Multilateral Price Level Measurement With Incomplete Data

Abstract: Multilateral price indices are widely used to estimate and compare price levels across units such as time periods or regions using observed prices and quantities of individual items. Besides ensuring transitivity and reducing chain drift, these methods are often assumed to mitigate the effects of missing price observations by exploiting information from multiple comparison units. This paper argues that this advantage can only be realized if item-level missingness is independent of the sensitivity of item prices to
overall unit price levels. Recent research has shown that this assumption is frequently violated in practice, resulting in biased price-level estimates. To address this issue, the paper develops a simple diagnostic procedure, the gap pattern test. For each item, the test quantifies the sensitivity of its prices to unit price levels and measures missingness by the number of absent observations. The relationship between these two variables is then examined, with statistical significance assessed using a permutation-based procedure. A significant correlation indicates that standard multilateral index methods may produce biased results and should therefore be interpreted with caution. The paper also discusses alternative estimation strategies and evaluates the performance of the proposed test through Monte Carlo simulation.