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, 1990-2013 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.

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

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 5216.0 (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.

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.

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

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

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.

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

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)

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.

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 2013. 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,

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.

Net Capital Stock, Ownership Transfer Costs

Net Capital Stock, Non-Dwelling Construction

Net Capital Stock, Machinery and Equipment

Net Capital Stock, Cultivated Biological Resources

Net Capital Stock, Intellectual Property Products

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

Further research and conclusion Productive Capital Stock series 1990-2015 to be completed in October 2015 The data should be treated with caution due to the sensitivity of the estimates to assumed PIM parameters

Thank you. Any questions?