# Experimental capital service indexes for non-market industries

New capital service indexes for Education and Health to facilitate productivity measures

Released
14/07/2021

Derek Burnell and Qinghuan Luo (Economic Statistics Research Section)¹

### Introduction

The Australian Bureau of Statistics (ABS) is undertaking a program of research and analysis to enhance measures of non-market economic activity in the Australian National Accounts. Non-market economic activity occurs when output is delivered to final consumers free of charge, or at ‘token’ prices set well below the cost of production. The lack of prices presents significant valuation and aggregation difficulties, which are articulated in a recent ABS research paper.²

This paper outlines the compilation of experimental rental prices and indexes of capital services for the education and health care industries, which will be used in constructing the experimental MFP measures referred to earlier. The ABS welcomes comments and suggestions on this approach. To provide feedback, please email economic.research@abs.gov.au.

Prime examples of non-market activity are services delivered by public hospitals and schools. The ABS recently published enhanced experimental measures of output for hospitals, schools and public universities, which considered methods of using costs of production data as a proxy for prices.³ ⁴ ⁵ The ABS intends to build on these experimental output measures by compiling experimental estimates of multifactor productivity (MFP) growth for the same areas of the economy, due for publication in 2021. This work will begin to address the long-standing gap in ABS productivity statistics for non-market industries.

Productivity growth is defined as growth in the volume of outputs relative to growth in the volume of inputs used to produce output. Partial measures of productivity take into consideration a single input like labour or capital. Labour productivity is frequently used as an indicator of productivity growth, which is usually measured as output per hour worked. When multiple inputs such as labour and capital are taken into consideration, estimates are referred to as multifactor productivity (MFP), which are measured as output per unit of a combined bundle of inputs.

The ABS publishes annual estimates of MFP growth for the market sector of the Australian economy, corresponding to industry Divisions A to N, plus Divisions R and S.⁶ The valuation and aggregation difficulties associated with measuring non-market activity are also present when measuring productivity growth. As a result, the ABS currently excludes three industry divisions in which there is a significant amount of non-market activity from the official multifactor productivity dataset.⁷ These industries are Division O – Public administration and safety; Division P – Education and training; and Division Q – Health care and social assistance.⁸ Enhancing the measurement of this portion of the economy is important, given the current size of the non-market sector (an estimated 18.6% of industry gross value added in 2019-20) which has been steadily increasing over time.⁹

To calculate MFP growth on a gross output basis, three inputs need to be accounted for – labour, capital, and intermediate goods and services ‘used up’ in the production process such as energy, materials and services.¹⁰ Figure 1 provides an overview of the types of productivity measures currently published by the ABS. To measure capital’s input to production, two variables are required – volume measures of productive capital stock (PKS), and the ‘price’ of a unit of capital, known as the rental price. While the ABS compiles PKS estimates for non-market industries, it does not currently compile rental prices for those industries.

Productivity typeGross Output based measuresGVA based measuresLabour inputsCapital services inputsIntermediate inputs
Labour Productivity-YY--
Capital Productivity-Y-Y-
Gross Ouput MFPY-YYY
KLEMS MFPY-YYY

### Footnote

[1] The authors would like to thank Jason Annabel and Katherine Keenan for their helpful comments on an earlier draft of this paper.

[7] In productivity statistics, a stylised definition of ‘market’ and ‘non-market’ sectors is used because estimates are compiled at the industry division level. It is acknowledged that market sector industries contain non-market activity, and that non-market industries contain market activity (e.g. services provided by private schools and private hospitals).

[8] The ABS publishes labour productivity measures for the non-market industries, just not MFP.

[10] For a more detailed discussion of gross output (KLEMS) based MFP, see the 2015 KLEMS Information paper.

## Capital service indexes

Capital service indexes are constructed by combining rental prices and volume measures of PKS. The fundamental assumption underpinning this approach is that the quantity of capital services is a fixed proportion of productive capital stock. That is, no adjustment is made for variations in the utilisation rate of capital, and so the growth in PKS provides an estimate of the flow of capital services for a given asset. Both rental prices and productive capital stock are compiled by asset type by industry division.

## Productive capital stock

The underlying volume measures of PKS required to estimate capital services are compiled using the Perpetual Inventory Model (PIM).¹¹ They are available for all industries including Divisions O, P and Q. The ABS produces separate estimates for land and ownership transfer costs, and these are used alongside the capital stock assets calculated in the PIM in estimating capital services.

### Footnote

[11] Details of capital stock estimation can be found in chapter 14 of the 2020-21 edition of Australian System of National Accounts: Concepts, Sources and Methods.

## Rental prices

Rental prices reflect the cost per unit of capital over time, held to the level of quality prevailing in a reference year. They differ from other price indexes such as the Consumer Price Index (CPI). Rental prices reflect the theory of user cost of capital for investment decisions, so the purpose is quite different. Not only do they reflect the change in price of new capital goods, but other factors such as depreciation and changes in the corporate taxation environment.

Four elements are required to calculate rental prices: investment rate of return (opportunity cost), depreciation, capital gains/losses (i.e. asset revaluations), and parameters to capture tax effects (e.g. elements such as company income tax rates and tax concessions for investment). The ABS imputes the rental price in period t using the following formula (Harper 1997, ABS 2015):

$$C_t=T_t (r_t P_{t-1}+δ_t P_t-ΔP_t )+x_t P_{t-1} \qquad{Equation\;1}$$

where

$$r_t$$ is the rate of return;

$$P_t$$ is the asset price;

$$δ_t$$  is the rate of economic depreciation (consumption of fixed capital);

$$ΔP_t=P_t-P_{t-1}$$ is the capital gain/loss due to revaluations;

$$T_t$$ is the income tax parameter; and

$$x_t$$ is the effective net indirect tax rate on production.

Rental prices are only currently calculated and published for each asset type within each market sector industry.¹²

For market sector industries, the ABS assumes an initial endogenous rate of return that fully exhausts capital income (gross operating surplus) and is consistent with the assumptions of constant returns to scale and the existence of efficient and competitive markets. That is, gross operating surplus (GOS) can be viewed as the ‘wages’ of capital services, just as compensation of employees are the wages of labour services. If the internal rate of return falls below CPI plus 4%,¹³ the latter rate is used. The lower bound CPI plus 4% ensures rental prices are always positive – this condition is needed in order to estimate aggregation weights.¹⁴

### Footnote

[13] The ABS has chosen a risk free long term discount rate of 4% for the lower bound rate of return in the rental price. This rate is consistent with the real rate of 4% used to discount future capital service flows in current productivity estimates, and originated from long-term RBA bond rates, after adjusting for CPI. The 4% rate also meets the practical requirements of ensuring rental prices remain positive for within industry aggregation.

[14] Details can be found in chapter 19 of the 2020-21 edition of Australian System of National Accounts: Concepts, Sources and Methods.

## Assumptions for constructing experimental rental prices for the health care and education industries

In contrast to the market sector, producing units in the general government sector, are assumed to have a  zero net operating surplus (NOS).¹⁵ For a significant proportion of the non-market sector industries, GOS is imputed using consumption of fixed capital as calculated in the PIM, meaning that GOS only covers the capital used up in production. Therefore, the usual method of assuming efficient and competitive markets to solve for the rate of return is not suitable.

To overcome this issue it is proposed to use the floor rate of CPI plus 4% as the nominal rate of return. While a real rate of 4% may seem too high given unprecedented low interest rates, Lane and Rosewall (RBA, 2015) noted private businesses reporting investment hurdle rates (the rates for investment projects to proceed as reported in their Business Liaison Program) did not follow the cash rate down, but remained around 10% or more.

This assumption allows rental prices to be compiled without assuming returns to capital over and above capital used up in the production process.  The advantage of using this approach for an exogenous rate of return is that it is consistent with the ABS’s current approach as the rate is already used as the lower limit for the market sector. It is also consistent with the real discount rate used to convert productive capital stock to net capital stock in the PIM.

To capture the influence of taxation, it has been assumed that taxes on capital for individual assets are the same as those from Division M – Professional, scientific technical services. This industry was chosen since it does not have any industry specific tax treatments, and shares some common characteristics with the health care and education industries, such as a high labour income share, and a significant proportion of professional employees working in scientific and technical non-market activity. For any given asset, tax treatments tend to be similar unless there are industry-specific tax incentives, such as those applying to industries such as Agriculture, Mining, Manufacturing, and Accommodation and food services.

Note that for each asset type, the level of rental price can vary by industry due to variation in composition and age profile of assets of the same type across industries, through the depreciation rate component.¹⁶

### Footnote

[15] 2008 System of National Accounts, paragraph 20.71. Also see ABS research paper at footnote 1.

[16] Since the quantity of capital services is not directly observable, the unit of rental price is the cost for services generated by one dollar (in the reference year) of productive capital stock.

## Experimental rental prices for the health care and education industries

Experimental rental prices for the health care and education industries were constructed for the period from 1995-96 to 2019-20 and presented in Tables 1 and 2 below.

These estimates are interpreted as “For a given year, what is the cost of $1 worth of capital services at 2018-19 quality”. For instance,$1 worth of capital services of computers in 2018-19 cost 51.5 cents to rent in the health care industry, whereas in 1995-96, $1 worth of capital services of 2018-19 quality cost$15.92 to rent.

Figures 2-5 present experimental rental prices for the health care and education industries, compared to published rental prices for the professional, scientific and technical services industry. Rental prices for computers, computer software, electrical and electronic equipment, and non-dwelling construction are presented.

Figures 2-4 show rapid declines in the rental prices of computers, computer software and electrical and electronic equipment, which is as expected. All three industries showed similar declining trends, which to a large extent validates the experimental indexes for the health care and education industries. While the short-term movement of rental prices across the three industries were not as close for non-dwelling construction (Figure 5), the experimental indexes for health care and education evolve similarly to those for the professional, scientific and technical services industry over the longer term.

Table 1: Experimental rental prices for the Education and Training industry ($cost per unit of capital in reference period 2018-19) Asset type1995-961996-971997-981998-991999-002000-012001-022002-032003-042004-052005-062006-072007-08 Computers 13.84511.7667.0466.2217.3443.1233.7383.9283.3782.2781.4872.0661.803 Electrical & electronic equipment 0.7260.7820.4370.4480.7490.3860.3240.4660.5980.5400.3960.4700.485 Industrial machinery & equipment 0.1570.1500.1300.1020.2370.1640.1070.1690.2120.1950.1540.2250.262 Land 0.0240.0160.0240.0170.0510.0260.0260.0310.0310.0460.0280.0370.084 Non-dwelling construction 0.0660.0510.0590.0540.1070.0640.0490.0410.0370.0700.0850.1120.070 Other plant & equipment 0.1420.1300.1180.1020.2050.1130.0960.1580.1680.1860.0520.2350.226 Other transport equipment 0.1700.1560.0680.0700.2240.0860.1350.2270.2910.2270.1790.2540.346 Ownership transfer costs 0.0240.0270.0210.0430.0560.0340.0010.0010.0010.0750.0760.0570.124 Research & development0.1310.1440.1480.1640.1860.1250.1380.1500.1690.1820.1690.2070.210 Road vehicles 0.1860.1960.1750.1620.2810.1610.1700.1540.2050.2560.1250.2770.287 Computer software 1.9851.7131.6110.9991.1140.8930.8730.8920.8940.9480.9550.9891.037 Table 1 continued: Experimental rental prices for the Education and Training industry ($ cost per unit of capital in reference period 2018-19)
Asset type2008-092009-102010-112011-122012-132013-142014-152015-162016-172017-182018-192019-20
Computers                                 1.0391.1941.0210.8510.8180.7220.6670.5830.5700.5140.5110.442
Electrical & electronic equipment               0.2210.3330.3810.3320.2760.1730.1880.1610.3030.2710.1930.201
Industrial machinery & equipment 0.0880.1610.2530.2040.2010.0980.1710.1100.2160.2090.1840.163
Land                                                              0.0200.0370.0720.0560.0660.0570.0640.0670.0660.0690.0840.071
Non-dwelling construction                                         0.0580.1050.1160.1380.1360.1140.0940.1070.1150.1180.1230.145
Other transport equipment         0.0860.2620.2810.2330.2200.1770.1670.1470.2570.2230.2110.205
Other plant & equipment  0.0970.2890.2100.1840.1620.0870.1100.0740.2250.2310.1470.187
Ownership transfer costs                                          0.1900.0130.0530.1890.1360.0740.0000.1120.1670.1290.2990.180
Research & development0.1500.1840.2350.2140.2240.2220.2170.2210.2350.2470.2660.263
Computer software0.6550.6370.7610.6550.6420.6090.6000.5210.5150.4980.4720.419
Table 2: Experimental rental prices for the Health Care and Social Assistance industry ($cost per unit of capital in reference period 2018-19) Asset type1995-961996-971997-981998-991999-002000-012001-022002-032003-042004-052005-062006-072007-08 Computers 15.92213.4028.0897.2478.3123.7844.2304.3323.8122.5421.8002.1151.925 Electrical & electronic equipment 0.8490.9050.5210.5420.8120.4910.3820.4980.6490.5810.4760.4930.532 Industrial machinery & equipment 0.1640.1560.1360.1080.2400.1610.1070.1720.2120.1950.1340.2300.262 Land 0.0240.0160.0240.0170.0510.0260.0260.0310.0310.0460.0280.0370.084 Non-dwelling construction 0.0670.0530.0590.0620.1060.0610.0470.0370.0370.0760.0950.1000.098 Other plant & equipment 0.1610.1440.1290.1120.2090.1300.0990.1580.1750.1910.0670.2350.242 Other transport equipment 0.1810.1670.0820.0850.2390.0970.1530.2460.3080.2440.1960.2720.361 Ownership transfer costs 0.0220.0260.0190.0410.0530.0300.0010.0010.0010.0700.0710.0510.118 Research & development0.1310.1440.1510.1660.1890.1280.1410.1550.1750.1890.1770.2110.215 Road vehicles 0.2410.2530.2270.2180.3140.2200.2190.1690.2470.2950.2450.2880.337 Computer software 2.0541.7581.6051.0441.1910.9840.9670.9810.9730.9970.9450.9361.002 Table 2 continued: Experimental rental prices for the Health Care and Social Assistance industry ($ cost per unit of capital in reference period 2018-19)
Asset type2008-092009-102010-112011-122012-132013-142014-152015-162016-172017-182018-192019-20
Computers                                 1.1081.1931.0260.8840.7970.7040.6700.6070.6060.5470.5150.438
Electrical & electronic equipment             0.2520.3460.4030.3570.2980.1970.2110.1810.3220.2900.2070.211
Industrial machinery & equipment              0.0920.1710.2650.2190.2110.1120.1860.1250.2340.2290.1990.176
Land                                                              0.0200.0370.0720.0560.0660.0570.0640.0670.0660.0690.0840.071
Non-dwelling construction                                         0.0430.1000.1130.1310.1250.1060.1000.1060.1140.1120.1170.142
Other plant & equipment                  0.0940.2580.2790.2350.2150.1740.1690.1520.2650.2320.2180.213
Other transport equipment                0.1120.3040.2290.2070.1840.1110.1310.0980.2500.2560.1650.201
Ownership transfer costs                                          0.1850.0100.0510.1870.1330.0710.0010.1060.1600.1210.2910.172
Research & development0.1570.1910.2410.2160.2250.2210.2160.2200.2290.2400.2580.255
Computer software                 0.6530.6770.6750.6670.6320.6080.6040.5450.5350.5210.4920.433

Note: The price of renting \$1 of capital services in 2018-19 dollars.

## Experimental indexes of capital services

Figure 6 shows volume indexes of capital services for the education and health care industries. The indexes were constructed as Törnqvist indexes, and are therefore additive in natural log growth.¹⁷ For comparison, Figure 6 includes the published aggregate capital service index for market sector industries.

The input of capital services for the health care industry grew at a compound annual rate of 5.4% from 1994-95 to 2019-20, considerably faster than for the education industry (around 3.5%). This compares to 4.1% compound annual growth for the aggregate of all market sector industries.

Figure 7 shows that for the education industry, the strongest overall contributors to growth in capital services were non-dwelling construction, followed by computers and software. The post-GFC acceleration in capital services provided by non-dwelling construction is largely due to public capital spending in schools.

Figure 8 shows the same for the health care industry. The strongest overall contributors to growth in capital services were non-dwelling construction, followed by computers and road vehicles. Capital services provided by these assets also tended to grow faster in the health care industry than in the education industry.

### Footnote

[17] See Concepts, Sources and Methods, paragraph 19.101.

## Sensitivity testing

Figures 9 and 10 show the results of sensitivity tests for the choice of rate of return, and the use of the tax parameter for the Professional, scientific and technical services industry (PST).

To test the sensitivity of capital services to the choice of rate of return, other rates of return were examined. The results in Figures 9 and 10 employ an 8% rate of return, and show that using a higher rate resulted in a slightly lower compound annual rate of 3.3% for the education industry (compared to 3.5% in Figure 9) and 5.2% for the health care industry (compared to 5.4% in Figure 10). That is, the impact on capital services between using a CPI plus 4% rate of return (blue line) and an 8% rate of return (black line) is very small. Given these two industries are labour-intensive, and the contribution of capital is relatively small, the choice of rate of return is not expected to have much of an impact on measures of MFP growth.

To test the sensitivity of capital services to the use of the PST tax parameter, the index was constructed with the tax parameter “switched off”, i.e.  $$T_t=1$$ in equation 1 above. The difference between using the professional, scientific and technical services industry’s tax parameter with a CPI plus 4% rate of return (blue line) and removing the tax parameter from the calculation with the same rate of return (orange line) is quite small, hence the use of the PST tax parameter is also not expected to impact MFP measurement.

## Conclusion

This paper has outlined the compilation of experimental rental prices and volume indexes of capital services for the education and health care industries which will be used in constructing experimental MFP measures for hospitals, schools and higher education, to be published later in 2021.

## References

Australian Bureau of Statistics (2021), “Australian System of National Accounts: Concepts, Sources and Methods”

Lane K and Rosewall T (2015), “Firms’ Investment Decisions and Interest Rates”, Reserve Bank of Australia Firms' Investment Decisions and Interest Rates (rba.gov.au)

Harper M J (1997), “Estimating capital inputs for productivity measurement: An overview of concepts and methods”, Capital Stock Conference, Canberra

Productivity Commission (2021), “Things you can’t drop on your feet: An overview of Australia’s services sector productivity”, PC Productivity Insight

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