## 1. Methods for compiling economic statistics such as the consumer price index (CPI)

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### Overview and motivation
- Pandemic created unprecedented challenges for compiling and interpreting economic statistics; CPI especially affected by product disappearances, outlet closures, sharp changes in consumers’ spending patterns, and declining incomes.
- Conceptual frameworks:
  - Cost-of-living index (COLI): product disappearances had an upward effect on the COLI (Diewert and Fox, 2020); reduced availability of varieties also had upward effects on COLI component indexes (Jaravel and O’Connell, 2020).
  - Cost-of-goods index (COGI): practical focus of this paper — objective is to track the prices that consumers actually pay.
- Empirical claim: selected advanced economies showed underestimation of inflation by the CPI in the early months of the pandemic; this paper finds underestimation occurs in nearly all regions.

### Why COVID-19 weights could tend to imply more inflation
- CPI construction and Lowe index mechanics:
  - CPI is a weighted average of micro-indexes; weights reflect base-period budget shares estimated from consumer expenditure surveys and sometimes national accounts data.
  - Lowe index formula updates base-period weights for price changes between base period b and starting month s:
    - I_s = Σ_i w_ib (p_is / p_ib).
    - Lowe index weight: w_is = w_ib (p_is / p_ib) / I_s.
    - Adjusted weight for t–1: w_i,t-1 = w_ib (p_i,t-1 / p_ib) / I_t-1.
- Under normal conditions:
  - Price-updated base-period shares approximate current budget shares if base period not too far in the past.
  - Consumer substitution causes Laspeyres (and Lowe-like) indexes to be ≥ Paasche indexes; Lowe indexes often have a small upward bias. Example: chained Törnqvist CPI tends to rise about a quarter-percent per year less than the Lowe index used for the headline CPI.
- Pandemic-specific effects:
  - Lockdowns and social distancing caused large declines in spending on items consumed outside the home and increased weight of food and housing in budgets.
  - Product disappearances: clear upward effect on COLI; ambiguous effect on Paasche vs pre-pandemic-weight index depending on price behavior and imputation.
  - Demand shifts likely produce an upward effect on the difference between a Paasche index and an index with pre-pandemic weights because:
    - Upward sloping supply curves imply prices of items with expanded demand tend to rise, and items with diminished demand tend to fall.
    - Examples: falling demand for motor fuel and airline tickets contributed to decline in transport price index; substitution toward food at home may have contributed to increase in food price index.
- Theoretical illustration:
  - Producer substitution in response to a shift in consumer preferences can make the Paasche index greater than the Laspeyres index (Varian, 1984); Lowe index expected to behave similarly to Laspeyres.
- Measurement error and benchmarks:
  - Gap between a COVID-19 index and the CPI indicates sign of CPI measurement error but likely overstates magnitude.
  - COVID-19 basket approximates a Paasche index for intervals starting before the pandemic; Fisher index (average of Laspeyres and Paasche) is a better “true” inflation estimate — implying only half the gap between COVID-19 index and CPI represents CPI measurement error.
  - Chained Törnqvist with monthly updated basket (with spike smoothing) would be an even better benchmark and expected to lie between COVID-19 index and CPI.
  - Empirical comparison: chained monthly indexes’ three-month growth exceeded the CPI by 0.22 percentage points, less than the 0.36 percentage points extra growth of the COVID-19 basket index for Canada (Mitchell et al., 2020).

### Empirical evidence on changes in spending patterns
- High-level patterns from card/payment data (early pandemic months, advanced economies):
  - Sharp declines: transport; restaurants and bars; hotels; recreational/cultural/sporting events; clothing.
  - Increases: food for home consumption; alcoholic beverages for home consumption.
  - Housing and utilities likely stable in expenditure amounts; stable expenditures increased budget shares because overall spending fell sharply.
- COVID-19 budget-share estimates (selected):
  - Canada (February / COVID-19 March / COVID-19 April / April–February Difference):
    - Food (including away from home): 16.54 / 20.68 / 20.84 / 4.30
    - Alcoholic beverages, tobacco and cannabis: 2.60 / 3.15 / 3.55 / 0.95
    - Clothing and footwear: 5.00 / 3.30 / 2.22 / -2.78
    - Shelter: 27.70 / 31.23 / 37.12 / 9.42
    - Household operations, furnishing, and equip.: 12.66 / 13.04 / 13.99 / 1.33
    - Health and personal care: 4.85 / 5.61 / 4.96 / 0.11
    - Transportation: 19.04 / 15.01 / 12.14 / -6.90
    - Recreation, education and reading: 11.62 / 7.97 / 5.18 / -6.44
    - Note: Expenditures on shelter are imputed from general spending.
  - United States (April 2020, COVID-19 Basket vs CPI Weight, differences):
    - Food at home: CPI Weight 7.6 / COVID Basket Weight 11.3 / COVID-19 Weight difference from CPI Weight 3.7
    - Alcoholic Beverages (at home)a: 1.0 / 1.5 / 0.5
    - Apparel: 2.8 / 2.2 / -0.6
    - Housingb: 42.1 / 55.8 / 13.7
    - Medical: 8.8 / 5.6 / -3.2
    - Transportation: 15.7 / 6.3 / -9.5
    - Recreation: 5.8 / 2.2 / -3.6
    - Education and Communication: 6.8 / 9.0 / 2.2
    - Food away from Home: 6.2 / 3.1 / -3.1
    - Other: 3.1 / 3.0 / -0.1
    - a. Change in alcoholic beverages inferred from change in food as measured by grocery store spending.
    - b. Housing adjustment is based on an assumption of stable expenditures.
- Limitations of card/payment data:
  - Fast but less detail and precision than CPI weight sources; lack of product detail; assumed constant mix within aggregates; may overstate items frequently purchased with cash.
- Dynamics:
  - Some sharp early spending changes moderated when lockdowns eased (example: Spain — Carvalho et al., 2020).
  - Longer-run expenditure patterns could partially revert; developing post-pandemic CPI weights is difficult while patterns remain in flux.

### Estimating the effect on the CPI of adjusting weights for COVID-19
- Potential CPI measurement-error sources during pandemic:
  - Obsolete upper-level weights.
  - Obsolete lower-level weights.
  - Price samples unrepresentative due to surge in online buying.
- Focus of analysis: calibrating likely effect of adjusting upper-level weights for pandemic purchasing-pattern changes; assumes net impact of lower-level weight and price-sample problems is zero due to lack of information (but notes these could add to impact).
- Mechanics:
  - A price index understates inflation if items whose weights are too small experienced rapid price growth and items whose weights are too large experienced below-average price growth.
  - An item’s contribution to total difference equals product of its weight adjustment and deviation of its index from the all-items CPI.
- Data: IMF CPI database, COICOP division (2-digit) level, data up to May 2020 for 83 economies in eight regions.
- Average component behavior up to May 2020 (12-Month % Change to May 2020 / 3-Month % Change to May 2020):
  - 01 Food and non-alcoholic beverages: 4.7 / 1.58
  - 02 Alcoholic beverages, tobacco, and narcotics: 4.9 / 1.03
  - 03 Clothing and footwear: 0.2 / 2.48
  - 04 Housing, water, electricity, gas and other fuels: 1.0 / -1.11
  - 05 Furnishings and household equipment and maintenance: 1.9 / 0.64
  - 06 Health: 2.5 / 0.74
  - 07 Transport: -2.9 / -3.18
  - 08 Communication: -0.1 / -0.12
  - 09 Recreation and culture: 1.0 / -0.07
  - 10 Education: 1.8 / -0.20
  - 11 Restaurants and hotels: 2.3 / 0.39
  - 12 Miscellaneous goods and services: 3.3 / 0.53
  - All-Items: 1.9 / 0.16
- Interpretation: food indexes rose substantially over both 12-month and 3-month intervals; transport declined substantially; clothing behavior depends on interval. The all-items CPI rose at a rate just over 0.6 percent per year in the three months ending in May 2020 (prose observation of very low inflation).

### Methodology for deriving COVID-19 basket weights (cross-country application)
- Components that straddle two COICOP divisions were disaggregated (Annex A).
- Canada’s COVID-19 basket and Mitchell et al. (2020) used to derive a basket classified by 12 COICOP divisions.
- For an economy c, with mi the ratio for item i in Canada or the United States, and sic the price-updated weight of item i in the CPI of economy c in the month furnishing the COVID-19 basket (May 2020 in practice):
  - s*ic = mi sic / Σj=1,...,12 mj sjc = (mi / m̄c) sic.
- Cross-country application assumes proportional change in spending on any item equals that observed in Canada or the United States, recognizing differences in emerging market and low-income countries.

### COVID-19 implied weights (Global averages from Table 4)
- CPI Weight, Price-updated to April 2020 — COVID-19 Weight (Canada-based) — COVID-19 Weight (US-based):
  - 01 Food and non-alcoholic beverages: 27.1 — 38.2 — 36.7
  - 02 Alcoholic beverages, tobacco, and narcotics: 4.0 — 5.1 — 5.6
  - 03 Clothing and footwear: 5.3 — 2.1 — 3.9
  - 04 Housing, water, electricity, gas and other fuels: 17.7 — 21.8 — 22.6
  - 05 Furnishings and household equipment and maintenance: 5.4 — 5.5 — 5.0
  - 06 Health: 4.1 — 3.9 — 2.5
  - 07 Transport: 11.9 — 7.0 — 4.6
  - 08 Communication: 3.5 — 3.8 — 4.4
  - 09 Recreation and culture: 5.6 — 1.3 — 2.1
  - 10 Education: 2.7 — 2.5 — 3.5
  - 11 Restaurants and hotels: 6.3 — 2.8 — 3.2
  - 12 Miscellaneous goods and services: 6.4 — 6.0 — 6.0

### Measurement framework for impact on inflation
- Comparison interval: three months starting in February (February just before COVID-19 affected spending).
- CPI change approximation: Σi sic (pitc / pi,t-3,c).
- COVID-19 index change: Σi s*ic (pitc / pi,t-3,c).
- Difference decomposed as: (COVID-19 index – CPI)c = Σi (s*ic – sic) (pitc / pi,t-3,c) = Σi (s*ic – sic) [(pitc / pi,t-3,c) – (Itc / I t-3,c)].
- Item contribution = weight adjustment (s*ic – sic) × price-change deviation from all-items CPI.

### Results: COVID-19 index versus CPI (February–May 2020 and 12-month)
- February–May 2020, weights based on Canada:
  - World average: COVID-19 3-month growth exceeds CPI by 0.23 percentage points.
  - Regional differences (Canada-based weights):
    - Middle East-North Africa-Pakistan (MENAP): 0.31 percentage points.
    - Eastern Europe: around 0.37 percentage points.
    - Western Hemisphere: around 0.37 percentage points.
    - Asia-Pacific: 0.42 percentage points.
    - Caucasus: 0.49 percentage points.
    - Southern Europe/Mediterranean: –0.36 percentage points.
    - Northwest Europe: 0.06 percentage points.
  - In individual economies, COVID-19 basket index rises more than the CPI in 65 of 83 cases.
  - Main positive contributors to world average gap:
    - Food: just over 0.16 percentage points.
    - Transport: just over 0.16 percentage points (transport prices fell relative to CPI except in Sub-Saharan Africa).
  - Main negative contributors to world average gap:
    - Housing: –0.028 percentage points.
    - Clothing: –0.075 percentage points (seasonality: February sale months cause CPI to rise more than COVID-19 index).
- Using U.S.-based spending changes:
  - Average CPI underestimation over three months ending in May: 0.32 percentage points.
  - COVID-19 index (US-based) exceeds CPI in 73 of 83 economies.
  - Southern Europe and Mediterranean: COVID-19 basket (US-based) exceeds CPI by 0.15 percentage points.
  - Sub-Saharan Africa: difference near zero.
- 12-month comparison (May 2020 vs May 2019):
  - World average: 12-month growth of COVID-19 index (Canada-based weights) exceeds CPI by almost 0.6 percentage points.
  - Clothing contributes positively to the 12-month difference in almost every region.
  - Food contributes on average 0.3 percentage points to faster growth of COVID-19 index.

### Robustness and sensitivity notes
- Differences between Canada-based and U.S.-based weight adjustments (notably clothing and transport) noticeably affect results.
- Delaying comparison start from February to March changes clothing contribution in Southern Europe/Mediterranean from –0.36 to +0.11 percentage points.
- Regional contributions are simple averages of included countries.
- Effects of altering assumed size of weight adjustments are linear and straightforward to calculate.

### Implications for CPI compilers and policy recommendations
- Interim updating of CPI weights:
  - Rapid interim adjustment of official CPI weights to pandemic spending patterns is inadvisable because:
    - Accurate, detailed CPI weights require lengthy survey processing; card/payment data lack necessary product detail and omit some items (e.g., housing); can overstate items previously purchased with cash.
    - Such data could be acceptable for a supplementary index but not for the official CPI.
  - Sub-annual chaining risks chain drift distortion over the longer run and can create inconsistencies with component indexes.
  - Pandemic is an inopportune time for sub-annual chaining because spending patterns are still in flux and may partially revert.
- Supplementary indices:
  - A supplementary COVID-19 index could provide useful information on consumer inflation during the pandemic and on inequality (larger weights to food and housing).
  - Examples cited: Essential Products CPI (Statistics South Africa, weekly index) and Statistics Canada’s COVID-19 index.
  - Rapid weights need special procedures using credit card and payments data supplemented by retailer product data; smoothing and careful construction required.
  - Users can approximate effects by re-weighting existing component indexes (increase food weight, decrease transport weight; consider housing up, clothing down).
- Planned rebasing:
  - If next scheduled rebasing is more than two years away, advancing its date could be appropriate.
  - A delay of a planned 2021 rebasing may be warranted if the base year would not represent post-pandemic patterns; a two-year base period of 2019 and 2020 could be considered.
  - If next rebasing would normally be after 2022, advancing timing should be considered because five-year intervals may be too long when spending patterns change rapidly.
  - Flux in spending patterns complicates development of representative new weights; special procedures may be needed for rebasing planned for 2021.

### Conclusions (concise)
- Pandemic shifted consumption away from transport, clothing and footwear, recreation and entertainment, and restaurants and hotels, toward food and housing.
- In early pandemic months, rising food prices and falling transport prices caused CPI to understate inflation in most regions.
- Adjusting CPI weights based on Canada’s spending changes adds 0.23 percentage points to estimated inflation over the first three months; using U.S. patterns adds 0.32 percentage points.
- These adjustments show the sign of measurement error from obsolete weights but do not imply the CPI understated inflation exactly by those amounts, because some difference may reflect COVID-19 indexes overstating inflation for an interval beginning before the pandemic.
- Recommendation summary:
  - Avoid rapid interim updates to official CPI weights based solely on payments data.
  - Consider producing a supplementary COVID-19 index using rapid payment and retailer data with special procedures.
  - Consider advancing rebasing schedules if normal cycles would delay next update past 2022, while acknowledging flux may argue for delaying a 2021 base year until representative patterns stabilize.

### Annex highlights
- Annex A (Canada breakout): Food (including away from home) — Budget share, February 16.54; Change in share, Feb. to April 4.30; Percent Change in Share 26.0; Food at homeb: 11.39; Change in share 7.20; Percent Change in Spending 63.2; Memo: Change in Spending in US Dataa 21.8; 12.3. Transportation (Transport): 19.04; Change in share -6.90; Percent Change in Share -36.2; Memo percent changes include -52.4 and -70.1 for related measures.
- Annex B (Canada-derived weights) selected country three-month percentage-point TOTAL IMPACT (three months ending May 2020) and components:
  - Canada: TOTAL IMPACT 0.36; 01 Food 0.15; 03 Clothing 0.15; 04 Housing 0.00; 07 Transport 0.17; 09 Recreation -0.11; 11 Restaurants & Hotels -0.02; All other 0.02
  - United States: TOTAL IMPACT 0.68; 01 Food 0.21; 03 Clothing 0.11; 04 Housing 0.14; 07 Transport 0.31; 09 Recreation -0.08; 11 Restaurants & Hotels -0.02; All other 0.02
  - Spain: TOTAL IMPACT -0.26; 01 Food 0.22; 03 Clothing -0.62; 04 Housing -0.18; 07 Transport 0.35; 09 Recreation 0.05; 11 Restaurants & Hotels -0.10; All other 0.02
  - Greece: TOTAL IMPACT -1.28; 01 Food -0.07; 03 Clothing -1.27; 04 Housing -0.16; 07 Transport 0.28; 09 Recreation 0.00; 11 Restaurants & Hotels -0.06; All other -0.01
  - Burkina Faso: TOTAL IMPACT 1.14; 01 Food 0.71; 03 Clothing 0.13; 04 Housing -0.09; 07 Transport 0.18; 09 Recreation 0.03; 11 Restaurants & Hotels 0.12; All other 0.07
- Annex C (US-derived weights) selected country three-month percentage-point TOTAL IMPACT:
  - United States: TOTAL IMPACT 0.77; 01 Food 0.18; 03 Clothing 0.04; 04 Housing 0.16; 07 Transport 0.47; 09 Recreation -0.06; 11 Restaurants & Hotels -0.02; All other -0.01
  - Canada: TOTAL IMPACT 0.36; 01 Food 0.13; 03 Clothing 0.05; 04 Housing 0.00; 07 Transport 0.28; 09 Recreation -0.09; 11 Restaurants & Hotels -0.02; All other 0.00
  - South Africa: TOTAL IMPACT 0.83; 01 Food 0.11; 03 Clothing 0.00; 04 Housing 0.06; 07 Transport 0.63; 09 Recreation -0.04; 11 Restaurants & Hotels 0.01; All other 0.05
  - Burkina Faso: TOTAL IMPACT 0.94; 01 Food 0.61; 03 Clothing 0.07; 04 Housing -0.18; 07 Transport 0.24; 09 Recreation 0.03; 11 Restaurants & Hotels 0.11; All other 0.07

*Source: Excerpt from wpiea2020224-print-pdf - 1. Methods for compiling economic statistics such as the consumer price index (CPI) (IMF).*

### 1.      Methods  for  compiling economic  statistics such  as  the  consumer  price  index  (CPI)

### 1.      Methods for compiling economic statistics such as the consumer price index (CPI)

### Overview and motivation
- Methods for compiling economic statistics such as the CPI were not designed for overnight transformations of economic conditions; the pandemic created unprecedented challenges for compiling and interpreting these statistics.
- The CPI is among the economic statistics most affected by sudden pandemic-driven changes: product disappearances, outlet closures, sharp changes in consumers’ spending patterns, and declining incomes.
- Conceptual frameworks:
  - Cost-of-living index (COLI): product disappearances had an upward effect on the COLI (Diewert and Fox, 2020); reduced availability of varieties also had upward effects on COLI component indexes (Jaravel and O’Connell, 2020).
  - Cost-of-goods index (COGI): practical focus of this paper — measurement objective is to track the prices that consumers actually pay.
- Empirical finding cited: selected advanced economies showed underestimation of inflation by the CPI in the early months of the pandemic; this paper investigates whether underestimation is a global problem and finds underestimation occurs in nearly all regions.

### Why COVID-19 weights could tend to imply more inflation
- CPI construction and Lowe index mechanics:
  - CPI is a weighted average of micro-indexes; weights reflect base-period budget shares estimated from consumer expenditure surveys and sometimes national accounts data.
  - Most countries use a Lowe index formula that updates base-period weights for price changes between base period b and starting month s. Key expressions:
    - I_s = Σ_i w_ib (p_is / p_ib).
    - Lowe index weight: w_is = w_ib (p_is / p_ib) / I_s.
    - Adjusted weight for t–1: w_i,t-1 = w_ib (p_i,t-1 / p_ib) / I_t-1.
- Under normal conditions:
  - Price-updated base-period shares approximate current budget shares if base period not too far in the past.
  - Consumer substitution causes Laspeyres (and Lowe-like) indexes to be greater than or equal to Paasche indexes; Lowe indexes often have a small upward bias. Example: chained Törnqvist CPI tends to rise about a quarter-percent per year less than the Lowe index used for the headline CPI.
- Pandemic-specific effects:
  - Lockdowns, staying at home, social distancing caused large declines in spending on items consumed/used outside the home and increased weight of food and housing in budgets.
  - Product disappearances have a clear upward effect on a COLI; their effect on the difference between a Paasche index with COVID-19 weights and an index with pre-pandemic weights is ambiguous and depends on price behavior of affected items and imputation methods.
  - Demand shifts (e.g., substitution of food at home for restaurants) are likely to produce an upward effect on the difference between a Paasche index and an index with pre-pandemic weights because:
    - Upward sloping supply curves imply prices of items with expanded demand tend to rise, and items with diminished demand tend to fall.
    - Examples: falling demand for motor fuel and airline tickets contributed to decline in transport price index; substitution toward food at home may have contributed to increase in the food price index.
- Theoretical illustration:
  - Producer substitution in response to a shift in consumer preferences can make the Paasche index greater than the Laspeyres index (Varian, 1984); Lowe index expected to behave similarly to Laspeyres.
- Measurement error and benchmarks:
  - The gap between a COVID-19 index and the CPI indicates sign of CPI measurement error but likely overstates magnitude.
  - A COVID-19 basket approximates a Paasche index for intervals starting before the pandemic; a Fisher index (average of Laspeyres and Paasche) is a better estimate of “true” inflation — implying only half the gap between COVID-19 index and CPI represents CPI measurement error.
  - Chained Törnqvist with monthly updated basket (with spike smoothing) would be an even better benchmark and expected to lie between COVID-19 index and CPI.
  - Empirical comparisons: Mitchell et al. (2020) find chained monthly indexes’ three-month growth exceed the CPI by 0.22 percentage points, less than the 0.36 percentage points extra growth of the COVID-19 basket index for Canada.

### Empirical evidence on changes in spending patterns
- High-level patterns from credit/debit card and payments data in early pandemic months (advanced economies):
  - Sharp declines in spending on transport, restaurants and bars, hotels, recreational/cultural/sporting events, and clothing.
  - Increased spending on food for home consumption (partly substitution from restaurants) and alcoholic beverages for home consumption.
  - Housing and electricity/water/other utilities likely stable in expenditure amounts (measured by amounts owed rather than amounts actually paid in cases of missed payments); stable expenditures increased budget shares because overall spending fell sharply.
- COVID-19 budget-share estimates from card/payments data:
  - Canada (using February–April differences from Mitchell et al., 2020):
    - Removing restaurants from total food implies increase of 7.2 percentage points in weight on food at home (Annex A).
    - Table 1: COVID-19 Budget Shares in Canada in March-April, 2020 (Percentages)
      - Derived weights, February / COVID-19 Basket in March / COVID-19 Basket in April / April-February Difference
      - Food (including away from home): 16.54 / 20.68 / 20.84 / 4.30
      - Alcoholic beverages, tobacco and cannabis: 2.60 / 3.15 / 3.55 / 0.95
      - Clothing and footwear: 5.00 / 3.30 / 2.22 / -2.78
      - Shelter: 27.70 / 31.23 / 37.12 / 9.42
      - Household operations, furnishing, and equip.: 12.66 / 13.04 / 13.99 / 1.33
      - Health and personal care: 4.85 / 5.61 / 4.96 / 0.11
      - Transportation: 19.04 / 15.01 / 12.14 / -6.90
      - Recreation, education and reading: 11.62 / 7.97 / 5.18 / -6.44
    - Note: Expenditures on shelter are imputed from general spending.
  - United States (Cavallo, 2020) — COVID-19 Basket weight differences from CPI Weight (April 2020):
    - Food at home: CPI Weight 7.6 / COVID Basket Weight 11.3 / COVID-19 Weight difference from CPI Weight 3.7
    - Alcoholic Beverages (at home)a: 1.0 / 1.5 / 0.5
    - Apparel: 2.8 / 2.2 / -0.6
    - Housingb: 42.1 / 55.8 / 13.7
    - Medical: 8.8 / 5.6 / -3.2
    - Transportation: 15.7 / 6.3 / -9.5
    - Recreation: 5.8 / 2.2 / -3.6
    - Education and Communication: 6.8 / 9.0 / 2.2
    - Food away from Home: 6.2 / 3.1 / -3.1
    - Other: 3.1 / 3.0 / -0.1
    - a. Change in alcoholic beverages inferred from change in food as measured by grocery store spending.
    - b. Housing adjustment is based on an assumption of stable expenditures.
- Limitations of card/payments data:
  - Fast estimation but less detail and precision than usual CPI weight sources.
  - Lack of product detail: grocery-store spending treated as food though stores sell non-food items.
  - Assumed constant mix of detailed products within aggregates; ignores substitution between detailed products (e.g., within clothing consumers bought more pajamas and shirts and less pants).
  - Card data may overstate increases in items frequently purchased with cash.
- Dynamics:
  - Some sharp early spending changes moderated when lockdowns eased (example: Spain — Carvalho et al., 2020 show types of spending that fell early later rebounded).
  - Longer-run expenditure patterns could partially revert to pre-pandemic configuration; developing CPI weights that reflect post-pandemic spending patterns is difficult while patterns remain in flux.

### Estimating the effect on the CPI of adjusting weights for COVID-19
- Potential sources of CPI measurement error due to pandemic:
  - Obsolete upper-level weights.
  - Obsolete lower-level weights.
  - Price samples for individual products unrepresentative due to surge in online buying.
- This section focuses on calibrating the likely effect of adjusting upper-level weights for pandemic purchasing-pattern changes; assumes net impact of lower-level weight and price-sample problems is zero due to lack of information (but notes these could add to the impact).
- Mechanics of impact:
  - A price index understates inflation if items whose weights are too small experienced rapid price growth and items whose weights are too large experienced below-average price growth.
  - An item’s contribution to the total difference between the COVID-19 index and the CPI equals the product of its weight adjustment and the deviation of its index from the all-items CPI.
- Data coverage and averages:
  - IMF CPI database used: major components at COICOP division (2-digit) level; data up to May 2020 for 83 economies in eight regions.
  - Average component behavior up to May 2020 (Table 3: Average Change in CPI Component Indexes):
    - COICOP Division / 12-Month % Change to May 2020 / 3-Month % Change to May 2020
    - 01 Food and non-alcoholic beverages: 4.7 / 1.58
    - 02 Alcoholic beverages, tobacco, and narcotics: 4.9 / 1.03
    - 03 Clothing and footwear: 0.2 / 2.48
    - 04 Housing, water, electricity, gas and other fuels: 1.0 / -1.11
    - 05 Furnishings and household equipment and maintenance: 1.9 / 0.64
    - 06 Health: 2.5 / 0.74
    - 07 Transport: -2.9 / -3.18
    - 08 Communication: -0.1 / -0.12
    - 09 Recreation and culture: 1.0 / -0.07
    - 10 Education: 1.8 / -0.20
    - 11 Restaurants and hotels: 2.3 / 0.39
    - 12 Miscellaneous goods and services: 3.3 / 0.53
    - All-Items: 1.9 / 0.16
  - Interpretation: on average, food indexes rose substantially over both 12-month and 3-month intervals; transport declined substantially; clothing behavior depends on measurement interval. The all-items CPI rose at a rate just over 0.6 percent per year in the three months ending in May 2020 (note: stated as "just over 0.6 percent per year" in prose), indicating very low inflation.

*Source: Excerpt from wpiea2020224-print-pdf - 1.      Methods for compiling economic statistics such as the consumer price index (CPI) (IMF).*

### 20.      Some components of the COVID-19 basket of Canada shown in Table 1 straddle two

### Some components of the COVID-19 basket of Canada shown in Table 1 straddle two

### Methodology for deriving COVID-19 basket weights
- Components that straddle two COICOP divisions were disaggregated to derive COICOP division weights (Annex A).
- Canada’s COVID-19 basket (Table 1) and Mitchell et al. (2020) were used to derive a basket classified by the 12 COICOP divisions.
- For creating an economy’s COVID-19 weights:
  - Let mi be the ratio for item i in Canada or the United States.
  - Let sic be the price-updated weight of item i in the CPI of economy c in the month furnishing the COVID-19 basket (in practice, May 2020).
  - The COVID-19 weight s*ic is given by s*ic = mi sic / Σj=1,...,12 mj sjc = (mi / m̄c) sic.
- Cross-country application assumes proportional change in spending on any item equals that observed in Canada or the United States, acknowledging potential differences in emerging market and low-income countries where work-from-home and lockdown incidence differ.

### COVID-19 implied weights (Global averages from Table 4)
- COICOP division — CPI Weight, Price-updated to April 2020 — COVID-19 Weight, based on Spending in Canada — COVID-19 Weight, based on Spending in the US
  - 01 Food and non-alcoholic beverages: 27.1 — 38.2 — 36.7
  - 02 Alcoholic beverages, tobacco, and narcotics: 4.0 — 5.1 — 5.6
  - 03 Clothing and footwear: 5.3 — 2.1 — 3.9
  - 04 Housing, water, electricity, gas and other fuels: 17.7 — 21.8 — 22.6
  - 05 Furnishings and household equipment and maintenance: 5.4 — 5.5 — 5.0
  - 06 Health: 4.1 — 3.9 — 2.5
  - 07 Transport: 11.9 — 7.0 — 4.6
  - 08 Communication: 3.5 — 3.8 — 4.4
  - 09 Recreation and culture: 5.6 — 1.3 — 2.1
  - 10 Education: 2.7 — 2.5 — 3.5
  - 11 Restaurants and hotels: 6.3 — 2.8 — 3.2
  - 12 Miscellaneous goods and services: 6.4 — 6.0 — 6.0

### Measurement framework for impact on inflation
- Comparison interval: three months starting in February (February just before COVID-19 affected spending).
- CPI change approximation: Σi sic (pitc / pi,t-3,c).
- COVID-19 index change: Σi s*ic (pitc / pi,t-3,c).
- Difference rearranged as sum of item contributions: (COVID-19 index – CPI)c = Σi (s*ic – sic) (pitc / pi,t-3,c) = Σi (s*ic – sic) [(pitc / pi,t-3,c) – (Itc / I t-3,c)].
- An item’s contribution equals its weight adjustment (s*ic – sic) times its price change deviation from the all-items CPI.

### Results: COVID-19 index versus CPI (February–May 2020 and 12-month)
- February–May 2020, weights based on Canada:
  - World average: COVID-19 3-month growth exceeds CPI by 0.23 percentage points.
  - Regional differences (Canada-based weights):
    - Middle East-North Africa-Pakistan (MENAP): 0.31 percentage points.
    - Eastern Europe: around 0.37 percentage points.
    - Western Hemisphere: around 0.37 percentage points.
    - Asia-Pacific: 0.42 percentage points.
    - Caucasus: 0.49 percentage points.
    - Southern Europe/Mediterranean: –0.36 percentage points.
    - Northwest Europe: 0.06 percentage points.
  - In individual economies, the COVID-19 basket index rises more than the CPI in 65 of 83 cases.
- Main contributors to positive gap (world average):
  - Food: just over 0.16 percentage points.
  - Transport: just over 0.16 percentage points (transport prices fell relative to CPI except in Sub-Saharan Africa).
- Main negative contributors to world average gap:
  - Housing: –0.028 percentage points.
  - Clothing: –0.075 percentage points (seasonality: February sale months cause CPI to rise more than COVID-19 index).
- Using U.S.-based spending changes:
  - Average CPI underestimation over three months ending in May: 0.32 percentage points.
  - COVID-19 index based on U.S. spending changes exceeds CPI in 73 of 83 economies.
  - Southern Europe and Mediterranean: COVID-19 basket (US-based) exceeds CPI by 0.15 percentage points.
  - Sub-Saharan Africa: difference near zero.
- 12-month comparison (May 2020 vs May 2019):
  - World average: 12-month growth of COVID-19 index (Canada-based weights) exceeds CPI by almost 0.6 percentage points.
  - Clothing contributes positively to the 12-month difference in almost every region.
  - Food contributes on average 0.3 percentage points to the faster growth of the COVID-19 index.

### Robustness and sensitivity notes
- Differences between Canada-based and U.S.-based weight adjustments (notably clothing and transport) can noticeably affect results.
- Delaying comparison start from February to March would change clothing contribution in Southern Europe/Mediterranean from negative outlier (–0.36) to +0.11 percentage points.
- The contribution in a region is calculated as a simple average of included countries.
- Effects of altering assumed size of weight adjustments are straightforward to calculate given the linear decomposition.

### Implications for CPI compilers and policy recommendations
- On interim updating of CPI weights:
  - Rapid interim adjustment of official CPI weights to pandemic spending patterns is inadvisable because:
    - Accurate, detailed CPI weights require lengthy survey processing; credit card and payments data lack necessary product detail and omit some items (e.g., housing), and can overstate items previously purchased with cash.
    - Such data could be acceptable for a supplementary index but not for the official CPI.
  - Sub-annual chaining to reflect pandemic weights risks chain drift distortion over the longer run and can create inconsistencies with component indexes.
  - The pandemic is an inopportune time for sub-annual chaining because spending patterns are still in flux and may partially revert.
- On supplementary indices:
  - A supplementary COVID-19 index could provide useful information on consumer inflation during the pandemic and on inequality (larger weights to food and housing).
  - Examples: Essential Products CPI (Statistics South Africa, weekly index) and Statistics Canada’s COVID-19 index.
  - Development of rapid weights needs special procedures using credit card and payments data supplemented by retailer product data; smoothing and careful construction required.
  - Users can approximate effects by re-weighting existing component indexes (increase food weight, decrease transport weight; consider housing up, clothing down).
- On planned rebasing:
  - If next scheduled rebasing is more than two years away, advancing its date could be appropriate.
  - A delay of a planned 2021 rebasing may be warranted if the base year would not represent post-pandemic patterns; a two-year base period of 2019 and 2020 could be considered.
  - If next rebasing would normally be after 2022, advancing timing should be considered because five-year intervals may be too long when spending patterns change rapidly.
  - However, flux in spending patterns complicates development of representative new weights; special procedures may be needed for rebasing planned for 2021.

### Conclusions (concise)
- The pandemic shifted consumption away from transport, clothing and footwear, recreation and entertainment, and restaurants and hotels, toward food and housing.
- In early pandemic months, rising food prices and falling transport prices caused CPI to understate inflation in most regions.
- Adjusting CPI weights based on Canada’s spending changes adds 0.23 percentage points to estimated inflation over the first three months; using U.S. patterns adds 0.32 percentage points.
- These adjustments show the sign of the measurement error from obsolete weights but do not imply the CPI understated inflation exactly by those amounts, because some difference may reflect COVID-19 indexes overstating inflation for a period beginning before the pandemic.
- Recommendation summary:
  - Avoid rapid interim updates to official CPI weights based solely on payments data.
  - Consider producing a supplementary COVID-19 index using rapid payment and retailer data with special procedures.
  - Consider advancing rebasing schedules if normal cycles would delay next update past 2022, while acknowledging flux may argue for delaying a 2021 base year until representative patterns stabilize.

*Source: Authors’ calculations and analysis in the provided IMF chapter excerpt.*

### References

### References (wpiea2020224-print-pdf)

### Key literature and themes cited
- Abramovich, Giselle, 2020. April Digital Economy Index: How COVID-19 Continues to Shift E-Commerce Trends, Adobe Blog (May 12).
- Alcorn, Chauncey, 2020. No one is buying pants, but pajama sales are soaring, CNN Business (May 12).
- Andersen, Asger Lau; Emil Toft Hansen; Niels Johannesen; Adam Sheridan, 2020. Consumer responses to the COVID-19 crisis.
- Bounie, David et al., 2020. Dynamiques de consommation dans la crise: les enseignements en temps réel des données bancaires, Conseil d’analyse économique Focus paper No. 049-2020 (October).
- Campelo Junior, Aloisio et al., 2020. Inflação brasileira ajustada para cesta de consumo pós-covid, FGV IBRE Blog.
- Carvalho, Vasco M. et al., 2020. Tracking the COVID-19 Crisis with High-Resolution Transaction Data, Cambridge-INET Working Paper Series No: 2020/16.
- Caselli, Francesca; Francesco Grigoli; Weicheng Lian; Damiano Sandri, 2020. The Great Lockdown: Dissecting the Economic Effects. In World Economic Outlook (October).
- Cavallo, Alberto, 2020. Inflation with Covid Consumption Baskets, NBER Working Paper 27352.
- Chronopoulos, Dimitris; Marcel Lukas; John Wilson, 2020. Real-time consumer spending responses to the COVID-19 crisis and government lockdown.
- Committee on National Statistics Panel on Conceptual, Measurement and other Statistical Issues in Developing Cost-of-Living Indexes, 2002. At What Price? Conceptualizing and Measuring Cost-of-Living and Price Indexes.
- Diewert, W. Erwin and Kevin Fox, 2020. Measuring Real Consumption and CPI Bias under Lockdown Conditions. NBER Working Paper 27144.
- Dunn, Abe; Kyle Hood; Alexander Driessen, 2020. Measuring the Effects of the COVID-19 Pandemic on Consumer Spending Using Card Transaction Data. BEA Working Paper WP2020-5.
- Ebrahimy, Ehsan; Deniz Igan; Soledad Martinez Peria, 2020. The Impact of COVID-19 on Inflation: Potential Drivers and Dynamics. IMF Special Notes Series on COVID-19 (September).
- Hacioglu, Sinem; Diego Känzig; Paolo Surico, 2020. Consumption in the time of Covid-19: Evidence from UK transaction data, CEPR Discussion Paper DP14733.
- Jaravel, Xavier; Martin O'Connell, 2020. Inflation spike and falling product variety during the Great Lockdown, Institute for Fiscal Studies Working Paper W20/17.
- Lasiy, Costa; Losaunne White; Vivek Pandya, 2020. Tracking the Impact of COVID-19 on the Online Economy in Real-Time. Presented at the 8th IMF Statistical Forum.
- Mitchell, Taylor et al., 2020. Consumer expenditures during COVID-19: An exploratory analysis of the effects of changing consumption patterns on consumer price indexes.
- Nutting, Rex, 2020. The government says there’s no inflation — except for the things people are actually buying.
- Seiler, Peter, 2020. Weighting Bias and Inflation in the Time of Covid-19: Evidence from Swiss Transaction Data.
- Shapiro, Adam, 2020. Monitoring the Inflationary Effects of COVID-19, FRBSF Economic Letter 2020-24.
- Shapiro, Adam, 2020. A Simple Framework to Monitor Inflation. Federal Reserve Bank of San Francisco Working Paper 2020-29.
- Statistics Canada, 2020. Adjusting the Consumer Price Index to the New Spending Realities during the Pandemic, The Daily (Oct. 8).
- Statistics South Africa, 2020. COVID-19: Deflation of essential product prices during Level 5 lockdown.
- Varian, Hal R., 1984. The non-parametric approach to production analysis. Econometrica 52, 579-597.

### Annex A — Break Out of COICOP Division Shares Changes from the Published Budget Share Changes for Canada (of Table 1)
- Description — Budget share, February; Change in share, Feb. to April; Percent Change in Share; Percent Change in Spending. Memo: Change in Spending in US Dataa
- Food (including away from home): 16.54; 4.30; 26.0
- Food at homeb: 11.39; 7.20; 63.2; 21.8; 12.3
- Food in restaurantsc: 5.15; -2.90; -56.3
- Alcoholic beverages, tobacco and cannabis: 2.60; 0.95; 36.5
- Alcoholic beverages, tobacco and narcotics at homeb: 2.46; 1.029; 41.8; 5.9; 12.3
- Alcoholic beverages at restaurants and barsc: 0.14; -0.08; -56.3
- Clothing and footwear: 5.00; -2.78; -55.6; -66.9; -41.0
- Shelter (Housing, water, electricity, gas, other fuels): 27.70; 9.42; 34.0; 0; 0
- Household operations, furnishing, and equipment: 12.65; 1.34; 10.6
- Communicationb: 3.43; 0.74; 21.5; -9.4; 0
- Furnishings, household equipment and routine household maintenanceb: 5.69; 0.60; 10.6; -17.5; -26.8
- Other household operationsc: 3.53; 0.00; 0.0
- Health and personal care: 4.85; 0.11; 2.3
- Healthb: 2.82; 0.06; 1.9; -23.9; -52.2
- Personal Carec: 2.03; 0.06; 2.7
- Transportation (Transport): 19.04; -6.90; -36.2; -52.4; -70.1
- Recreation, education and reading: 11.62; -6.44; -55.4
- Hotels, calculated as: 1.49; -0.59; -40.0
- Restaurants and hotelsb: 6.77; -3.57; -52.8; -64.8; -61.9
- LESS: Food + alcoholic beverages at restaurants: 5.29; -2.98; -56.3
- Educationb: 2.34; 0.00; 0.0; -25.4; 0
- Recreation and cultureb: 7.79; -5.85; -75.0; -81.4; -71.1
- Miscellaneous goods & services; calculated as sum of: 5.56; 0.06; 1.0; -24.6; -26.8
  - Other household operations: 3.53; 0.00; 0.0
  - Personal Care: 2.03; 0.06; 2.7
- Notes:
  - a. Percent change in spending estimates for the U.S. are from Cavallo (2020).
  - b. Price-updated CPI weight from IMF database (rescaled by a factor of 0.97 in cases of Education and Recreation and Culture).
  - c. Estimated as a residual.

### Annex B — Contributions to the Impact of COVID-19 (Weights derived from Spending Changes in Canada) on the Growth of the CPI over 3 Months Ending May 2020 (Percentage points)
- Table structure: Economy; TOTAL IMPACT; 01 Food; 03 Clothing; 04 Housing; 07 Transport; 09 Recreation; 11 Restaurants & Hotels; All other.
- Selected country entries (exact values as presented):
  - Canada: 0.36; 0.15; 0.15; 0.00; 0.17; -0.11; -0.02; 0.02
  - United States: 0.68; 0.21; 0.11; 0.14; 0.31; -0.08; -0.02; 0.02
  - China, P.R.: Hong Kong: -0.18; -0.18; -0.05; 0.03; 0.01; 0.01; -0.03; 0.02
  - Japan: 0.08; 0.11; -0.11; -0.01; 0.12; -0.09; 0.04; 0.01
  - Spain: -0.26; 0.22; -0.62; -0.18; 0.35; 0.05; -0.10; 0.02
  - Greece: -1.28; -0.07; -1.27; -0.16; 0.28; 0.00; -0.06; -0.01
  - South Africa: 0.56; 0.13; 0.01; 0.05; 0.43; -0.05; 0.01; -0.02
  - Burkina Faso: 1.14; 0.71; 0.13; -0.09; 0.18; 0.03; 0.12; 0.07
  - Mexico: 0.63; 0.39; 0.07; -0.08; 0.32; -0.03; -0.07; 0.03
  - United Kingdom: 0.09; 0.03; 0.04; 0.03; 0.06; -0.04; -0.06; 0.02
- The Annex contains full country-by-country percentage-point contributions across categories for the specified 3-month period.

### Annex C — Impact of COVID-19 (Weights derived from Spending Changes in the United States) on the Growth of the CPI over 3 Months Ending May 2020 (Percentage points)
- Table structure: Economy; TOTAL IMPACT; 01 Food; 03 Clothing; 04 Housing; 07 Transport; 09 Recreation; 11 Restaurants & Hotels; All other.
- Selected country entries (exact values as presented):
  - United States: 0.77; 0.18; 0.04; 0.16; 0.47; -0.06; -0.02; -0.01
  - Canada: 0.36; 0.13; 0.05; 0.00; 0.28; -0.09; -0.02; 0.00
  - China, P.R.: Hong Kong: -0.10; -0.14; -0.02; 0.03; 0.02; 0.01; -0.02; 0.03
  - Japan: 0.17; 0.09; -0.05; -0.01; 0.19; -0.08; 0.04; -0.02
  - Spain: 0.36; 0.19; -0.19; -0.20; 0.58; 0.04; -0.09; 0.02
  - Greece: -0.34; -0.06; -0.47; -0.19; 0.44; 0.00; -0.05; -0.01
  - South Africa: 0.83; 0.11; 0.00; 0.06; 0.63; -0.04; 0.01; 0.05
  - Burkina Faso: 0.94; 0.61; 0.07; -0.18; 0.24; 0.03; 0.11; 0.07
  - Mexico: 0.69; 0.33; 0.03; -0.10; 0.48; -0.02; -0.06; 0.03
  - United Kingdom: 0.14; 0.03; 0.01; 0.03; 0.11; -0.03; -0.05; 0.04
- The Annex contains full country-by-country percentage-point contributions across categories for the specified 3-month period using U.S.-derived spending-change weights.

*Source: wpiea2020224-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020224-print-pdf.pdf_