hours worked as the result of change in FTE.

To derive the weights in (B2), a university’s total expenditure on staff is split between academic and non-academic staff,

$$E^t_i=E^t_{AC,i}+E^t_{NAC,i}, \quad\quad\quad\quad (B4)$$

where expenditure on academic versus non-academic staff is available from the Department of Education financial performance data set.

Expenditure on academic staff can be further split by academic levels, i.e. $$E^t_{AC,i,a}=x^t_{i,a}E^t_{AC,i}$$, with

$$x^t_{i,a}=\displaystyle{{(Salary)^t_{i,a}*FTE^t_{i,a}\over\sum_a(Salary)^t_{i,a}*FTE^t_{i,a}}},\quad\quad\quad (B5)$$

where $$a=A$$, $$B$$, $$C$$, and $$D$$. Academic salaries can be normalised to the average salary for category $$a=D$$  (i.e. Level D and above), denoted by $$(Salary)_{i,D}$$. Relative weights between academic levels were estimated by combining relative scales of salaries and FTE by academic levels.²³  Assuming $$R^t_{i,a}=(Salary)^t_{i,a}/(Salary)^t_{i,D}$$ with $$R^t_{i,D}=1$$, Equation (B5) can be written as

$$x^t_{i,a}=\displaystyle{{R^t_{i,a}*FTE^t_{i,a}\over\sum_aR^t_{i,a}*FTE^t_{i,a}}}.\quad\quad\quad\quad (B6)$$

Ideally, Equation (B6) should be estimated using a time series of salary for each university. However, such time series are not readily available. In this paper, $$R^t_{i,A}$$, $$R^t_{i,B}$$, $$R^t_{i,C}$$ are estimated based on the Group of Eight universities and are assumed to be time invariant. So, weights for academic staff can be calculated as

$$w^t_{i,a}=\displaystyle{E^t_{AC,i,a}\over\sum_iE^t_i}=\displaystyle{{E_{AC,i}\over\sum_iE^t_i}{R_a*FTE^t_{i,a}\over\sum_aR_a*FTE^t_{i,a}}},\quad\quad\quad (B7)$$

where the simplified notation $$R^t_{i,a}\equiv R_a$$ is used.

The weight for non-academic staff can be calculated as

$$w^t_{i,NAC}=\displaystyle{E^t_{NAC,i}\over\sum_i E^t_i}.\quad\quad\quad\quad\quad (B8)$$

Figure B1 shows period-to-period compositional change (as percentage), defined as [(period-to-period adjusted index)/(period-to-period unadjusted index)-1]*100%. There was shifts in both directions with a marginal net shift toward higher paid staff categories, because the number of academic FTE grew slightly faster than non-academic FTE (i.e. at annual rate 2.6% versus 2.5% over the period from 2008-09 to 2018-19).²⁴

A limitation of this labour composition index is that as it covers only universities, it may not be representative for non-university institutions. Another limitation is that compositional change in non-academic staff is not captured.

### Footnote

[22] Above senior lecturer includes Level D (Associate professor) and Level E (Professors).

[23] For each academic classification (or level), a relative salary scale is defined as a ratio of average salary of this classification to that of Level D and above. The ratios for A, B, and C were estimated to be 0.5, 0.66 and 0.79 based on average salary scales in 2021 for the group of eight universities. These ratios were assumed to be time invariant and fixed across all universities.

[24] The proportion of academic staff across each category remained relatively stable, say over the period from 2013-2017 (TEQSA 2019).