# Experimental hospital multifactor productivity estimates

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

Released
30/08/2021

## 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 such as health care.¹ Non-market sector industries have a large portion of output provided at prices that are not economically significant; that is, where goods and services are provided to final consumers at prices below the cost of provision, such as 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 hospitals, a sub-division of the health and social assistance industry.

The estimates show that between 2008-09 and 2018-19, hospital labour productivity grew on average 0.5% per annum. Increased use of intermediate inputs per hour worked contributed about 0.3 percentage points per annum. The average annual growth rate of multifactor productivity was 0.1%. Labour input was a main driver for output growth, contributing about 1.8 percentage point to annual growth of 3.5% in output. This reflects that hospital output is labour intensive.

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 hospital 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) of Australian and New Zealand Standard Industrial Classification (ANZSIC).

## Hospitals

Hospital output plays an important role in the Australian economy. According to the Australian Government’s 2021 Intergenerational Report, the impact of an ageing population, technological advancement and rising incomes is expected to increase Commonwealth health expenditure from 19% of total government spending in 2021-22 to 26% in 2060-61. Commonwealth funding for public hospitals is expected to double between 2020-21 and 2031-32.²

Hospitals are classified under the Australian and New Zealand Standard Industrial Classification (ANZSIC) Subdivision 84 in Industry Division Q (Health care and social assistance). Hospitals are significant to Division Q as hospital services comprise over one third of the industry’s output. Australian hospitals employed around 597,000 people in 2018-19.³

The Australian hospital system consists of public and private hospitals. Public hospitals deliver around 60% of hospital separations in admitted patient care, as well as most emergency department activity and non-admitted patient care.⁴

The ABS classifies public hospitals as non-market producers because the majority of their output is provided to patients free of charge, or at prices which are not economically significant.  In contrast, private hospitals are considered to be market producers, though some private hospitals are contracted to provide public hospital services and provide services directly to public patients.

### Footnote

[4] The proportion of non-admitted care services delivered by private hospitals is relatively small (footnote 6).

## Productivity measures

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).⁵ The output measure is based on the ABS’s recently published output index for hospitals.⁶ Input measures were based on the Labour Account hours worked data,⁷ newly constructed experimental capital services index for the health industry,⁸ and intermediate input indexes constructed from administrative data and the Government Finance Statistics (GFS) dataset.

### Footnote

[5] See Chapter 19, Australian System of National Accounts: Concepts, Sources and Methods.

[7] The annual labour accounts data, which is used to construct the labour input index used in this paper, will be revised in December 2021. An impact on the experimental productivity analysis presented in this paper would be expected to be small. Readers are directed to the Labour Accounts page on the ABS website for more details. Labour Account Australia, March 2021 | Australian Bureau of Statistics (abs.gov.au)

## Measuring hospital output

The ABS recently published experimental volume indexes for hospital output, which enhances coverage compared to the existing volume index used in the National Accounts.⁶ The experimental index includes public hospital emergency department activity and non-admitted care. This coverage enhancement also enables measurement of shifts across categories of care for public hospitals over time. For private hospitals, the index covers admitted patient care only.

The inclusion of non-admitted patient care in the index is especially important with an increasing shift from admitted care to non-admitted care as the result of advances in medical technology (Gu & Morin 2014). Such shifts can be regarded as efficiency gains as less labour is used in treating patients in an outpatient clinic than in a hospital ward.

The approach underpinning these experimental indexes is the direct volume index approach, where an annually chained Laspeyres index was calculated by combining output quantity indicators and cost weights.

Although private hospitals are regarded as market producers, the same direct volume index approach was used.  A deflation approach would require detailed price indexes matching the level of disaggregation of output quantity, to control for quality change. In practice, such price indexes were not available. Therefore, the direct volume index approach was preferred. It is noted that US Bureau of Labour Statistics also used the direct volume index approach to measuring output of private hospitals (Chansky, et al 2015).⁹

Table 1 shows the quantity indicators used.

Table 1: Output of hospitals
Output of hospitalsQuantity indicator
Public hospitals:
- Admitted patient careNumber of hospital separations
- Emergency department activityNumber of emergency department presentations
Private hospitals:
- Admitted patient careNumber of hospital separations

Quantity and cost data were sourced mainly from the Australian Institute and Welfare (AIHW) and Independent Hospital Pricing Authority (IHPA).

A volume index for the hospital sub-industry as a whole was estimated as aggregation of the private and public hospital output indexes. The weight for public hospital output was calculated from public hospital expenditure via the GFS dataset.¹⁰ The weight for private hospital output was based on private hospital revenue, sourced from the ABS Australian Industry dataset.¹¹ ¹²

Figure 1 shows volume indexes for public hospital output, private hospital output, and total aggregate hospital output over the period from 2004-05 to 2018-19. Aggregate hospital output growth tracks closely to public hospital output growth because the public hospital sector is larger.

### Footnote

[9] The US Bureau of Labour Statistics also used the direct volume index approach to measuring output of private hospitals (Chansky, et al 2015). The paper noted that the usual deflation method may not be suitable for hospitals as prices patients face may not reflect marginal costs due to the lack of a competitive market.

[10] GFS expenditure may include expenses on contracted public hospital services in private hospitals. Such services are part of private hospital output, already captured in the private hospital data. As these services are usually contracted by health authorities (they are not treated an intermediate input in public hospitals), this should be excluded from public hospital expenditure, but this is not feasible for the purposes of this analysis. Nonetheless, as the proportion of separations in this category to total public hospital separations is small (less than 3% in 2018-19), impacts on aggregation of total output should be immaterial.

[11]  In the previous research paper (footnote 6), the weights were based on the AIHW published health expenditure by area. This was to enable a comparison between the two hospital systems. For the purposes of this paper, private hospital activity is weighted by sales revenue because private hospitals are considered to be market producers. The use of revenue instead of expenditure for private hospitals did not make material differences to the total index, because the public hospital sector is significantly larger.

## Labour input

The ABS currently compiles productivity estimates using ABS Labour Account hours worked as the labour input measure. For hospitals, ANZSIC Subdivision 84 total annual hours worked were used.   The Labour Account estimates are aligned with the production concept in the National Accounts in terms of both coverage and methodology.¹³

### Accounting for change in labour composition

The ABS also compiles quality adjusted hours worked in the official productivity statistics to take into account change in labour quality over time.¹⁴ However, quality adjusted hours worked are only available at the ANZSIC division level. In this paper, a simplified method of stratification by occupation was used. For example, medical doctors are considered as having different level of education and skill sets compared to nurses.¹⁵ The relative proportion between doctors and nurses can change over time.

A quality adjusted index of hours worked for hospitals was derived by splitting total number of hours worked between public hospitals and private hospitals according to their relative proportion in full time equivalent (FTE) employment. This derivation assumed there was no difference in average hours worked per FTE between public and private hospitals. Public hospital FTE were sourced from the Australian Institute of Health and Welfare (AIHW) publication of hospital resources.¹⁶ Private hospital FTE were sourced from the ABS publication – Private Hospitals.¹⁷

Employed staff was disaggregated into five broad categories of occupations:

• salaried medical officers;
• nurses;
• diagnostic and allied health professionals;
• administrative staff and personal care staff; and
• other.

The proportion of hours worked for each category was approximated by the relative proportion of FTE employment. A labour composition index was calculated as a Törnqvist index based on FTE weighted by wages. Wages for public hospitals were sourced from the AIHW, however wages data for private hospitals were not available, so wages for public hospitals were also used for relative weights for private hospitals.¹⁸ The composition indexes for public and private hospitals were aggregated to total composition index based on their respective total labour costs.

A quality adjusted index of hours worked was calculated as the product of an index of hours worked and the labour composition index (see Appendix A for details of the method).

### Trends in labour input

Figure 2 compares three different labour input indexes: an unadjusted index of total hours worked, quality adjusted hours worked, and an index based on the sum of FTE employment. The three indexes followed similar trends, though the FTE index generally grew at a faster rate. The hours worked index increased by an average of 3.0% annually over the period from 2008-09 to 2018-19, compared to 3.4% for the FTE index. This means that average hours worked per FTE has decreased.

The quality adjusted hours worked index increased at an average annual rate of 3.2% compared to 3.0% for the unadjusted index of total hours worked. Higher growth in the quality adjusted hours worked was due to an increasing proportion of salaried medical staff with higher wages in the staff FTE composition.

### Footnote

[14] Hours worked are disaggregated according to workers’ education and age and sex based on the data from the Census. The quality adjusted index is calculated as a Törnqvist index where wages are used as weights.

[15] Staff employed in hospitals who are paid wages or salaries. For public hospitals, this excludes visiting medical officers. Payments to visiting medical officers are considered to be intermediate input.

[17] Private Hospitals, Australia, 2016-17 financial year | Australian Bureau of Statistics (abs.gov.au). Private hospital FTE collected by the ABS is available up to 2016-17. FTE from 2017-18 onwards was imputed based on the growth in the number of persons employed. The data on persons employed in private hospitals was sourced from ABS Australian Industry (footnote 12).

[18] Wages were used as relative weights within the sector.

## Capital services

The ABS only currently measures capital services (for purposes of compiling multifactor productivity statistics) 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 health care industry as a whole (Division Q). The methodology for the new capital services indexes is described in a separate paper,⁸ and these indexes are used in this paper as a proxy for growth in hospital capital services.

A limitation of using the Division Q capital services index for hospitals is that the composition of assets providing capital services in hospitals may differ from the average of the health care industry. However, the impacts on productivity measures are expected to be immaterial, given hospital activity is labour intensive.

## Intermediate inputs

Intermediate inputs are goods and services consumed in the production process such as energy, materials and services. While estimates for intermediate inputs for ANZSIC Division Q are available from the National Accounts, they also include intermediate inputs consumed by non-hospital units of the health care industry, which are outside the scope of this paper. For this analysis, estimates for only the hospital component of the industry were constructed.

For public hospitals, total current price expenditure on intermediate inputs were estimated using GFS expenditure data for hospitals. This expenditure was then disaggregated into categories according to AIHW public hospital expenditure data (e.g. AIHW 2019).¹⁹ For each expenditure category, volume growth was estimated by deflating current price expenditure by an appropriate price index. An annually chained Laspeyres volume index was then calculated by aggregating across all the expenditure categories.

For private hospitals, total current price expenditure on intermediate inputs were sourced from the ABS Australian Industry publication.¹² These were then disaggregated into expenditure categories using the ABS Private Hospital Statistics publication.²⁰ An annually chained Laspeyres volume index was then calculated by aggregating across all the expenditure categories in the same way as for public hospitals.

A total volume index for intermediate input for all hospitals was calculated as a Laspeyres index by aggregating the public hospital and private hospital indexes.²¹

The methodology for calculating the intermediate input indexes is described in Appendix B.

### Footnote

[19] Data Table 2.7 Recurrent expenditure on public hospitals in AIHW (2019).

[20] The expenditure categories for private hospitals were closely aligned with those for public hospitals.

[21] Use of the Laspeyres index aligns with the National Accounts approach for calculating volume measures for output and intermediate input.

## Aggregate input of labour, capital, and intermediate use

An aggregate input of labour inputs, capital inputs and intermediate inputs was constructed as a Törnqvist index using cost shares as weights. 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.²²  The cost share for intermediate inputs is the ratio of expenditures on intermediate inputs to current price value of gross output.

COE and GOS are only compiled at ANZSIC division level in the National Accounts, therefore cost shares for public hospitals were estimated using GFS data. As public hospitals are classified as non-market producers, GOS is set equal to consumption of fixed capital (COFC).²³

In theory, the weight for capital should include opportunity costs (return of investment on capital) regardless of whether a producer is market or non-market. Setting GOS to equal COFC may underestimate the contribution of capital services to public hospital output.²⁴

Cost shares for private hospitals were estimated in the same way as for market producers where GOS is estimated based on sales revenue and operating expenses. The revenue and expenses data were sourced from the ABS Australian Industry.

Figure 3 shows the average cost shares for each component of public hospitals, private hospitals, hospital as a sub-industry, and the total health care industry (Division Q).²⁵ The capital cost weight for public hospitals is considerably lower than that for private hospitals and Division Q as a whole. In comparison, the capital cost weight for private hospitals is similar to Division Q. It is worth noting that private hospitals have a lower labour cost share and higher intermediate input cost share.

The total input volume index and the hours worked index grew at similar rates (Figure 4), reflecting that hospitals are labour intensive, with labour comprising around 60% of total inputs (Figure 3). The total aggregate input index based on hours worked rose by an average of 3.4% per year, compared to 3.0% for the hours worked index and 3.8% for the intermediate input index. The total aggregate input index based on quality adjusted hours worked increased by an average of 3.5% per year, due to shifts to higher quality labour over time.

### Footnote

[22] It is reasonable to assume that hospitals are either non-financial corporations or general government units. This implies gross mixed income (GMI) is zero. Taxes net subsidies have immaterial impacts.

[23] GFS depreciation is used as a proxy measure for consumption of fixed capital (COFC).

[24] Because the overall cost share for capital services is much smaller than labour input, the impact of any differences on multifactor productivity estimates should be minor.

[25] The relative weights for labour versus capital for the whole hospital system was estimated by weighting the estimates for each hospital component by the current price value of their respective output.

[26] Unless explicitly indicated otherwise, labour input was based on unadjusted hours worked.

## Productivity

Figures 5 and 6 summarise the productivity estimates.

Between 2008-09 to 2018-19, labour productivity for the hospital sub-industry grew by an average of 0.5% per year. The average annual growth rate of labour productivity between 2008-09 and 2013-14 was 0.8%.

Labour productivity based on the quality adjusted hours worked grew at an average annual rate of 0.3%. Compositional change in labour input accounted for about 0.2 percentage points of annual growth in labour productivity per year on average, compared to labour productivity growth estimated on the unadjusted hours worked basis.

Hospital multifactor productivity increased by an average of 0.1% per year, with most of the growth occurring in earlier periods. The average annual growth rate of multifactor productivity between 2008-09 and 2013-14 was about 0.7%.

Capital productivity fell by 1.3% annually on average. The declining trend in capital productivity was driven by rapid growth in capital services for the health care industry. Because the overall weight for capital input was small, this decline only had minor impacts on multifactor productivity.  Capital services grew faster than hours worked, therefore hospitals generally experienced capital deepening, i.e. an increase in use of capital services per unit hour worked.

Figure 7 shows a breakdown of sources for growth in labour productivity (calculated in terms of hours worked). In terms of log growth, increased use of intermediate inputs per hour worked contributed about 0.3 percentage points of growth on average annually, while capital deepening contributed an annual average 0.1 percentage point.

Figure 8 shows that labour input was the main driver for growth in hospital output, contributing 1.8 percentage points annually on average, compared to a 1.3 percentage point contribution from intermediate inputs.

Figure 9 shows that growth in labour input accounted for more than half of total cumulative output growth over the period from 2008-09 to 2018-19.

### Footnote

[27] In Figures 7-9, the y-axis is natural log growth*100%, and labour input is based on unadjusted hours worked.

## Limitations

There are some limitations which could affect the interpretation of the results, in addition to limitations discussed in an earlier paper on hospital output measures.⁶

The hospital output measure used in this analysis have not been explicitly quality adjusted from the patient’s perspective. Improvements in treatments over time that deliver quality-related benefits to patients may not be fully captured. Although some National Statistical Offices have experimented in this area, there is no internationally agreed framework for incorporating explicit quality adjustments in output measures from a national accounts perspective.²⁸

To estimate hospital intermediate input indexes in volume terms, experimental deflators were developed. Ideally, input producer price indexes should be used to deflate each component of these deflators, but these were not available in all cases. See Tables B1 and B2 in Appendix B for details of price indexes used.

Capital services were measured using the Division Q capital services index. A limitation of using the Division Q capital services index for hospitals is that composition of assets providing capital services in hospitals could differ from the average of the health care industry. However, as mentioned earlier, the impacts of such differences on productivity measures are expected to be immaterial, due to the small capital cost share. Nonetheless, for completeness, it would be desirable to measure capital services using data specific to hospitals (ABS 1997).

### Footnote

[28] For example, UK Office of National Statistics has incorporated explicit quality adjustment in their measures of health care output (ONS 2012).

## Conclusion

Hospital productivity growth has generally been lower than Australian productivity growth, although health care is an area of the economy where there has been technological progress (such as the development of new or improved procedures and new drugs in treating patients). Labour productivity grew at an annual rate of 0.5% over the period from 2008-09 to 2018-19, lower than the market sector average. Increased use of intermediate inputs (per hours worked) was a major contributor to labour productivity growth.

Multifactor productivity grew at an even slower rate of about 0.1% per year. This means the contribution of multifactor productivity to hospital output was relatively minor, with the majority of output growth attributed to growth in labour input. This reflects the fact that hospital services are labour intensive.

Improving output measures for hospitals will continue to be a challenging area. Future work could include refinement of output indexes by using a finer level of stratification and allowing for the presence of comorbidities. Other possibilities include constructing indexes from an integrated dataset covering all three categories of patient care, experimenting with explicit quality adjustment, and extending the time series to incorporate the full time span of labour accounts data.

The multifactor productivity estimates could be improved by developing a capital services index specifically for hospitals.

## Acknowledgements

This paper was authored by Qinghuan Luo and Jason Annabel. The authors would like to thank Derek Burnell, Katherine Keenan and Jacqui Jones for their comments and input.

## References

Australian Institute of Health and Welfare (AIHW) (2019) Hospital resources 2017-18: Australian hospital statistics.

Australian Bureau of Statistics (ABS) (1997), Measuring outputs, inputs and productivity for Australian public acute care hospitals.

Australian Bureau of Statistics (ABS) (2015) Australian System of National Accounts Concepts, Sources and Methods.

Chansky B, Garner C A, Raichoudhary R (2015), New measure of labour productivity for private community hospitals: 1993–2012, Monthly Labour Review, U.S. Bureau of Labour Statistics, October 2015.

Gu W, Morin S (2014), Experimental measures of output and productivity in the Canadian hospital sector, 2002 to 2010, in Measuring Economic Sustainability and Progress, edited by D.W. Jorgenson, J.S. Landefeld and P. Schreyer, 575-594. Chicago: University of Chicago Press.

Office of National Statistics (ONS) (2012), Quality adjustment of public service health output: current method, ONS.

## Appendix A: Quality adjusted labour input in hospitals

This appendix outlines the method for adjusting hours worked by occupation categories using hospital staff FTE.

Total annual hours worked for ANZSIC Subdivision 84 (Hospitals) is available from the Labour Account. Total number of hours worked is disaggregated into public and private hospital sectors using their respective proportions of FTE, i.e. total hours worked for hospital sector $$s$$ is  $$H^t_s=H^t(FTE^t_s/FTE^t_{total})$$, where $$H^t$$ is total hours for Subdivision 84.

A Törnqvist index of hours worked, adjusted for change in labour composition, can be calculated as the product of an unadjusted index and labour composition index $$Q^t_s$$ , that is

$$L^t_s=\displaystyle{{H^t_s\over H^{t-1}_s}}Q^t_s=\displaystyle{{H^t_s\over H^{t-1}_s}{FTE^t_s\over FTE^t_{total}}{FTE^{t-1}_{total}\over FTE^{t-1}_s}}Q^t_s,\quad\quad\quad\quad (A1)$$

where the labour composition index $$Q^t_s$$ is given by

$$Q^t_s=\displaystyle{\prod_i\left({h^t_{s,i}\over h^{t-1}_{s,i}}\right)^{w^t_{s,i}+w^{t-1}_{s,i}\over 2}},\quad\quad\quad\quad (A2)$$

where $$h^t_{s,i}$$ is share of hours worked by workers in category $$i$$ in hospital sector $$s$$, given by

$$h^t_{s,i}=\displaystyle{FTE^t_{s,i}*(average\,\,hours)^t_{s,i}\over \sum_i FTE^t_{s,i}*(average\,\, hours)^t_{s,i}}.\quad\quad\quad\quad (A3)$$

The weights can be estimated using average salary for each category:

$$w^t_{s,i}=\displaystyle{FTE^t_{s,i}*(average\,\,salary)^t_{s,i}\over \sum_i FTE^t_{s,i}*(average\,\, salary)^t_{s,i}}.\quad\quad\quad\quad (A4)$$

In this paper, the average hours per FTE is assumed to be fixed across occupation categories. Equation (A3) is simplified to

$$h^t_{s,i}=\displaystyle{FTE^t_{s,i}\over\sum_iFTE^t_{s,i}}. \quad\quad\quad\quad (A5)$$

Finally, total quality adjusted index is calculated as a Törnqvist index, that is

$$L^t=\displaystyle{\prod_s\left({L^t_s\over L^{t-1}_s}\right)^{w^t_s+w^{t-1}_s\over 2}}\equiv \displaystyle{H^t\over H^{t-1}}Q^t,\quad\quad\quad\quad (A6)$$

$$Q^t\equiv\displaystyle{\prod_s\left({FTE^t_s\over FTE^t_{total}}{FTE^{t-1}_{total}\over FTE^{t-1}_s}{Q^t_s\over Q^{t-1}_s}\right)},\quad\quad\quad\quad (A7)$$

where $$w^t_s$$ are the relative labour costs between two hospital sectors, which can be estimated as their labour cost share within each sector multiplied by their output weight.

The total composition index (A7) measures combined effects of a composition shift within each sector and a shift between sectors.

## Appendix B: Volume indexes for intermediate inputs in hospitals

This appendix describes the method for estimating volume indexes of hospital intermediate inputs.

### Intermediate inputs for public hospitals

Total current price expenditure on intermediate inputs for public hospitals was estimated from the GFS. The total expenditure was disaggregated using the administrative data on hospital expenditure from the AIHW Publication of Hospital Resources. Table B1 summarises expenditure categories and their average proportions from 2014-15 to 2018-19. The third column lists price indexes/IPDs used as deflators.

Table B1: Public hospital expenditure categories and deflators
Expenditure category%Deflator
Payments to visiting medical officers6.4CPI doctor services
Drug supplies13.1PPI ANZSIC 184 Pharmaceutical and medicinal product manufacturing
Medical and surgical supplies21.6IPD Medical aids, equip (excl x-ray) and therapeutic appliances
Food supplies2.5PPI ANZSIC 11 Food product manufacturing
Domestic services5.9Wage Price Index Div Q
Repair and maintenance6.0IPD Repair and maintenance
Patient transport3.1Wage Price Index Div Q
Administrative expenses - other13.6Wage Price Index Div Q
Lease costs1.5PPI ANZSIC 66 Rental and hiring services (except real estate)
Other26.3All Groups CPI
Total100

An intermediate input volume index from $$t-1$$ to $$t$$ can be calculated by aggregating all categories using the following formula:

$$X^t=\displaystyle{\sum_i w^{t-1}_i{(CP^t_i/CP^{t-1}_i)\over(P^t_i/P^{t-1}_i)}},\quad\quad\quad\quad (B1)$$

where for each category, $$w^t_i$$ is the expenditure weight, $$CP^t_i$$ is current price expenditure, and $$P^t_i$$ is the corresponding price index.

Due to volatility in prices around the GFC period (2008-09 to 2009-10), total implicit price deflator (IPD) for the Division Q intermediate inputs was used for both public and private hospitals in 2009-10.

### Intermediate inputs for private hospitals

Total current price expenditure on intermediate inputs for private hospitals was sourced from the ABS Australian Industry. The total expenditure was disaggregated using private hospital expenditure categories derived from the ABS Private Hospitals (Table B2). As the private hospital expenditure data does not have a split between drug supplies, and medical and surgical supplies, the split between these two categories was based on public hospitals.

Similarly, an intermediate input volume index for private hospitals can be calculated using equation (B1).

Table B2: Private hospital expenditure categories and deflators
Expenditure category%Deflator
Contract services15.0Wage Price Index Div Q
Drug supplies22.1PPI ANZSIC 184 Pharmaceutical and medicinal product manufacturing
Medical and surgical supplies38.5IPD Medical aids, equip (excl x-ray) and therapeutic appliances
Food supplies2.7PPI ANZSIC 11 Food product manufacturing
Repair and maintenance2.7IPD Repair and maintenance
Fuel and power2.4IPD Fuel and power
Patient transport0.3Wage Price Index  Div Q
Other16.3All Groups CPI
Total100

### Total intermediate input volume index

Total intermediate input volume index was aggregation of the public hospital intermediate input index $$X^t_{public}$$ and private hospital intermediate input index $$X^t_{private}$$, i.e.

$$X^t_{total}=\displaystyle{w^{t-1}_{X,public}{X^t_{public}\over X^{t-1}_{public}}}+\displaystyle{w^{t-1}_{X,private}{X^t_{private}\over X^{t-1}_{private}}},\quad\quad\quad\quad (B2)$$

where $$w^t_{X,public}$$ and $$w^t_{X,private}$$ are the relative weights of intermediate inputs between public and private hospitals. The weights were calculated as their respective intermediate input cost share ($$C^t_X$$) multiplied by their output weight ($$W^t$$):

$$w^t_{X,public}=\displaystyle{C^t_{X,public}W^t_{public}\over C^t_{X,public}W^t_{public}+C^t_{X,private}W^t_{private}},\quad\quad w^t_{X,private}=1-w^t_{X,public}.\quad\quad\quad (B3)$$