Extension Methods for Multilateral Index Series: A Comparative Study by Antonio Chessa

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This study by Antonio Chessa delves into the characterization of extension methods for multilateral index series, highlighting the impact of various factors such as product definition, index formula, weighting schemes, and length of time windows on the index. It addresses the challenges of revising indices in the Consumer Price Index (CPI) and explores different linking methods for index series across subsequent time windows. The comparative study also examines data sets, product categories, and methodology choices made in the analysis.

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Extension methods for multilateral index series Antonio Chessa CPI unit, Statistics Netherlands ag.chessa@cbs.nl 16thOttawa Group meeting Rio de Janeiro, 8-10 May 2019

Overview Problem statement Characterisation of extension methods Comparative study Results Conclusions 2

Its one out of many choices Product definition ( relaunches ) Index formula + weighting schemes Length of time window (ML methods) Index extension method Important: Impact of all these factors on index! 3

The revision problem ML methods allow us to compute transitive indices on a fixed time interval/window The window must be adapted in order to accommodate data of the next month Previously calculated indices may change However, indices cannot be revised in the CPI How could we link index series of subsequent windows? 4

Characterisation of extension methods Time window: Length: e.g. 13 months, 25 months, Window type 1: Fixed-length rolling Window type 2: Monthly expanding (with a fixed base month) Linking month Index in the linking month: Linking on a recalculated index Linking on a published index 5

Extension methods illustrated Full window splice Movement splice Published indices Published indices Windows: Windows: FBEW method FBRW method Published indices Published indices Index published in base month Index published in base month Windows: Windows: FBEW = Fixed Base month, Expanding Window; FBRW = same, with rolling window; x = linking month and index 6

Comparative study: (1) Data Data set # months COICOPs # product categories Supermarket chain 48 01, 05, 12 11 Department store chain 47 01, 03, 05, 11, 12 34 Pharmacy store chain 43 06, 12 20 7

Comparative study: (2) Methods and choices Choice aspect Choices made in this study Splicing: Window and movement splice (WS, MS) Fixed base methods: FBEW and FBRW Index extension method Geary-Khamis (GK) Time Product Dummy (TPD), only for supermarkets Index method Window length 13 months By GTIN: COICOP 01, non-clothing items (dept.stores) By characteristics: clothing, pharmacy products Product definition 8

Results: (1) Splicing, GK, chain level Supermarkets Pharmacy stores 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 Movement splice Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M7 M9 M3 M5 M3 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M3 M5 M7 M9 M5 M7 Window splice Window splice Movement splice 9

Results: (2) FB methods, GK, chain level Supermarkets Pharmacy stores 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y1M1 Y2M1 Y3M1 Y4M1 Y1M1 Y2M1 Y3M1 Y4M1 FBRW M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M7 M9 M3 M5 M3 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M3 M5 M7 M9 M5 M7 13-month benchmark FBEW FBRW 13-month benchmark FBEW 10

Results: (3) Splicing, GK, lower aggregates Coffee and tea (supermarkets) Hair care (pharmacy stores) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 Movement splice Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M7 M9 M3 M5 M3 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M3 M5 M7 M9 M5 M7 Window splice Window splice Movement splice 11

Results: (4) Splicing, GK, lower aggregates Menswear (dept. stores) Sugar and confectionery (supermarkets) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y2M1 Y2M1 Y3M1 Y1M1 13-month benchmark Y3M1 Y4M1 Movement splice Y1M1 13-month benchmark Y4M1 Movement splice M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M3 M9 M7 M5 M3 M9 M5 M9 M3 M9 M3 M7 M5 M5 M7 M3 M5 M9 M3 M7 M9 M5 M7 Window splice Window splice 12

Results: (5) FB methods, GK, lower aggrs Coffee and tea (supermarkets) Hair care (pharmacy stores) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y1M1 Y2M1 Y3M1 Y4M1 Y1M1 Y2M1 Y3M1 Y4M1 FBRW M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M7 M9 M3 M5 M3 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M3 M5 M7 M9 M5 M7 13-month benchmark FBEW FBRW 13-month benchmark FBEW 13

Results: (6) FB methods, GK, lower aggrs Menswear (dept. stores) Sugar and confectionery (supermarkets) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y2M1 Y2M1 Y3M1 Y1M1 Y3M1 Y4M1 Y1M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M3 M9 M7 M5 M3 M9 M5 M9 M3 M9 M3 M7 M5 M5 M7 M3 M5 M9 M3 M7 M9 M5 M7 13-month benchmark FBEW FBRW 13-month benchmark FBEW FBRW 14

Results: (7) Splicing, TPD method Supermarkets Coffee and tea 120 130 115 120 110 110 105 100 100 95 90 90 80 85 80 70 Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 Movement splice Y1M1 13-month benchmark Y2M1 Y3M1 Y4M1 Movement splice M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M3 M7 M5 M5 M9 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M5 M9 M3 M7 M9 M3 M7 Window splice Window splice 15

Results: (8) Window length, GK, chain level Supermarkets Department stores, clothing excluded 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y2M1 Y2M1 Y3M1 Y1M1 Y3M1 Y4M1 Y1M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M3 M7 M5 M5 M9 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M5 M9 M3 M7 M9 M3 M7 13-month benchmark Full period 13-month benchmark Full period Pharmacy stores Department stores, clothing 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y1M1 Y3M1 Y4M1 Y2M1 Y3M1 Y2M1 Y1M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M7 M9 M5 M7 M3 M7 M3 M9 M3 M7 M5 M5 M9 M3 M5 M3 M9 M5 M7 M9 M3 M5 M5 M7 M5 M9 M3 M7 M9 M3 M7 13-month benchmark Full period 13-month benchmark Full period 16

Summary of first results Splicing methods: Significant drift Downward drift in WS, mixed behaviour for MS Large deviations in year on year indices at chain level Can be much larger for lower aggregates Fixed base methods: Free of drift by construction Much better performance, also for lower aggregates 17

Pitfalls with splicing: Clearance prices Hair conditioner 200 180 160 140 120 100 80 60 40 20 0 Y2M1 Y3M1 Y1M1 Y4M1 M11 M11 M11 M3 M5 M7 M9 M3 M5 M7 M5 M7 M9 M3 M5 M7 M9 M3 Price Number of products sold 18

Pitfalls with splicing: Clearance prices Clearance prices dominate window Hair conditioner 200 180 Reference price decreases 160 140 120 100 Price index is pushed down 80 60 40 20 Linking is on recalculated indices 0 Y2M1 Y3M1 Y1M1 Y4M1 M11 M11 M11 M3 M5 M7 M9 M3 M5 M7 M5 M7 M9 M3 M5 M7 M9 M3 Price Number of products sold Drift is likely to persist 19

Pitfalls with splicing: Clearance prices Clearance prices dominate window Hair conditioner 200 180 Reference price decreases 160 140 120 100 Price index is pushed down 80 60 40 20 Linking is on recalculated indices 0 Y2M1 Y3M1 Y1M1 Y4M1 M11 M11 M11 M3 M5 M7 M9 M3 M5 M7 M5 M7 M9 M3 M5 M7 M9 M3 Price Number of products sold Drift is likely to persist 20

Pitfalls with splicing: Clearance prices Clearance prices dominate window Hair conditioner 200 180 Reference price decreases 160 140 120 100 Price index is pushed down 80 60 40 20 Linking is on recalculated indices 0 Y2M1 Y3M1 Y1M1 Y4M1 M11 M11 M11 M3 M5 M7 M9 M3 M5 M7 M5 M7 M9 M3 M5 M7 M9 M3 Price Number of products sold Drift is likely to persist 21

Illustration of window splice WindowSplice.ppsx 22

An amended proposal to splicing Behaviour of published series is what matters Linking on published indices: Calculated year on year index = Published index This is not the case in classical window splice! Drift in published series is excluded over the length of time window Two splicing methods studied: Window splice, with a 13-month window Half splice, with a 25-month window The half splice also links on published indices of 12 months ago 23

Splicing on published indices Splicing_On_Published_Indices.ppsx 24

Results: (9) Window splice, GK, chain level Supermarkets Pharmacy stores 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y2M1 Y1M1 Benchmark (13M) Y4M1 Y1M1 Benchmark (13M) Y3M1 Y4M1 Y2M1 Y3M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M9 M5 M7 M3 M7 M5 M9 M3 M9 M3 M7 M5 M3 M5 M7 M3 M9 M5 M7 M9 M3 M5 Classical WS WS on published indices Classical WS WS on published indices 25

Results: (10) WS, GK, lower aggregates Coffee and tea (supermarkets) Hair care (pharmacy stores) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y2M1 Y1M1 Benchmark (13M) Y4M1 Y1M1 Benchmark (13M) Y3M1 Y4M1 Y2M1 Y3M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M9 M5 M7 M3 M7 M5 M9 M3 M9 M3 M7 M5 M3 M5 M7 M3 M9 M5 M7 M9 M3 M5 Classical WS WS on published indices Classical WS WS on published indices 26

Results: (11) WS, GK, lower aggregates Menswear (dept. stores) Sugar and confectionery (supermarkets) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y2M1 Y2M1 Y3M1 Y1M1 Benchmark (13M) Y3M1 Y4M1 Y1M1 Benchmark (13M) Y4M1 M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M3 M9 M7 M5 M3 M9 M5 M9 M3 M9 M3 M7 M5 M5 M7 M3 M5 M9 M3 M7 M9 M5 M7 Classical WS WS on published indices Classical WS WS on published indices 27

Results: (12) Half splice, GK, chain level Supermarkets Pharmacy stores 120 120 115 115 110 110 105 105 100 100 95 95 90 90 85 85 80 80 Y2M1 Y1M1 Y4M1 Y1M1 Y3M1 Y4M1 Y2M1 Y3M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M9 M5 M7 M3 M7 M5 M9 M3 M9 M3 M7 M5 M3 M5 M7 M3 M9 M5 M7 M9 M3 M5 13 months Full period HS on published indices 13 months Full period HS on published indices 28

Results: (13) HS, GK, lower aggregates Coffee and tea (supermarkets) Hair care (pharmacy stores) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y1M1 Y2M1 Y3M1 Y4M1 Y1M1 Y2M1 Y3M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M3 M7 M7 M5 M9 M3 M9 M3 M9 M7 M9 M3 M5 M3 M5 M9 M3 M5 M9 M3 M7 M5 M7 M5 M7 M3 M5 M7 M9 M5 M7 13 months Full period HS on published indices 13 months Full period HS on published indices 29

Results: (14) HS, GK, lower aggregates Menswear (dept. stores) Sugar and confectionery (supermarkets) 130 130 120 120 110 110 100 100 90 90 80 80 70 70 Y2M1 Y2M1 Y3M1 Y1M1 Y3M1 Y4M1 Y1M1 Y4M1 M11 M11 M11 M11 M11 M11 M11 M11 M3 M7 M5 M7 M5 M9 M3 M7 M9 M3 M9 M7 M5 M3 M9 M5 M9 M3 M9 M3 M7 M5 M5 M7 M3 M5 M9 M3 M7 M9 M5 M7 13 months Full period HS on published indices 13 months Full period HS on published indices 30

Conclusions Fixed base extension performs (very) well (no drift) Classical splicing methods may lead to severe drift Splicing should be done on published indices: Drift is avoided over the length of the time window Window splice shows some variability in MoM changes Half splice is more accurate and stable 31

Additional remarks on half splice Calculated YoY = Published YoY (also for WS) Product contributions to index: Easier to compute for YoY Probably more difficult for MoM 25M window advantageous for (strongly) seasonal items YoY indices should not suffer from switches to new data sources and/or methods in CPI Will differences between ML methods be reduced? 32