Generalized Logarithmic Index Numbers with Demand Shocks: Bridging the Gap between Theory and Practice

There has long been a gap between theory and practice for measuring aggregate price changes. As Samuelson and Swamy (1974, AER) stated, deflators must satisfy transitivity to make real consumption expenditures consistent with consumer theory. To date, few well-known indices are transitive. Building on Redding and Wenstein (2020), we consider a generalized logarithmic index with demand shocks and establish its monotonicity and transitivity properties, which fills the gap. We also derive conditions under which the logarithmic price index is unique. Analysis of Japanese weekly scanner data shows that the traditional chained Sato-Vartia index has 4.86 percent downward bias per annum.