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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!
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