Regression composite estimation for the Finnish LFS from a practical perspective Riku Salonen

Outline Design of the FI-LFS The idea of RC-estimator Empirical results Conclusions and future work LFS Workshop in Rome May 15 - 16, 2014

The FI-LFS Monthly survey on individuals of the age 15-74 Sample size is 12 500 divided into 5 waves It provides monthly, quarterly and annual results Sampling design is stratified systematic sampling The strata: Mainland Finland and Åland Islands In both stratum systematic random selection is applied to the frame sorted according to the domicile code Implicit geographic stratification LFS Workshop in Rome May 15 - 16, 2014

Rotation panel design Partially overlapping samples Each sample person is in sample 5 times during 15 months The monthly rotation pattern: 1-(2)-1-(2)-1-(5)-1-(2)-1 No month to month overlap 60% quarter to quarter theoretical overlap 40% year to year theoretical overlap Independence: monthly samples in each three-month period quarterly sample consists of separate monthly samples LFS Workshop in Rome May 15 - 16, 2014

Sample allocation (1) The half-year sample is drawn two times a year It is allocated into six equal part - one for the next six months The half-year sample (e.g. Jan-June 2014) The monthly sample (e.g. Jan 2014) ”Sample bank” Jan Wave (1) Feb Wave (2) Mar Earlier samples Wave (3) Apr Wave (4) May June Wave (5) LFS Workshop in Rome May 15 - 16, 2014

Sample allocation (2) The monthly sample is i) divided into five waves wave (1) come from the half-year sample waves (2) to (5) come from ”sample bank” ii) distributed uniformly across the weeks of the month (4 or 5 reference weeks) The quarterly sample (usually 13 reference weeks) consist of three separate and independent monthly samples. LFS Workshop in Rome May 15 - 16, 2014

Weighting procedure The weighting procedure (GREG estimator) of the FI-LFS on monthly level is whole based on quarterly ja annual weighting also. For this purpose i) the monthly weights need to be divided by three to create quarterly weights and ii) the monthly weights need to be divided by twelve to create annual weights. This automatically means that monthly, quarterly and annual estimates are consistent. LFS Workshop in Rome May 15 - 16, 2014

The idea of RC-estimator Extends the current GREG estimator used FI-LFS. To improve the estimate by incorporating information from previous wave (or waves) of interview. Takes the advantage of correlations over time. LFS Workshop in Rome May 15 - 16, 2014

RC estimation procedure The technical details and formulas of the RC estimation method with application to the FI-LFS are summarized in the workshop paper and in Salonen (2007). RC estimator introduced by Singh et. al, Fuller et. al and Gambino et. al (2001). Examined further by Bocci and Beaumont (2005). LFS Workshop in Rome May 15 - 16, 2014

RC estimation system implementation The RC estimator can be implemented within the FI-LFS estimation system by adding control totals and auxiliary variables to the estimation program. It can be performed by using, with minor modification, standard software for GREG estimation, such as ETOS. It yields a single set of estimation weights. LFS Workshop in Rome May 15 - 16, 2014

Control totals of auxiliary variables Population control totals Assumed to be population values Composite control totals Estimated control totals LFS Workshop in Rome May 15 - 16, 2014

Population control totals Population totals taken from administrative registers sex (2) age (12) region (20) employment status in Ministry of Labour's job-seeker register (8) Obs! Weekly balancing of weights on monthly level is also included in the calibration (4 or 5 reference weeks). LFS Workshop in Rome May 15 - 16, 2014

Composite control totals Composite control totals are estimates from the previous wave of interview Employed and unemployed by age/sex groups (8) Employed and unemployed by NUTS2 (8) Employment by Standard Industrial Classification (7) LFS Workshop in Rome May 15 - 16, 2014

Table 1. Population and composite control totals for RC estimation LFS Workshop in Rome May 15 - 16, 2014

Composite auxiliary variables Overlapping part of the sample Variables are taken from the previous wave of interview Non-overlapping part of the sample The values of variables are imputed LFS Workshop in Rome May 15 - 16, 2014

Example 1. Overlapping January 2014 Wave 1 Wave 2 Wave 3 Wave 4 Wave 5 Previous interview none October 2013 (July 2013) Dependence: Theoretical overlap wave-to-wave is 4/5 (80%) LFS Workshop in Rome May 15 - 16, 2014

Empirical results We have compared the RC estimator to the GREG estimator in the FI-LFS real data (2006-2010) Here we have used the ETOS program for point and variance estimation (Taylor linearisation method). Relative efficiency (RE) can be formulated as A value of RE greater than 100 indicates that the RC estimator is more efficient than the GREG estimator. LFS Workshop in Rome May 15 - 16, 2014

Table 2. Distribution of calibrated weights for GREG and RC estimators (e.g 2nd quarter of 2006) The calibrated weights are obtained by the ETOS program. The results show that the variation of the RC weights is smaller than that of the GREG weights. LFS Workshop in Rome May 15 - 16, 2014

Table 3. Relative efficiency (RE, %) of estimates for the quarterly level of employment and unemployment by sex LFS Workshop in Rome May 15 - 16, 2014

Table 4. Relative efficiency (RE, %) of estimates for the monthly level of employment and unemployment by industrial classification LFS Workshop in Rome May 15 - 16, 2014

Table 5. Relative efficiency (RE, %) of estimates for the quarterly level of employment and unemployment by industrial classification LFS Workshop in Rome May 15 - 16, 2014

Conclusions (1) For the variables that were included as composite control totals, there are substantial gains in efficiency for estimates For some variables it is future possible to publish monthly estimates where only quarterly estimates are published now? Leading to internal consistency of estimates Employment + Unemployment = Labour Force Labour Force + Not In Labour Force = Population 15 to 74 LFS Workshop in Rome May 15 - 16, 2014

Conclusions (2) It can be performed by using, with minor modification, standard software for GREG estimation, such as ETOS It yields a single set of estimation weights The results are well comparable with results reported from other countries Chen and Liu (2002): the Canadian LFS Bell (2001): the Australian LFS LFS Workshop in Rome May 15 - 16, 2014

Future work Analysis of potential imputation methods for the non-overlapping part of the sample? Analysis of alternative variance estimators (Dever and Valliant, 2010)? Incorporating information from all potential previous waves of interview LFS Workshop in Rome May 15 - 16, 2014

MAIN REFERENCES BEAUMONT, J.-F. and BOCCI, C. (2005). A Refinement of the Regression Composite Estimator in the Labour Force Survey for Change Estimates. SSC Annual Meeting, Proceedings of the Survey Methods Section, June 2005. CHEN, E.J. and LIU, T.P. (2002). Choices of Alpha Value in Regression Composite Estimation for the Canadian Labour Force Survey: Impacts and Evaluation. Methodology Branch Working Paper, HSMD-2002-005E, Statistics Canada. DEVER, A.D., and VALLIANT, R. (2010). A Comparison of Variance Estimators for Poststratification to Estimated Control Totals. Survey Methodology, 36, 45-56. FULLER, W.A., and RAO, J.N.K. (2001). A Regression Composite Estimator with Application to the Canadian Labour Force Survey. Survey Methodology, 27, 45-51. GAMBINO, J., KENNEDY, B., and SINGH, M.P. (2001). Regression Composite Estimation for the Canadian Labour Force Survey: Evaluation ja Implementation. Survey Methodology, 27, 65-74. SALONEN, R. (2007). Regression Composite Estimation with Application to the Finnish Labour Force Survey. Statistics in Transition, 8, 503-517. SINGH, A.C., KENNEDY, B., and WU, S. (2001). Regression Composite Estimation for the Canadian Labour Force Survey with a Rotating Panel Design. Survey Methodology, 27, 33-44. LFS Workshop in Rome May 15 - 16, 2014