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Biases in Price Indexes

Producer and International Trade Price Indexes: Concepts, Sources and Methods
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A price index may be described as biased if it produces estimates that depart consistently from the 'true' measure as a ‘pure price index’. There are several methodological and practical issues that may give rise to a biased price index and these forms of bias are outlined below, together with the review and maintenance strategy employed in such situations.

Elementary Index Bias

Elementary index bias (or within elementary aggregate (EA) bias) results when the formulae used to compile index numbers at the elementary aggregate level does not allow index movements to appropriately reflect substitution behaviour.

For example, consider an illustrative model for the an output price index, where producers have fixed inputs. Under this model, it is assumed producers aim to sell more high-priced products as opposed to lower-priced products. This behaviour is revenue maximising (and for fixed inputs revenue maximising is profit maximising, an expected behaviour of producers). A fixed basket price index measuring price changes for this economic model would exhibit bias. This bias arises because the quantities in the basket are fixed, but the behaviour exhibited in the marketplace has producers selling more of the relatively more expensive products - that is, quantities change. The failure of the price index to account for this shift is the extent to which the index is biased.

For an input price index example, consider an illustrative model where producers have fixed outputs. Under this model, it is assumed producers aim to purchase more low-priced intermediate inputs as opposed to higher-priced products. This behaviour is cost minimising (and for fixed outputs, cost minimising is profit maximising, an expected behaviour of producers). A fixed basket price index measuring price changes for this economic model would exhibit bias. This bias arises because the quantities in the basket are fixed, but the behaviour exhibited in the marketplace has producers purchasing more of the relatively more of the cheaper products - that is, quantities change. The failure of the price index to account for this shift is the extent to which the index is biased.

There are two strategies that can be adopted to further protect these price indexes from elementary aggregate bias. The first of these strategies is to frequently update the weights in the basket (assuming we are using the Lowe price index, with differentially weighted specifications). This can be achieved through regular sample maintenance.

The second strategy that can be employed is to adopt a different price index formula that better reflects such behaviour. The Jevons, or geometric mean, price index is a formula that is unbiased if the price behaviour is¹, a condition which is not universally applicable for every product.

"Between Component" substitution bias

Substitution bias arises from using formulae at levels above the elementary aggregates which do not allow for substitution in response to changes in relative prices. Substitution may occur outside elementary aggregates in response to price changes or changes in taste. For example, producers may substitute between natural and synthetic fibres, between steel and ceramic parts for machinery, between wooden and aluminium window frames and so forth. This substitution again results in a quantity shift, and the failure of a fixed basket price index to account for this shift is again the extent to which the index is biased.

The sample and index review processes described above result in new components and updated weights and are the key mechanism by which the ABS mitigates between component substitution bias. Industry reports, media and other information sources collected by index managers provides an annual picture of change across all products in the Producer and International Trade Price Indexes, and an assessment of this change allows resources to be targeted to those areas that are most susceptible to this type of bias.

Outlet/Customer biases

Outlet/Customer biases occur because the transactions in the elementary aggregates are generally fixed to specific suppliers and/or specific customers. In an input price index, bias occurs when the price index does not detect when purchasers shift from higher cost suppliers to lower cost suppliers for the same product. In an output price index, bias arises when the index does not detect when producers practise price discrimination and shift the sales from customers with lower prices to customers who pay higher prices for the same product.

The bias that arises due to change in supplier or customer is mitigated in several ways in the Producer and International Trade Price Indexes. For the Input to the Manufacturing Industries Producer Price Index, prices are generally observed by surveying the purchaser. If the purchaser changes supplier (and pays a lower price) then this is detected in the quarterly Survey of Producer Prices and, after being adjusted for any appropriate quality changes, appears as a movement in the price index. Similarly, for the output price indexes, prices are generally observed by surveying the producer, and any price rises resulting from changes to new customers will similarly appear in the price indexes. Much but not all of the risk of bias is mitigated by this approach to sample selection.

There are two situations where potential biases can arise.

The first is in the Input to House Construction Producer Price Index. This input price index measures prices paid by builders by surveying the businesses supplying the products rather than the builders themselves. This practise is far more practical and efficient than attempting to survey a sample of individual builders. However, one drawback to this approach is that this price index becomes susceptible to outlet (supplier) substitution bias. For example, if builders begin purchasing from a chain wholesaler outside the sample that offers materials at substantial discount, the price index would exhibit an upward bias.

The second case where biases arise is where counterpart pricing is utilised. Counterpart pricing is a term used to reflect using a transaction price observed on a pricing basis that differs from the conceptual base of the price index. For example, within the manufacturing price indexes, some suppliers provide the prices they receive for their products and these are included in the input price index. Aside from the appropriateness of the underlying assumptions regarding distributive trade margins, this practise also has the potential to introduce outlet substitution bias, since it does not always detect when purchasers change their point of supply (at lower prices). A similar issue arises when purchasers provide prices for incorporation into an output index (although in this case the bias is more suitably termed ‘customer substitution’).

Regardless of where such practises occur, the potential for bias is mitigated through index reviews and sample maintenance reviews. As detailed above, such reviews measure expenditure and revenue for different products and involve consultation, both with industry bodies and producers themselves. Regular activity of this kind detects changes in sales or purchasing markets and allows price indexes to be updated to reflect the shift in the quantities and revenue/expenditure.

Quality adjustment bias

Failure to adequately adjust prices to account for changes to quality results in volume changes being inappropriately measured as price changes, with a resulting bias in the price index. Pricing to constant quality, and the mechanisms by which quality adjustments are made, are described in detail in the Quality change section.

With a set of tools to enable quality adjustments to be made, the remaining risk for quality adjustment bias occurs through failing to detect changes in products or conditions of sale. This risk is mitigated through forms design of the Survey of Producer Prices, and through the initial enrolment process for selected providers. As described above, a key feature of the enrolment process is to convince selected providers of the importance of pricing to constant quality. Capturing the detailed specification of products together with their condition of sale is also protection against quality change since it allows providers to inform the ABS directly of variations in characteristics.

New product bias

The issues surrounding new products were discussed in the Quality change section, which noted that the bias arising from the introduction of new products is exacerbated through delays in introducing such products into the price basket. Sample reviews and index reviews provide opportunities to incorporate new products into the price baskets. If such reviews are carried out regularly, the risk from the emergence of new products is substantially mitigated. Sample reviews and index reviews provide further protection against new product bias in that they allow an assessment of market trends and conditions.


¹ “Unit elasticity” means that quantities respond proportionally to changes in prices, such that value remains constant. For example, if 5 units of a product are sold at $4.00 each, the value is 5 x $4 = $20. If a price rise of 25% to $5.00 sees a commensurate fall of 20% in the units sold, or 1 unit, so that 4 units are exchanged, the total value is then 4 x $5 = $20. In these circumstances, the total value is constant and the product is exhibiting unit elasticity. This approach is used in the PPIs and ITPIs when markets are evolving very quickly, or detailed level value data is unavailable in a timely manner. Such a strategy is often adopted only in those cases where the price behaviour is reasonably matched by the properties of the index formula. 

As per the “Choosing an index number formula” found in the Price index theory section, other factors aside from elasticity are also useful in determining suitability of index formulae.