Global properties of well-behaved demand systems: A generalized logit model specification

Global negative semidefiniteness of the Hicks-Slutsky substitution matrix limits the range of the elasticities with respect to own-price (E(ii)), cross-price (E(ij)) and expenditure or income (E(iI)) for many standard demand systems. In a two-good model, the results for the translog and AIDS are qualitatively identical, namely, E(ii) is less than - 1; E(ij) is greater than 0; and E(iI) equals 1 (homothetic preferences). The results for the generalized Leontief and minflex Laurent are also qualitatively identifical, namely, E(ii) is equal to the negative of the own expenditure share; E(ij) is equal to the negative of the expenditure share of the other good; and E(iI) equals 1 (homothetic preferences and zero Hicksian substitutability). Thus, these standard flexible functional forms can be globally well behaved but at the expense of losing their flexibility property. The generalized logit model presented in this paper is also a flexible functional form and can be globally well behaved while retaining flexibility.