Download - L08 - Benchmarking Techniques (ENG)
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1Quarterly National Accounts CourseJoint Vienna InstituteAugust 5 - 16, 2013
L-8: Benchmarking Techniques
Reproductions of this material or any parts of it should refer to the IMF Statistics Department as the source
Lecture Outline
Benchmarking Principles in QNABenchmarking Principles in QNAThe Denton PFD method
Enhanced formula for extrapolation
Benchmarking and revisions
JVI/QNA/L8 : 2IMF Statistics Department
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2IntroductionQuarterly compilation involves:Q y p
Establishing a set of quarterly national accounts for periods the annual estimates are available
Construction of historical quarterly accountsUpdating a set of quarterly national accounts -derivation of quarterly estimates for most current periods with no annual estimatescurrent periods with no annual estimates
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Discrepancy Between QNA and ANA
Discrepancies occur due to:Discrepancies occur due to:Independent collection of quarterly and annual data sources for the same phenomena
Quarterly data based on (smaller) sample surveys using simplified questionnairesAnnual data based on censuses/larger sample surveys using more comprehensive questionnairesAnnual data based on data from audited business accounts
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3Discrepancy Between QNA and ANA
Discrepancies occur due to:Discrepancies occur due to:More information, and more detailed information, available annuallyQuarterly estimates based on:
Fixed input output coefficientsTrend extrapolationsTrend extrapolationsGuesstimates
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Discrepancy Between QNA and ANA
Discrepancies occur due to:Discrepancies occur due to:Compilation procedures for annual and quarterly national accounts estimates may differ
Annual accounts more detailedAnnual accounts more completeUse of supply and use tables as compilation tool for Use o supp y a d use tab es as co p at o too othe annual accountsUse of simplified methods in the quarterly accounts
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4Discrepancy Between QNA and ANADiscrepancies removed byp y
Benchmarking the quarterly data to the ANA estimates
So thatTime series of quarterly and annual data for the same phenomena are consistentAccuracy and quality of the quarterly data areAccuracy and quality of the quarterly data are increasedQuarterly data could be used to forecast annual data
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Benchmarking: Basic ApproachesManual reconciliation and revision of independent annual and quarterly data sources, and annual and quarterly estimatesMechanical methods
Pro-rata distribution breaks in series (the step problem)Time series method no breaks in seriesTime series method no breaks in series
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5Pro Rata Distribution and Step Problem
Distribution presentation Xq is the level of theDistribution presentation Xq, is the level of the QNA estimate for quarter q of year
Iq, is the level of the indicator in quarter q of year
q q
qq I
IAX
,, .
q y A is the level of the
ANA estimate for year
q qI ,
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Pro Rata Distribution and Step Problem
Benchmark-to-indicator Xq is the level of theBenchmark to indicator ratio presentation
Xq, is the level of the QNA estimate for quarter q of year
Iq, is the level of the indicator in quarter q of year
qqq I
AIX
,, . q y
A is the level of the ANA estimate for year
q qI ,
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6Pro Rata Distribution and Step Problem
Both equations are algebraically equivalent
Only the presentation differs
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Extrapolation with an IndicatorFor the quarters of the current year or even the q ymost recent year, independent ANA data are not available.QNA estimates for these periods should be consistent with the QNA estimates for previous periods that are benchmarked to the annual data.M t i th t l i di t i d tMovements in the quarterly indicator is used to extrapolate/update the QNA estimates (benchmarked to the ANA) to derive the QNA estimates for quarters with no ANA estimates.
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7Extrapolation with an Indicator
Extrapolation presentation Xq is the level of theExtrapolation presentation Xq, is the level of the QNA estimate for quarter q of year
Iq, is the level of the indicator in quarter
IIXX qq
,4
1,,41, .
indicator in quarter q of year
,4
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Extrapolation with an Indicator
Benchmark-to-indicator Xq is the level of theBenchmark to indicator presentation
Xq, is the level of the QNA estimate for quarter q of year
Iq, is the level of the indicator in quarter
IXIX qq
,4
,41,1, .
indicator in quarter q of year
,4
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8Pro Rata Distribution: Step Problem
98 0
100.0
102.0
104.0
106.0
108.0 -------------------------Back Series-------------------------
980
1000
1020
1040
1060
1080-------Forward series-----
96.0
98.0
1997 1998 1999960
980
Indicator (left hand scale)QNA estimates derived using pro rata distribution (right hand scale)
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Pro Rata Distribution: Step Problem
Benchmark-to-indicator ratioBenchmark to indicator ratio
9.8
10.3
1997 1998 1999
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9Golden rules of BenchmarkingA benchmarking procedure should satisfy two g p y
requirements at the same time:Preserve as much as possible the short-term movements in the quarterly source data under the restrictions provided by the annual dataEnsure, for the forward series, that the sum of the four quarters of the current year is as close
ibl t th k f t l d tas possible to the unknown future annual data
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Benchmarking Methods That Avoid Steps
Time series method avoiding stepsTime series method avoiding stepsVarious, but same purposeKeeps the movements of the short-term benchmarked series as proportional as possible to those in the original series
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Benchmarking Methods That Avoid Steps
Proportional Denton methodProportional Denton methodKeeps the movements in the benchmarked QNA series as proportional as possible to those in the quarterly indicator series using a least square technique to minimize the difference in relative adjustment to neighboring quarters subject to annual total constraint.
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Optimal Benchmarking SolutionFor the back series, the method ,recommended in the IMF QNA manual is the Proportional First Differences (PFD) solution proposed by Denton (1971) which
Preserves the short-term movements in the indicators keeping the quarterly estimates as proportional to the indicator as possible (avoid the step problem)Considers the annual benchmarks as binding constraints
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Denton PFD methodIn mathematical terms, the benchmarked ,series Xt is the solution of the following minimization problem:
NtforYX
YXN tt 4,...,2,1min
241
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NTforAXtsYY
TTt
t
t tt
,...,2,1..2 1
Proportional Denton Method
Benchmarking without Step ProblemsBenchmarking without Step Problems
98.0
100.0
102.0
104.0
106.0
108.0
980
1000
1020
1040
1060
1080------------------ Back series ------------------------------- ----Forward series ----
96.01997 1998 1999
960
Indicator (left hand scale)QNA estimates derived using pro rata distribution (right hand scale)1997-98 distributed 1999 extrapolated using Proportional Denton (right hand scale)
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Proportional Denton Method
Benchmark-to-Indicator Ratios
10.3
9.81997 1998 1999
1997-98 distributed 1999 extrapolated using Proportional Denton Annual step change
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Improving extrapolation of QNA results
Using proportional Denton method implies thatUsing proportional Denton method implies that the B-I ratio for the fourth quarter of the last benchmarked year is used to prepare the forward QNA seriesThe B-I ratios for quarters with ANA data are usually different and change smoothly y g y
Depends on the movements in the annual B-I ratios
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Improving extrapolation of QNA resultsFor the forward series, the Denton PFD ,method results in quarter-to-quarter rates of change that are identical to those in the indicator series. But
When there is a bias between the movements of the target variable and those of the indicator, extrapolations should be adjusted to better predict the next annual growth rate of the target variable
An adjustment (or enhancement) to the original Denton method is proposed in the IMFs QNA manual (chapter 6)
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Improving extrapolation of QNA results
The B-I ratios for quarters with no ANA data canThe B I ratios for quarters with no ANA data can be improved by
Forecasting annual B-I ratios Deriving quarterly B-I ratios taking into account the forecasted annual B-I ratio
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Denton PFD method with enhancement for extrapolation
The minimization problem changes into:
4 2
1
2 1
4min for 1, 2, , ,t tt t t
N s X X tI I
N s
p g
B-I forecast for year N+1
4 14
4 1 1
,
s.t.
for 1, 2,3, 4
, for 1,2, ,t Tt TN s
t Nt
t N t N
X A T N
X Aw sI I
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Benchmarking and Revisions
When the ANA data becomes available:When the ANA data becomes available:The QNA data for that year are benchmarked to the ANA dataThe QNA data for the quarters of the subsequent years are revisedThe QNA data for earlier years are revised
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Benchmarking and Revisions
When ANA data for previous years are revised:When ANA data for previous years are revised:The QNA data for those years are benchmarked to the revised ANA dataThe QNA data for the quarters of the subsequent years are revisedThe QNA data for earlier years are revised
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Benchmarking and RevisionIncorporation of new annual data for one yearp ywill generate revisions of quarterly data for neighboring yearsThe Denton method is optimal because revisions for one year are distributed smoothlyover several quarters, not just within the same yearyearThe enhanced Denton method tries to improve the B-I forecast for the next year, and then reduce revisions to preliminary QNA data
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