1. Dr Serguei Mikhailitchenko Lecturer Holmes Institute, Brisbane
11/27/2018 4:58 AM
Net Capital Stock and Consumption of Fixed Capital for the Australian States and Territories,
Dr Serguei Mikhailitchenko
Lecturer
Holmes Institute, Brisbane
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

2. 11/27/2018 4:58 AM
Introduction
This is a data development paper that extends previous studies by
Following the Perpetual Inventory Model used by ABS as close as possible
Presenting the Consumption of Fixed Assets series for the first time
Used age-specific depreciation rate
Used Winfrey survival function rather than a simultaneous exit assumption
Pre-tested the model on published NCS data for Australia before applying it

3. Perpetual Inventory Model (PIM)
11/27/2018 4:58 AM
Perpetual Inventory Model (PIM)
Perpetual Inventory Model (PIM) to estimating NCS series as per Holten (1999) and ABS (2012)
𝑲 𝒕 𝒊𝒋 = 𝑲 𝒕−𝟏 𝒊𝒋 + 𝑰 𝒕 𝒊𝒋 − 𝑫 𝒕 𝒊𝒋 where
𝐾 𝑡 𝑖𝑗 is NCS of asset type i in region j in period t,
𝐾 𝑡−1 𝑖𝑗 is NCS in period t-1; it accounts for accumulated NCS less retirement during the period
𝐼 𝑡 𝑖𝑗 is Gross Fixed Capital Formation (GFCF) (or investment) of asset type i in region j in period t,
𝐷 𝑡 𝑖𝑗 is Consumption of Fixed Capital of asset type i in region j in period t.
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

4. Hyperbolic Age-Efficiency function
𝑬 𝒕 = 𝑴− 𝑨 𝒕 𝑴−𝒃 𝑨 𝒕
where
𝑬 𝒕 is efficiency of a capital asset at a point of time t,
𝑴 is the service life of an asset according to the Winfrey (1938) distribution,
𝑨 𝒕 is the current age of an asset,
b is the asset-specific efficiency reduction parameter.

5. An alternative form of PIM
𝑲 𝒕 𝒊𝒋 = 𝝉=𝟎 𝑻 𝑰 𝒕−𝝉 𝒊𝒋 (𝟏− 𝜹 𝝉 𝒊𝒋 )(𝟏− 𝜽 𝝉 𝒊𝒋 )
𝑰 𝒕−𝝉 𝒊𝒋 is the real value of investment of type i in a region j with the remaining service life of t-τ;
𝜹 𝝉 𝒊𝒋 is the cumulated loss in value of an asset when it reaches the age τ;
𝜽 𝝉 𝒊𝒋 is the cumulated value of retired assets

6. Consumption of Fixed Capital
𝑫 𝒕 𝒊𝒋 = 𝑨 𝒕 =𝟎 𝑻 𝑰 𝒕 𝒊𝒋 𝜹 𝝉 𝒊𝒋 − 𝜹 𝝉−𝟏 𝒊𝒋

7. Winfrey survival function
𝑭 𝑻 = 𝑭 𝟎 (𝟏− 𝑻 𝟐 𝒂 𝟐 ) 𝒎
where
𝑭 𝑻 is the proportion of the cohort retiring at the time period T,
𝑭 𝟎 is the proportion of the cohort retiring at the mean asset service life,
a the parameter that determines the time periods (e.g. a = 10 for decile),
m is the parameter that determines the flatness of the distribution.

8. PIM parameters by type of asset
Winfrey Survival function
Mean service life
Efficiency reduction parameter
Dwellings S3 60
0.75
Alterations and additions S0 35
0.50
Ownership transfer costs 13
Non-dwelling construction
Machinery and equipment 12
Cultivated biological products 6
Intellectual property products
0.00
Public assets 40

9. Data availability
For the states and territories the data for Gross Fixed Capital Formation (GFCF) is available only from 1990 with an exception for Weapons (N/A)
The GFCF data by type for states are available only for the private sector; public sector GFCF series are not disaggregated by type
Intellectual Property GFCF series for the states are not disaggregated by sub-type (R&D, MPE, CS and AO)

10. Estimates of Total Net Capital Stock
This is an unadjusted series. Despite the complexities of the Chain Volume Measures, the additivity of CVM NCS should hold in the base year, which is not the case here (for 2012 the percentage error is 3.7%). The percentage error is diminishing from 6.7% in 1990 to 2.2% in 2008 and then gradually increases to 4.1% in 2013.

11. Estimates of Consumption of Fixed Capital
COFC results are not as good as for NCS. I overestimate COFC by 13% in 1990 and underestimate it by 17% in Some causes might be related to the the stock composition and incorrect assumptions regarding the PIM parameters. The most serious cause of errors might come from NDC estimates due to a large variability in PIM parameters of assets in this class. Also, the changing proportion of computers and peripherals in M&E might have resulted in significant decline of an average service life of M&E stock. Further, with no detailed information about second-hand items and only with the expenditure information, it was impossible to take into account the vintage of these items.
Finally, in the absence of information about assets transferred from public ownership into the private sector,

12. Net Capital Stock, Dwellings
As can be seen, the proportion of private dwellings in the total NCS has declined for Australia as a whole but was slightly up in QLD, TAS and NT. However, for all states, NCS of private dwellings per capita has increased indicating a better quality of life across Australia.

13. Net Capital Stock, Ownership Transfer Costs

14. Net Capital Stock, Non-Dwelling Construction

15. Net Capital Stock, Machinery and Equipment

16. Net Capital Stock, Cultivated Biological Resources

17. Net Capital Stock, Intellectual Property Products

18. Public Net Capital Stock
The growth in public GFCF for Tas was the lowest in Australia and averaged around 2% compared to 7% for Australia as a whole

19. Further research and conclusion
Productive Capital Stock series to be completed in October 2015
The data should be treated with caution due to the sensitivity of the estimates to assumed PIM parameters

20. Thank you.
Any questions?