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Product Substitution Effect: 2011 and 2009 Basket Updates

Waruna Wimalaratne
Statistics Canada, Consumer Prices Division

The Canadian Consumer Price Index (CPI) is a fixed-basket Laspeyres-type index for which the weights in the basket are periodically updated. On March 27, 2013, the 2009 weighting pattern was replaced with one from 2011. This marked the first time in the Canadian CPIís history that weights were updated at a two-year interval.

Due to its use of fixed weights, a Laspeyres-type index is typically subject to an upward bias brought on by product substitutions made by consumers. This arises in a fixed quantity index when consumers change their purchasing behaviour in response to relative price changes. For example, if the price of chicken increases substantially between basket updates, consumers may opt away from chicken and substitute other meats such as beef. In cases such as these, a fixed-quantity Laspeyres-type price index cannot correctly reflect this expenditure change until basket weights are updated. This can lead to an overstatement of the importance of changes in the price of chicken in the index and, hence, an upward bias.

One aspect of the CPI Enhancement Initiative, a five-year project to improve the quality of the CPI, is to take into account, as rapidly as possible, changes in consumer behaviours and therefore minimize the substitution effect. This is achieved by updating basket weights at more frequent two-year intervals, instead of at the four-year interval which has been the most recent practice.

A basket update provides the opportunity to measure the magnitude of the effect of product substitutions in consumer purchases.

A straightforward method of estimating this effect is to measure the difference between the Laspeyres and Fisher indexesNote1. The Fisher index formula is the geometric mean of the base period-weighted Laspeyres price index and the current period-weighted Paasche price index. This incorporates, in a symmetrical and balanced manner, weight information from both the beginning and ending periods for which data on consumers’ purchasing patterns are available. This ensures a more representative reflection of spending patterns and effectively avoids the bias issue noted above.

It should be noted that, despite having this desirable feature, constructing a CPI using a Fisher (or any other symmetrically-weighted) index is not feasible in a timely monthly production environment because of the long lags in obtaining current-period weights. However, it can be calculated retrospectively and with a lag when new weight information is obtained.

It follows that the Fisher index, once calculated, can be used as a reference or benchmark, representing the path the CPI would have taken had there been no substitution effects. The magnitude of substitution effects over a given period can be measured as the difference between the fixed-weighted Laspeyres index and the symmetrically-weighted Fisher index.

The effect of product substitutions was estimated as part of the 2011 basket update by calculating the relevant indexes using weights from 2009 and 2011 at the published class level for Canada as a whole. The results are shown in the following table, with those obtained from a comparison of 2005 and 2009 spending patterns for reference purposes:

Calculation of the Product Substitution Effect
Table summary
This table displays the results of tab 1 all-items cpi: laspeyres index value , all-items cpi: paasche index value, all-items cpi: fisher index value and implied annual upward substitution effect, calculated using data and % units of measure (appearing as column headers).
All-items CPI: Laspeyres index value All-items CPI: Paasche index value All-items CPI: Fisher index value Implied annual upward substitution effectTable Note 1
2005 – 2009Table Note 2
106.42 104.72 105.57 0.20
2009 – 2011Note 3
104.82 104.51 104.66 0.07
1. The implied annual upward rate of substitution is measured by the difference between the Laspeyres and the Fisher indexes, expressed as the growth rate per annum. Using the table index values to calculate the implied annual upward substitution effect may not equal the implied annual upward substitution figure in the table due to rounding.
2. Note that some adjustments were made to the 2009 basket in order to align with that from 2005, mainly due to the addition of two published classes in 2009.
3. In this analysis, the homeowners’ replacement cost component was excluded from both periods because it is the only product that is not an out-of-pocket expense, but rather is an imputed expenditure value. Moreover, its price movement is imputed from the New Housing Price Index (NHPI), and therefore we should not expect any meaningful interaction between changes in prices and changes in quantities.

The results show a product substitution effect of 0.07% per year between 2009 and 2011. This is significantly less than the average annual upward bias of 0.20% that was observed between the 2009 and 2005 baskets. This difference underlines the benefits of more frequent basket updates. The impact of using a less representative set of weights is minimized by its more frequent replacement.

A more detailed analysis of the component parts of the CPI revealed that the two largest contributors to the divergence between the Laspeyres and Paasche indexes were gasoline and women’s clothing. These two products exhibited large price change and quantity shifts in the opposite direction. From 2009 to 2011, gasoline prices increased by 31.0%, while the quantities purchased decreased by 9.2%. Gasoline is relatively inelastic, with a price elasticity of demand of -0.36 from 2009 to 2011. Over the same period, women’s clothing prices decreased by 7.7% whereas quantities increased by 24.8%, with a price elasticity of -2.75.Note2


  1. White, Alan G. “Measurement Biases in Consumer Price Indexes.” International Statistical Review 67.3 (1999): 301-325.
  2. Due to rounding, quality and seasonal adjustments, the published indexes may differ from internal data. From 2009 to 2011, the published CANSIM series indicates gasoline has increased 30.9% and women’s clothing prices have decreased by 7.5%. The primary source of expenditures for the CPI is the Survey of Household Spending (SHS). The SHS collects expenditures (price*quantity). The quantity change was derived by the following method: [1-((1/(P2009Q2009)(P2011Q2011)*(P2011/P2009))]. The price elasticity of demand was calculated using the midpoint method. By using average prices and quantities one avoids the value of elasticity being dependent upon whether a price change reflects a price increase or decrease.