Statistics Iceland has published a working paper on the treatment of bias in the Icelandic CPI (Meðhöndlun bjaga í vísitölu neysluverðs á Íslandi). The paper is in Icelandic but has an English summary.

This working paper explores the reasons for biases and how they can be treated. There are four types of different biases described in this Working paper. Three of them are within the scope of consumer behaviour (substitution bias, shopping substitution bias and new goods and services bias). Methods for treating these biases are all in line with economic consumer theory. The fourth type of bias (quality bias) is not connected to consumer behaviour. This bias is rooted in the production characteristics of goods and services. The bias’s size is unknown, but the bias changes over time, it can increase or decrease, be positive or negative. Various methods are used for treating bias of different origin. Measurements of price changes, which are systematically too high or too low compared to the absolute values measured are biased. Measuring correctly and avoiding bias is a constant challenge in all price indices. The Icelandic CPI is no exception. Statistics Iceland takes this challenge seriously and works determinately on minimizing the bias.

Substitution bias
The cost of living index relates to consumers that maximize their utility and minimize their associated cost. Ordinarily it is presumed that quantity and price are negatively related. It follows that individuals maximize their utility and modify their consumption by substituting for cheaper or at least relatively cheaper products.

When bias is discussed in a cost of living index, an index value is compared to the value obtained by the theoretically correct cost of living index for two periods. A distinction is drawn between the calculating methods for the aggregate index (upper level) and for the elementary aggregate (lower level), which is the index's lowest level.

• Results aggregate index (upper level): Findings for 10 years interval in the Icelandic CPI indicate that this bias is -0.01 per cent to +0.02 per cent on average. The lowest yearly bias is -0.8 per cent and the highest yearly bias +0.9 per cent.

• Results elementary aggregate (lower level): The level of bias is not known. In the Icelandic CPI Statistics Iceland applies both geometric mean and superlative indexes to cure the substitution bias. Both methods cover 77 per cent of the index weights. For this reason this bias is assumed low.

Shopping substitution bias
Consumers constantly face the situation that store prices for identical or similar goods can vary widely. If consumer price indices are to be correct, they should measure the prices of the goods that households obtain to measure the price changes in household purchases. When households modify their purchasing patterns, the average price of their purchases may change without anything happening in the store; in fact, prices might even remain unaltered and if these changes are not corrected there will be shopping substitution. The method for correction in the price measurement is by direct quality adjustment. Results: Bias is 0 per cent. Shopping substitution bias has been corrected in the Icelandic CPI yearly since 2001. The total effect of shopping substitution corrections in 2001-2018 amounts to a 0.75 per cent lowering of the CPI.

New goods and services bias
When new or improved goods and services enter the market they are not taken into account nor the welfare gains for the consumers of their entrance. Results: The level of new goods and services bias is not known. New goods are systematically incorporated in the CPI. The main method used is overlapping that should ensure that the price history of the good is measured. For this reason this bias is not considered high.

Quality bias
Quality bias arises from the situation where the basket of goods and services is updated without consideration to quality changes of new items. This can occur either because the changes in quality are not noticed or are not properly measured.

Results: The level of quality bias is unknown. Statistics Iceland uses similar methods as other statistical offices with overlapping the most commonly used method. Many quality adjustments, explicit or implicit, are applied regularly but an overview of its extent is not available. There is an uncertainty of the magnitude of the quality change which is not accounted for in the index.

Treatment of bias in the Icelandic CPI - Working paper