Transcript Bias (PPS)
ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING PERSPECTIVE ICES III, June, 2007 Zdenek Patak & Jack Lothian, Statistics Canada Outline Motivation Catalyst for change A word on sample design Canadian Service Producer Price Index (SPPI) – 2 Wholesale component Simulation study Remarks Motivation 3 Discussion with methodologists on best probability sample design for index surveys – Stratified Probability Proportional to Size (PPS) – Stratified Simple Random Sampling Without Replacement (SRSWOR) 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 – 4 Could lead to outlier problems Stratified SRSWOR Size measure less important – – 5 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 Catalyst for change Boskin report (1996) on state of US CPI – Impetus for revision of procedures – 6 More emphasis on data quality More emphasis on reacting to change More emphasis on quality indicators Impetus for enhancing methodology A word on sample design Historically most common sample designs – – Probability sample designs – – 7 Purposive Cut-off Stratified PPS Stratified SRSWOR ? a possibility Judgmental and Cut-off sample designs Easy to implement but requires good industry knowledge – – Cannot compute statistical quality indicators – – 8 Which units to select – different experts may select different samples What represents satisfactory coverage Sampling bias may be difficult to estimate Variance = 0 Probability sample designs Can produce statistical quality indicators – – 9 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? Canadian SPPI – Wholesale component Probability sample – Stratified PPS – – Frame stratified by NAICS ~ 33,000 est Sample ~ 3,000 est Collect monthly prices for 3 representative items on quarterly basis – 10 Size variable – Revenue Complete “triplets” form basis for frame used for simulation study Simulation study Only complete observations – triplets – used – – Data replicated to approximate original frame – – 11 Observations pooled across time Largest outliers removed More where small revenue Less where larger revenue Laspeyres index pn q0 E pn LP p q w0 00 p0 12 Base period economic weights Index is weighted mean Upward economic bias typically Paasche index PP pq p q n n 0 n 13 1 pn w p 0 1 E n Current period economic weights Index is weighted harmonic mean Downward economic bias typically 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 – 14 Neyman X-proportional Simulation study – Stratified PPS Generate 5,000 samples Compute Laspeyres index at national and industry levels Vary simulation parameters – Economic weight – 15 Revenue Gross margin Weight adjustment Simulation study – Stratified SRSWOR Use Lavallée-Hidiroglou for optimal stratification – – 16 Take-all stratum Two take-some strata Neyman allocation (3,000 units) Repeat steps as described in Stratified PPS section Simulation results I Geomean at unit level Trade Group 17 Bias (SRS) Std Dev (SRS) Bias (PPS) Std Dev (PPS) A 0.006 0.009 0.006 0.008 B -0.024 0.004 -0.024 0.004 C -0.004 0.005 -0.004 0.001 D 0.017 0.006 0.018 0.001 E -0.003 0.004 -0.002 0.004 F 0.009 0.005 0.009 0.004 G 0.017 0.011 0.016 0.010 H 0.001 0.004 0.001 0.004 I -0.092 0.008 -0.093 0.003 J 0.007 0.002 0.007 0.001 Overall -0.007 0.002 -0.006 0.001 Simulation results II Arithmetic mean at unit level (~ Laspeyres) Trade Group 18 Bias (SRS) Std Dev (SRS) Bias (PPS) Std Dev (PPS) A 0.016 0.010 0.015 0.010 B -0.016 0.004 -0.016 0.004 C -0.001 0.005 -0.001 0.001 D 0.021 0.006 0.021 0.001 E 0.003 0.004 0.003 0.004 F 0.020 0.005 0.021 0.004 G 0.042 0.012 0.040 0.011 H 0.007 0.004 0.007 0.005 I -0.072 0.009 -0.073 0.004 J 0.017 0.002 0.017 0.002 Overall 0.001 0.002 0.000 0.001 Remarks Negligible differences between Stratified PPS (Poisson) and Stratified SRSWOR – – – 19 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 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: Statistique Canada Courriel / Email: 20 Statistics Canada Zdenek Patak [email protected]