ChainLinking in Quarterly National Accounts and the Business
Chain-Linking in Quarterly National Accounts and the Business Cycle The 2008 World Congress on National Accounts and Economic Performance Measures for Nations Washington D. C. , 12 th to 17 th May 2008 May 14 Session 3 E: Expert Seminar Session on Index Number Theory Key Bridge Marriott, The Francis Scott Key Ballroom Salon A Marcus Scheiblecker
Whereas chain-linking of annuals in previous years prices is unambiguous, it is not at quarterly frequencies. Contrary to the US, annuals as well as quarters are calculated at average prices of the whole previous year in the EU. For the consecutive construction of quantity indexes, there exist three different methods: n The over-the-year method 28. 02. 2021
n The annual-overlap method n The quarterly-overlap method 28. 02. 2021
Three different chain-linking methods Austrian GDP in million € Date nominal (at prices of the current quarter) at average prices of the current year at average prices of the previous year 2004 -01 55316. 88 55883. 83 54749. 82 2004 -02 58206. 69 58323. 31 57223. 87 2004 -03 60165. 13 60055. 64 59066. 67 2004 -04 62129. 84 61555. 77 60727. 75 2005 -01 57257. 14 57433. 55 56310. 32 2005 -02 60614. 11 60743. 55 59604. 40 2005 -03 62513. 27 62528. 67 61398. 34 2005 -04 64718. 30 64397. 05 63324. 27 2006 -01 59452. 31 58996. 74 2006 -02 63595. 43 62623. 76 2006 -03 65441. 57 64489. 25 2006 -04 67899. 57 66494. 52 blue = over-the-year method green = quarterly-overlap method red = annual-overlap method 28. 02. 2021
Time series properties n n n Over-the-year method: Breaks in the series (compared to the previous quarter) occur every quarter. Does not represent a time series in a narrower statistical sense. Annual-overlap method: Breaks in the series (compared to the previous quarter) occur every first quarter of a year. Represents a time series in a narrower statistical sense only within a year. Quarterly-overlap method: No breaks in the series (compared to the previous quarter) occur. Represents a time series in a narrower statistical sense. 28. 02. 2021
Time consistency (additivity) property n n n Over-the-year method: approximately time consistent even away from the reference period Annual-overlap method: fully time consistent Quarterly-overlap method: not time consistent, especially away from the reference period ⇨ Splitting-up annual discrepancies over quarters by a method generating time series in a narrower sense (proportional Denton procedure, spline functions) does not interfere with the time series properties of the benchmarked series. Note: Quarterly-overlap method + pro-rata distribution of annual discrepancies ≙ annual-overlap method. According to the IMF‘s Quarterly National Accounts Manual (2001, p. 84): ‘Because of the step problem, the pro-rata distribution technique is not acceptable. ‘ 28. 02. 2021
Differences between the sum of the quarters and annual data in Austrian GDP 28. 02. 2021
Relative differences between the AO- and the Denton benchmarked QO-method 28. 02. 2021
Distribution of annual chain-linkingdifferences by the AO and the B-QO-method 28. 02. 2021
Consequences for time series modelling of QNA data chain-linked by different methods Why time series modelling of QNA series? n n Outlier detection procedures for preparing time series for a following seasonal adjustment are based on time series analysis. For seasonal adjustment an extrapolation of the series beyond the time series horizon is necessary to apply filter techniques for the recent observations (which are in the focus of interest). All extrapolation methods rely on time series properties. For TRAMO-SEATS the seasonal component is extracted by factorization of the time series model. For X-12 instead, mathematical filters are applied (making this procedure slightly less dependent on neat time series properties). For some kind of business cycle analysis (Beveridge-Nelson decomposition, unobserved components models, …) 28. 02. 2021
Models suggested by TRAMO-SEATS Over-the-year method 28. 02. 2021
Annual-overlap method 28. 02. 2021
Quarterly-overlap method 28. 02. 2021
Denton benchmarked quarterly-overlap method 28. 02. 2021
Overview over time series models OTY AO QO B-QO time-series model (0, 1, 1)(0, 1, 1) (0, 1, 0)(0, 1, 1) outlier detected none AO 1993 Q 1 TC 1993 Q 1 AO 1993 Q 1 28. 02. 2021
Quarter-to-quarter percentage changes seasonally and working day adjusted 28. 02. 2021
BC extraction n n Seasonally adjusted OTY, AO and B-QO series (by time-series modelling techniques) HP 1600 -filtered Unadjusted series (not modelled) BK 32 -8 filterd 28. 02. 2021
Austrian chained GDP HP-1600 filtered 28. 02. 2021
Log differencies of HP-1600 -transformed series 28. 02. 2021
Co-movement of cyclical components Coherence Average Spectrum Mean Delay 2 Y-8 Y r 0 rmax tmax (1) GDPao 0. 98 0. 41 -0. 01 0. 96 0 GDPqo 0. 88 0. 42 0. 1 0. 92 0 Series Cross-correlation Note: The + (-) sign refers to a lead (lag) vis-à-vis the reference series. 28. 02. 2021
Bry-Boschan BC turning points in HP-1600 filtered series 28. 02. 2021
Business cycle turning points 1992 1 1993 2 3 4 1 2 1994 3 4 1 2 1995 3 4 1 2 1996 3 4 1 2 1997 3 4 1 2 3 4 Austria HP ▲ ▼ ▲ ▼ BK ▲ ▼ ▲ ▼ HP Dyn Fact ▲ ▼ ▲ BK Dyn Fact ▼ ▲ Breuss (1984) Hahn et (1992) Artis et M. (2004) ▼ ▲ ▼ Artis et K. (2004) ▼ HP ▼ ▲ ▼ BK ▼ ▲ ▼ Mönch et (2004) ▲ ▼ Forni et (2000) ▼ ▲ ▼ Artis et M. (2004) ▼ ▲ ▼ Artis et K. (2004) ▲ ▼ CEPR (2003) ▼ ▲ Euro area 28. 02. 2021
Capacity utilisation in the Austrian industry 28. 02. 2021
Baxter-King 32 -8 -filtered series 28. 02. 2021
Bry-Boschan BC turning points for BK 32 -8 filtered series 28. 02. 2021
Conclusions n n Different quarterly chain-linking methods generate different time series. Their different time series properties can potentially interfere with modelling outliers, seasonalfactors, BC-components, … This can lead to different results for analysis based on model pre-processed series. The turning point detection process itself (not based on data pre-processed or pre-adjusted by timeseries models) seems to be rather robust to different quarterly chain-linking methods. 28. 02. 2021
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