Extrapolation and benchmarking
Vu quang Viet
UNSD consultant
Why extrapolation and benchmarking?
• Normally data, even annual, are not available on time
and comprehensive enough to compile a definite annual
data set.
• As a rule, economic statistics and national accounts are
estimates that are extrapolated from a base year using
indicators.
• Data from a base year is considered the most reliable as
they are based on economic census that covers the
complete population.
• Indicators are based on survey (or administrative report)
of a limited number of units in an activity thus are less
reliable.
• When a new base year is compiled, the estimates must
What are normally benchmarked?
• Quarterly values are benchmarked so that the sum of
quarterly values is the same of the annual value. This
will not be the focus of this workshop.
• Annual estimates should be benchmarked so that the
last annual estimate should match the benchmark value.
• These benchmarking applies to an individual statistics or
a composite statistics such as quarterly GDP and annual
GDP.
• Preferred approach: benchmark each individual statistic
series.
Indicators
• Economic performance indicators are mostly drawn from
annual or quarterly accounts and therefore are fully
consistent with one another and provide useful overview
of the economy, its strength as well as weakness.
• All indicators would be more meaningful in the context of
changes over time, therefore, time series of statistics are
required.
Indicators that are used to national
accounts aggregates
• Industrial production indexes.
• Crop yield indexes.
• Employment indexes, based on:
Establishment survey that captures only
employment in formal activities that are
covered by updated census frame
Labor force survey (based on surveying
households) that captures employment in
informal activities.
• Retail sale indexes.
• Investment (GCF) indexes.
Some indicators for Compensation of
employees
• Labor Force Survey (LFS): statistical unit of LFS is the household.
In this case, LFS covers data on employees for both corporations
and unincorporated enterprises and government. Provide:
– unemployment rate, employment rate and the participation rate.
– Wage rates by industry, occupation, public and private sector,
hours worked and much more, all cross-classifiable by a variety
of demographic characteristics.
• Establishment Survey (ES): This survey is also normally carried
out monthly and annually that provides data to produce production
indexes and labor by establishments (covered in business registers).
• Informal employment: Informal employment is estimated as the
difference between employment in LFS and in ES. It is used to
estimate mixed income for the household sector beyond agriculture.
• Financial reports of corporations.
• Corporate income taxes from tax authority.
Some indicators for final
consumption
• Household final consumption of market goods and services:
– Indexes of retail sales
– Administrative data on water, gas and electricity, communication, etc.
– Employment data collected by monthly Labor Force Survey (LFS) on
health, education and personal services.
• Household final consumption of nonmarket goods and
services:
•
•
•
– Administrative on government expenditures
Household gross capital formation: data on construction of
residential building and estimation of own-account construction based on
construction materials. Increase in machinery and equipment for
unincorporated enterprises may be based on benchmark capital/output
ratios.
Compensation of employees: extrapolated by LFS.
Mixed income: extrapolated by informal employment estimated as the
difference between employment in LFS and in Establishment Survey (ES).
Extrapolation for income approach
Benchmark
compensation of
employees (COE) of
corporations
Administrative data,
particularly
government payment
of COE
Benchmark value of
corporate profits (gross
operating surplus)
Extrapolation by
Labor Force
Surveys
Surveys of corporate
profits or estimated
from tax returns
By production
approach
Household unincorporated
enterprises
Estimated annual or
quarterly COE of
corporate sectors and
government
Annual and quarterly corporate
profits (gross operating surplus)
Benchmark value of private
gross capital formation
Household
mixed income
Use of indicators for extrapolation
• Base year: 2000.
• It-1,t : Volume index indicating growth from
t-1 to t.
• Q: Value in constant prices.
Q2000,t = Q2000,t-1*It-1,t
Benchmarking annual data to
base year data
• Benchmarking a series of values of annual
estimates to match the new annual value of the
benchmark year: growth rate approach.
• A general rule for benchmarking GDP is to
benchmark each component separately. A
component is made up as the sum of
benchmarked sub-components. Revised GDP is
the sum of benchmarked components.
Scheme for growth and value
benchmarking of annual data
Benchmark
year 2 =13
Benchmark
year 1 =10
Annual
Estimates
Conditions:
• New rates of growth are close to the old rates of growth
• The new rates of growth should permit the obtaining of
the new benchmark value at the new benchmark period.
Example for benchmarking annual
values
Time period
Preliminary GDP
Actual benchmark
value
GDP after
benchmarking
1
10
2
11
3
11.5
4
12
13
10
11.3
12.1
13
Method for mechanical benchmarking
• Find the percentage growth difference between the
estimate and the new benchmark for the same
benchmark year.
= 13/12=1.083
• Distribute that percentage difference to the n-years in
the old series.
• = (1.083)^(1/3) = 1.027
• New rate of growth = old rate * ig
Time period
Preliminary GDP
Preliminary growth index
1
2
3
4
10
11
11.5
12
100
Preliminary growth rates
110
1.1
115
1.045
Actual new benchmark value
120
1.043
Original values
Index with period
1=100
Index with previous
period =1
13
Actual benchmark growth index
130
Compared 13 to 10
Accumulated incremental growth rate
1.083
Compared 13 to 10
Annual incremental growth factor equally distributed to
each year
1.027
(1.083)^(1/3)
1.072
Preliminary growth
rates*Increment
al growth
130
New growth rate
applied to period
1 = 100
New growth rates
New growth index
New value
1.13
100
10
113
11.3
1.074
121.3
12.13
13
New growth index
applied to base
year value
Linking
Time series
1 in t=0
Time series
2 from t=1
Linking requires that data in the two time series
overlap at least for one year.
Linking
• Each time series is based on a base (benchmark) year.
• In constant prices, a time series is normally at the prices
of the base year.
• It is more convenient to connect times series of many
base years into one for analysis.
• Linking is a simple and mechanical way to link one base
year to another by using a given time series as a base.
Growth rates (in constant prices) are used to connect
backward and forward.
• Additivity problem: The problem with linking is that the
extrapolated total is not equal to the sum of the
extrapolated components, i.e. destroying the accounting
relationship.
• As growth rates are used for analyses, each individual
time series (total and components) should be linked
separately.
Difference between linking and chain index
(rebasing)
Rebasing
• As the base for an index series moves farther from the current year,
the structure in the components changes. Relative prices of a distant
base year period become less relevant to later periods,
– Growth rates tend to be higher than they should be with an outdated
base year.
• It is necessary to update the base year to be closer to current
period.
• However using the same information, every time the base year is
changed, growth rates change: This is like rewriting history.
Annual chain index
• Annual Chain index is basically the change of the base year yearly.
In this way, growth rates will not be rewritten as in using a fixed base
year.
• Linking will allow the connection of chain time series to a given
reference year (for which any year of continence for an analyst can
be picked. Linking produces the additivity problem as discussed.