Extrapolation and benchmarking

Vu quang VietUNSD 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 be

benchmarked to the data of the new base year.

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 approachBenchmark compensation of employees (COE) of corporations

Extrapolation byLabor Force

Surveys Estimated annual or

quarterly COE of corporate sectors and

government

Administrative data, particularly government payment of COE

Benchmark value of corporate profits (gross operating surplus)

Annual and quarterly corporate profits (gross operating surplus) Benchmark value of private gross capital formation

Surveys of corporate profits or estimated

from tax returns

Household unincorporated enterprises

Household mixed income

By production approach

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

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.

Benchmark year 1 =10

Benchmark year 2 =13

Annual Estimates

Example for benchmarking annual values

Time period 1 2 3 4Preliminary GDP 10 11 11.5 12Actual benchmark value 13GDP after benchmarking 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 1 2 3 4

Preliminary GDP 10 11 11.5 12 Original values

Preliminary growth index 100 110 115 120 Index with period

1=100

Preliminary growth rates 1.1 1.045 1.043 Index with previous

period =1

Actual new benchmark value 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)

New growth rates 1.13 1.074 1.072

Preliminary growth rates*Incremental growth

New growth index 100 113 121.3 130

New growth rate applied to period 1 = 100

New value 10 11.3 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.