Experimental capital service indexes for non-market industries

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.

Figure 1: Summary of Productivity measures published by the ABS
Productivity type	Gross Output based measures	GVA based measures	Labour inputs	Capital services inputs	Intermediate inputs
Labour Productivity	-	Y	Y	-	-
Capital Productivity	-	Y	-	Y	-
Value added MFP	-	Y	Y	Y	-
Gross Ouput MFP	Y	-	Y	Y	Y
KLEMS MFP	Y	-	Y	Y	Y

Footnote

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

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

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

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 type	1995-96	1996-97	1997-98	1998-99	1999-00	2000-01	2001-02	2002-03	2003-04	2004-05	2005-06	2006-07	2007-08
Computers	13.845	11.766	7.046	6.221	7.344	3.123	3.738	3.928	3.378	2.278	1.487	2.066	1.803
Electrical & electronic equipment	0.726	0.782	0.437	0.448	0.749	0.386	0.324	0.466	0.598	0.540	0.396	0.470	0.485
Industrial machinery & equipment	0.157	0.150	0.130	0.102	0.237	0.164	0.107	0.169	0.212	0.195	0.154	0.225	0.262
Land	0.024	0.016	0.024	0.017	0.051	0.026	0.026	0.031	0.031	0.046	0.028	0.037	0.084
Non-dwelling construction	0.066	0.051	0.059	0.054	0.107	0.064	0.049	0.041	0.037	0.070	0.085	0.112	0.070
Other plant & equipment	0.142	0.130	0.118	0.102	0.205	0.113	0.096	0.158	0.168	0.186	0.052	0.235	0.226
Other transport equipment	0.170	0.156	0.068	0.070	0.224	0.086	0.135	0.227	0.291	0.227	0.179	0.254	0.346
Ownership transfer costs	0.024	0.027	0.021	0.043	0.056	0.034	0.001	0.001	0.001	0.075	0.076	0.057	0.124
Research & development	0.131	0.144	0.148	0.164	0.186	0.125	0.138	0.150	0.169	0.182	0.169	0.207	0.210
Road vehicles	0.186	0.196	0.175	0.162	0.281	0.161	0.170	0.154	0.205	0.256	0.125	0.277	0.287
Computer software	1.985	1.713	1.611	0.999	1.114	0.893	0.873	0.892	0.894	0.948	0.955	0.989	1.037

Table 1 continued: Experimental rental prices for the Education and Training industry ($ cost per unit of capital in reference period 2018-19)
Asset type	2008-09	2009-10	2010-11	2011-12	2012-13	2013-14	2014-15	2015-16	2016-17	2017-18	2018-19	2019-20
Computers	1.039	1.194	1.021	0.851	0.818	0.722	0.667	0.583	0.570	0.514	0.511	0.442
Electrical & electronic equipment	0.221	0.333	0.381	0.332	0.276	0.173	0.188	0.161	0.303	0.271	0.193	0.201
Industrial machinery & equipment	0.088	0.161	0.253	0.204	0.201	0.098	0.171	0.110	0.216	0.209	0.184	0.163
Land	0.020	0.037	0.072	0.056	0.066	0.057	0.064	0.067	0.066	0.069	0.084	0.071
Non-dwelling construction	0.058	0.105	0.116	0.138	0.136	0.114	0.094	0.107	0.115	0.118	0.123	0.145
Other transport equipment	0.086	0.262	0.281	0.233	0.220	0.177	0.167	0.147	0.257	0.223	0.211	0.205
Other plant & equipment	0.097	0.289	0.210	0.184	0.162	0.087	0.110	0.074	0.225	0.231	0.147	0.187
Ownership transfer costs	0.190	0.013	0.053	0.189	0.136	0.074	0.000	0.112	0.167	0.129	0.299	0.180
Research & development	0.150	0.184	0.235	0.214	0.224	0.222	0.217	0.221	0.235	0.247	0.266	0.263
Road vehicles	0.198	0.228	0.238	0.224	0.236	0.197	0.179	0.166	0.222	0.226	0.227	0.197
Computer software	0.655	0.637	0.761	0.655	0.642	0.609	0.600	0.521	0.515	0.498	0.472	0.419

Table 2: Experimental rental prices for the Health Care and Social Assistance industry ($ cost per unit of capital in reference period 2018-19)
Asset type	1995-96	1996-97	1997-98	1998-99	1999-00	2000-01	2001-02	2002-03	2003-04	2004-05	2005-06	2006-07	2007-08
Computers	15.922	13.402	8.089	7.247	8.312	3.784	4.230	4.332	3.812	2.542	1.800	2.115	1.925
Electrical & electronic equipment	0.849	0.905	0.521	0.542	0.812	0.491	0.382	0.498	0.649	0.581	0.476	0.493	0.532
Industrial machinery & equipment	0.164	0.156	0.136	0.108	0.240	0.161	0.107	0.172	0.212	0.195	0.134	0.230	0.262
Land	0.024	0.016	0.024	0.017	0.051	0.026	0.026	0.031	0.031	0.046	0.028	0.037	0.084
Non-dwelling construction	0.067	0.053	0.059	0.062	0.106	0.061	0.047	0.037	0.037	0.076	0.095	0.100	0.098
Other plant & equipment	0.161	0.144	0.129	0.112	0.209	0.130	0.099	0.158	0.175	0.191	0.067	0.235	0.242
Other transport equipment	0.181	0.167	0.082	0.085	0.239	0.097	0.153	0.246	0.308	0.244	0.196	0.272	0.361
Ownership transfer costs	0.022	0.026	0.019	0.041	0.053	0.030	0.001	0.001	0.001	0.070	0.071	0.051	0.118
Research & development	0.131	0.144	0.151	0.166	0.189	0.128	0.141	0.155	0.175	0.189	0.177	0.211	0.215
Road vehicles	0.241	0.253	0.227	0.218	0.314	0.220	0.219	0.169	0.247	0.295	0.245	0.288	0.337
Computer software	2.054	1.758	1.605	1.044	1.191	0.984	0.967	0.981	0.973	0.997	0.945	0.936	1.002

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 type	2008-09	2009-10	2010-11	2011-12	2012-13	2013-14	2014-15	2015-16	2016-17	2017-18	2018-19	2019-20
Computers	1.108	1.193	1.026	0.884	0.797	0.704	0.670	0.607	0.606	0.547	0.515	0.438
Electrical & electronic equipment	0.252	0.346	0.403	0.357	0.298	0.197	0.211	0.181	0.322	0.290	0.207	0.211
Industrial machinery & equipment	0.092	0.171	0.265	0.219	0.211	0.112	0.186	0.125	0.234	0.229	0.199	0.176
Land	0.020	0.037	0.072	0.056	0.066	0.057	0.064	0.067	0.066	0.069	0.084	0.071
Non-dwelling construction	0.043	0.100	0.113	0.131	0.125	0.106	0.100	0.106	0.114	0.112	0.117	0.142
Other plant & equipment	0.094	0.258	0.279	0.235	0.215	0.174	0.169	0.152	0.265	0.232	0.218	0.213
Other transport equipment	0.112	0.304	0.229	0.207	0.184	0.111	0.131	0.098	0.250	0.256	0.165	0.201
Ownership transfer costs	0.185	0.010	0.051	0.187	0.133	0.071	0.001	0.106	0.160	0.121	0.291	0.172
Research & development	0.157	0.191	0.241	0.216	0.225	0.221	0.216	0.220	0.229	0.240	0.258	0.255
Road vehicles	0.230	0.222	0.240	0.229	0.241	0.202	0.183	0.167	0.223	0.226	0.237	0.197
Computer software	0.653	0.677	0.675	0.667	0.632	0.608	0.604	0.545	0.535	0.521	0.492	0.433

Figure 2: Rental prices: Computers
	Education	Health care	Professional services
1995-96	13.84450274	15.92170455	19.7811
1996-97	11.76591444	13.40246316	16.7334
1997-98	7.046379713	8.089338322	9.9038
1998-99	6.220929664	7.246830831	8.6578
1999-00	7.344145348	8.311670906	8.6093
2000-01	3.123409026	3.783638209	5.4158
2001-02	3.738015021	4.229541239	5.4444
2002-03	3.927935002	4.33245606	5.3282
2003-04	3.377837376	3.812059662	4.5674
2004-05	2.277527275	2.542225125	2.7893
2005-06	1.486606605	1.799908714	2.2429
2006-07	2.066351955	2.115215551	2.0972
2007-08	1.80264194	1.925041881	1.9359
2008-09	1.03926578	1.107528515	1.3748
2009-10	1.194218096	1.19302927	1.3721
2010-11	1.020651212	1.026179812	1.1154
2011-12	0.850856192	0.884005547	0.9267
2012-13	0.818466399	0.796655774	0.856
2013-14	0.722017056	0.703948592	0.7787
2014-15	0.666588731	0.670380318	0.7038
2015-16	0.582502771	0.606947108	0.6173
2016-17	0.569636109	0.606473384	0.6082
2017-18	0.51387801	0.546851519	0.5384
2018-19	0.511077788	0.515108293	0.5161
2019-20	0.441970662	0.438283983	0.4353

Figure 2: Rental prices: Computers

["","Education","Health care","Professional services"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[13.844502739999999],[11.76591444],[7.0463797130000003],[6.2209296639999998],[7.3441453479999996],[3.123409026],[3.7380150209999998],[3.9279350019999999],[3.377837376],[2.2775272750000002],[1.486606605],[2.066351955],[1.80264194],[1.03926578],[1.194218096],[1.020651212],[0.85085619199999996],[0.81846639899999996],[0.72201705599999999],[0.66658873100000005],[0.58250277100000003],[0.56963610899999995],[0.51387801],[0.51107778800000003],[0.44197066200000001]],[[15.921704549999999],[13.40246316],[8.0893383219999997],[7.2468308309999996],[8.3116709059999998],[3.7836382089999998],[4.2295412389999996],[4.3324560600000002],[3.8120596619999998],[2.5422251249999999],[1.7999087140000001],[2.1152155509999999],[1.9250418810000001],[1.107528515],[1.19302927],[1.0261798120000001],[0.884005547],[0.79665577399999998],[0.70394859200000004],[0.67038031799999998],[0.60694710799999996],[0.60647338399999995],[0.54685151899999995],[0.51510829300000005],[0.43828398299999999]],[[19.781099999999999],[16.7334],[9.9038000000000004],[8.6577999999999999],[8.6092999999999993],[5.4157999999999999],[5.4443999999999999],[5.3281999999999998],[4.5674000000000001],[2.7892999999999999],[2.2429000000000001],[2.0972],[1.9359],[1.3748],[1.3721000000000001],[1.1153999999999999],[0.92669999999999997],[0.85599999999999998],[0.77869999999999995],[0.70379999999999998],[0.61729999999999996],[0.60819999999999996],[0.53839999999999999],[0.5161],[0.43530000000000002]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Rental price (see note)","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

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

Figure 3: Rental prices: Computer software
	Education	Health care	Professional services
1995-96	1.984854053	2.053921527	1.9826
1996-97	1.712836641	1.757823064	1.7322
1997-98	1.610984501	1.605395091	1.5328
1998-99	0.998678839	1.043855026	1.0085
1999-00	1.114209575	1.190586092	1.0263
2000-01	0.892673414	0.984241356	1.056
2001-02	0.873138133	0.96739244	1.0287
2002-03	0.892083311	0.981127322	0.9418
2003-04	0.894172683	0.973095724	0.9129
2004-05	0.948138655	0.996579308	0.8841
2005-06	0.954558159	0.945267494	0.8808
2006-07	0.988850376	0.936185363	0.8644
2007-08	1.037240413	1.002162566	0.8678
2008-09	0.655291796	0.653167235	0.7049
2009-10	0.637291523	0.677380194	0.7689
2010-11	0.761339119	0.67490376	0.7328
2011-12	0.655346668	0.667472038	0.6932
2012-13	0.64209174	0.632453057	0.679
2013-14	0.608838555	0.60795687	0.6865
2014-15	0.600240921	0.604385002	0.6352
2015-16	0.520592331	0.54525009	0.558
2016-17	0.515356083	0.535033227	0.5338
2017-18	0.497793294	0.520701888	0.4934
2018-19	0.47222976	0.49233447	0.4451
2019-20	0.418582317	0.432847514	0.3862

Figure 3: Rental prices: Computer software

["","Education","Health care","Professional services"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[1.9848540530000001],[1.712836641],[1.6109845009999999],[0.99867883899999998],[1.1142095750000001],[0.892673414],[0.87313813299999998],[0.89208331100000005],[0.89417268299999997],[0.94813865500000005],[0.95455815899999996],[0.98885037600000003],[1.0372404129999999],[0.65529179599999998],[0.63729152300000003],[0.76133911899999995],[0.65534666799999997],[0.64209174000000002],[0.60883855499999995],[0.60024092100000004],[0.52059233100000002],[0.51535608300000002],[0.497793294],[0.47222976],[0.41858231699999998]],[[2.053921527],[1.7578230640000001],[1.6053950910000001],[1.0438550259999999],[1.190586092],[0.98424135599999996],[0.96739244000000002],[0.98112732199999997],[0.973095724],[0.99657930800000005],[0.94526749399999999],[0.93618536299999999],[1.002162566],[0.65316723499999996],[0.67738019400000005],[0.67490375999999996],[0.66747203799999999],[0.63245305699999999],[0.60795686999999998],[0.604385002],[0.54525009000000002],[0.535033227],[0.52070188799999995],[0.49233447000000002],[0.43284751399999999]],[[1.9825999999999999],[1.7322],[1.5327999999999999],[1.0085],[1.0263],[1.056],[1.0286999999999999],[0.94179999999999997],[0.91290000000000004],[0.8841],[0.88080000000000003],[0.86439999999999995],[0.86780000000000002],[0.70489999999999997],[0.76890000000000003],[0.73280000000000001],[0.69320000000000004],[0.67900000000000005],[0.6865],[0.63519999999999999],[0.55800000000000005],[0.53380000000000005],[0.49340000000000001],[0.4451],[0.38619999999999999]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Rental price","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

Figure 4: Rental prices: Electrical and electronic equipment
	Education	Health care	Professional services
1995-96	0.725553831	0.848920506	0.868
1996-97	0.782474051	0.904598661	0.9482
1997-98	0.436780331	0.521399306	0.4803
1998-99	0.447945141	0.542157241	0.5309
1999-00	0.74947688	0.811695908	0.6868
2000-01	0.385639127	0.490719139	0.6392
2001-02	0.324171383	0.381525566	0.4743
2002-03	0.465946911	0.497572092	0.6028
2003-04	0.597999994	0.649483312	0.713
2004-05	0.540031341	0.581240204	0.55
2005-06	0.395781164	0.476430427	0.4835
2006-07	0.470350838	0.493488292	0.4487
2007-08	0.485089911	0.53177219	0.4802
2008-09	0.220885289	0.252362576	0.3443
2009-10	0.332951243	0.346147923	0.4151
2010-11	0.38135944	0.40272317	0.4221
2011-12	0.331997055	0.356514385	0.368
2012-13	0.276297488	0.298280885	0.3118
2013-14	0.17296305	0.197255642	0.2405
2014-15	0.188466838	0.210680915	0.2489
2015-16	0.16127513	0.181237475	0.2086
2016-17	0.303273084	0.321906087	0.3459
2017-18	0.271147496	0.289701491	0.3002
2018-19	0.193404221	0.206854135	0.2068
2019-20	0.200642685	0.211270345	0.2048

Figure 4: Rental prices: Electrical and electronic equipment

["","Education","Health care","Professional services"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[0.72555383100000004],[0.782474051],[0.43678033100000002],[0.44794514099999999],[0.74947688000000001],[0.38563912700000003],[0.32417138299999998],[0.46594691100000002],[0.59799999400000003],[0.54003134100000005],[0.39578116400000002],[0.47035083799999999],[0.48508991099999998],[0.22088528900000001],[0.33295124300000001],[0.38135943999999999],[0.33199705499999999],[0.27629748799999998],[0.17296305000000001],[0.188466838],[0.16127512999999999],[0.30327308400000003],[0.27114749599999999],[0.19340422099999999],[0.20064268499999999]],[[0.84892050600000002],[0.90459866099999997],[0.52139930599999995],[0.54215724099999996],[0.81169590800000002],[0.49071913900000003],[0.38152556599999998],[0.49757209200000002],[0.64948331199999998],[0.58124020399999998],[0.47643042699999999],[0.493488292],[0.53177218999999998],[0.25236257600000001],[0.34614792300000002],[0.40272317000000002],[0.35651438499999999],[0.298280885],[0.19725564200000001],[0.210680915],[0.18123747500000001],[0.32190608700000001],[0.28970149099999998],[0.20685413499999999],[0.211270345]],[[0.86799999999999999],[0.94820000000000004],[0.4803],[0.53090000000000004],[0.68679999999999997],[0.63919999999999999],[0.4743],[0.6028],[0.71299999999999997],[0.55000000000000004],[0.48349999999999999],[0.44869999999999999],[0.48020000000000002],[0.34429999999999999],[0.41510000000000002],[0.42209999999999998],[0.36799999999999999],[0.31180000000000002],[0.24049999999999999],[0.24890000000000001],[0.20860000000000001],[0.34589999999999999],[0.30020000000000002],[0.20680000000000001],[0.20480000000000001]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Rental price","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

Figure 5: Rental prices: Non-dwelling construction
	Education	Health care	Professional services
1995-96	0.06627198	0.066822117	0.0624
1996-97	0.051456575	0.05333557	0.0572
1997-98	0.058684236	0.059329144	0.0429
1998-99	0.054026741	0.062414867	0.059
1999-00	0.107252248	0.106003487	0.0595
2000-01	0.064233029	0.060829999	0.082
2001-02	0.048997123	0.047096629	0.0715
2002-03	0.040563546	0.037000287	0.0635
2003-04	0.037215802	0.037203131	0.0437
2004-05	0.070137243	0.075869378	0.0499
2005-06	0.085164423	0.095031798	0.0816
2006-07	0.112195293	0.100439825	0.068
2007-08	0.070489338	0.097511216	0.0649
2008-09	0.057691175	0.042815138	0.0912
2009-10	0.104792276	0.099909614	0.136
2010-11	0.115595941	0.113086655	0.1127
2011-12	0.138180677	0.130845631	0.142
2012-13	0.135602629	0.125232408	0.1212
2013-14	0.114471122	0.10567185	0.1305
2014-15	0.093992139	0.099587334	0.1156
2015-16	0.106607466	0.106142861	0.1217
2016-17	0.114951442	0.114066176	0.1287
2017-18	0.117516623	0.112331749	0.1255
2018-19	0.122755837	0.11659897	0.1085
2019-20	0.144857428	0.142249779	0.1244

Figure 5: Rental prices: Non-dwelling construction

["","Education","Health care","Professional services"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[0.066271979999999994],[0.051456574999999997],[0.058684236000000001],[0.054026741000000003],[0.10725224799999999],[0.064233028999999997],[0.048997122999999997],[0.040563545999999999],[0.037215801999999999],[0.070137243000000002],[0.085164423000000003],[0.112195293],[0.070489337999999999],[0.057691174999999997],[0.104792276],[0.11559594099999999],[0.138180677],[0.135602629],[0.11447112199999999],[0.093992139000000002],[0.106607466],[0.114951442],[0.117516623],[0.12275583700000001],[0.14485742800000001]],[[0.066822117],[0.053335569999999999],[0.059329144],[0.062414866999999999],[0.10600348699999999],[0.060829999000000003],[0.047096629000000001],[0.037000287],[0.037203131],[0.075869378000000001],[0.095031798000000001],[0.100439825],[0.097511215999999998],[0.042815138000000003],[0.099909613999999994],[0.11308665499999999],[0.13084563099999999],[0.12523240799999999],[0.10567185],[0.099587334],[0.10614286100000001],[0.11406617600000001],[0.11233174899999999],[0.11659897],[0.14224977899999999]],[[0.062399999999999997],[0.057200000000000001],[0.042900000000000001],[0.058999999999999997],[0.059499999999999997],[0.082000000000000003],[0.071499999999999994],[0.063500000000000001],[0.043700000000000003],[0.0499],[0.081600000000000006],[0.068000000000000005],[0.064899999999999999],[0.091200000000000003],[0.13600000000000001],[0.11269999999999999],[0.14199999999999999],[0.1212],[0.1305],[0.11559999999999999],[0.1217],[0.12870000000000001],[0.1255],[0.1085],[0.1244]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Rental price","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

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

Figure 6: Capital service indexes
	Education	Health care	Market sector industries
1994-95	100	100	100
1995-96	103.1628352	103.7031606	103.974047
1996-97	106.8054567	108.8183345	108.7050554
1997-98	111.0029861	116.1720422	114.4363341
1998-99	114.5282227	121.6281043	119.9783725
1999-00	117.9580837	127.5636467	125.6826169
2000-01	121.7787233	134.04322	130.467694
2001-02	126.276202	141.0041599	134.7120843
2002-03	131.8079609	149.1573198	140.4703974
2003-04	138.2410206	159.8398276	148.0129765
2004-05	144.6909187	170.8574725	156.3395512
2005-06	149.4149254	181.2598213	165.6123277
2006-07	154.1086461	193.1482051	174.9662071
2007-08	159.3486455	206.3379587	186.6180049
2008-09	166.0485083	221.9761593	195.5934036
2009-10	181.0972351	238.4550513	203.406326
2010-11	193.926762	253.8374688	212.1113815
2011-12	201.6444934	264.5437682	224.6553122
2012-13	206.5122324	277.2693108	236.063801
2013-14	211.0261204	290.1660837	244.5255474
2014-15	214.6733524	303.420577	251.5274398
2015-16	217.4631914	315.5590628	256.4206542
2016-17	221.2441432	327.6102269	261.2057313
2017-18	226.1647151	341.3929845	266.044877
2018-19	230.174704	356.0749455	270.343336
2019-20	234.4321581	370.7236918	273.0467694

Figure 6: Capital service indexes

["","Education","Health care","Market sector industries"]

[["1994-95","1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[100],[103.1628352],[106.80545669999999],[111.0029861],[114.5282227],[117.9580837],[121.7787233],[126.276202],[131.80796090000001],[138.24102060000001],[144.6909187],[149.41492539999999],[154.10864609999999],[159.3486455],[166.04850830000001],[181.09723510000001],[193.926762],[201.64449339999999],[206.51223239999999],[211.0261204],[214.6733524],[217.4631914],[221.2441432],[226.1647151],[230.17470399999999],[234.43215810000001]],[[100],[103.7031606],[108.81833450000001],[116.17204220000001],[121.6281043],[127.56364670000001],[134.04321999999999],[141.00415989999999],[149.15731980000001],[159.83982760000001],[170.8574725],[181.2598213],[193.14820510000001],[206.3379587],[221.97615930000001],[238.45505130000001],[253.83746880000001],[264.54376819999999],[277.26931080000003],[290.1660837],[303.42057699999998],[315.55906279999999],[327.61022689999999],[341.39298450000001],[356.07494550000001],[370.72369179999998]],[[100],[103.974047],[108.70505540000001],[114.4363341],[119.97837250000001],[125.6826169],[130.46769399999999],[134.71208429999999],[140.4703974],[148.01297650000001],[156.33955119999999],[165.61232770000001],[174.96620709999999],[186.61800489999999],[195.59340359999999],[203.40632600000001],[212.11138149999999],[224.6553122],[236.06380100000001],[244.52554739999999],[251.5274398],[256.4206542],[261.20573130000002],[266.04487699999999],[270.34333600000002],[273.04676940000002]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Index (1994-95=100)","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

Figure 7: Contribution to capital services: education
	Computers	Electrical eqp	Non dwelling construction	Other assets	R&D	Road vehicles	Software
1995-96	0.007292869	0.000710937	0.008205401	0.001725072	0.004194869	0.001944656	0.007064673
1996-97	0.01620566	0.00161408	0.017591534	0.003429445	0.009120617	0.003445146	0.014432349
1997-98	0.031362634	0.002847232	0.024448276	0.004308171	0.014480711	0.004028193	0.022911701
1998-99	0.040132169	0.003514775	0.030180802	0.005494785	0.020356498	0.005425399	0.030546665
1999-00	0.048828981	0.004190054	0.038343219	0.006826348	0.025000929	0.006438919	0.035530701
2000-01	0.055794537	0.005034594	0.046536248	0.009419362	0.028503123	0.007297632	0.044449972
2001-02	0.061401879	0.005880009	0.060310908	0.012237662	0.033113473	0.008275215	0.052082256
2002-03	0.070008956	0.007746841	0.071602557	0.015837289	0.039109472	0.009691494	0.062179226
2003-04	0.082059821	0.011386512	0.080419013	0.020178253	0.045904724	0.011960507	0.071919671
2004-05	0.091981563	0.015037262	0.08949911	0.024976527	0.052005926	0.014722224	0.081207074
2005-06	0.096715965	0.017563302	0.101772497	0.027745618	0.057322834	0.016643665	0.083793102
2006-07	0.101841996	0.019942988	0.116780051	0.030334119	0.060890394	0.018487436	0.084210678
2007-08	0.108197879	0.021549644	0.130346017	0.034030783	0.064835818	0.021521024	0.085443189
2008-09	0.11779743	0.023717901	0.14270496	0.037135995	0.068398394	0.025775807	0.091579291
2009-10	0.126996	0.025159972	0.195530059	0.046223708	0.070982498	0.030272438	0.098699236
2010-11	0.132263586	0.026523218	0.239674692	0.053896528	0.073321808	0.033322106	0.103308448
2011-12	0.136975386	0.027882817	0.258634075	0.057669066	0.075071859	0.036347563	0.108755261
2012-13	0.137782006	0.028663154	0.274437598	0.058583018	0.076019045	0.037890487	0.111814154
2013-14	0.138460271	0.029242678	0.288895803	0.060223773	0.07632501	0.039376331	0.114287867
2014-15	0.139694273	0.029849622	0.298781839	0.062914348	0.07610086	0.041076869	0.115529584
2015-16	0.140450592	0.030231535	0.30560831	0.064912595	0.075674507	0.042637908	0.117343969
2016-17	0.14112472	0.030720493	0.316370168	0.067492008	0.074956975	0.044319337	0.119112925
2017-18	0.142194094	0.031468012	0.329922717	0.070929491	0.074006273	0.046215095	0.121357694
2018-19	0.142952757	0.03173237	0.342413099	0.073152406	0.072917616	0.047469403	0.123030765
2019-20	0.143710821	0.031863394	0.357007001	0.074774632	0.071915964	0.04824342	0.124480823

Figure 7: Contribution to capital services: education

["","Computers","Electrical eqp","Non dwelling construction","Other assets","R&D","Road vehicles","Software"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[0.0072928689999999996],[0.01620566],[0.031362634],[0.040132169000000002],[0.048828981],[0.055794536999999998],[0.061401878999999999],[0.070008955999999997],[0.082059821000000005],[0.091981563000000002],[0.096715965000000001],[0.101841996],[0.108197879],[0.11779742999999999],[0.126996],[0.13226358599999999],[0.136975386],[0.13778200600000001],[0.138460271],[0.13969427300000001],[0.14045059200000001],[0.14112472000000001],[0.14219409399999999],[0.14295275700000001],[0.14371082099999999]],[[0.00071093700000000003],[0.0016140799999999999],[0.0028472319999999999],[0.0035147749999999999],[0.0041900540000000003],[0.0050345939999999999],[0.0058800090000000003],[0.007746841],[0.011386512],[0.015037261999999999],[0.017563301999999999],[0.019942987999999998],[0.021549644],[0.023717901],[0.025159971999999999],[0.026523218000000001],[0.027882817000000001],[0.028663154],[0.029242678000000001],[0.029849621999999999],[0.030231535],[0.030720493000000001],[0.031468011999999997],[0.031732370000000003],[0.031863394000000003]],[[0.0082054009999999993],[0.017591533999999999],[0.024448276000000001],[0.030180802],[0.038343218999999998],[0.046536248000000002],[0.060310908000000003],[0.071602556999999997],[0.080419012999999998],[0.089499110000000007],[0.101772497],[0.116780051],[0.13034601700000001],[0.14270495999999999],[0.19553005900000001],[0.23967469199999999],[0.25863407500000002],[0.274437598],[0.28889580300000001],[0.29878183899999999],[0.30560830999999999],[0.31637016800000001],[0.32992271699999998],[0.342413099],[0.35700700099999999]],[[0.001725072],[0.0034294450000000001],[0.0043081710000000004],[0.0054947850000000003],[0.0068263480000000003],[0.0094193620000000006],[0.012237662],[0.015837289000000001],[0.020178253],[0.024976526999999998],[0.027745618],[0.030334119],[0.034030783000000002],[0.037135994999999998],[0.046223708000000002],[0.053896527999999999],[0.057669065999999998],[0.058583018000000001],[0.060223773000000001],[0.062914347999999995],[0.064912595000000003],[0.067492008000000006],[0.070929490999999997],[0.073152406000000003],[0.074774631999999994]],[[0.0041948690000000004],[0.0091206169999999993],[0.014480711],[0.020356498000000001],[0.025000929000000002],[0.028503122999999998],[0.033113472999999997],[0.039109471999999999],[0.045904724000000001],[0.052005926000000001],[0.057322834000000003],[0.060890394],[0.064835818000000003],[0.068398394000000001],[0.070982498000000005],[0.073321808000000002],[0.075071859000000005],[0.076019044999999993],[0.076325009999999999],[0.076100860000000006],[0.075674507000000002],[0.074956974999999995],[0.074006272999999997],[0.072917616000000005],[0.071915963999999999]],[[0.0019446559999999999],[0.0034451460000000001],[0.0040281930000000002],[0.005425399],[0.0064389190000000004],[0.0072976320000000001],[0.0082752150000000007],[0.0096914940000000002],[0.011960507],[0.014722224000000001],[0.016643664999999998],[0.018487435999999999],[0.021521024],[0.025775807000000001],[0.030272437999999999],[0.033322105999999997],[0.036347562999999999],[0.037890487],[0.039376331000000001],[0.041076869000000002],[0.042637908000000002],[0.044319337],[0.046215094999999998],[0.047469403],[0.048243420000000002]],[[0.0070646729999999996],[0.014432349000000001],[0.022911701],[0.030546665000000001],[0.035530700999999998],[0.044449971999999997],[0.052082256],[0.062179225999999997],[0.071919671000000004],[0.081207074000000004],[0.083793101999999994],[0.084210677999999997],[0.085443189000000003],[0.091579290999999993],[0.098699235999999996],[0.103308448],[0.10875526100000001],[0.111814154],[0.114287867],[0.115529584],[0.11734396900000001],[0.11911292499999999],[0.121357694],[0.123030765],[0.124480823]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Cumulative growth","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

Figure 8: Contribution to capital services: health care
	Computers	Electrical eqp	Non dwelling construction	Other assets	R&D	Road vehicles	Software
1995-96	0.008348319	0.001801723	0.009901691	0.003427863	0.002051149	0.001905978	0.008925683
1996-97	0.020940328	0.004486462	0.021732883	0.007691037	0.003988153	0.005702578	0.019968209
1997-98	0.039377333	0.009099418	0.039467345	0.011055517	0.005839219	0.008972065	0.036091132
1998-99	0.050332597	0.0109614	0.05518966	0.014427939	0.007433518	0.012553905	0.044898857
1999-00	0.060495525	0.013564771	0.076185709	0.018476626	0.008689234	0.017063864	0.048969515
2000-01	0.070235666	0.017091227	0.092390601	0.026058205	0.009640393	0.020358728	0.057217279
2001-02	0.079844489	0.021026657	0.110524755	0.032574302	0.010575123	0.025023175	0.064050705
2002-03	0.092264355	0.02903808	0.127765188	0.039766047	0.01138837	0.029574401	0.070034961
2003-04	0.109531937	0.043498015	0.141211812	0.049065103	0.011892499	0.036746769	0.077055915
2004-05	0.123058248	0.057538323	0.154141611	0.059150572	0.01201513	0.047226181	0.082529464
2005-06	0.132676687	0.068732833	0.16861753	0.066541086	0.012196713	0.058922973	0.087073471
2006-07	0.142708309	0.079615646	0.186841159	0.073364064	0.012229544	0.071180936	0.09234795
2007-08	0.153738939	0.087754094	0.206062364	0.083212589	0.012562472	0.085981166	0.09503359
2008-09	0.166074046	0.096575063	0.223210459	0.093413206	0.012958734	0.102772233	0.102396058
2009-10	0.179416305	0.101649373	0.240795788	0.101956953	0.013411358	0.124340067	0.107440799
2010-11	0.186802557	0.10432714	0.260106715	0.111632723	0.013881772	0.133543145	0.121229938
2011-12	0.191000599	0.106275009	0.276694607	0.117096175	0.014416808	0.140153417	0.127199911
2012-13	0.194513379	0.108531607	0.297274092	0.123433598	0.014872371	0.146820162	0.13437388
2013-14	0.196581645	0.110115453	0.318920845	0.129623439	0.015096111	0.154858243	0.140087539
2014-15	0.197660005	0.112551947	0.342409936	0.136643663	0.015290104	0.162172245	0.1432218
2015-16	0.196759038	0.113659044	0.369270342	0.142145548	0.015527515	0.168076407	0.143737788
2016-17	0.195562757	0.114441086	0.395165184	0.146888349	0.015819316	0.172437558	0.146340133
2017-18	0.195256363	0.11533507	0.422033087	0.152347078	0.016148652	0.177886941	0.148856884
2018-19	0.196129622	0.11693241	0.44524049	0.158735449	0.016399739	0.185973375	0.150559959
2019-20	0.197042213	0.117996531	0.470370329	0.163088081	0.016597554	0.192686972	0.152505153

Figure 8: Contribution to capital services: health care

["","Computers","Electrical eqp","Non dwelling construction","Other assets","R&D","Road vehicles","Software"]

[["1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[0.0083483189999999999],[0.020940328000000001],[0.039377333],[0.050332597],[0.060495525000000001],[0.070235666000000002],[0.079844489000000005],[0.092264355000000006],[0.109531937],[0.123058248],[0.13267668699999999],[0.14270830900000001],[0.15373893899999999],[0.166074046],[0.179416305],[0.18680255700000001],[0.19100059899999999],[0.19451337899999999],[0.196581645],[0.197660005],[0.196759038],[0.195562757],[0.19525636299999999],[0.196129622],[0.19704221299999999]],[[0.0018017230000000001],[0.0044864620000000001],[0.0090994179999999997],[0.0109614],[0.013564771],[0.017091227000000001],[0.021026657000000001],[0.029038080000000001],[0.043498015000000001],[0.057538323000000002],[0.068732832999999993],[0.079615645999999998],[0.087754094000000005],[0.096575063000000003],[0.101649373],[0.10432714],[0.106275009],[0.108531607],[0.110115453],[0.112551947],[0.113659044],[0.114441086],[0.11533507],[0.11693241],[0.117996531]],[[0.0099016910000000007],[0.021732883000000001],[0.039467345000000001],[0.055189660000000001],[0.076185709000000004],[0.092390601000000003],[0.110524755],[0.127765188],[0.14121181199999999],[0.15414161100000001],[0.16861752999999999],[0.18684115900000001],[0.206062364],[0.223210459],[0.24079578800000001],[0.26010671499999999],[0.27669460699999998],[0.29727409199999999],[0.31892084500000001],[0.34240993600000003],[0.36927034199999997],[0.395165184],[0.42203308699999997],[0.44524048999999999],[0.47037032899999998]],[[0.0034278630000000002],[0.0076910370000000004],[0.011055517000000001],[0.014427939000000001],[0.018476625999999999],[0.026058205000000001],[0.032574301999999999],[0.039766046999999999],[0.049065102999999999],[0.059150571999999998],[0.066541085999999999],[0.073364064000000007],[0.083212589000000003],[0.093413205999999999],[0.101956953],[0.111632723],[0.117096175],[0.12343359800000001],[0.12962343900000001],[0.136643663],[0.14214554800000001],[0.146888349],[0.152347078],[0.158735449],[0.163088081]],[[0.0020511489999999999],[0.0039881530000000004],[0.0058392189999999997],[0.0074335180000000001],[0.0086892340000000005],[0.0096403930000000006],[0.010575123000000001],[0.01138837],[0.011892499000000001],[0.012015130000000001],[0.012196713],[0.012229544],[0.012562472],[0.012958734],[0.013411358],[0.013881772000000001],[0.014416808],[0.014872371000000001],[0.015096111000000001],[0.015290104000000001],[0.015527515],[0.015819316],[0.016148651999999999],[0.016399739],[0.016597554]],[[0.001905978],[0.0057025779999999998],[0.0089720649999999996],[0.012553905000000001],[0.017063864000000002],[0.020358728],[0.025023175000000002],[0.029574401],[0.036746768999999999],[0.047226180999999999],[0.058922972999999997],[0.071180936],[0.085981165999999998],[0.102772233],[0.124340067],[0.133543145],[0.140153417],[0.146820162],[0.15485824300000001],[0.16217224499999999],[0.16807640700000001],[0.17243755799999999],[0.17788694099999999],[0.185973375],[0.19268697200000001]],[[0.0089256830000000002],[0.019968209000000001],[0.036091131999999998],[0.044898857],[0.048969514999999998],[0.057217279000000003],[0.064050704999999999],[0.070034961000000007],[0.077055915000000003],[0.082529463999999997],[0.087073471],[0.092347949999999998],[0.095033590000000001],[0.102396058],[0.107440799],[0.121229938],[0.127199911],[0.13437388],[0.14008753900000001],[0.14322180000000001],[0.14373778800000001],[0.14634013300000001],[0.14885688399999999],[0.15055995899999999],[0.152505153]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Cumulative growth","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

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.

Figure 9: Capital services for the education industry using different rates of return
	Education	Education (8% return)	Education (tax parameter off)
1994-95	100	100	100
1995-96	103.1628352	103.2011637	103.3688432
1996-97	106.8054567	106.5622621	107.1744108
1997-98	111.0029861	110.1377103	111.5507972
1998-99	114.5282227	113.3219856	115.3245817
1999-00	117.9580837	116.8356418	119.1149565
2000-01	121.7787233	120.750724	123.3651489
2001-02	126.276202	124.7326363	128.1447096
2002-03	131.8079609	129.1958885	133.9833369
2003-04	138.2410206	134.2965779	140.6775928
2004-05	144.6909187	140.0703947	147.4361191
2005-06	149.4149254	144.8100632	152.5077762
2006-07	154.1086461	149.549604	157.4338237
2007-08	159.3486455	155.3297409	162.9969456
2008-09	166.0485083	162.3337688	170.0875944
2009-10	181.0972351	176.4393805	185.3137725
2010-11	193.926762	188.6331132	198.3582838
2011-12	201.6444934	195.9285169	206.4497931
2012-13	206.5122324	200.5860612	211.5009592
2013-14	211.0261204	204.8560386	216.1021369
2014-15	214.6733524	208.1812443	219.7511439
2015-16	217.4631914	210.6726679	222.5756635
2016-17	221.2441432	214.2048846	226.4274674
2017-18	226.1647151	218.812318	231.4406167
2018-19	230.174704	222.6571378	235.4958084
2019-20	234.4321581	226.769927	239.8002129

Figure 9: Capital services for the education industry using different rates of return

["","Education","Education (8% return)","Education (tax parameter off)"]

[["1994-95","1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[100],[103.1628352],[106.80545669999999],[111.0029861],[114.5282227],[117.9580837],[121.7787233],[126.276202],[131.80796090000001],[138.24102060000001],[144.6909187],[149.41492539999999],[154.10864609999999],[159.3486455],[166.04850830000001],[181.09723510000001],[193.926762],[201.64449339999999],[206.51223239999999],[211.0261204],[214.6733524],[217.4631914],[221.2441432],[226.1647151],[230.17470399999999],[234.43215810000001]],[[100],[103.2011637],[106.5622621],[110.13771029999999],[113.3219856],[116.8356418],[120.75072400000001],[124.7326363],[129.1958885],[134.29657789999999],[140.07039470000001],[144.8100632],[149.54960399999999],[155.32974089999999],[162.3337688],[176.4393805],[188.6331132],[195.92851690000001],[200.58606119999999],[204.85603860000001],[208.1812443],[210.67266789999999],[214.20488460000001],[218.812318],[222.65713779999999],[226.769927]],[[100],[103.3688432],[107.1744108],[111.55079720000001],[115.3245817],[119.11495650000001],[123.36514889999999],[128.1447096],[133.98333690000001],[140.67759280000001],[147.43611910000001],[152.5077762],[157.4338237],[162.9969456],[170.0875944],[185.3137725],[198.35828380000001],[206.44979309999999],[211.50095920000001],[216.1021369],[219.75114389999999],[222.57566349999999],[226.42746740000001],[231.44061669999999],[235.49580839999999],[239.80021289999999]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Index (1994-95=100)","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

Figure 10: Capital services for the health care industry using different rates of return
	Health care	Health care (8% return)	Health care (tax parameter off)
1994-95	100	100	100
1995-96	103.7031606	103.7378521	103.6991702
1996-97	108.8183345	108.5536254	108.7590022
1997-98	116.1720422	115.2376707	115.9220224
1998-99	121.6281043	120.3950753	121.3991756
1999-00	127.5636467	126.3976116	127.4574019
2000-01	134.04322	132.9739407	134.1768485
2001-02	141.0041599	139.3654617	141.1904278
2002-03	149.1573198	146.5711551	149.3076227
2003-04	159.8398276	155.6677231	159.8101584
2004-05	170.8574725	165.8044255	170.6800867
2005-06	181.2598213	176.2568484	181.1853113
2006-07	193.1482051	188.4370059	193.1747175
2007-08	206.3379587	202.6084438	206.540286
2008-09	221.9761593	217.7381072	222.2792959
2009-10	238.4550513	231.5667495	238.8114905
2010-11	253.8374688	245.3790345	254.5603811
2011-12	264.5437682	255.4812052	265.5385008
2012-13	277.2693108	267.4904296	278.5531177
2013-14	290.1660837	279.5412928	291.585799
2014-15	303.420577	291.9802693	304.8003002
2015-16	315.5590628	303.8940735	316.7179246
2016-17	327.6102269	315.6802117	328.5742952
2017-18	341.3929845	329.0719941	342.2008095
2018-19	356.0749455	343.0941809	356.9266615
2019-20	370.7236918	357.1322034	371.6186635

Figure 10: Capital services for the health care industry using different rates of return

["","Health care","Health care (8% return)","Health care (tax parameter off)"]

[["1994-95","1995-96","1996-97","1997-98","1998-99","1999-00","2000-01","2001-02","2002-03","2003-04","2004-05","2005-06","2006-07","2007-08","2008-09","2009-10","2010-11","2011-12","2012-13","2013-14","2014-15","2015-16","2016-17","2017-18","2018-19","2019-20"],[[100],[103.7031606],[108.81833450000001],[116.17204220000001],[121.6281043],[127.56364670000001],[134.04321999999999],[141.00415989999999],[149.15731980000001],[159.83982760000001],[170.8574725],[181.2598213],[193.14820510000001],[206.3379587],[221.97615930000001],[238.45505130000001],[253.83746880000001],[264.54376819999999],[277.26931080000003],[290.1660837],[303.42057699999998],[315.55906279999999],[327.61022689999999],[341.39298450000001],[356.07494550000001],[370.72369179999998]],[[100],[103.7378521],[108.5536254],[115.2376707],[120.3950753],[126.3976116],[132.97394070000001],[139.3654617],[146.5711551],[155.66772309999999],[165.80442550000001],[176.2568484],[188.4370059],[202.6084438],[217.7381072],[231.56674949999999],[245.37903449999999],[255.48120520000001],[267.49042960000003],[279.54129280000001],[291.98026929999997],[303.89407349999999],[315.68021169999997],[329.07199409999998],[343.09418090000003],[357.13220339999998]],[[100],[103.6991702],[108.7590022],[115.9220224],[121.39917560000001],[127.45740189999999],[134.17684850000001],[141.19042780000001],[149.3076227],[159.81015840000001],[170.6800867],[181.1853113],[193.17471750000001],[206.54028600000001],[222.27929589999999],[238.81149049999999],[254.5603811],[265.53850080000001],[278.55311769999997],[291.58579900000001],[304.80030019999998],[316.7179246],[328.57429519999999],[342.20080949999999],[356.92666150000002],[371.61866350000003]]]

[]

[{"axis_id":"0","tick_interval":"","axis_min":"","axis_max":"","axis_title":"","precision":-1,"axis_units":"","tooltip_units":"","table_units":"","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

[{"value":"0","axis_id":"0","axis_title":"Index (1994-95=100)","axis_units":"","tooltip_units":"","table_units":"","axis_min":null,"axis_max":null,"tick_interval":null,"precision":"-1","data_unit_prefix":"","data_unit_suffix":"","reverse_axis":false}]

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

APA

Citation

Experimental capital service indexes for non-market industries

APA

Citation

Introduction

Footnote

Capital service indexes

Productive capital stock

Footnote

Rental prices

Footnote

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

Footnote

Experimental rental prices for the health care and education industries

Experimental indexes of capital services

Footnote

Sensitivity testing

Conclusion

References

Provide feedback