Revealing fundamental demand parameters: A new theoretically consistent meta-regression approach to US food demand elasticities

Demand elasticities are critical inputs for estimating the impacts of many food policies, yet efforts to derive these key parameters from past studies suffer from underlying inconsistencies. Typical demand elasticities drawn from meta-analyses often fail to deliver fundamental parameters consistent with economic theory. This practice could cause at least three drawbacks: (1) demand elasticities might violate symmetry, adding up, or other requirements of applied demand theory, (2) demands do not integrate into a utility function and cannot support welfare analysis, and (3) parameters often violate the theoretical underpinnings of the source studies from which they are drawn.

We propose a new meta-analysis approach that is consistent with demand theory. Using elasticities of past studies and market data as inputs, we estimate the fundamental parameters of a Quadratic Almost Ideal Demand System using nonlinear least squares augmented by a wild bootstrap for bias correction and to allow for heteroskedasticity across studies and products. The theoretically consistent matrix of price and expenditure elasticities for the seven major food categories in the United States is calculated from fundamental demand parameters and consequently can readily be updated. We compare this new approach to an atheoretical, purely statistical meta-analysis and find some departures from a statistics-driven approach. This approach overcomes the limitations of sparse data, supports practical applications in welfare and market analysis, and offers applied economists a more theory-consistent alternative.