Folie 1

1
How similar are different calibration estimators
in the presence of a zero-inflated auxiliary
variable? Evidence from the German job vacancy
survey Hans Kiesl Institute for Employment
Research (IAB), Germany hans.kiesl_at_iab.de
NTTS 2009 New Techniques and Technologies for
Statistics Brussels February 18-20, 2009
2
Background

• Regulation (EC) No. 453/2008 of the European
  Parliament and of the Council of 23 April 2008 on
  quarterly statistics on Community job vacancies
• Member states have to provide
• quarterly data on job vacancies (broken down to
  NACE section level)
• quality reports
• In Germany, the data will be provided by the IAB.

3
Background (2)

• Information on job vacancies in Germany
• Business units might report job vacancies to the
  Federal Employment Agency
• Federal Employment Agency publishes monthly
  statistics on number of registered job vacancies
  (by NACE-sector)
• Since 1989, IAB conducts a yearly (4th quarter)
  sample survey among business units to estimate
  number of job vacancies (registered or not) and
  to get additional information (e.g. about
  recruiting strategies)
• Mail questionnaire (8 pages in length) voluntary
• CATI interviews in quarters 1 - 3

4
Basic estimation strategy

• stratified simple random sampling (by size
  classes and industry sector)
• calculate design weights as inverse (realized)
  sampling rate within each stratum
• calibrate design weights to known totals from
  external data
• number of business units by size
• number of business units by industry sector
• number of employees by size
• number of employees by industry sector
• number of registered vacancies by industry sector
  

5
Calibration estimators (1)

• RAKCON
• raking estimator with weight restrictions
• within each stratum only two different weights
  allowed
• units with vacancies, units without vacancies
• reason control variance of weights and variance
  of estimates
• start with design weights and repeat following
  two steps until convergence of weights
• proportional fitting of weights for units with
  vacancies to number of registered vacancies by
  sector
• iterative proportional fitting of all weights to
  number of units by size and by sector

6
Calibration estimators (2)

• Generalized regression estimator (GREG)
• minimizes
  so that
• GREG1 calibrated to
• number of units by size
• number of units by sector
• number of registered vacancies by sector
• GREG2 additionally calibrated to
• number of employees by size
• number of employees by sector

7
Calibration estimators (3)

• Generalized regression estimator (GREG) with
  weight restrictions
• GREGCON1 N1 set of units with vacancies
• GREGCON2 N1 set of units with registered
  vacancies

8
Result of different calibration estimators

• 4th quarter 2007, Germany (west)
• realized sample size 7,485 (response rate 20)

9
Highly skewed distribution of job vacancies
of 0s 91 97 86 96 77 91 68 86 48 75
36 71
size
10
Simulation study

• Create synthetic population by sampling with
  replacement from original sample
• Draw 300 samples from synthetic population with
  same sampling design and realized sample sizes as
  original sample
• Calculate all estimators described above
• Repeat for different nonresponse models
• RHG1 equal response probability within strata
• RHG2 equal response probabilities within two
  group (units with and without vacancies) in every
  stratum
• RHG3 equal response probabilities within two
  group (units with and without registered
  vacancies) in every stratum

11
Sampling distributions under RHG 1

12
Sampling distributions under RHG 2

13
Sampling distributions under RHG 3

14
Two step GREG estimation

• If we accept RHG2, unconstrained GREG is biased.
• No information in the frame or among
  non-responding units to directly estimate the
  response probabilities.
• Suggestion two step GREG estimation.
• First step GREG estimation, calibrating to
  registered vacancies
• Using the calibrated weights, we can get
  estimates for response probabilities.
• Second step adjust design weights for different
  response probabilities, add another GREG
  estimation step

15
How do we estimate response probabilities?
population
1st stage equal inclusion probabilities
sample
(model RHG 2)
respondents
16
Sampling distributions under RHG 1

17
Sampling distributions under RHG 2

18
Sampling distributions under RHG 3

19
Conclusions

• Weight restrictions lead to larger variance of
  estimators.
• Calibration estimators work under an implicit
  nonresponse model.
• Two step GREG estimator applicable if
• theory suggests certain response homogeneity
  groups,
• there is no complete information about RHG
  membership in the frame or among the
  non-responding units,
• the only information is an auxiliary variable
  applicable for calibration which identifies part
  of the RHG group.
• Special case existence of a zero-inflated
  calibration variable with the property that units
  with a value greater than zero are in the same
  RHG, but units with a value of zero might be in
  different RHGs.

20
Thank you very much for your attention!
NTTS 2009 New Techniques and Technologies for
Statistics Brussels February 18-20, 2009