Quarterly NA
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: GDP(O) = Output - Intermediate consumption + Product taxes – Product subsidies, by ISIC activities
Expenditure approach: GDP(E) = Final consumption + Gross capital formation + Exports - Imports
Income approach: 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
General government
Household sector (including NPISH)
Rest of the world
The accounting system 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. But before going into details let’s see what special features NA Builder has to offer when it comes to quarterly accounting.
QNA and NA Builder
We can distinguish between a tabular presentation of a particular NA area and a time-series presentation of some of the parts of the table. In the latter case the table cells need to be "collapsed" to either the header or the stub of the time-series table. Whereas most of the NA structures have a tabular layout (SUT, SIOT, SAM, Sector Accounts) with time-series derived, the “natural” presentation for QNA is often by time-series, with the tabular presentation being derived. NA Builder contains functionality to "switch" between the tabular and the time-series perspectives so that the compilar can work on the same data using both perspectives.
First, it is easy to create a time-series sheet for any collection of cells for a table which (based on the same template) has been implemented in various sheets. Suppose we have the following year sheets and we want to have column totals for all years in a “time-series” sheet "TS":
In one of the sheets (here Y2012) select the column totals:
Then press <ctrl>Q (tab “Actions” and then “Code cells to Scrt”); this will set up the view in sheet Scrt:
After entering the name “TS” in cell A1 and then capturing the table with <ctrl>E, the sheet TS is created:
Setting up such a time-series sheet can also be done with the CROSSCUT rule. This rule converts the cells of the range given in arg.1 into the stub (arg.3=1) or header (arg.3=2) in a new sheet with the name given in arg.2; these cells will be coded in the following triples: <partition name>|<row code>|<column code>, with the codes coming from the template of the sheet that contained the cells; the other axis will contain the sheet names of all sheets that share the same template, except for those sheets listed in arg.6, arg.7,...; if arg.4 contains a number n (n=1,2,3,...) a sum formula will be set up after n rows/columns; if arg.5=1 then corresponding FOLD / UNFOLD rules (more on these below) will be set up when the crosscut rule is saved, enabling the data migration between the included sheets and the new crosscut sheet. There is an example of this rule in the application:
This example sets up the following sheets:
Use the following CROSSCUT rule to create the sheet TS (set up by hand earlier):
After playing this rule, the sheet list contains the sheet “TS”:
The following FOLD rule has also been set up by the CROSSCUT rule:
The FOLD rule converts the values from a set of sheets with a common template (of the sheet given in arg.1) into one single sheet given in arg.2; This single sheet must have the sheet names in column B or row 2; the other row / column must have as codes the following triples: <partition name>|<row code>|<column code>, with the codes coming from the template of the sheets that are folded; these triples can be created with <ctrl>Q on multi-selected cells in the sheet Scrt; if arg.3=1 then the values are appended, otherwise they replace the originals; if arg.4=1 then formulas linking to the sheet cells will be set up.
This rule will “fold” tabular sheet data into the time-series view (here using formulas):
The reverse is also possible with the UNFOLD rule. This rule carries out the reverse of the FOLD rule, i.e. it takes the values in the arg.2 sheet, coded in header / stub by sheet names / code triples (or vice versa) and appends or replaces them in the designated sheet + cell; arg.2=1 appends the values, instead of the default replacement
Let’s set up another time-series view TS2 as follows:
Next, enter some data in this time-series view:
Then the following UNFOLD rule will copy the data in the individual tables (here as values; formulas are also possible):
In summary, by using the FOLD and UNFOLD rules data can be copied between the tabular and time-series views at any time. If the direction is always one-way, then this can be accomplished most easily using formulas; otherwise data need to be copied as values.
Next, there is also some functionality in NA Builder to enable "benchmarking", i.e. adjusting quarterly time-series to annual time-series. This is possible with the DENTON rule which implements the proportional Denton method (explained below), using the solution given in Annex 6.3 of the Quarterly National Accounts Manual, IMF, 2001. The application contains an example in rule 27 in the SIMPLE framework:
If we have the following data:
Then playing rule 27 will give:
Some other NA Builder rules which may be useful when working with timeseries and QNA:
COMPARE: Given ranges for current values in periods T-1 and T, and a range with values in T in prices of T-1 ("constant values"), this rule sets up implicit value, volume and price indexes referenced to T-1.
INDEX: Calculates indexes from the values in the range in arg.1 either vertically (arg.3 = 1) or horizontally (arg.3 = 2); results will be written to the range in arg.2; the lag of the index is in arg.4 (default 1); the offset for the reference period (=100) is in arg.6 (default 1); the length of the reference period is in arg.5 (default 1); the results will be multiplied with the scalefactor in arg.7; if arg.8 = 1 then the results will be set up as formulas.
DISTRIBUTE: Distributes the values in the range in arg.1 either vertically (arg.3 = 1) or horizontally (arg.3 = 2); results will be written to the range in arg.2; the results will be multiplied with the scalefactor in arg.4; if arg.5 = 1 then the results will be set up as formulas.
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. Chain-linking is the technique to express the estimates in previous years’ prices in terms of prices of a fixed reference year. 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
An example of these three methods can be found here
It is not difficult to implement chain-linking techniques in formulas in NA Builder, no dedicated rules are therefore needed. Typically this is done using a number of different FORMULA rules, which can be collected in a script.
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 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 “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 2010 – 2012 for which the annual totals for 2010 and 2011 are known The example is based on the example 6.1 of the IMF QNA Manual (2001). A simple way to adjust the quarterly series so that the sum of the quarterly values equals the annual given total is by “pro-rating” as is illustrated in the following table.
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 Q4 2010 – Q1 2011 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.
The following table gives an example using the same data as before
Columns (1) to (4) are the same as before. The entries in column (5) are now obtained by using the proportional Denton method. The yearly averages of these entries are equal to the BI ratio in column (4). Note that for 2012 the entry for Q4 2011 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).
This method is implemented in NA Builder in the DENTON rule.
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 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.
Some background information on seasonal adjustment can be found here
There are no special features related to seasonal adjustment in NA Builder since there are dedicated software packages for this.
GDP compilation
At the heart of QNA we have quarterly GDP (QGDP) compilation by the two main methods (production approach and expenditure approach) at current and constant prices.
GDP by industries is compiled by the GDP by production (output) method (GDP(O), broken down by ISIC industries. This compilation is based on:
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.
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:
We can also obtain GDP(O) in constant prices (in the example given here we use average prices of the 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
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)
Again, compilations are carried out in both current and constant prices. To continue with the earlier numerical example, the following tables give the expenditure approach data for the three years.
Because of the equality of total product supply and total product use we must have:
GDP(O) = GDP(E)
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.
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). Once the SUT is balanced GDP(O) will automatically be equal to GDP(E).
Indexes
Indexes play a major role in QGDP compilation and have been introduced elsewhere. 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:
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.
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 which has already been introduced. Recall that 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 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.
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.
Both of the above balances in these figures 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 the figure below. 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.
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. Quarterly volume measures for GDP are among the most important short term growth rate indicators published by the national accounts.
QGDP compilation issues
Recall that 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, 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.
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:
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.
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). 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.