Hicksian separability does not hold over space: Implications for the design of household surveys and price questionnaires

If relative prices of goods within a commodity group are constant, Hicksian separability lets the price of a single good represent the group price level. This is relied on by price questionnaires used with household surveys in developing countries and when constructing temporal and spatial deflators. Methods of estimating demand systems from household survey data also rely on Hicksian separability. Yet this restriction remains untested in cross-sections. We use unique data from Vietnam with multiple specifications from within the same food groups to test if within-group relative prices are constant over space. The data firmly reject these restrictions. Some guidelines for survey design are discussed, in terms of the characteristics of commodity groups that should be disaggregated and those that should have more elementary goods added to their linked price questionnaire.