1. ICES III, June, 2007 Zdenek Patak & Jack Lothian, Statistics Canada ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING PERSPECTIVE

2. Outline Motivation Catalyst for change A word on sample design Canadian Service Producer Price Index (SPPI) – Wholesale component Simulation study Remarks 2

3. Motivation Discussion with methodologists on best probability sample design for index surveys – Stratified Probability Proportional to Size (PPS) – Stratified Simple Random Sampling Without Replacement (SRSWOR) 3

4. Stratified PPS Large units selected with higher probability believed to drive index If economic weight inversely proportional to sampling weight index is simple average Possible drawback – Accuracy of size measure – Could lead to outlier problems 4

5. Stratified SRSWOR Size measure less important – Reduces outlier problem – Stratum jumpers easy to handle Wealth of literature on all aspects of design Largest units selected as take-alls Larger units selected with high probability 5

6. Catalyst for change Boskin report (1996) on state of US CPI – Impetus for revision of procedures More emphasis on data quality More emphasis on reacting to change More emphasis on quality indicators – Impetus for enhancing methodology 6

7. A word on sample design Historically most common sample designs – Purposive – Cut-off Probability sample designs – Stratified PPS – Stratified SRSWOR ? a possibility 7

8. Judgmental and Cut-off sample designs Easy to implement but requires good industry knowledge – Which units to select – different experts may select different samples – What represents satisfactory coverage Cannot compute statistical quality indicators – Sampling bias may be difficult to estimate – Variance = 0 8

9. Probability sample designs Can produce statistical quality indicators – Coefficients of Variation – Confidence intervals Handle non-response, imputation and outlier detection in a consistent, scientific manner Do not depend on judgment Typically stratified PPS but is stratified SRSWOR a viable alternative? 9

10. Canadian SPPI – Wholesale component Probability sample – Stratified PPS – Frame stratified by NAICS ~ 33,000 est – Sample ~ 3,000 est Size variable – Revenue Collect monthly prices for 3 representative items on quarterly basis – Complete triplets form basis for frame used for simulation study 10

11. Simulation study Only complete observations – triplets – used – Observations pooled across time – Largest outliers removed Data replicated to approximate original frame – More where small revenue – Less where larger revenue 11

12. Laspeyres index Base period economic weights Index is weighted mean Upward economic bias typically 12

13. Paasche index Current period economic weights Index is weighted harmonic mean Downward economic bias typically 13

14. Simulation study – Stratified PPS Stratified PPS sampling (Poisson) – Proportional to revenue available on most frames – Proportional to variable of interest gross margin (available on simulation frame) – Allocate 3,000 units Neyman X-proportional 14

15. Simulation study – Stratified PPS Generate 5,000 samples Compute Laspeyres index at national and industry levels Vary simulation parameters – Economic weight Revenue Gross margin – Weight adjustment 15

16. Simulation study – Stratified SRSWOR Use Lavallée-Hidiroglou for optimal stratification – Take-all stratum – Two take-some strata Neyman allocation (3,000 units) Repeat steps as described in Stratified PPS section 16

17. Simulation results I Geomean at unit level Trade GroupBias (SRS)Std Dev (SRS)Bias (PPS)Std Dev (PPS) A0.0060.0090.0060.008 B-0.0240.004-0.0240.004 C-0.0040.005-0.0040.001 D0.0170.0060.0180.001 E-0.0030.004-0.0020.004 F0.0090.0050.0090.004 G0.0170.0110.0160.010 H0.0010.0040.0010.004 I-0.0920.008-0.0930.003 J0.0070.0020.0070.001 Overall-0.0070.002-0.0060.001 17

18. Simulation results II Arithmetic mean at unit level (~ Laspeyres) Trade GroupBias (SRS)Std Dev (SRS)Bias (PPS)Std Dev (PPS) A0.0160.0100.0150.010 B-0.0160.004-0.0160.004 C-0.0010.005-0.0010.001 D0.0210.0060.0210.001 E0.0030.0040.0030.004 F0.0200.0050.0210.004 G0.0420.0120.0400.011 H0.0070.0040.0070.005 I-0.0720.009-0.0730.004 J0.0170.0020.0170.002 Overall0.0010.0020.0000.001 18

19. Remarks Negligible differences between Stratified PPS (Poisson) and Stratified SRSWOR – True in ideal setting? need to expand simulation study – What happens when real life phenomena are incorporated? imperfect size measure, non-response, misclassification, etc. – Holds for Laspeyres would same hold for true index? Another option Stratified PPSWOR 19

20. 20 ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING PERSPECTIVE Pour de plus amples informations ou pour obtenir une copie en anglais du document veuillez contacter… For more information, or to obtain an English copy of the presentation, please contact: StatistiqueStatisticsCanada Zdenek Patak Courriel / Email: zdenek.patak@statcan.ca