# Checking negativity condition in demand system model

Let's assume you want to estimate a demand system model, e.g. the AIDS, based on observational data. Then you usually test first whether the homogeneity and symmetry condition hold in order to check whether the consumer act according the neoclassical demand theory. For the AIDS the negativity condition holds by design, so you do not have to test this. But if we use a model that caries less prior structure from demand theory, then it is not clear whether own-price effect acutally turn out negative. Maybe we want to estimate a model, inluding log prices and log income, equation-by-equation with OLS.

So my question is how to check whether the negativity condition is satsified if we do not use a model with much prior structure, such as the AIDS? Do we simply check whether the estimated own-price effects are negative and significant? Can we do something like a joint test in addition?

Estimating demand equations with OLS is never done due to some major problems (endogeneity, assumptions of homogeneous coefficients for all consumers, assumptions of a linear demand curve).

Most modern demand estimation is based in random-coefficient logit and follows the methods of Berry, Levinsohn, and Pakes (1995) and Nevo (2001). That GMM estimation would result in a coefficient estimate for the price elasticity. We could then do a hypothesis test.

I'm not sure what you mean by a "joint test" and would need more context.

• Thanks for your answer. By "joint test" I mean something like a F-test. The homogeneity condition we test with a F-test "equation-by-equation" typically.
– timm
Apr 25, 2022 at 10:34
• Are you saying there is a different equation for each product in OLS? Apr 25, 2022 at 16:13
• Yeah, there is. I guess one has to estimate it with SUR...
– timm
Apr 26, 2022 at 20:02
• You could pool all data, and have fixed effects for products, then interact the fixed effects for products with price. Apr 27, 2022 at 7:59