Reviewing the ONS’ Perpetual Inventory Model and Capital Stock EstimationChris 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 timeGross 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 guidanceSystem 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 periodicitye.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 standardsMoved 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

Inter-mediate

Weibull geometric yes mid 1 1, ex 0.96 0.70

ONSstandard

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 indexe.g. 0.96 means ‘intermediate method gives a total

gross stock of 4% less than the R&D method in 2012’

• Differences are bigcareful 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 environmentmay 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/method-quality/specific/gss-methodology-series/ons-working-paper-series/index.html

• Capital Stocks, Consumption of Fixed Capital 2013 ONS Statistical Bulletin

Available at: http://www.ons.gov.uk/ons/rel/cap-stock/capital-stock--capital-consumption/index.html