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

Internal coherence of SA chain indices 2/16 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

Internal coherence of SA chain indices 3/16 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

Internal coherence of SA chain indices 4/16 The problem (1) The Italian hourly LCI system (EC 450/2003) BCD...LMNBCD...LMN B-N Wages Other Costs Total Cost Elementary indices Chain Laspeyres indices

Internal coherence of SA chain indices 5/16 The problem (2) Seasonal adjustment of the LCI system (a) Direct approach Independent treatment of wages, other costs and total 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)

Internal coherence of SA chain indices 6/16 The problem (3) Seasonal adjustment of the LCI system (b) Indirect approach total cost = f 1 ( wages, other costs )  section B-N = f 2 ( sections )  component f 1 and f 2 ~ weighted average Unknowns of the problem  weights of f 1 and f 2 Internal coherence always fulfilled

Internal coherence of SA chain indices 7/16 The proposal: sectorial total cost (sC)  Elementary indices  Proposal: indices as weighted averages

Internal coherence of SA chain indices 8/16 The proposal: B-N chain indices (Sc) The starting point definitions  Laspeyres indices in the previous year base (a-1)  Chain linked indices in the fixed base (b) L Sc, l, l+1  annual average of quarterly l LCI Sc, t l+1 Chain linking  non-additivity Weights unsuited to the indirect approach

Internal coherence of SA chain indices 9/16 A new weighting system  Indirect approach for seasonal adjustment f  weighted average  Weights to “restore” additivity in the LCI system if The proposal: B-N chain indices (Sc)

Internal coherence of SA chain indices 10/16 Results (1) B-N total cost - direct and indirect approach (a)

Internal coherence of SA chain indices 11/16 Results (2) B-N total cost - direct and indirect approach (b)

Internal coherence of SA chain indices 12/16 Results (3) Assessment of the quality of seasonal adjustment  Residual seasonality  Smoothness measures  Stability Sliding spans Revisions history

Internal coherence of SA chain indices 13/16 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

Internal coherence of SA chain indices Thank you!

Internal coherence of SA chain indices 15/16 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%) % H (9.0%) % J (5.2%)1230.8% M (4.3%)717.9% Labour cost components – B-N aggregate Wages00% Other costs 00% Total cost00%

Internal coherence of SA chain indices 16/16 T2 – Revisions history Mean absolute differences on q-on-q changes Labour cost components – B-N aggregate Direct approach 1 step2 steps3steps4steps Wages Other costs Total cost Indirect approach 1 step2 steps3steps4steps Wages Other costs Total cost