L12 - Chain-linking in QNA (ENG)

8/11/2019 L12 - Chain-linking in QNA (ENG)

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Quarterly National Accounts Course

Joint Vienna Institute

August 5 - 16, 2013

L-12: Chain-Linking in QNA

Reproductions of this material or any parts of it should refer to the IMF Statistics Department as the source

Lecture Outline

Main conce ts of chain-linkin

Index number formulas

Techniques for annual chain-linking

Chain-linking and nonadditivity

IMF Statistics Department JVI/QNA/L12 : 2


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Main Concepts of Chain Linking

1993 SNAand 2008 SNA recommend movin fromfixed-base year constant price estimates to chain-linkedvolume measures

Changing/updating the base year and time series?

Linking the old base data to data on the new base?

SNA recommends changing the base period annually



Base eriod

Weight period

Reference period

Chain-linked indices do not have a particularbase or weight period

Reference period free to choose

0 0 ( ) ( )t t h t h t I I I



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If t =10 and h= 5 a five-year chain-linkedannual index measuring the change from year 0to year 10

Growth rates and indices for series that contain

net exports) meaningless


Choice of Index Number Formulas

Annually chain-linked quarterly Laspeyres volume index:

, 1 , ,i y i q yp q ( 1) ( , )

, 1 , 1

y q y

i y i yip q



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Annually chain-linked quarterly Paasche volume index:

, , , ,

( 1) ( , )

i q y i q yip q

PQ

, , , 1i q y i yi



Annually chain-linked quarterly Fisher volume index:

( 1) ( , ) ( 1) ( , ) ( 1) ( , )q y y q y y q yFQ LQ PQ



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Laspeyres versus Fisher?

Annually chain-linked quarterly Fisher index does notaggregate to the corresponding direct annual index, whileannually chain-linked quarterly Laspeyres index linkedby annual overlap technique does aggregate!

Annually chain-linked Laspeyres volume measures inmonetary terms are additive in the reference year and the

, .

Laspeyres formula is simpler to work and explain.


Techniques for Annual Chain-Linking of

Quarterly Data

2 alternative techniques:Annual overlap

One-quarter overlap

A third technique sometimes is used over-the-year technique

Should be avoided



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The Annual Overlap Technique

Compiling estimates for each quarter at the weightedannual average prices of the previous year

Subsequent linking using the correspondent annual datato provide linking factors


The Annual Overlap Technique

Handout 1



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The One-Quarter Overlap Technique

Compiling estimates of each quarter of year t at theweighted average prices of previous yearCompiling estimates for the overlap quarter (4th quarter ofyear t-1) at the weighted average prices of the same yeart-1The ratio between the estimates for the linking quarter atthe average prices of year t-1 and average prices of year- prov es e n ng ac or o sca e own o e pr ces

of t-2) the quarterly estimates of year t at prices of year

t-1.


The One-Quarter Overlap Technique

Handout 2



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The Over-the-Year Technique

Compi ing estimates or eac quarter at weig te annuaaverage prices of the current year.Compiling estimates for each quarter at weighted annualaverage prices of the previous year.The year-on-year changes derived from these constantprice data are used for extrapolating the quarterlyconstant price data of the reference period.


The Over-the-Year Technique

Handout 3



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The Three Techniques

Chain linked indices (Average 1999=100)

Period Annual overlap

technique

One-quarter

overlap

technique

Over-the-year

technique

2001 Q1 131.14 132.25 128.48

. . .

2001 Q3 138.47 139.61 137.33

2001 Q4 185.67 187.23 187.17


Chain-Linked Measures and Nonadditivity

Additivity consistency in aggregation for indexnumbers

Temporal aggregationAnnual overlap technique applied to Laspeyres-type index guarantees temporal additivity

Cross-sectional a re ation

No chain-linking techniques guarantee additivityAll chain-linked volume measures are nonadditive

Example Handout 4



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Which Technique to Choose?Two chain-linking approaches:

One-quarter overlap technique, combined withbenchmarking to eliminate temporal discrepancy

Annual overlap techniqueIn many cases the two approaches give similar results

The over-the-year technique should be avoided(distorted seasonal pattern in the linked series)


L12 - Chain-linking in QNA (ENG)

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