Estimation of preliminary unemployment rates by

means of multiple imputation

UN/ECE-Work Session on Data Editing

Vienna, April 2008

Thomas Burg, Statistics Austria

www.statistik.at

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Outline

Description of the problem

Methods of Estimation

Preliminary estimation using MI

Results

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Quickness of results

Today policy makers want to receive results as early as possible

Challenging for official statistics

Final results only after field work is completed

Can I get figures earlier?

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Austrian Labor Force Survey

Survey performed quarterly based on a rotatingsample of households. Every quarter one fifthof the sample is exchanged

Data collection is distributed to 13 weeks of a quarter andrespondents are questioned about their labor status withreference to the week before.

Most important figures: Unemployment rates

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Situation during field work

End of quarter

Estimation on data available on first day afterQuarter ends.

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The Problem

Is it possible to estimate preliminary unemploymentRates on the basis of the data already received?

AvailableData ~70%

Missing Records ~30%

Unemploymentfigures

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Missing Records

For missing records not everything is missing……

Rotating sample Basic socio demographic information (Age, Sex, etc…

Information from sampling frame Assumed household size, residence..

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Estimation Methods

Weighting on basis of available data Raking procedure involving marginal distributions

of the Austrian population

Imputing labor status for records still to come

Assumption on the set of records necessary

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Imputing labour status

AvailableData ~70%

Missing Records ~30%

To impute values on a record I definitely needrecords on which I can impute!

Informationfrom priorrotations and from the sampling frame

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Multiple imputation

In official statistics not very common:

There you like to have authentic databaseswith stored values

Multiple imputation rather focuses on concrete estimation problems

=> Here I have a concrete estimation problem!

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Multiple imputation – single imputation step Analysis (I)

Labour status:

4 possible values (1=’employed’, 2=’unemployed’, 3=’not relevant for employment’, 4=’military person’).

Analysis of distributional differences of labour status between known and expected records based on poststratificationincluding Sex , Age-groups, and Citizenship

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Multiple imputation – single imputation step Analysis (II)

Results were also depending on the quarter.

Even incorporating this figures were not satisfactory

=> There must be an additional factor

=> Weight of a person delivered desired result.

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Multiple imputation – single imputation step

Identify stratum s

Get distribution Y forLabour Status in sratum s

Correct Y by estimateddistribution differences C

Generate random numberx and assign imputedvalue for Labour Status according to Y+C

Single Imputation for a record not received

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Multiple imputation

Multiple Imputation smoothes out Variability of estimators

Estimation of differences of distribution between known records and expected records of the specified quarter on the basis of quarters already processed. Weighting of the dataset based on certain socio-demographic assumptions concerning the records still to come. Computation of the distribution of labour status of the already known records 25 times single imputation of the item labour status according to the algorithm above and calculation of the unemployment rate on the basis of imputed and non-imputed values for every single imputation. Final estimation of the unemployment rate by the mean value over all imputation runs.

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Results (I)

Results for the MI-Estimation of preliminary figures compared to the real data

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Results (II)

Umemployment Rate

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Real data 5.2 5.2 5.0 5.1 5.5 4.7 4.3 4.5

Grossing up 5.2 5.2 5.3 5.0 5.3 4.6 4.3 4.4

MI 5.3 5.2 5.4 5.1 5.4 4.7 4.2

q1_2005 q2_2005 q3_2005 q4_2005 q1_2006 q2_2006 q3_2006 q4_2006

Umemployment Rate

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Real data 5.2 5.2 5.0 5.1 5.5 4.7 4.3 4.5

Grossing up 5.2 5.2 5.3 5.0 5.3 4.6 4.3 4.4

MI 5.3 5.2 5.4 5.1 5.4 4.7 4.2

q1_2005 q2_2005 q3_2005 q4_2005 q1_2006 q2_2006 q3_2006 q4_2006

Comparison of estimation of unemployment rate – MI, Grossing up and Real data

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Conclusions – Critical remarks

Multiple imputation is a possible estimation strategy for preliminary figures

Problematic assumptions concerning expected records

Time series are very thin now