Chapter 6. Methodological chapter

Productivity measures for the total economy

Productivity measures at industry level

The conceptual approach used to estimate productivity at industry level follows that for the total economy. However the same quantity (and quality) of data that is available for the whole economy estimates is not always available at the detailed industry level. Hence some approximations are necessary and, so, some differences may prevail between the whole economy estimates and those at industry level.

Productivity measures at industry level are computed for 14 economic activities, each defined in accordance with the International Standard Industrial Classification of All Economic Activities (ISIC) Rev.4.

Further reading

OECD (2001), Measuring Productivity – OECD Manual: Measurement of Aggregate and Industry-Level Productivity Growth, OECD Publishing, Paris, https://doi.org/10.1787/9789264194519-en.

OECD (2009), Measuring Capital – OECD Manual, Second edition, OECD Publishing, Paris, https://doi.org/10.1787/9789264068476-en.

Colecchia, A. and P. Schreyer (2002), “The contribution of information and communication technologies to economic growth in nine OECD countries”, OECD Economic Studies, Vol. 2002/1, https://doi.org/10.1787/eco_studies-v2002-art5-en.

Schreyer, P. (2002), “Computer Price Indices and International Growth and Productivity Comparisons”, Review of Income and Wealth, Series 48, Number 1.

Schreyer, P. (2004), “Capital Stocks, Capital Services and Multi-Factor Productivity Measures”, OECD Economic Studies, Vol. 2003/2, https://doi.org/10.1787/eco_studies-v2003-art11-en.

Schreyer, P., P. Bignon and J. Dupont (2003), “OECD Capital Services Estimates: Methodology and a First Set of Results”, OECD Statistics Working Papers, No. 2003/06, OECD Publishing, Paris, https://doi.org/10.1787/658687860232.

Hours worked for productivity analysis – main definitions

Within the OECD Productivity Statistics (database)(PDB), the underlying concept for labour input is total hours actually worked by all persons engaged in production. It is instructive to consider the relationship between this concept and related measures of working time (Table 6.1):

• Hours actually worked – hours actually spent on productive activities;

• Hours usually worked – the typical hours worked during a short reference period such as a week over a longer observation period;

• Hours paid for – the hours worked for which remuneration is paid;

• Contractual hours of work – the number of hours that individuals are expected to work based on work contracts;

• Overtime hours of work – the hours actually worked in excess of contractual hours; and

• Absence from work hours – the hours that persons are expected to work but do not work.

Table 6.1. Relationship between different concepts of hours worked

Total economy, percentage point contributions at annual rate

Note: Establishing the relationship between normal hours and the five other concepts is not possible, as normal hours are established on a case-by-case basis.

Source: ILO (2008), Measurement of working time, 18^th ICLS.

 https://doi.org/10.1787/888933477593

Because productivity analysis is interested in measuring the inputs used in producing a given output, the underlying concept for labour input should include all hours used in production, whether paid or not. They should exclude those hours not used in production, even if some compensation is received for those hours. As such the relevant concept for measuring labour input is hours actually worked. The productive or non-productive characteristic of an activity is determined by its inclusion in, or exclusion from, the SNA production boundary. Hours actually worked are defined as (ILO, 2008):

• the hours spent directly on productive activities or in activities in relation to them (maintenance time, cleaning time, training time, waiting time, time spent on call duty, travelling time between work locations);

• the time spent in between these hours when the person continues to be available for work (for reasons that are either inherent to the job or due to temporary interruptions); and

• short resting time.

Conversely, hours actually worked should exclude:

• annual leave and public holidays;

• longer breaks from work (e.g. meal breaks);

• commuting time (when no productive activity is performed); and

• educational activities other than on-the-job training time.

Measuring hours worked

In general, Labour Force Surveys (LFS) are the main source used to compile hours worked data in a majority of countries. LFS is most often also the principal underlying source for total hours worked estimates in National Accounts – the main source ultimately used in the OECD Productivity Statistics (database). LFS include questions on the number of hours actually and usually worked in the reference period, i.e. questions concerning the differences between the time usually spent working and the time actually worked during the reference week. Additional LFS questions concerning working time components such as work at home, commuting time, short breaks, overtime and absence from work are also often available.

Continuous labour force surveys are especially appropriate for measuring working time as they allow direct collection of data on hours actually worked throughout the year. This method is known as the direct method, as it is based on a direct measure of average actual hours of work during each week of the year, effectively taking into account all types of absences from work and overtime.

However, when LFS are not continuous, the direct method to measure actual hours worked during the year is not applicable. In these cases, estimates are built using the component method. Thereby, data are collected for a specific reference week (e.g. one week during a month) and complemented with other data to build annual estimates of actual hours worked during the year. The component method starts with the usual hours of work collected in the LFS and then adjusts for absences from work such as holidays, bank holidays, illness, maternity leave, overtime, etc. Annual totals are then derived by scaling up the weekly estimate.

In some countries, LFS are not used or are complemented with information from other sources. Among such other sources are the following:

• Establishment (and enterprise) surveys. These are typically the main source of information for hours worked estimates by industry. One of the main drawbacks of this source is that the data collected generally refer to hours paid rather than actual hours worked, hence include paid absences and exclude unpaid overtime.

• Population census. These cover the whole population and are often used as a benchmark for most household surveys including LFS. The main disadvantage is the low frequency of data collection (normally carried out every 5 or 10 years).

• Administrative records, such as social security and tax registers. These are the main sources of information for adjusting data from labour force surveys and establishment surveys to obtain estimates of absences from work due to illness, maternity leave, occupational injuries, strikes and lockouts.

• Time Use Surveys. These are useful to compare the results from other sources but their irregularity, low frequency and limited international comparability is a drawback. Labour force survey based estimates of working time typically over-report hours worked when compared with estimates from time use surveys.

For the purposes of productivity analysis, consistency of LFS based data on hours worked with National Accounts concepts needs to be ensured (OECD, 2009; Ypma and van Ark, 2006). This implies adjusting the coverage of activities included in the LFS to that used to compute GDP, and adapting the geographical and economic boundaries of employment to GDP. The notion of economic territory used to compute GDP refers to the domestic concept, i.e. resident persons working outside the country are excluded. Some of these adjustments can be considered as negligible for most countries although they are made in all countries. Likewise, measures of hours actually worked should refer to productive activities within the SNA production boundaries (by definition); persons spending time on productive activities excluded from the original sources should therefore be included.

In general, when LFS is the main source of information for employment, adjustments concern persons outside the LFS universe but who need to be included as persons engaged in production, as defined in the SNA. The causes for differences between these two measures are:

• age threshold: for example, people under 15 engaged in production are generally not included in LFS estimates;

• non-coverage of particular groups: persons living in collective households, armed forces, and non-resident persons working within the economic territory of the country are generally not surveyed in LFSs;

• non-coverage of certain activities: the LFS may not include hours worked in certain activities such as subsistence work and volunteer work;

• non-coverage of some territories: the LFS may not cover the entire economic territory covered in GDP.

• Table 6.2 describes the main strengths and limitations of the primary sources typically used to compute hours worked and employment estimates in national accounts.

• In practice, the effective quantity of labour input depends not only on the total number of hours actually worked but also on the characteristics of those performing the work, like education, working experience, business function and sex. The measure of labour input used in this publication, i.e. total number of hours worked, does not account for the composition or heterogeneity of the labour force, thus ignoring changes in the quality of labour (i.e. human capital). This implies treating workers as perfect substitutes: an hour worked by a highly-experienced surgeon and an hour worked by an eighteen-year old student employed in a fast-food are treated as equal amounts of labour. Unadjusted measures of labour input, i.e. total number of hours worked, underestimate the effective use of labour in production affecting cross-country comparability.

Hours worked data in the OECD Productivity Statistics (database) (PDB)

In the PDB, the main requirement is that the most internationally comparable hours worked data are used (OECD, 2007). The preferred source for total hours worked is National Accounts, which are presented in the OECD National Accounts Statistics (database), both for the total economy and for aggregate economic activities. However, long time series of hours worked are not available for a number of countries; in which case, the Secretariat estimates hours worked using the OECD Employment and Labour Market Statistics (database). Total economy estimates of average hours actually worked per year and per person employed are currently available on an annual basis, for all 35 OECD member countries and some key partner economies as follows:

• Actual hours worked are primarily sourced from the OECD National Accounts Statistics (database) for Australia, Austria, Belgium, Canada, Costa Rica, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Israel, Italy, Korea, Latvia, Lithuania, Luxembourg, Mexico, the Netherlands, Norway, Poland, Portugal, the Slovak Republic, Slovenia, South Africa, Spain, Sweden, Switzerland, the United Kingdom and the United States.

• Actual hours worked are sourced from the OECD Employment and Labour Market Statistics (database) for Chile, Iceland, Japan, New Zealand, the Russian Federation and Turkey.

• For some countries, longer time series and/or more recent estimates of total hours worked are derived from the OECD Economic Outlook: Statistics and Projections (database) and national sources.

Further reading

Ahmad, N. et al. (2003), “Comparing Labour Productivity Growth in the OECD Area: The Role of Measurement”, OECD Science, Technology and Industry Working Papers, No. 2003/14, https://doi.org/10.1787/126534183836.

ILO (2008), Measurement of working time, 18th ICLS.

OECD (2007), “Factors explaining differences in hours worked across OECD countries”, Document prepared for the Working Party No. 1 on Macroeconomic and Structural Policy Analysis, September 2007.

OECD (2009), “Comparability of labour input measures for productivity analysis”, Document prepared for the OECD Working Party on National Accounts, November 2009, www.oecd.org/officialdocuments/publicdisplaydocumentpdf/?doclanguage=en&cote=std/cstat/wpna(2009)11.

Ypma, G. and B. van Ark (2006), “Employment and Hours Worked in National Accounts: A Producer’s View on Methods and a User’s View on Applicability”, EU KLEMS Working Paper No. 10.

Introduction

Two key measures of capital stock exist. The first is the productive capital stock, which looks at capital in its function as a provider of capital services in production. The second is gross (or net) capital stock, which captures the role of capital as a store of wealth.¹ This section provides supplementary information on these two measures, on the approaches used to estimate them and on capital measures available at the OECD.

Definitions

Measuring capital input

In general, capital stock series are not directly measured. In common with most measures presented in the national accounts, they are estimated by national statistics institutes using available data on gross fixed capital formation (investment) with local methodology and assumptions – although there is increasing convergence towards international standards. There are heavy data requirements for the estimation of capital stocks which include the following:

• a benchmark level of capital stock for at least one year (preferably by asset type);

• a long-time-series of investment volumes and price deflators (preferably by asset type);

• as much asset type detail as possible;

• depending on the type of capital stock being estimated, estimates of average services lives by asset and/or depreciation rates for each asset;

• industry-by-asset-type investment matrices for capital stock by industry.

Capital measures in OECD statistics

Several OECD databases, described below, contain capital stock data. However some differences exist between them:

• The origin of the data. In some of the databases described below only official data made available to the OECD by national statistics institutes are used. In other databases however, particularly those that are considered more analytical databases, such as the OECD Productivity Statistics (database), other sources are often used to estimate missing data or to create estimates based on comparable estimation techniques.

• The coverage of the data. As shown in Table 6.3 below, some databases are confined to aggregate statistics, such as the OECD Economic Outlook: Statistics and Projections (database) or OECD Productivity Statistics (database). Others provide a break-down by industry, such as the OECD Structural Analysis Statistics (database) and the OECD National Accounts Statistics (database).

• The capital stock variable. The OECD Productivity Statistics (database) measures productive capital stocks (and therefore, capital services) whereas the OECD Structural Analysis Statistics (database) and OECD National Accounts Statistics (database) contain measures of net and/or gross (wealth) capital stocks.

How to access OECD capital input measures

• Aggregate capital services series in the OECD Productivity Statistics (database), along with methodological information and analytical papers and publications can be found on the OECD Productivity Statistics website on www.oecd.org/std/productivity-stats/ or on the OECD Productivity Statistics (database) on OECD.Stat, within the theme Productivity, then selecting Growth in GDP per capita, productivity and ULC, and then Growth in capital input;

• Data on gross/net capital stocks by industry can be found in the OECD Structural Analysis Statistics (database) on: www.oecd.org/sti/stan;

• Gross/net capital stocks in the OECD National Accounts Statistics (database) can be found under the theme of the national accounts via: http://stats.oecd.org/, then selecting Annual National Accounts; Main Aggregates; Detailed Tables and Simplified Accounts; Fixed Assets by Activity and by Type of Product;

• Data used for the OECD Economic Outlook, such as the total economy productive capital stock volume series, are published separately and can be found under the item Supply Block through the current Economic Outlook theme on OECD.Stat (http://stats.oecd.org/).

Notes

For more information on capital measures and their uses see OECD (2001, 2009) and Schreyer (2004).

In the PDB, the following average service lives are currently assumed for the different assets: 7 years for computer hardware, 15 years for telecommunications equipment, other machinery and equipment and weapons systems and transport equipment, 40 years for non-residential construction, 3 years for computer software and databases, 10 years for research and development and 7 years for other intellectual property products.

Further reading

OECD (2001), Measuring Productivity - OECD Manual: Measurement of Aggregate and Industry-Level Productivity Growth, OECD Publishing, Paris, https://doi.org/10.1787/9789264194519-en.

OECD (2009), Measuring Capital – OECD Manual, Second edition, OECD Publishing, Paris, https://doi.org/10.1787/9789264068476-en.

OECD (2010), OECD Handbook on Deriving Capital Measures of Intellectual Property Products, OECD Publishing, Paris, https://doi.org/10.1787/9789264079205-en.

Colecchia, A. and P. Schreyer (2002), “The contribution of information and communication technologies to economic growth in nine OECD countries”, OECD Economic Studies, Vol. 2002/1, https://doi.org/10.1787/eco_studies-v2002-art5-en.

Schreyer, P. (2002), Computer Prices Indices and International Growth and Productivity Comparisons, Review of Income and Wealth, Number 1, Series 48.

Schreyer, P. (2004), “Capital Stocks, Capital Services and Multi-Factor Productivity Measures”, OECD Economic Studies, Vol. 2003/2, https://doi.org/10.1787/eco_studies-v2003-art11-en.

Schreyer, P., P. Bignon and J. Dupont (2003), “OECD Capital Services Estimates: Methodology and a First Set of Results”, OECD Statistics Working Papers, No. 2003/06, OECD Publishing, Paris, https://doi.org/10.1787/658687860232.

System of National Accounts (SNA) 2008, New York, http://unstats.un.org/unsd/nationalaccount/sna2008.asp.

The 2008 SNA – changes from the 1993 SNA

In 2009, The United Nations Statistical Commission endorsed a revised set of international standards for the compilation of national accounts: the System of National Accounts (SNA) 2008, replacing the 1993 version of the SNA. For Chile and Colombia, the indicators presented in this publication are in line with the 1993 SNA. For the Russian Federation, the indicators are in line with the 1993 SNA until 2013 and with the 2008 SNA from 2014 onwards. For all the other countries, the indicators are based on 2008 SNA. The 2008 SNA includes a number of changes from the 1993 SNA and was adopted by most OECD countries at the end of 2014.

Changes affecting whole economy levels of income

For the United States, the adoption of the 2008 SNA in 2013 raised the level of GDP by 3.6 per cent, mainly due to the recognition of new forms of gross fixed capital formation (GFCF), notably Research and Development (R&D). The revision was also an opportunity for countries to implement some additional changes made in the 1993 SNA, which recognised entertainment originals as fixed assets. In addition changes were also made for the 2008 SNA recommendations on ownership transfer costs (see below). Current consumption expenditures of government in recent years were also revised downwards, reflecting 2008 SNA recommendations on defined benefit pensions plans as well as the net (of depreciation) effects of removing R&D expenditures from current consumption (see also below).

Re-allocating income across categories

Further reading

System of National Accounts (SNA) 1993, New York, http://unstats.un.org/unsd/nationalaccount/sna1993.asp.

System of National Accounts (SNA) 2008, New York, http://unstats.un.org/unsd/nationalaccount/sna2008.asp.

Van de Ven, P. (2015), “New standards for compiling national accounts: What’s the impact on GDP and other macro-economic indicators?”, OECD Statistics Brief, No. 20, OECD Publishing, Paris, www.oecd.org/std/na/new-standards-for-compiling-national-accounts-SNA2008-OECDSB20.pdf.

The price index-productivity link

Empirical evidence presented in this publication points to relatively low productivity growth rates over long periods for several service industries. This is true even for some business sector services for which rapid technological change and increasing competitive pressures may argue for an opposite trend. However, for some services, this evidence may reflect an under-estimation of service productivity growth, linked to difficulties measuring price indices, and hence volume series of services value added (Wölfl, 2003). While problems estimating an appropriate price index may arise in several manufacturing industries, there are reasons that measurement problems may be stronger in the service sector than in manufacturing.

Because of the difficulty in measuring services producer price indices (SPPIs), different methods are used in OECD countries to compute volume series of value added. Moreover, even if producer price indices can be computed, different methods are typically used depending on the type of the service under consideration as well as data and availability. Over the past 10 years, much progress has been made by OECD countries in measuring SPPIs, in particular in business sector services. This has significantly increased the availability of SPPIs and has improved their comparability across countries. However, even where SPPIs have been computed, they are based on different pricing methods across industries and countries, potentially affecting comparability of productivity growth estimates.

General measurement issues when tracking price changes for services

Measurement of price changes in services is not trivial, in large part complicated by the way businesses provide and charge for services, by problems identifying quality change, through the provision of bundled services, and by the difficulty identifying separate price indices per end-user.

The potential role of price measurement for measured productivity growth

Table 6.4 provides some indication of the potential effects on volume series of value added that may result from using different deflators for two services “telecommunication services”, on the one hand, and “legal and accounting services”, on the other.¹ These services provide two interesting examples of how price index measurement could impact on measured productivity growth.² They are i) characterised by very different factors of service output and the way they are provided, and ii) by different availability of producer price indices and underlying methods.

The table provides evidence for France and the United States, for which time series data are available for a large range of input and output variables, such that several different price and volume indices can be derived. The different deflators compared are those that are commonly used in countries either directly for a deflator of value added or as a reference for the computation of producer price indices:

• Services Producer Price Indices (SPPI). From a methodological point of view, using SPPIs, especially in the form of a price of final service output as defined above, would represent the most appropriate way to deflate value added if the aim is the computation of productivity growth. Ideally, SPPIs would exist for both, gross output and intermediate inputs used in producing the good or service under consideration, and SPPIs would adjust for quality changes so that the resulting value added volume series reflect productivity growth changes properly.

• Consumer Price Indices (CPI), for goods or services that are close to the services analysed, or the CPI All items. Using CPI’s for deflation may result in measurement biases vis-à-vis SPPIs as they cover only household consumption and are not valued in basic prices. This may be particularly relevant for those services where the share of final household consumption in total output is low, and where price changes differ significantly between intermediate (business) and final use (consumption) (Eurostat, 2001).

• Wage rate indices per employed person or per hour worked (WRIE, WRIH). The latter can be seen as a proxy for a time-based producer price index as defined above. Productivity growth rates based on wage rate indices may underestimate true productivity developments.

The table suggests that the choice of the implicit value added deflator, or the pricing method for computing producer price indices, may matter significantly for measured labour productivity growth. For instance, in telecommunication services, average annual labour productivity growth rates over the 2000-11 period would differ by between 5 percentage points (United States, both periods) and 10 percentage points (France, 2005-11) using different deflators. In the case of legal services, the overall variation is with 1 to 4 percentage points lower, but still significant, especially given the generally lower level of productivity growth in this services activity.

This exercise is of a purely hypothetical nature. Its aim is merely to illustrate the sensitivity of value added volume series and hence productivity growth to price index methods.

In the empirical results presented in Table 6.4, labour productivity growth has been calculated as real value added per employment and not per hour worked. While hours worked is typically the more appropriate measure of labour input, employment has been chosen here for data availability reasons.

Further reading

Loranger, A. (2012), “Quality Change for Services Producer Price Indexes”, paper presented at the Group of Experts on Consumer Price Indices, Geneva, Switzerland, 30 May 30-1 June 2012.

Eurostat (2001), Handbook on price and volume measures in national accounts, Eurostat, Luxemburg.

Wölfl, A. (2003), “Productivity Growth in Service Industries: An Empirical Assessment of Recent Patterns and the Impact of Measurement”, Science, Technology and Industry Working Paper 2003-07, OECD Publishing, Paris, https://doi.org/10.1787/086461104618.

Definition

Purchasing power parities (PPPs) are the rates of currency conversion that equalise the purchasing power of different currencies by eliminating the differences in price levels between countries. In their simplest form, PPPs are price relatives which show the ratio of the prices in national currencies of the same good or service in different countries. In this sense, they are spatial price comparisons.

Levels of GDP in a given year, when converted with PPPs, measure the size of economies in volume terms and so provide a more meaningful measure of the relative size of countries than simple exchange-rate based comparisons. Indeed, exchange rates reflect so many more influences than the direct price comparisons that are required to make volume comparisons. Furthermore, they tend to exhibit large movements over short periods of time, implying rapid changes in living standards which cannot have possibly occurred.

GDP and its components, converted using PPPs, provide a snapshot of relative volumes in a particular year. For many analytical purposes, the interest is in the evolution of GDP volumes between countries and over time. There are at least two ways of setting up such a comparison, each with its specific interpretation and use.

Current PPPs and expenditures (comparison at current international prices)

One approach for combining spatial and temporal observations is to use a sequence of current PPPs, i.e., a new set of price data for every period, compiled, weighted and aggregated to yield rates of currency conversion for total GDP and its expenditure components. With current PPPs, prices and price structures are allowed to vary over time. Volume levels of GDP are then obtained by applying these current PPPs, for every period, to GDP measures at current national prices. For a given year, (spatial) comparisons between countries are straightforward – volumes are measured with the same price structure. Comparisons of the resulting series over time, however, incorporate several effects: relative volume changes, changes in relative prices between countries and, possibly, changes in definitions and methodologies. The approach can also be described as comparisons at current international prices or current PPPs.

Constant PPPs and expenditures (comparison at constant international prices)

A second approach is to generate time series at constant prices and constant PPPs. With constant PPPs, a single year is chosen for the comparison of GDP levels and all other observations are obtained by applying relative rates of GDP growth, consistent with those derived in national currencies. This procedure ensures transitivity over space and time. The approach can also be described as comparisons at constant international prices or at constant PPPs. The key conceptual difference between using current and constant PPPs is that the former capture changes in volume as well as changes in weights, whereas the latter only capture volume changes. Put differently, even if the volumes of goods and services remain identical over time, a GDP comparison based on current PPPs may change over time if prices and price structures shift. Ignoring such shifts over longer periods can generate a biased picture of economic developments. This factor comes into play when some countries are large producers and exporters of products with marked price changes, for example Norway, which is an important oil exporter. Another consequence of fixing price structures to a base year is the sensitivity of results to the choice of the base year.

How are PPPs calculated?

PPPs are calculated in three stages:

• first for individual products,

• then for groups of products or basic headings and,

• finally, for groups of basic headings or aggregates.

The PPPs for basic headings are un-weighted averages of the PPPs for individual products. The PPPs for aggregates are weighted averages of the PPPs for basic headings.

The weights used are the expenditures on the basic headings. PPPs at all stages are price relatives. They show how many units of currency A need to be spent in country A to obtain the same volume of a product or a basic heading or an aggregate that X units of currency B purchases in country B.

In the case of a single product, the “same volume” means “identical volume”. But in the case of the complex assortment of goods and services that make up an aggregate such as GDP, the “same volume” does not mean an “identical basket of goods and services”.

The composition of the basket will vary between countries according to their economic, social and cultural differences, but each basket will provide equivalent satisfaction or utility.

• Values at constant international prices of period t₀ (at PPPs of period t₀)

Values at constant international prices of period t0 (at PPPs of period t0) are series at current domestic prices converted to a common currency by way of constant PPPs of a given year.

Constant PPPs capture volume changes only.

A value index of this kind corresponds to a weighted average of the value changes in domestic prices, as PPPs are held fixed.

• Values at constant international prices of period t_-1 (at PPPs of period t_-1)

Values at constant international prices of period t_-1 (at PPPs of period t_-1) are series at current domestic prices converted to a common currency by way of PPPs of year t_-1.

A value index of this kind corresponds to a weighted average of the value changes in domestic prices, as PPPs are held fixed at their previous year’s value. However, weights are continuously updated.

• Values at current international prices (at current PPPs)

Values at current international prices (at current PPPs) are series at current domestic prices converted to a common currency by way of current PPPs. Because PPPs are price relatives of goods and services, this implies substituting the set of domestic prices by a set of international prices.

Current PPPs capture changes in volumes and in relative prices.

PPPs produced at the OECD are intended for whole economy cross-country comparisons of GDP and consumption across countries. They are derived through a collection of prices of final demand components and, as such, while they provide a sound basis for whole economy comparisons, they should not be used for comparisons across industries, especially for sectors whose prices are determined internationally.

Further reading

OECD/Eurostat (2012), Eurostat-OECD Methodological Manual on Purchasing Power Parities (2012 Edition), OECD Publishing, Paris, https://doi.org/10.1787/9789264189232-en.

OECD (2008), OECD Glossary of Statistical Terms, OECD Publishing, Paris, https://doi.org/10.1787/9789264055087-en.

OECD, Purchasing Power Parities (PPP), www.oecd.org/std/prices-ppp/.

Bournot S., F. Koechlin and P. Schreyer (2011), “2008 Benchmark PPPs Measurement and Uses”, OECD Statistics Brief, No. 17, OECD Publishing, Paris, www.oecd.org/std/47359870.pdf.

Schreyer, P. and F. Koechlin (2002), “Purchasing power parities – measurement and uses”, OECD Statistics Brief, No. 3, OECD Publishing, Paris, www.oecd.org/std/prices-ppp/2078177.pdf.

The Hodrick-Prescott filter

The HP filter is the best known and most widely used method to separate the trend from the cycle (Hodrick and Prescott, 1997). The method has been first presented in a working paper in 1981 (Hodrick and Prescott, 1981). The filter is defined as the solution to the following optimisation problem:

where y_t is the original series, t _t is the trend component and c_t is the cyclical component. The method consists in minimising the deviation of the original series from the trend (the first term of the equation) as well as the curvature of the estimated trend (the second term). The trade-off between the two goals is governed by the smoothing parameter λ. The higher the value of λ, the smoother is the estimated trend.

For quarterly data it has been typically assumed a value of λ = 1600, as recommended by Hodrick and Prescott (1997). However, there is less agreement on the value to be used when the filter is applied to other frequencies (e.g. annual, monthly). Backus and Kehoe (1992) used λ = 100 for annual data, while Ravn and Uhlig (2002) propose an adjustment of the standard value of 1600 that consists of multiplying that value by the fourth power of the frequency of observations relative to quarterly data. The latter results in a value of λ equal to 6.25 (= 1600*(1/4)⁴) for annual data.1

The HP-filter can be interpreted in the frequency domain. In this formulation the λ parameter can be associated with the cut-off frequency of the filter – the frequency at which it halves the impact of the original cyclical component. It can be shown that the Ravn-Uhlig rule for selecting the value of λ corresponds to a cut-off frequency of approximately 10 years, assuming annual data (Maravall and Del Río 2001). Nonetheless, Nilsson and Gyomai (2011) point out that the HP-filter has strong leakages (i.e. letting cyclical components from the stop band appear in the filtered series), and this feature may affect the choice of the filter parameter depending on the goal of the study and sensitivity to filter leakage.

In this publication, the target frequency for trend estimation was no different than in the above studies (10 years and beyond). However an additional objective is to minimize the leakage from shorter business-cycle frequencies into the estimated trend. Accordingly, the value of the smoothing parameter selected here is λ = 54.12. This value has been determined by calibrating the Hodrick-Prescott filter in such a way that the frequency response at 9.5 years is equal to 0.10. This means that with λ = 54.12, cycles with a wavelength lower than 9.5 years would be attenuated by 90% or more.

In comparison with other ideal filters, the trend estimated with the HP filter is more sensitive to transitory shocks or short-term fluctuations at the end of the sample period. This results in a sub-optimal performance of the HP filter at the endpoints of the series (Baxter and King, 1999). In view of this property, in order to lessen revisions of the published estimates, trend series are not published for the first two years and the last two years for which data on the original series are available. Even though, the choice of the HP filter is based on its interpretability and widespread use in the literature.

The frequency of observations relative to quarterly data is 1/4 for annual data and of 3 for monthly data.

Further reading

Backus, D. and P. Kehoe (1992), “International evidence on the historical properties of business cycles”, The American Economic Review, Vol. 82, No. 4.

Baxter and King (1999), “Measuring business cycles: approximate band-pass filters for economic time series”, The Review of Economics and Statistics, Vol. 81, No. 4.

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