1. Item 18: Quarterly National Accounts
ESTP course on National Accounts ESA 2010
Luxembourg, 30 May June Eurostat

2. Structure of the presentation …
0) Prologue: Frequency of (national) accounting?
I) QNA scope
II) QNA vs. ANA: basic principles
III) QNA data sources
IV) Compilation practices in Europe
to be continued …

3. … Structure of the presentation
... V) Quarterly chain-linking VI) Benchmarking VII) Seasonal and calendar adjustment VIII) QNA presentation issues IX) QNA release and revision policy

4. 0) Frequency of (national) accounting?
Year is an evident accounting period, but not the only possible one.
Quarter (possibly even month) – a natural choice for more up-to-date accounting period
Quarterly accounts form a quick compact picture for the economic development in the new quarters for
- economic analysis and decision-making
Comprehensive in past periods (in line with ANA  benchmarked to ANA figures)

5. I) QNA scope. goods and services account,. production & income account
I) QNA scope goods and services account, production & income account employment, capital accumulation

6. I)… QNA scope in data transmissions
ESA 2010 TP requires transmission of:
101: GVA 10 industries, Taxes less subsidies on products.
102: FCE (HH,NPISH,GG), GFCF (6 assets), Changes in Inventories, exports and imports (goods and services).
103: CoE & WS (& SC) 10 industries, GOS, Taxes less subsidies on production
110: Population & (national) employment (EMP/SELF) in persons
111: Domestic employment (EMP/SELF) 10 industries in persons/hours
117: HH Final Consumption by durability
120/121: geographical breakdown exports/imports

7. II) QNA and ANA: basic principles
QNA are a higher frequency version of ANA:
follow the same rules and use the same classifications and definitions
integration with ANA, first ANA is a sum QNA, later QNA benchmarked to (structural) ANA
The time series perspective dominates the structural perspective in QNA (structure from the ANA, updated with new ANA).
Volume growth rates are more important in QNA than levels.
Seasonally adjusted figures are more important than original series.
Timeliness is more important in QNA.
QNA follow the same principles as ANA and in theory they could be compiled at the same level of detail. But sources usually don’t allow that and they are a lighter version of ANA.
QNA were developed after ANA except on the US and UK were both ANA and QNA were started at the same time.
QNA are used for forecasting and time series techniques. For that long series without breaks are needed.
Current prices are less interesting than volume data in the short term, SA is more important than NSA data.
Timeliness pressure is higher. In many cases some of the information needed is not available and has to be forecasted/extrapolated by the QNA department.
Short “life” of QNA compared to ANA. Some shortcuts are unavoidable.

8. II)… Some issues are more relevant for QNA than ANA
Higher frequency and shorter reference period create some issues specific to quarterly NA.
Time of recording (interests, dividends, work in progress, agricultural production)
Consistency in recording (work-in-progress; Out/Inc/Exp)
SEASONS INSIDE A YEAR  SEASONAL COMPONENT
Maybe all data from different sources are not on accrual basis
Production of goods and services over accounting periods (>3 months). Record them as work in progress. Particularly relevant for construction and some services
Transactions that occur infrequently and irregularly during the year (interest payments)

9. II)… QNA and ANA: compilation
Many source statistics are annual, i.e. available only well after Q4. (e.g. A: SUT transmission in 3 years)
Quarterly statistics have a smaller sample size and/or reduced coverage (STS vs. SBS) QNA: Use of indicators of economic activity
Many available monthly/quarterly source statistics do not follow ESA concepts.
Problems in QNA resemble those in early estimates of ANA.
Some detailed sources are only annual and are available too late. E.g. SUT product group deflation and balancing. Direct sources for Intermediate consumption usually not available at QNA timeliness.
STS coverage lower than SBS, smaller companies (10/50) not covered on infra-annual surveys.
Some other statistics (FTS, HICP,LFS) calculate the annuals from infra-annual observations. This is not the case for ANA/QNA, in many cases QNA and ANA sources are different.

10. III) QNA data sources for t+60d publication
Output approach (O):
good quarterly sources for many (Nace) branches. (STS)
not necessarily for all (e.g. some services).
Expenditure approach (E):
Good sources in C, G, X-M(goods); issues in GFCF (I') and inventories. Sometimes output indicators used for expenditure items (C).
Income approach (I):
good sources for wages, taxes (possibly only late in the quarter).
difficult for operating surplus (= often residual).
Most reliable approach (O or E) in balancing depends on the data sources in the country
- Output: either based on quarterly surveys or monthly (production) indicators, also administrative data, VAT, etc. In some cases indicators (transport= tonnes, kms, passengers). For some services in some countries hours worked or persons employed used as a proxy for economic activity
Expenditure: good data for Exports/imports (BOP/FTS), government consumption, private consumption (HBS, retail sales,).Problem is to differentiate between Final/intermediate consumption. Investment and particularly change in inventories are the most difficult part.
Income: Difficulties for GOS, specially Mixed income of self-employed
What about statistical discrepancy?

11. IV) QNA: compilation practices in Europe
Same principles used for compiling ANA can be used for QNA (even SUT framework) but at a less disaggregated level.
Methods that benchmark preliminary quarterly estimates of a QNA variable, or a quarterly indicator, to the corresponding ANA. (Direct GVA extrapolation by indicator in QNA, after ANA benchmark QNA to ANA figures)
Temporal Disaggregation Methods that impute values for a QNA variable by modeling the relationship between (annualized) preliminary quarterly estimates of a QNA variable, or a quarterly indicator, and the corresponding ANA. (Indirect GVA extrapolation by modelling quarterly indicator and annual variable relation)
There are three broad ways to compile QNA:
Quarterly SUT: need of a lot of sources, quite demanding. NL does it for 120 industries, 200 products and 17 expenditure categories. Time series are restricted (12 quarters) variables subject to constraints.
Simplified approach: a quarterly good approximation of the annual variable is available. Extrapolating quarterly variable + benchmarking. Revisions of time series are more limited.
Either a good indicator is not available or the NSI has a preference for econometric techniques.

12. V) Quarterly Chain Linking
Annual Overlap is the common practice EU countries use
- Pros: easier computation, consistency with annual CLV data
- Cons: Break between Q4 and Q1
One-quarter-overlap method also possible

13. V) … The annual-overlap method (AO)
A quarter at average prices of the previous year is related to the average of the four quarters of year t-1 at (average) prices of t-1
E.g. from data CUP_Q1_t
1) Deflate the price change from average (quarter) T-1 price (P_T-1 /4) for receiving => PYP_Q1_t
2) Calculate (AO) LINK:
PYP_Q1_t / CUP_av.Q_T-1
3) Using the link derive CLV_Q1_t
= LINK * CLV_av.Q_T-1
= [PYP_Q1_t / CUP_av.Q_T-1] * CLV_av.Q_T-1

14. V) ..The one-quarter-overlap method (1QO)
A quarter at average prices of the previous year is related to the fourth quarter of year t-1 at average prices of t-1.

15. VI) QNA: benchmarking quarterly variable with annual
Simple pro-rata approach ? (annual to quarters in proportions of quarterly figures) to benchmark to the annuals
 will create a step problem between Q4 and Q1 of the next year. NOT RECOMMENDED, problems in SA.

16. VI) …QNA: benchmarking quarterly variable with annual …
Denton
In differences nb: in parenthesis min 𝑡=1 𝑛 (( 𝑏 𝑡 − 𝑝 𝑡 )−( 𝑏 𝑡−1 − 𝑝 𝑡−1 ) ) 2 (𝑏 𝑡 − 𝑏 𝑡−1 )− (𝑝 𝑡 − 𝑝 𝑡−1 )
Subject to the annual constraints
Proportional nb: in parenthesis in LN
min 𝑡=2 𝑛 ( 𝑏 𝑡 𝑝 𝑡 − 𝑏 𝑡−1 𝑝 𝑡−1 ) (𝐿𝑁 𝑏 𝑡 −𝐿𝑁 𝑏 𝑡−1 )− (𝐿𝑁 𝑝 𝑡 −𝐿𝑁 𝑝 𝑡−1 )
The aim is to receive a quarterly benchmarked variable bt that closely follows the development of the quarterly indicator pt
Denton solves an optimisation problem for creating a benchmarked target variable so that changes to QoQ growth (absolute diff or relative growth) from the indicator are minimized
Benchmarked variable follows as closely as possible the indicator development
Denton in First Differences of Levels applied usually if e.g. the Ann GDP and the indicator have more or less the same level
Proportional Denton
*e.g. if indicator is and INDEX and has a different level than GDP
* if B/I ratio is changing in different years
NB: if growth rates have changing signs (+ - ) proportional Denton does not work straight-forwardly

17. VI) … QNA: benchmarking quarterly variable with annual …
What about regression based methodology? A simplified introduction: ∆ 𝑦 𝑡 =𝑐+𝛽∆ 𝑥 𝑡 + 𝑢 𝑡
xt is an indicator for QNA yt, (Q GDP): - regress Δxt's annual average with annual ΔYt (annual GDP) - use the equation (c and β with xt) information in allocating annual GDP to quarters (temporal disaggregation)
For a new quarter, use the received equation (c and β) to extrapolate the new quarter yt growth from Δxt
We have an indicator xt for QNA variable yt (for simplicity QGDP)
How to extrapolate a new quarter growth rate for yt
Estimate the above equation between growth of xt and yt for the past years so that yt is benchmarked to the ANA GDP numbers (with more data sources)
- For a new quarter: use the equation to extrapolate quarterly growth of yt with quarterly growth of indicator xt
B=1 will hold on average through the time series, btw. Consecutive individual years B will slightly differ from 1
This is because corr (d yt, d xt) throughout the time series is one number, however varies a little bit in different individual years (QNA has a 'sample' of ANA data sources.

18. VI) …QNA: benchmarking quarterly variable with annual…
Optimal methods using one-step calculation
Chow and Lin (1971) worked out a least-square optimal solution on the basis that a linear regression model involving the quarterly QNA variable yt and one or more related quarterly indicators xt can be estimated using the annual data for the QNA variable and the annualised quarterly data for the indicator(s). This model can be written as: 𝑦 𝑡 𝑎 =𝑐+𝛽 𝑥 𝑡 𝑎 + 𝑢 𝑡 𝑎
Extensions of the general model assume different structures for the residual term, like AR(1).
Optimal methods using two-steps or dynamic 𝑦 𝑡 𝑎 =𝛾 𝑦 𝑡−1 𝑎 +𝑐+ 𝛽 1 𝑥 𝑡 𝑎 + 𝛽 2 𝑥 𝑡−1 𝑎 + 𝑢 𝑡 𝑎
Original Chow-Lin operates in Levels
For simplicity using GDP variable as an example:
The 'orig' equation is estimated with yt = Ann GDP, xt = annualised quarterly GDP indicator
The final output is however * a quarterly GDP that sums up to Ann GDP * one B parameter value
For extrapolation of a new quarterly GDP value (e.g. 2014Q1), without annual GDP for that year, one can use in C-L the final equation parameter values for B and c
Extensions assume some time series model structure for the residual, Random Walk: Fernández, Random Walk-Markov: Litterman
Later Optimal dynamic models work typically in growth rates (dynamic)
A second step often needed to ensure levels to sum up to annuals

19. VII) Seasonal and calendar adjustment … - Why?
Business cycle analysis
To improve comparability:
-Over time:
example: how to compare the first quarter (with February) to the fourth quarter (with Christmas) ?
-Across space:
Never forget that when we are freezing at work, Australians are burning on the beach !
Very important to compare European national economies (convergence of business cycles) or industrial activities

20. VII)…Seasonal and calendar adjustment …
A time series is considered to consist of three main components:
- Trend-cycle (TC): long-term trend (T) + business cycle (C)
- Seasonal and calendar effect (S, K):
Seasonal effect: reasonably stable in terms of annual timing (Christmas, holidays, administrative deadlines, weather) Part of the seasonal effect is calendar-induced (fixed holidays, length of month).
Non-seasonal calendar effects: not stable in terms of annual timing (number and composition of working days, leap year effect, moving holidays e.g. Easter)
- Irregular component (I): effects that are unpredictable in terms of timing, impact and duration (outliers, natural disasters, strikes…)

21. VII)…Decomposing time series Y=TC*(S*K)*I …

22. VII)… Seasonally and calendar adjusted series ...
SA, decomposition in more detail:
the seasonally adjusted series is logically defined as the raw series from which the seasonality (St) has been removed.
SCA (or old expression SAWD)
The seasonally and calendar (or working-day) adjusted series is defined as the raw data from which the seasonal and calendar effects (St , TDt, MHt) have been removed.

23. VII) SA: TRAMO/SEATS, Reg-ARIMA-X12/-X13SEATS …

24. VII) Seasonal and calendar adjustment
Proper Seasonal Adjustment requires a lot expertise
In many NSIs SA is done/guided by a particular Department
Heterogeneity across MS:
Method: X12/X13 – TRAMO/SEATS
Sources: Monthly/Quarterly indicators – QNA
Direct/indirect
SA series benchmarked or not to AN-A/AC-A

25. VIII) QNA presentation issues (i)
Which volume series?
Chain-linked levels (based on reference year Mio Eur cup levels)
Index series (reference year = 100)
Growth rates
Previous year‘s price volumes
Which form for the growth rate?
Quarter-on quarter (from s.a.)
Year-on-year (from raw or s.a.)
Annualised growth rate (from s.a.)
Cumulated growth (from raw or s.a)

26. VIII) QNA presentation issues (ii)
Carry-over effect
Annual rate of growth (for the year) that would result if the level reached in the fourth quarter of a given year remained constant throughout the following year.
It is equivalent to the percentage difference between the level in the fourth quarter and the average level for that year.

27. IX) QNA release and revision policy
Very heterogeneous across MS
ESA 2010TP: QNA at 60 days (from 2014Q3 onwards)
Almost all countries produce a flash between days
In some cases flash includes O/E/I (FR, NL, AT)
Flash + one or two releases
Limited revisions or all the time series might be revised depending on the compilation method

28. Some current issues
GDP flash at t+30 days for the euro area and EU, - a long discussed issue accomplished 29 April 2016 (2016Q1)
Eurostat Handbook on Quarterly National Accounts (2013)
Discussion on component growth contributions (See Eurostat Handbook on QNA (2013))
JDemetra+ (2.00) official version published in Feb 2015 JEcotrim: a series of NA plug-ins for Jdemetra+
Task Force on data validation

29. Item 18: Quarterly National Accounts
- THANK YOU FOR YOUR ATTENTION ! -
Item 18: Quarterly National Accounts
ESTP course on National Accounts ESA 2010
Luxembourg, 30 May June Eurostat