Quarterly National Accounts, part 1: Main issues 1

Transcription

1 Quarterly National Accounts, part 1: Main issues 1 Introduction This paper continues the series dedicated to extending the contents of the Handbook Essential SNA: Building the Basics 2. One of the main themes in this series has been GDP compilation since GDP (Gross Domestic Product) is the most important single indicator measuring economic activity in a country. Earlier in this series we reviewed the three main approaches to GDP compilation the production approach, the expenditure approach and the income approach, both in current prices and in prices of a previous year. A closely related goal is to make the estimates of GDP exhaustive. We examined some of the reasons for non-exhaustiveness, such as lack of coverage of the illegal economy, the underground economy and the informal economy. Once exhaustive estimates for GDP are in place, the system of national accounts (NA) can be expanded in two directions. First, production processes can be more closely investigated, following outputs or imports through the economy either to final demand or back into the system of production in the form of intermediate demand, leading to further production. This is studied in supply and use tables and input-output tables, to which we have dedicated a number of papers earlier in this series. Second, we can embed the traditional GDP decompositions - by ISIC activities, by expenditure categories and by income components - in a full system of institutional sector accounts, where the main productive, distributive, capital and financial transactions are presented in a series of accounts for the main institutional sectors of the economy. We have also explored the full SNA system of institutional sector accounts earlier in this series. So far the frequency of compilation in our explorations has been annual. But the system of NA does not essentially depend on this annual frequency. In principle the same compilations can be done at quarterly frequency as well if data sources allow this. In this paper we want to explore quarterly national accounts (QNA) compilation 3. Rather than repeat many of the topics that were reviewed in earlier papers on annual national accounts (ANA), we want to single out three issues that are specific to quarterly compilation, having no equivalent in ANA: Chain-linking of quarterly time-series; Benchmarking and reconciliation of quarterly time-series to annual estimates; Seasonal adjustment of quarterly estimates. In this first part of the paper we will present an overview of these three issues and explore chainlinking and benchmarking in some detail. In later parts we will examine seasonal adjustment and the 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: 2 Henceforth called the Handbook ; this paper is based on the third (2013) edition; it can be found at the following link: 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. 1

2 way chain-linking, benchmarking and seasonal adjustment can be reconciled in a QNA compilation strategy. What are Quarterly National Accounts? The aim of a system of Quarterly National Accounts (QNA) is to provide a picture of current economic developments that is more timely than that provided by the Annual National Accounts (ANA) 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. Although QNA are less timely than individual short-term indicators, they provide a more comprehensive picture of current economic developments organized in an integrated national accounts (NA) framework. 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. 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 QNA compilation. Also, 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. The core of a system of QNA consists of the three methods of GDP compilation: Output approach 4 : GDP(O) = Output - Intermediate consumption + Product taxes Product subsidies, by ISIC activities; Expenditure approach 5 : GDP(E) = Final consumption + Gross capital formation + Exports - Imports; Income approach 6 : GDP(I) = Compensation of employees + Production taxes - Production subsidies + Consumption of fixed capital + Net operating surplus (mixed income) + Product taxes - Product subsidies, by ISIC activities. The output approach and the expenditure approach are compiled in both current and constant prices, the income approach only in current prices. The breakdown of ISIC industries, expenditure categories and income components is typically less detailed than in the ANA case. As with the annual accounts, the quarterly ones are broken down by institutional sectors as well. Usually, a simplified breakdown into four macro-sectors is used: Corporations; 4 See the papers: 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. 5 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. 6 See the papers: Annual GDP by income approach in current prices: Main issues; Compensation of employees and related labour concepts; Operating Surplus, Mixed Income and Consumption of Fixed Capital. 2

3 General government; Household sector (including NPISH); Rest of the world. The accounting system 7 is also more simple, usually consisting of: Production account; Generation of income account; Distribution of income account; Use of income account; Capital account. Quarterly volume growth of GDP is an often used figure of national accounts. Compared to ANA there are specific problems related to the quarterly frequency. In particular, chain-linking in quarterly national accounts requires more complex calculations than annual data. Furthermore, once the most suitable index formula has been chosen, alternative approaches for its implementation can be used. We will explore in some detail chain-linking in the context of QNA in the next section. Chain-linking: the three methods Constant price estimates of output and intermediate consumption by ISIC activities or of expenditure categories are typically compiled in prices of the previous year. For QNA we can use either annual (average) prices or quarterly prices (corresponding quarter of the previous year). Both methods are used in practice, but there is a tendency to prefer the use of annual prices 8. Chain-linking is the technique to express the estimates in previous years prices in terms of prices of a fixed reference year 9. Even with the choice of annual average prices there are three different methods to chain-link: Annual overlap method; One quarter overlap method; Over-the-year method. We will illustrate these three methods with a very simple example, using quarterly production data and annual price data for the years for two goods, here called A and B 10. Annual data are also available for Annual overlap method In this method the average price data from the previous year are used as weights for each of the quarters in the current year, with the linking factors being derived from the annual data. The following table presents a simple example of the annual overlap method. For both goods A and B we have data on quantities (Q) in columns (1) and (2) and prices (P) in columns (3) and (4). There are rows for quarters Q1, Q2, Q3 and Q4 and a row for the year (Y). Note that we use annual average prices in columns (3) and (4). 7 See the papers: Introduction to the SNA 2008 Accounts, part 1: Basics; Introduction to the SNA 2008 Accounts, part 2: Current Accounts; Introduction to the SNA 2008 Accounts, part 3: Accumulation Accounts. 8 This is required in the EU 9 For index and chain-linking background see the papers: National Accounts in Constant Prices, part 1: Elementary Indexes; National Accounts in Constant Prices, part 2: Aggregated Indexes. 10 The example is based on the examples 9.4a, 9.4b and 9.4c of the IMF QNA Manual (2001). 3

4 Q A Q B P A P B Pt.Qt Pt-1.Qt Links Chained Q-Q change (1) (2) (3) (4) (5) (6) (7) (8) (9) 2009 Y , , Q % 2010 Q % 2010 Q % 2010 Q % 2010 Y , , Q % 2011 Q % 2011 Q % 2011 Q % 2011 Y , , Q % 2012 Q % 2012 Q % 2012 Q % 2012 Y , , Table 1 Chain-linking using the annual overlap method (yellow cells: calculation explained in the text) Column (5) gives the total annual value (multiplying price and quantity) for both goods (e.g. for 2010: 3594 = 282 * * 9). Column (6) gives the total quarterly value using the previous year price (e.g. for Q1, 2012: = 85.5* * 11.5). In column (7) we calculate the links, by comparing the quarterly value in previous years prices with the quarterized annual value in current prices of the previous year (e.g. for Q1, 2012: = 100 * / (3779/4)). Quarterized means dividing the annual value equally over the quarters by dividing by 4. Finally, we chain-link these individual links into the series in column (8) given now in prices of the year 2009 by multiplying the links (e.g. for Q1, 2012: = * * / (100*100)). Column (9) gives the percentage change of the quarter with respect to the previous quarter. Note that the annual indexes in columns (7) and (8) are averages of the quarterly indexes. The annual overlap technique is a time consistent method in the sense that the average of quarterly volume indexes is equal to the annual index, as we see in the following table (1) (2) (3) (4) Cur (1) 3, , , Con (PPY) (2) 3, , , Links (3) Chained (4) Table 2 Annual indexes (yellow cells: calculation explained in the text) In this table current annual values are given in row (1) (corresponding to column (5) of table 1) and values in prices of the previous year (PPY) are given in row (2) (corresponding to column (6) of table 1). The links in row (3) are calculated by dividing the PPY value by the current value of the previous year (e.g. for 2010: = 100 * 3336 / 3173). The annual chain-linked series (expressed in changes with respect to the reference year 2009) is obtained by multiplying the links (e.g. for 2011: = * / 100). Time consistency means that for each year the annual index of row (4) equals the corresponding annual average of the quarterly indexes in column (8) of table 1, which is indeed true in this example. It can be shown that this is always true for the annual overlap method. As we will see below, this is not true for the other methods. 4

5 In practice we usually do not work with quantity and price data as in columns (1), (2), (3) and (4) of table 1. Instead we use a variety of techniques to prepare PPY data as in column (6) of table The chain-linking can then be done as in columns (7) and (8) of table 1. Applying the chain-linked indexes to the current value for 2009 in column (5) of table 1 will convert the index series into a value series. One quarter overlap method For the one quarter overlap method one quarter of the year (e.g., the fourth quarter) is compiled at both the average prices of the current year and the average prices of the previous year, which than provides the linking factor for the current year. This technique gives the smoothest transition between each link, in contrast to annual overlap technique that may introduce a step between each link (in the first quarter) due to the change from one annual link to the next. The following table presents the calculations for this method, using the same data as in table 1. Q A Q B P A P B Pt.Qt Pt-1.Qt Links Chained Q-Q change (1) (2) (3) (4) (5) (6) (7) (8) (9) 2009 Y , , Q % 2010 Q % 2010 Q % 2010 Q % 2010 Y , , Q % 2011 Q % 2011 Q % 2011 Q % 2011 Y , , Q % 2012 Q % 2012 Q % 2012 Q % 2012 Y , , Table 3 Chain-linking using the one quarter overlap method (yellow cells: calculation explained in the text) For Q4 two values are calculated: in current years prices (e.g. Q4 2011: = 83.1 * * 11.5) and in previous years prices (e.g. Q4 2011: = 83.1 * * 9). The links for all quarters are then calculated with respect to this Q4 value (e.g. Q1 2012: = 100 * / 948.8). The chained index is then built up from the links via multiplication of the link with the Q4 value of the previous year (e.g. Q1 2012: = * / 100). The annual indexes are the same as in table 2. The index for the first year 2010 is the same as the average of the quarterly indexes, but those for 2011 and 2012 are not. The quarterly chained indexes are no longer time consistent with the annual ones, which is a disadvantage of this method. The advantage of this method is that the step-problem has been eliminated, with Q4 serving as pivot. Over-the-year method For the over-the-year method all quarters (rather than only Q4) are compiled at the weighted average prices of both the current and the previous year. This technique doesn t meet time 11 See the papers listed in footnote 9 for details 5

6 consistency as well, even though the differences are smaller than in one the quarter overlap method and it is also affected by the step problem. The following table presents the calculations for this method, again using the same data as in table 1. Q A Q B P A P B Pt.Qt Pt-1.Qt Links Chained Q-Q change (1) (2) (3) (4) (5) (6) (7) (8) (9) 2009 Y , , Q % 2010 Q % 2010 Q % 2010 Q % 2010 Y , , Q % 2011 Q % 2011 Q % 2011 Q % 2011 Y , , Q % 2012 Q % 2012 Q % 2012 Q % 2012 Y , , Table 4 Chain-linking using the over-the-year method (yellow cells: calculation explained in the text) For each quarter two values are calculated: in current years prices (e.g. Q2 2011: =78.3 * * 11.5) and in previous years prices (e.g. Q2 2011: = 78.3 * *9). The links for all quarters are then calculated with respect to the value of the corresponding quarter a year earlier (e.g. Q2 2012: = 100 * / 943.4). The chained index is then built up from the links via multiplication of the link with the value of the corresponding quarter a year earlier (e.g. Q2 2012: = * * / (100 * 100)). The annual indexes are again the same as in table 2. As for the previous method the index for the first year 2010 is the same as the average of the quarterly indexes, but those for 2011 and 2012 are not, although they are much closer than for the one quarter overlap method. The three chained index series have been plotted in the following graph. Figure 1 Chained indexes series for the annual overlap method (AO), the one quarter overlap method (QO) and the over-the-year method (OY) 6

7 The step problem affects the AO and OY methods, but not the QO method. Time consistency is met by the AO method, but not by the QO and OY methods, although for the OY method differences between the annual indexes and the averages of the quarterly indexes are typically very small. With respect to the step problem QO is the preferred method, with respect to the time consistency AO is the preferred method (see table 5). AO is the method of choice for many countries. Annual overlap One quarter overlap Over-the-year Abbreviation AO QO OY Step problem Yes No, preferred Yes Time consistency Yes, preferred No No, small differences Table 5 Overview of the three methods Benchmarking and reconciliation Given the independent compilation of QNA and ANA a next problem pertains to the consistency between the two compilations. 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. Benchmarking deals with the problem of combining series of quarterly (or other highfrequency) 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 quarterize annual data to construct time series of QNA estimates. 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. To illustrate the benchmarking technique let us take a simple case of a quarterly time-series for the years for which the annual totals for 2010 and 2011 are known 12. A simple way to adjust the quarterly series so that the sum of the quarterly values equals the annual given total is by prorating as is illustrated in the following table. Indicator Q-Q ch Year ratio Q-Q ch (1) (2) (3) (4)=(3)/(1) (5)=(4) (6)=(1)*(5) (7) 2010 Q Q Q Q Y Q Q Q Q Y Q Q Q Q Y Table 6 Example of benchmarking by pro-rating (yellow cells: calculation explained in the text) 12 The example is based on the example 6.1 of the IMF QNA Manual (2001). 7

8 Here we have a quarterly indicator series in column (1) and an annual level series in column (3). Column (4) gives the pro rate ratio (the benchmark-to-indicator or BI ratio) which is the ratio of the annual to the quarterly data (e.g. for 2010: 9.95 = 4000 / 402). Column (5) assigns this annual BI ratio to each quarter of the corresponding year. Note that for 2012 (the year for which the annual total is not yet known) the BI ratio of 2011 is used as proxy. The benchmarked estimate is then given in column (6) as the product of the indicator value and the BI ratio. A drawback of this pro-rating method is that the quarterly growth rate Q Q in the original series is -1.8% (column 2) and in the pro-rated series 1.5% (column 7). This discontinuity is known as the step problem and is caused by suddenly changing from one pro-rate ratio to another. To avoid this distortion, the pro-rate ratios should change smoothly from one quarter to the next. One well known method that achieves such a smooth adjustment is the proportional Denton benchmarking technique. This method keeps the benchmarked series as proportional to the indicator as possible by minimizing the difference in relative adjustment to neighboring quarters subject to the constraints provided by the annual benchmarks 13. The following table gives an example using the same data as in table 5. Indicator Q-Q ch Year ratio Q-Q ch (1) (2) (3) (4)=(3)/(1) (5) (6)=(1)*(5) (7) 2010 Q Q Q Q Y Q Q Q Q Y Q Q Q Q Y Table 7 Example of benchmarking by proportional Denton method Columns (1) to (4) are the same as in table 5. The entries in column (5) are now obtained by using the proportional Denton method 14. The yearly averages of these entries are equal to the BI ratio in column (4). Note that for 2012 the entry for Q is used as proxy. The benchmarked estimates are then given in column (6) as before, as the product of the indicator value and the BI ratio (now adjusted by the proportional Denton method). Seasonality The last issue important in QNA compilation we want to explore is seasonality. Human activity is subject to different rhythms, both natural and social. Examples of natural rhythms are day and night 13 Technical details can be found in chapter 6 of the IMF QNA Manual (2001). 14 We will not show here how to obtain these values. We will come back to implementation issues (including software) in a later part of this paper. 8

9 on account of the Earth s 24-hour rotation and the succession of seasons due to the Earth s yearly rotation around the sun. Examples of social rhythms are the Friday or Sunday as rest day and national and religious holidays. The seasonal component in time series corresponds to the regular movements observed in quarterly (and monthly) time series during a twelve-month period. It represents the systematic, persistent, predictable, and identifiable effects in the series. Examples are increases in retail sales data associated with the Christmas period or the fall in industrial activity during vacation periods. Note that seasonality does not apply to annual data. There can of course be temporal patterns in annual data as well. These are called (economic or business) cycles. Another type of seasonal variation which is also linked to the calendar is the trading day effect for flow data which arises because of differences in the number of such days in the month. Production in February will be lower than in January or March simply because there are fewer working days in this month. But also in months with an equal number of calendar days, the number of working days may be different, because different numbers of rest days may be included in them. To compare data between two months or quarters for which the seasonal pattern is different we want to eliminate the seasonal effect. This is called seasonal adjustment. Typically, seasonally adjusted quarterly data are used in economic modeling and cyclical analysis. We will explore techniques for seasonal adjustment of quarterly time-series in the next part of this paper. Concluding remarks The aim of this paper is to identify a number of issues in quarterly national accounting that arise because of the quarterly frequency of the compilation and therefore are not encountered in annual national accounting. We identified three such issues: chain-linking, benchmarking and reconciliation and seasonal adjustment. For chain-linking we reviewed the three methods available: annual overlap, one quarter overlap and over-the-year. The annual overlap method is a widely used method because it has the desirable property that the annual indexes are equal to the averages of the quarterly indexes. A drawback of this method is the step between the fourth quarter and the first quarter of the next year that arises because of the shift in the annual price weights. For benchmarking we introduced the widely used proportional Denton method and illustrated how this method can be used to benchmark quarterly estimates to annual totals. Reconciliation strategies will be further explored in part 4 of this paper. Seasonal adjustment will be the topic of parts 2 and 3 of this paper. 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,