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```									Benchmarking

United Nations Statistics Division
What is benchmarking?
 Benchmarking is a statistical technique aimed at
correcting inconsistencies between estimates of
the same variable obtained from data collected at
different frequencies
Why do we need benchmarking?
 Low frequency data (e.g. results of annual
surveys) are more comprehensive and accurate
than high frequency data (e.g. monthly/
quarterly survey results)
 Different sample sizes etc.

 Therefore, aligning high frequency data
(Indicators) with low frequency data
(Benchmark) is desirable
Example:
India                                                                   Malaysia
180.0
160.0             Annual MVA index
Annual MVA index
170.0
150.0             Monthly average
160.0             Monthly average
140.0
150.0
130.0
140.0

130.0                                                      120.0

120.0                                                      110.0

110.0                                                      100.0
2002   2003     2004   2005      2006   2007   2008   2009
100.0
2002   2003    2004   2005      2006   2007   2008   2009

Source: UNIDO MVA Database, UNSD Monthly IIP statistics
Major reasons for differences between
annual and monthly series
 Difference in coverage and sample
 Annual survey has broader coverage and a more
representative sample
 Differences in frame may exist
 Difference in definition and variables
 Value added replaces output for growth measures
 Accounting period
 Calendar year versus accounting year effect
 Inventory valuation
 Estimation method, non-response treatment,
imputation etc.
Purpose of benchmarking
 Create a coherent high-frequency data series
by correcting the difference between
benchmark and indicator values
 “Combine the relative strengths of low- and
high-frequency data while preserving as much
as possible the short-term movements” (IRIIP
2010)
 Improve quality of production data in terms of
comparability and coherence in time series

 Often discussed for QNA and IIP, but can also
apply to other indicators
Benchmarking methods
 Main benchmarking methods described in
existing recommendations (IRIIP 2010, OECD
manuals and IMF QNA Manual) include:
   Pro Rata distribution
   Proportional Denton Method
   ARIMA-model based methods
   General Least-squares regression models
Pro Rata distribution
 Annual value is distributed in direct proportion of
quarterly/monthly values

                                     
 I q, y                   Aq , y     
X q, y    Ay                I q, y               
  I q, y                  I q, y   
 q                        q          

I – indicator
X – new indicator estimate
A – annual value
Example of Pro Rata distribution method

Indicator                                  Derived quarterly VA
Quarterly       Qt to qt        Annual Annual                                 Qt to qt
a         b       c=a*b
indices         change in %     MVA    BI ratio                               change in %
101.0                                        101.0   14.507   1465
103.4           2.38                         103.4   14.507   1500            2.38
103.8           0.39                         103.8   14.507   1506            0.39
105.4           1.54                         105.4   14.507   1529            1.54
413.6                      6000 14.507                        6000
102.3           -2.94                      102.3 14.972       1532             0.17
103.5            1.17                      103.5 14.972       1550             1.17
104.5            0.97                      104.5 14.972       1565             0.97
103.8           -0.67                      103.8 14.972       1554            -0.67
414.1                      6200 14.972                        6200
Step problem caused by change of BI ratio

Source: IMF QNA manual
Pro Rata Distribution – step problem

Source: IMF QNA manual
Benchmark-to-indicator ratio
Pro Rata Distribution

Easy to compute and interpret    Smoothens quarterly estimates
only within a year.
No special software needed.
Concentrates bias in one
Quarterly estimates can be       quarter and cause abrupt
derived each year                change (“step problem”).
independently
Not recommended for longer
Estimates are well aligned to    time series.
benchmark value and are fairly
reliable when BI ratios are
stable
Proportional Denton method
 Goal: Find new estimates with minimal deviation
from original indicator series
2
4y
 X t X t 1 
min                                   t   ,..., 4 y
1
t 2  It  I t 1 
( X1 ,..., X 4 y )

under restriction (for flow series):

4y

X         t    Ay , y   ,..., 
1
t  4 y 3
Example of proportional Denton
method

No big jump
in year
change

Source: IMF QNA manual
Proportional Denton method – step problem
Benchmark-to-indicator ratio
Proportional Denton method

Smoothens the benchmark-to-        More difficult to compute.
indicators ratio.
Requires longer series.
Avoids “step problem”.
Calculation for new period
Is “optimal” for the given         results in revision of previous
objective.                         benchmarked series.

Modifications/variations exist to take into account additional
known information.
 Benchmarking is done retrospectively when
annual survey data are available
 Benchmarking is a part of temporal
disaggregation that also comprises
Interpolation and Extrapolation
 Interpolation is done when no measures
currently exists for the target variable
 Extrapolation provides an estimate of the
monthly/quarterly indicator when the annual
estimate is not yet available
 Usually by applying last available BI ratio or by
forecasting new BI ratio

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