The Gap Pattern Coefficient: Diagnosing Missing-Data Bias in Multilateral Price Level Measurement

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. For each item, the procedure quantifies the sensitivity of its prices to unit price levels and measures missingness by the number of absent observations. The association between price-level sensitivity and missingness is then quantified by the gap pattern coefficient. A non-zero gap pattern coefficient indicates that standard multilateral index methods are likely to produce biased results. If desired, the analysis can be complemented by a permutation-based assessment of the statistical significance of the gap pattern coefficient. Monte Carlo simulations evaluate the performance of the proposed diagnostic procedure. The paper further presents simulation evidence showing that GEKS price-level estimates are more sensitive to missing observations than those obtained from CPD or GK.