This chapter explores the measurement of price indices using the Engel curve, which reflects the relationship between food expenditure and total expenditure (Engel coefficient). Ernst Engel’s 1857 study found that as income increases, the proportion of income spent on food decreases. Recent studies leverage this relationship to measure price index biases, suggesting significant biases in existing indices. The chapter details the Almost Ideal Demand System (AIDS), introduced by Deaton and Muellbauer (1980), as a central model for such measurements. The AIDS model provides a second-order approximation to any expenditure function, making it a robust tool for analyzing consumption patterns and estimating price indices. Nakamura (1996), Hamilton (2001), and Costa (2001) found significant biases in historical consumer price statistics in the US, using the Engel curve to analyze changes in food expenditure relative to income and prices. Almås (2012) extended this approach internationally, revealing substantial biases in purchasing power parity, particularly for developing countries. Despite the method’s simplicity and the substantial body of literature supporting it, official price indices have not adopted the Engel curve approach. The chapter highlights criticisms, including the model’s reliance on invariant preference parameters across time and regions, and the omission of factors like savings and home production. These issues cast doubt on the method’s reliability for official statistics, even as it gains traction in academic research.