Reviewing the ONS’ Perpetual
Inventory Model and Capital
Stock Estimation
Chris Stapenhurst - National Accounts
Strategy, Change and Support
Capital Stocks
• An asset which is (intended to be) used as a factor of
production for more than one year is classified as a
capital asset.
• Capital stock refers to the value of all stocks in an
economy at a given point in time
Gross stock – purchase value of existing stocks
Net stock – sale value of existing stocks
Consumption of Fixed Capital (flow) – value of capital
depreciation over a period
• Relevant to questions about:
National wealth
Rates of return (on capital)
Productivity measures
ONS’ Capital Stocks Review
• ONS is reviewing its methods of measuring
capital stocks in the context of recent Quality
Review (NSQR) and international guidance
System of National Accounts 2008
European System of Accounts 2010
Measuring Capital OECD manual 2009
• Developing an offline prototype system in R
trial new methods
carry out sensitivity analysis
possibly an open source PIM package
Perpetual Inventory Model (PIM)
• Direct estimation (surveying all assets in the
stock) is expensive
• Instead sum up previous expenditure on
capital assets (accumulated investment)
deducting retirement gives gross stock
deducting depreciation gives net stock
• Typically applied to a specific class
(industry/sector/type) of asset with a given
periodicity
e.g. spanners purchased by cycle industry in
financial sector every year
Perpetual Inventory Method
Vintage columns are summed to give stock
Degree of saturation indicates value of assets
Assumptions Underlying the PIM
• The Retirement Distribution describes when
assets cease to be used in production (as a
result of wear and tear or obsolescence)
• An age-price profile describes how the value
of a single asset changes over the course of
its life
• These can be combined to describe how the
value of a cohort of assets changes over time
• C.f. A note on distributions used when
calculating estimates of consumption of fixed
capital
Price profile of a cohort
Method 1
Method 2
Generalised PIM
• Previous PIM only allows for normally
distributed retirement and linear depreciation
combined by method 1
• Prototype gives a choice of
normal, lognormal, gamma and Weibull retirement
distributions
linear, geometric, hyperbolic and double declining
balance depreciation
Method 1 or method 2 profile combinations
• Allows for sensitivity analysis and more
representative modeling
Comparison of methods results
• An experimental PIM method for Research
and Development (R&D) was developed in
line with international standards
Moved into production in 2014
• We compare this method with standard ONS
method using the R&D dataset
Comparison of methods
retire
deprecate
right
truncate
purchase
time
price
type
min,
max
Gross
Net
R&D
Weibull
geometric
no
start
2
0, ex
1
1
Intermediate
Weibull
geometric
yes
mid
1
1, ex
0.96
0.70
ONS
standard
normal
linear
yes
mid
1
μ±4·σ
1.01
1.38
• Sum up the stocks of all assets in 2012 under
each method and divide by the same sum of
assets under R&D method to give stock index
e.g. 0.96 means ‘intermediate method gives a total
gross stock of 4% less than the R&D method in
2012’
• Differences are big
careful parameter choice is important
Conclusion
• Parameter choices can have substantial
impacts on stocks and capital consumption
• Also looking at impacts of
purchases of second hand assets
recording of terminal costs
premature scrappage and catastrophic losses
• Incorporate capital stocks into value index of
capital service (VICS)
• Able to work using open source software
outside of production environment
may make open source PIM available
References
• McLaren,C. And Stapenhurst, C. (2014) A note on
distributions used when calculating estimates of
consumption of fixed capital ONS Working Paper Series 3.
Available at: http://www.ons.gov.uk/ons/guide-method/methodquality/specific/gss-methodology-series/ons-working-paperseries/index.html
• Capital Stocks, Consumption of Fixed Capital 2013 ONS
Statistical Bulletin
Available at: http://www.ons.gov.uk/ons/rel/cap-stock/capitalstock--capital-consumption/index.html