The range of admissible price and income elasticity estimates is materially reduced in this investigation of a variety of procedures, including new methods for analyzing deflation bias. Mostly small effects are found for choice of index formula, base year, logarithmic versus linear form, definition of food consumption (e.g., physical versus expenditure measure), procedures related to time, and aggregation. However, the supply elasticity of food is found to be identifiable and to have a value greater than many have believed, providing a basis for deciding whether to favor demand estimates based on consumption-dependent or price-dependent regressions. The most frequently used deflators are inconsistent with the Slutsky-Schultz relation. Estimates are developed of three types of bias due to improper deflation (weight of food in deflator, correlation of deflator with residual, and formula nonconformities).