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Effect of the Cut-off Size on International Comparability of Industrial Statistics

Shyam Upadhyaya

International workshop on industrial statistics

8 – 10 July, Beijing

unido.org/statisticsOutline

• Why cut-off sampling

• Various thresholds and cut-off point

• Cut-off size and problems of data comparability

• UNIDO databases and estimation of cut-off portion

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Characteristics of the industrial survey

Target population highly heterogeneous by kinds of activitiesThere are more than 150 activity groups in manufacturing at 4-digit

Highly skewed distribution

A few large companies account for a significant amount of major variables of interest (employment, output, capital formation)

Statistical units are not uniformVary from hardly identifiable family business to huge industrial enterprise with a complex corporate structure

Specific geographical distribution

Designated industrial estates, export processing zones, area of mineral resources or other raw materials

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Size and distribution of manufacturing sector of Nepal

0.00

20.00

40.00

60.00

80.00

100.00

'0 up to 9 10-19 20-49 50-99 100-199 200 andmore

Employment size class

Perc

enta

ge

Number of units

Value added

Example of the distribution pattern

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Cut-off sampling – theoretical framework

Use of cut-off in two ways:

Designate a cut-off size to divide population into two sub-populations -W. Edwards Deming (1960)

Exclude smaller units from the survey

“Cut-off is a sampling procedure in which a predetermined threshold is established with all units in the universe at or above the threshold being included in the sample and all units below the threshold being excluded… In the case of establishments, size is usually defined in terms of employment or output.”

- OECD Glossary of statistical terms

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Design considerations for cut-off sampling

Deming applied cut-off sampling in manufacturing survey by dividing

the target population N into two sub-populations 1N and 2N

Sample for first part was taken as 11 Nn

Second part was determined by: 2

222

xCx

Pn

Where, 2P - proportion of units in percent to total, i.e. 10021 PP

2 - variance for sub-population N2

x - estimated mean of a variable for total population

xC - coefficient of variation.

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Decision on cut-off point

An indicative cut-off point can be determined by where mj is the size measure

and n is sample size

For an economy with 150 000 employees a sample of 500 establishments would mean that establishments with 300 and more employees can be selected with certainty

More precise cut-off size for certainty - Vijaya Verma (1991), SIAP

πj is the selection probability and Mj - the cumulative value of size measure of j-th unit.

Application of this method shows that units larger than a particular size gets the selection probability exceeding 1 which determines the cut-off point for certainty

n

mK j

jjj

j mMmjn

MMm 1

Njm

mn

j

jj ...1

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Size class Number of units

Share in total (in %)

Number of employees

Share in total (in %)

Selection probability

Sampling decision

500 and more 17 1.46 17725 34.07 Equal to 1 Take All 100 - 499 41 3.53 12089 23.23 0.41 - 0.99

Take

sample of some

50 – 99 50 4.30 6465 12.43 0.21 - 0.40 20 - 49 76 6.54 5252 10.09 0.10 - 0.20 10 - 19 168 14.46 4645 8.93 0.04 - 0.10 5 – 9 230 19.79 3299 6.34 0.02 - 0.04

Less than 5 580 49.91 2557 4.91 Less than 0.02 Take none (Cut-off)

Grand Total 1162 100.00 52032 100.00

Illustration of two sides cut-off ...

Two sides cut-off:1. For selection of units with certainty2 . For exclusion of units from sample

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Estimation of cut-off portion1. Assume that the cut-off portion is really negligible so estimates of the

surveyed population are accepted with the relative bias of

Where t0 and t are estimators for surveyed and total population

2. Apply the ratio of a variable y from a surveyed population to another variable x observed earlier for entire population to estimate the cut-off portion

Assuming thatIts estimator can be used to estimate with an approximate relative bias of:

t

t

t

ttE 00 1)ˆ(

0

00 )(

x

yNR

NRNR )( 0

1)(

)( 0 NR

NR

)(ˆ0NR )(ˆ NR

- Särndal, Swensson, Wretmann (1991)

unido.org/statisticsSurvey thresholds in

practice

All industrial activities

Below the Registry threshold Very small and not identifiable units

Above the Registry threshold Identifiable units

Business register

Small units

Other large and medium units

Very large units

Cut-off point

Registry threshold

Certainty threshold

Lower the cut-off point better the coverage and more accurate are survey estimates

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Cut-off as a threshold for two independent surveys …

Survey of larger units

Based on the list frame from the business register

Information needed for stratification normally available

A detail questionnaire on a large range of data items is implemented

Data collection through mail or web-based questionnaire

Survey of smaller units

• Area-cum-list frame

• Limited information for stratification

• A smaller version of the questionnaire with basic data items

• Extensive field survey through direct interview

A threshold may divide the population into sub-populations for independent surveys

unido.org/statisticsPros and cons of two independent

surveys

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• Single estimates of entire industry cannot be produced

• Larger establishments survey gets priority and survey of smaller units is ignored

• Results of larger establishment survey are de facto presented as the estimates for total industry

• Design flexibility

• Better planning

• More applicable survey instruments

unido.org/statisticsCut-off size and problems of

international data comparability

1. Size measure applied to different statistical unitsEnterprise - in European countriesEstablishment – in North America, Japan and most of the developing countries

2. Cut-off size varies by countryBangladesh, Nepal 10 persons engaged

India - units using power and employing 10 or more workers; all others employing 20 or more workers.

Sri Lanka - 25 persons or more engaged

3. Cut-off size changes over time in the same countrySwitch over from employment to output criteria

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Number of countries by type of cut-off size

Type of cut-off size In % to total No cut-off size or no exclusion in estimation 46.5 With cut-off size (no estimation for cut-off portion)

53.5

Out of which Employment based 29.8

Less than 5 persons 0.9 5 persons 9.6 10 persons 15.8 20 persons 3.5

Multiple criteria (e.g. employment and capital)

7.0

Other criteria (Ownership, license)

4.4

Cut-off size not adequately specified 12.3 Total 100.0

Source: UNIDO Metadata

Mostly developed statistical system

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Problems and solutions

• No standard cut-off point across the countries (not a solution !)

• Data represents varying portions of industry if no estimation is made for cut-off portion

• Detail information about the cut-off size is missing in international reporting

• Results without estimation for cut-off portion become incomplete and incomparable

Lower cut-off size produces more comparable estimates - US cut-off for ASM is 1 paid employee

Cut-off based on the contribution of units to total value added

- 1% cut-off means smallest units with total combined contribution less than 1 percent are excluded

An established estimation procedure for establishments below the cut-off point

unido.org/statisticsEstimation at international

level

0.0

50.0

100.0

150.0

200.0

250.0

500 and

more

200-499 100-199 50-99 20-49 10-19 Less than

10Employment size classV

alue

added

per

em

plo

yee,

mil $

Value added per employee

Log linear regression line

Source: UNIDO Size-class database

• Additional data on ratio from other survey data for entire population is rarely available to UNIDO

• Instead, UNIDO uses its size class database to get such ratio as VA per employee to estimate the value for cut-off portion.

• A regression model is used to predict the VA per employee for smaller establishments.

unido.org/statisticsIn conclusion:

• Designation of a threshold or cut-off in industrial surveys is a convenient approach, but not an ideal one. It has trade off between the time and cost on one hand and the precision of results on the other hand.

• Cut-off sampling should be applied with some precaution:

- whether cut-off portion is really negligible

- if not, whether data are available for estimation of cut- off portion and how the estimates will be produced for cut-off portion

• For international organizations like UNIDO it is necessary that any cut-off point applied to survey should be reported so that any necessary estimation could be made.