Anna Ciammola and Donatella Tuzi ISTAT - Italy

1. Internal Coherence in Seasonally Adjusted Chain Laspeyres Indices An Application to the Italian Hourly Labour Cost Indicators Anna Ciammola and Donatella Tuzi ISTAT - Italy European Conference on Quality in Official Statistics Q2010 Helsinki, 4-6 May 2010

2. Layout • Objectives of the presentation • The problem: Seasonal Adjustment (SA) of Italian hourly Labour Cost Indicators (LCI) • The solution: a proposal to aggregate chain linked Laspeyres indices • Results and conclusions

3. Objectives • Internal coherence in a system of SA time series • Number of components  few or many • Approach for SA  direct or indirect • Implemention of the indirect approach for chain Laspeyres indices • Chain linking non-additivity • A proposal to “restore” additivity

4. The problem (1) The Italian hourly LCI system (EC 450/2003) Wages Other Costs Total Cost B C D . . . L M N Elementary indices Chain Laspeyres indices B-N

5. The problem (2) Seasonal adjustment of the LCI system (a) Direct approach Independent treatment of wages, other costs andtotal cost total cost < min (wages, other costs) total cost > max (wages, other costs) Internal coherence not fulfilled (more evident to users for period-on-period changes)

6. The problem (3) Seasonal adjustment of the LCI system (b) Indirect approach total cost = f1(wages, other costs)  section B-N = f2(sections)  component f1andf2 ~ weighted average Unknowns of the problem  weights of f1 and f2 Internal coherence always fulfilled

7. The proposal: sectorial total cost (sC) • Elementary indices • Proposal: indices as weighted averages

8. The proposal: B-N chain indices (Sc) The starting point definitions • Laspeyres indicesin the previous year base(a-1) • Chain linked indices in the fixed base (b) • LSc, l, l+1 annual average of quarterly l LCISc, tl+1 • Chain linking non-additivity • Weights unsuited to the indirect approach

9. The proposal: B-N chain indices (Sc) A new weighting system • Indirect approach for seasonal adjustment • f  weighted average • Weights to “restore” additivity in the LCI system • if

10. Results (1) B-N total cost - direct and indirect approach (a)

11. Results (2) B-N total cost - direct and indirect approach (b)

12. Results (3) Assessment of the quality of seasonal adjustment • Residual seasonality • Smoothness measures • Stability • Sliding spans • Revisions history

13. Conclusions • Direct and indirect approach almost equivalent in terms of residual seasonality and smoothness • Sliding spans computable only for some NACE sections • Indirect approach slightly outperforms the indirect one in terms of revisions history Internal coherence as crucial criterion in the choice of the indirect approach

14. Thank you!

15. T1 - Incoherencies in the LCI system Number of incoherencies on q-on-q changes (2000Q2-2009Q4) NACE Rev. 2 Sections – Total cost aggregate F (9.8%) 16 41.0% H (9.0%) 6 15.4% J (5.2%) 12 30.8% M (4.3%) 7 17.9% Labour cost components – B-N aggregate Wages 0 0% Other costs 0 0% Total cost 0 0%

16. T2 – Revisions history Mean absolute differences on q-on-q changes Labour cost components – B-N aggregate Direct approach 1 step 2 steps 3steps 4steps Wages 0.13 0.21 0.36 0.67 Other costs 0.09 0.21 0.30 0.54 Total cost 0.14 0.24 0.39 0.68 Indirect approach 1 step 2 steps 3steps 4steps Wages 0.12 0.12 0.13 0.25 Other costs 0.07 0.06 0.10 0.26 Total cost 0.10 0.10 0.12 0.25