5900.0.00.003 - University output measures in the Australian National Accounts: experimental estimates, 2008 to 2017  
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Technical appendix


The formulae underlying construction of the composite university output index are outlined below.

Output of a university is composed of teaching output and research output. In the indexes proposed in this paper, research output is proxied by research degree completions and research activity funded by government and industry through research grants, where research grants (deflated by the Consumer Price Index) act as a proxy for the real amount of research funding. So, at the lowest level of disaggregation, university output can be thought to comprise three components: teaching, research degree completions, and research grants.


Year-to-year Laspeyres quantity index

A Laspeyres quantity index from year t - 1 to t for university output activity component a can be calculated as

Equation 1: Laspeyres quantity index for university output
Where:

    • q is the output quantity indicator for activity component a;
    • a is teaching (teaching), a is research grants (research grants) or a is research degree completions (research degree completions);
    • w is the individual university iweight for activity with weights adding to 1
    • the aggregation in (1) is across all universities in the university sector.

The following output quantity indicators are used:
    • Teaching: Full time student load;
    • Grants: CPI deflated research grant income; and
    • Completions: The number of research degree completions, where PhDs are counted as equivalent to two research master degrees.


Derivation of university weights

The weights in (1) are based on the university’s operating expenditure. For each university i the total expenditure e is split into three components: teaching teaching, grants grants, and completions completions, where the splits teaching weight, grants weight, and completions weight can be considered as relative cost proportions within a university with

Equation 2: expenditure weights for teaching, grants and completions add to 1

The weights w in Eq (1) can be written in the following form for activity a, at the i'thuniversity, at time t:

Equation 3: weights for each university, for each activity, at time t

The weights can be derived in two steps.

First, the university’s total expenditure is split using proportions of teaching teaching weight and research research weight where teaching and research weight for each university adds to 1. The proportion of expenditure on research is estimated using the ratio of academic staff full time equivalent (FTE) in research to total academic staff FTE (all academic staff). Assume that research only staff (research only academic staff) have 100% FTE in research. For academics with a combined role in teaching and research (combined academic staff), assume that fraction of their FTE in research is x Total academic staff FTE in research is research only staff, plus x percent of combined academic staff. The split between research and teaching can be written as

Equation 4: weights for teaching and research based on academic designation

In this analysis, x equals0.25.

Second, research expenditure is further split into grants and completions using proportions derived as follows:

Equation 5: weights for research expenditure (grants and completions)

where grants proportion of research and completions proportion of research are the relative proportions of funding based on research grant success and completions of research degrees within in a university.

In this paper, grants proportion of research and completions proportion of research are assumed to be constant across the university sector and estimates of these proportions are based on how Australian government allocates block funding to universities for research. There are currently two government funds: the Research Support Program (RSP) and the Research Training Program (RTP).

The proportion grants proportion of research is estimated as follows. In the recent funding rule, 100% of the RSP is allocated based on universities’ performance in attracting research grant income, while only 50% of the RTP is allocated based on research grant income, with the other 50% based on research degree completions. Using the 2017 funding, RSP equals $879 million and RTP equals $1012 million, thus grants proportion of research and completions proportion of research are estimated to be

Equation 6: derivation of proportions for grants and completions components of research


Calculation of quantity indexes for various components and aggregates

(i) Teaching index

The teaching index is calculated directly from Eq (1) with a = teaching:

Equation 7: quantity index for teaching

(ii) Grant index

The grant index follows from Eq (1) with a = grants:

Equation 8: quantity index for grants

Where the second equality holds for constant grants proportion of research across the university sector.

(iii) Completion index

Similar to (8), the completion index can be calculated from Eq (1) with a = completions:

Equation 9: quantity index for completions

Where the second equality holds for constant completions proportion of research across the university sector.

(iv) Research index

The research index is calculated as the weighted aggregate of the grant index (8) and completion index (9):

Equation 10: composite index for research

where the second equality is a direct consequence of grants proportion of research and completions proportion of research being constant across the university sector.

(v) Total university index

A total university index is calculated as aggregate of the teaching index (7) and research index (10):

Equation 11: quantity index for total university output

Alternatively, the following aggregate of teaching, grant, and completion leads to the same result as (11):

Equation 12: alternative to equation 11

(vi) Annually chained index

An annually chained index from time zero to time t can be constructed from year-to-year indexes growth in Q from t-1 to t as

Equation 13: annually chained index



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