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 1Method 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 retiredeprecateright truncate purchase time price type min, max GrossNet R&DWeibullgeometricnostart20, ex11 Inter- mediate Weibullgeometricyesmid11, ex ONS standard normallinearyesmid1μ±4·σ 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 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: quality/specific/gss-methodology-series/ons-working-paper- series/index.html Capital Stocks, Consumption of Fixed Capital 2013 ONS Statistical Bulletin Available at: stock--capital-consumption/index.html