Quarterly National Accounts, part 4: Quarterly GDP Compilation 1

Quarterly National Accounts, part 4: Quarterly GDP Compilation 1 Introduction This paper continues the series dedicated to extending the contents of the Handbook Essential SNA: Building the Basics 2. In this part of the series we want to explore quarterly national accounts (QNA) compilation 3. We have singled out three issues that are specific to quarterly compilation, having no equivalent in annual national accounts (ANA): Chain-linking of quarterly time-series; Benchmarking of quarterly time-series to annual estimates; Seasonal adjustment of quarterly estimates. In the first paper dedicated to QNA compilation we presented an overview of these three issues and explored chain-linking and benchmarking in some detail 4. We then proceeded to examine seasonal adjustment 5. To complete the exploration of QNA we want to focus on the topic that will be of main interest to the targeted audience of these papers: quarterly GDP compilation. Before going into specific issues related to quarterly compilation we will review some main issues in GDP compilation in general. GDP compilation At the heart of QNA we have quarterly GDP (QGDP) compilation by the two main methods we encountered in earlier papers (production approach and expenditure approach) at current and constant prices. Figure 1 GDP time-series prepared for the production and expenditure approaches GDP by industries is compiled by the GDP by production (output) method (GDP(O), broken down by ISIC industries. This compilation is based on: 1 This paper was initiated and financed by EUROSTAT through the Project Essential SNA: Building the Basics, implemented by DevStat Servicios de Consultoría Estadística in consortium with ICON Institute, for which information can be found at the following link:http://circa.europa.eu/irc/dsis/snabuildingthebasics/info/data/website/index.html 2 Henceforth called the Handbook ; this paper is based on the third (2013) edition; it can be found at the following link: http://epp.eurostat.ec.europa.eu/portal/page/portal/product_details/publication?p_product_code=ks-ra-13-003 3 An upcoming new edition of the Handbook will contain a new chapter on QNA; the aim of this paper is to focus on topics not covered by this new chapter. 4 Quarterly National Accounts, part 1: Main issues 5 Quarterly National Accounts, part 2: Introduction to Seasonal Adjustment; Quarterly National Accounts, part 3: Model based Seasonal Adjustment. 1

Value Added = Gross Output minus Intermediate Consumption To obtain GDP(O), value added is summed over all ISIC industries and net product taxes (taxes minus subsidies) is added 6. We will first illustrate the annual case, which in the next section we will expand to the quarterly frequency. Our example uses the following breakdown: Agriculture (Agri): ISIC section A; Manufacturing (Man) : ISIC section B E ; Services (Serv): all remaining ISIC sections; Product taxes minus product subsidies (Tx). The following table gives an example for the compilation for the years 2010 2012: Agri Man Serv Tx GDP(O) 2010 30 84 68 36 218 2011 33 96 71 40 240 2012 35 110 75 44 264 Table 1 GDP by production approach in current prices We can also obtain GDP(O) in constant prices (in the example given here we use average prices of the previous year). Agri Man Serv Tx GDP(O) 2010 29 83 67 36 215 2011 33 95 70 40 238 2012 34 108 73 43 258 Table 2 GDP by production approach in constant prices (prices previous year) The second approach to GDP compilation used in QNA is the GDP by expenditure method. In this approach we look at the expenditure categories on which income generated from value added is spent. Value added created by production is used up either on final consumption or on gross capital formation, with additional flows from and to ROW (Rest-of-the-World) supplying imports and using up exports. GDP(E) = Final consumption + Gross capital formation + Exports Imports Final consumption consists of: Household Final Consumption Expenditure (HH); NPISH Final Consumption Expenditure (Non-profit Institutions serving households); we will ignore this part here; 6 The GDP by production method in current and constant prices is examined in the following papers in this series: Annual GDP by production approach in current and constant prices: main issues; Agriculture in National Accounts: Value added in current and constant prices; Industry and Construction in National Accounts: Value added in current and constant prices; Services in National Accounts, part 1: Value added in current prices; Services in National Accounts, part 2a: Value added in constant prices; Services in National Accounts, part 2b: Value added in constant prices. 2

Government Final Consumption Expenditure (Gov). The other expenditure categories are: Gross Capital Formation (GCF), consisting of Gross Fixed Capital Formation and Changes in inventories; Exports minus imports (Exp-Imp). Figure 2 Categories distinguished for the expenditure approach Again, compilations are carried out in both current and constant prices 7. To continue with the earlier numerical example, the following tables give the expenditure approach data for the three years. GDP(E) HH Gov GCF Exp-Imp 2010 218 132 52 44-10 2011 240 142 56 47-5 2012 264 152 63 39 10 Table 3 GDP by expenditure approach in current prices GDP(E) HH Gov GCF Exp-Imp 2010 215 131 51 42-9 2011 238 141 55 46-4 2012 258 149 62 37 10 Table 4 GDP by expenditure approach in constant prices (prices previous year) Because of the equality of total product supply and total product use we must have: GDP(O) = GDP(E) 7 See the papers: Annual GDP by expenditure approach in current and constant prices: Main issues; Final Consumption Expenditures in current and constant prices, part 1: Households; Final Consumption Expenditures in current and constant prices, part 2: Government, NPISH; Gross Capital Formation in current and constant prices, part 1: Gross Fixed Capital Formation; Gross Capital Formation in current and constant prices, part 2: Changes in Inventories; Exports and Imports in current and constant prices. 3

So for each year the GDP totals for the two approaches should be equal, as is illustrated for the year 2011 in the following figure. Figure 3 Balancing the two approaches: GDP(O) = GDP(E) (yellow cells should be equal) In practice this will never be true due to the fact that data sources used in both compilations are different. In practice we therefore have a statistical discrepancy = GDP(O) - GDP(E). Note that the balance between GDP(O) and GDP(E) has to be achieved in both current and constant prices for each year. Note also that this balance can be achieved within the framework of a supply and use table (SUT) 8. Once the SUT is balanced GDP(O) will automatically be equal to GDP(E). Indexes Indexes play a major role in QGDP compilation 9. We can distinguish between three types of indexes: Value index (VIDX) Price index (PIDX) Volume index (QIDX) The important relationship between these types of indexes is given by: Value index = Volume index x Price index Using the abbreviations CUR for current prices and CON for constant prices we can define the implicit versions of these indexes as follows (T stands for time period, year or quarter): QIDX(T) = CON(T) / CUR(T-1) PIDX(T) = CUR(T)/CON(T) VIDX(T) = CUR(T)/CUR(T-1) Once the compilations in current and constant prices have been prepared these implicit indexes can be calculated and assessed for their plausibility. These checks serve an important role in constant price estimation. For our GDP(O) example the indexes are as follows: Agri Man Serv Tx GDP(O) 2011 110 114 104 110 110 2012 106 115 106 110 110 Table 5 Value indexes (previous year = 100) 8 See the papers: Introduction to Supply and Use Tables, part 1 Structure Introduction to Supply and Use Tables, part 2 Data Sources and Compilation 9 Indexes were explored in the papers: National Accounts in Constant Prices, part 1: Elementary Indexes National Accounts in Constant Prices, part 2: Aggregated Indexes. 4

Agri Man Serv Tx GDP(O) 2011 109 113 103 109 109 2012 104 112 103 107 107 Table 6 Volume indexes (previous year = 100) Agri Man Serv Tx GDP(O) 2011 101 101 101 101 101 2012 102 102 103 102 102 Table 7 Price indexes (previous year = 100) Similar implicit indexes can be prepared for the GDP(E) example. Note that the year 2010 disappeared from the time-series since we now work with annual changes. QGDP compilation Ideally, ANA should be derived as the sum (or average for stock variables) of the corresponding quarterly data. In this scenario the focus would be on quarterly data collection. Unfortunately, sources for ANA are generally different, more exhaustive, reliable and comprehensive than the corresponding ones for QNA. So in practice ANA are prepared independently from QNA. In many cases, data are collected only at the annual frequency, and at the quarterly frequency only indicators or proxies are available. Therefore ANA play a leading role and serve as a reference benchmark for QNA, and QNA generally follow annual estimates. The QGDP compilation procedure is in principle the same as for annual compilation, although the breakdowns of the ISIC industries and the expenditure components may be less detailed than for the annual case. Balances between GDP(O) and GDP(E) now need to be achieved for each quarter as well as for the whole year, as is indicated for the second quarter of 2010 in the following figure. Figure 4 Balancing the two approaches: GDP(O) = GDP(E) for each quarter Given the independent compilation of QNA and ANA the consistency between the two compilations is not guaranteed. Typically, the annual compilations provide the most reliable information on the overall level and long-term movements in the series, while the quarterly estimates provide the only available explicit information about the short-term movements in the series. Given that data sources will usually be different (see next section) the sum of the quarterly values will in general not be eqaul to the annual values. Ensuring consistency between quarterly and annual values is achieved by benchmarking. Benchmarking deals with the problem of combining series of quarterly (or other high-frequency) data with series of annual (or other less frequent) data when the two series show inconsistent movements and the annual data are considered the more reliable. Benchmarking can be used to revise preliminary QNA estimates to align them to new annual data when they become available. Additionally, in the absence of quarterly source data, benchmarking can be used to allocate annual 5

data over quarters. Finally, benchmarking is used as extrapolation method to update the quarterly series for the most current period for which annual data are not yet available. We therefore see that for each ISIC industry and for each expenditure component included in the QGDP compilation the sum of quarterly values should be made equal to the corresponding annual value, as is depicted for services value added and for government consumption in the following figure. Figure 5 Balancing QNA and ANA in time (benchmarking) It is important to remember that ANA typically become available a long time after the end of the quarter compiled by QNA. The following figure represents a sistuation in which QNA become available at T+60 (i.e. 60 days after the end of the reporting quarter), whereas the ANA appear nine months into the next year. So for a number of quarters the benchmarking with ANA figures is not yet possible. Figure 6 Possible publication schedule for QNA (Q1, Q2, Q3, Q4) and ANA (A) Both of the above balances in figures 4 and 5 need to apply at the same time, in both current and constant prices. So for each quarter GDP(O) should be equal to GDP(E) and for each transaction the sum of the quarters should equal the yearly total coming from ANA. Full balancing of QGDP means that these two balances need to apply in both current and constant prices at the same time, as is illustrated in figure 7. These transaction and time balances apply to the whole time-series for which ANA totals are available. For the latest quarters for which ANA totals are not yet available only the transaction balances apply. Figure 7 Balancing QGDP in current and constant prices 6

Once ANA for a certain year become available, the QNA for that year need to be revised, to ensure that the sum of the quarters for all transactions included in the QNA is equal to the ANA value. In this respect QNA will be more prone to revisions than ANA. As for the annual case implicit value, volume and price indexes can be calculated for each transaction and for each quarter. Such calculations are somewhat more complex in the sense that quarters can be compared with previous quarters, with corresponding quarters a year earlier or with the annual average of the year before 10. Quarterly volume measures for GDP are among the most important short term growth rate indicators published by the national accounts. QGDP compilation issues The aim of a system of Quarterly National Accounts is to provide a picture of current economic developments that is more timely than that provided by the Annual National Accounts and more comprehensive than that provided by individual short-term indicators. Whereas ANA are produced with a considerable time lag, QNA are usually available within three months after the end of a quarter and therefore more relevant to analysts and policy makers. In practice, the constraints of data availability, time, and resources mean that QNA are usually less complete than ANA. Data collection for QGDP compilation can be either direct, using source data similar in nature to ANA or indirect, using proxy indicators. From a NA viewpoint there is little methodological difference between ANA and QNA. Concepts and definitions in QNA are based on SNA 2008 just as those of ANA are. For the direct method, the same data sources that are used annually may also be available on a quarterly basis, such as foreign trade data, central government data, and financial sector data. Also, specific data sources may only be available at quarterly frequency, with annual totals being derived as sums of quarters. Commonly, QNA direct data sources are more limited in detail and coverage than those available for the ANA because of issues of data availability, collection cost, and timeliness. Given the fact that QNA need to be published relatively soon after the end of the reporting period, the use of price and volume measures takes on a prominent role in QGDP compilation. The application of such indirect indicators in annual compilation has been explored in previous papers 11, but applies without modification to the quarterly case as well. Generally, in order to express aggregates in constant prices we can use volume indicators for extrapolation or price indicators for deflation. We can use the extrapolation approach with quarterly volume indicators to obtain quarterly estimates in constant prices. We can then invert the deflation approach into an inflating approach by multiplying price indexes with the constant prices estimates to obtain current prices estimates. Using the earlier symbols this can be expressed as (T now stands for quarters; here we illustrate extrapolation with the value from a year earlier): CON(T) = CUR(T-4) * QIDX (volume extrapolation) CUR(T) = CON(T) * PIDX (inflation) In case value indexes are available we can first obtain current prices estimates and then apply deflation with price indexes. Quarterly current prices values may also be directly observed and used. 10 See the section on chain-linking in the paper Quarterly National Accounts, part 1: Main issues 11 See the papers mentioned in footnote 9. 7

CUR(T) = CUR(T-4) * VIDX (direct observation or value extrapolation) CON(T) = CUR(T) / PIDX (deflation) For each component, the available data source that best captures the movements (growth rates) in the target variable in the past constitutes the best indicator. Let us examine a simple example. The aim is to construct quarterly volume indexes for 2011 for the industry Hotels and Restaurants. We do this by constructing separate volume indexes for Hotels and for Restaurants and then constructing the weighted average, using weights of the year before based on value added taken from financial statements. Let the share of value added of both industries in the total for Hotels and Restaurants in 2010 be as follows: 2010 Hotel 0.79 Restaurants 0.21 1.00 Table 8 Value added shares in Hotels and Restaurants By way of example let the index for Hotels be constructed from quarterly data on nights spent in hotels. And let the index for Restaurants be constructed from quarterly data on food and drinks consumption. Using data for 2010 and 2011 the indexes for nights spent and food and drinks consumed for 2011 can be constructed as changes with respect to the average of 2010 (see table 9). Q1-11 Q2-11 Q3-11 Q4-11 Nights 86.3 113.2 138.6 101.3 Food + Drinks 75.1 91.6 179.8 84.4 Hotels and restaurants 83.9 108.6 147.4 97.7 Table 9 Volume indexes The volume index for Hotels and restaurants (calculated with 2010 = 100) can then be obtained as weighted average of the two volume indexes with the weights coming from table 8 (last row in table 9) 12. We can then use the extrapolation method with this volume index to extrapolate average 2010 figures on value added for Hotels and restaurants to obtain quarterly value added figures in constant prices. Using a suitable price index (e.g. CPI hotels and restaurants, or a general cost of living index) we can come to quarterly current prices values. Concluding remarks This paper concludes our coverage of QNA in this series of methodological papers. The intention has been to provide some additional information on topics specific to QNA, next to the information that can be found in the new chapter on QNA in the Handbook. We singled out the following topics: Chain-linking of quarterly time-series; Benchmarking of quarterly time-series to annual estimates; Seasonal adjustment of quarterly estimates; Quarterly GDP compilation in current and constant prices. 12 This is a Laspeyres volume index, since the weights from the previous year are used. 8

In this paper we examined the last topic. We tried to make clear that QGDP compilation is in principle no different from annual GDP compilation with respect to both the production and the expenditure methods. In practice issues of availability of data sources and the need for timely publication will typically imply that QGDP methods will rely to a greater extent on price and volume indicators. Also, the QGDP system faces an additional constraint in that for all transactions the sum of the quarterly values needs to be equal to the annual value, if available. Furthermore, quarterly time-series are usually compiled with indicators referenced to the previous year (and compiled using previous years weights) so that consistent time-series back to a particular reference year will need to be prepared by chain-linking techniques. Finally, there is the need for publishing seasonally corrected quarterly time-series to enable users to better assess long-term developments in GDP. To find out more, The 2008 SNA, European Commission, IMF, OECD, UN, World Bank, 2009, Chapter18, part D Quarterly National Accounts Manual concepts, data sources, and compilation, A.M. Bloem, R.J. Dippelsman, N. Maehle IMF, 2001 Handbook on Quarterly National Accounts, Eurostat, 2013 9