S T A T I S T I K A U S T R I A11/10/2007 1

Model based estimation of enterprises below thresho lds

www.statistik.at

Seminar on

Reengineering of Business Statistics

11-12 October 2007, Lisbon

Sabine Zachsabine.zach@statistik.gv.at

11.10.2007© STATISTIK AUSTRIA

i n f o r m a t i o n s

We move

Model based estimation of enterprises below thresholds for SBS

in Austria

S T A T I S T I K A U S T R I A11/10/2007 2

Model based estimation of enterprises below thresho lds

� Objectives

� SBS Strategy

� Mathematical model

� Model effects

� Quality aspects

S T A T I S T I K A U S T R I A11/10/2007 3

Model based estimation of enterprises below thresho lds

Objectives:

� fulfill the requirements of the Austrian Federal Statistics Act 2000 and of SBS-Regulation

� reduce burden for small enterprises

� retain high data quality

� use synergies between statistical products

� use information from external sources (administrative sources)

� introducing model based estimation in business statistics

S T A T I S T I K A U S T R I A11/10/2007 4

Model based estimation of enterprises below thresho lds

SBS Strategy in Austria (from 2002 onwards):

� Statistical survey for enterprises exceeding certain threshold values

� Employment thresholds in production

� Turnover thresholds in services

� Use of administrative sources

� Social security authority

� Tax authority

� Model based estimation for enterprises below thresholds on micro level

S T A T I S T I K A U S T R I A11/10/2007 5

Model based estimation of enterprises below thresho lds

91% 9%

87% 13%

85% 15%

76% 24%

12% 88%

survey estimation

Principle of concentration

S T A T I S T I K A U S T R I A11/10/2007 6

Model based estimation of enterprises below thresho lds

new SBS conceptnew SBS concept

thresholds

enterprises above thresholds enterprises below thresholds

conducted by

final results

new SBS concept

thresholds

enterprises above thresholds

survey

enterprises below thresholds

estimation

methods registers, classifications and methods division

directorate business statistics

S T A T I S T I K A U S T R I A11/10/2007 7

Model based estimation of enterprises below thresho lds

turn

over

empl

oyee

s

Inve

stm

ent

about 280.000 active enterprises

survey

estimation

responsenonresponse [~5%]

~35.000 enterprises [12,5%]

~245.000 enterprises [87%]

…

:::::::::::::::::::::::: ::::::

threshold

external sources

data matrix

stoc

ks…~ 120 different variables

S T A T I S T I K A U S T R I A11/10/2007 8

Model based estimation of enterprises below thresho lds

� Data analysis

� Parameter estimation based on the survey results of the reporting year

� No recent information from enterprises below thresholds available

� Select model base to obtain most suitable parameter s

� to take into account the size range distinction of some variable

� Specify a suitable general model

� Produce synthetic model parameters

� for each of the 595 NACE-classifications

� to estimate micro data information for enterprises below thresholds

Mathematical model - Decision making

S T A T I S T I K A U S T R I A11/10/2007 9

Model based estimation of enterprises below thresho lds

MM

0

10

20

30

40

50

60

GrKl

0 1 2 3 4 5 6 7 8 9

observable array

legal threshold

size range ofemployees

model basis for parameter estimation

none observable array

personnel expenditures per employee

Conceptual approach

S T A T I S T I K A U S T R I A11/10/2007 10

Model based estimation of enterprises below thresho lds

� Consideration of the economic sector distinction

� by selecting on the most detailed NACE classification level (6-digits)

� Consideration of the size range distinction

� by applying a threshold that is raised step by step

� starting with a threshold of 999.000 € turnover

� all units below the threshold are included

� generally 15 units are required (model dependent)

� raise the threshold step by step by 1 Mio €

� turn to the next classification level by 5 Mio €

Model basis selection

S T A T I S T I K A U S T R I A11/10/2007 11

Model based estimation of enterprises below thresho lds

Model basis selection

thresholds in 1.000 EURO

num

ber

of b

ranc

hes turnover<=4.999

turnover<=3.999

turnover<=2.999

turnover<=1.999

turnover<= 999

0

20

40

60

80

100

120

140

160

1-digit 2-digit 3-digit 4-digit 6-digit

Turnover < = 4999Turnover < = 3999Turnover < = 2999Turnover < = 1999Turnover < = 999

S T A T I S T I K A U S T R I A11/10/2007 12

Model based estimation of enterprises below thresho lds

� for main variables

� by using linear regression

� limited to the regressors turnover and employees

� Outlier influence �

� Therefore a robust model (LTS= least trimmed squares regression)

� for detailed variables

� by using ratio estimation

� which breaks down all main variables (e.g. turnover, investment, stocks)

Calculation of model parameters

S T A T I S T I K A U S T R I A11/10/2007 13

Model based estimation of enterprises below thresho lds

Branche= 0y1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000

Regr

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Regressi onsgl ei chung y1 = 252. 8782 + 0. 550137*Regr y2 = -4. 139025 + 1. 072434*Regr

OLS: y = 252,8782 + 0,550137 * turnoverLTS: y = -4,13902 + 1,072434 * turnover

y

turnover

ordinary least squares regression

robust regression (LTS)

Example: robust and non robust model

S T A T I S T I K A U S T R I A11/10/2007 14

Model based estimation of enterprises below thresho lds

gross comp.

business register

Micro data calculation

expendituresexpenditures

in some cases model modification due to expert rati ng

regression parameter ß ij

parameter estimation based on adjusted survey data [model basis]

expenditures without gross wages& salaries

turnovertax authorities

income

investment .

stocks

research

. . .

purchases

expenditures

employeessocial security

authority

part time employee

regression parameter ßij

ratio estimator p ij

.

.

.

interest paid

depreciation

p. of services …

expand.for freight ..

input of raw & aux..

rental expanses

duties, taxes …

financial leasing

other expendit.gross w. & s.

gross wages

gross salaries

soc. sec. contr.

other expendit.

active enterprise

.

.

.

S T A T I S T I K A U S T R I A11/10/2007 15

Model based estimation of enterprises below thresho lds

� Quality of the business register

� timeliness and completeness of links to external registers

� Quality of the collected basic data [survey]

� sufficient survey coverage, also on detailed classification level

� usability for the parameter estimation

� Quality of the data from external sources

� accordance to the SBS definition (fiscal turnover)

� Quality of the model based estimation

� sufficient collected units for the parameter estimation

� suitability of the chosen mathematical model

� parameter transferability

Quality aspects

S T A T I S T I K A U S T R I A11/10/2007 16

Model based estimation of enterprises below thresho lds

� Model respectively data adjustment

� by experts for business statistics

� subjective examination and modification of values and parameters

� due to structural analysis of corresponding economic sections

� if systematic deviations are known

� Reasons

� low covered inhomogeneous economic sectors

� economic sectors with high structural size range deviation

� to less collected units of an economic sector

Expert rating

S T A T I S T I K A U S T R I A11/10/2007 17

Model based estimation of enterprises below thresho lds

Thank you for your attention!