Tourism Almost Ideal Demand System

A single-equation model estimates demand for one destination in isolation, so it cannot consistently capture how spending on competing destinations is interdependent. AIDS models the whole budget allocation as a system of share equations that must add up to one, so a price change in one destination is allowed to shift shares toward or away from all others. This delivers a complete, theory-consistent matrix of own- and cross-price elasticities and respects the logical constraints of consumer choice, which single-equation approaches generally cannot guarantee.

The exact AIDS uses a price index that makes the system nonlinear and harder to estimate. The Linear Approximate AIDS replaces that index with the simpler Stone price index, turning the share equations into a linear system that standard methods can estimate easily. Most applied tourism studies, including Li, Song, and Witt's, use LAIDS, often in a dynamic error-correction form. The trade-off is that the Stone-index approximation can introduce some bias and sensitivity to units, so its limitations should be acknowledged.

These are restrictions that consumer theory implies any valid demand system should satisfy: shares must sum to one (adding-up), demand should not change if all prices and the budget scale together (homogeneity), and cross-price substitution effects should be symmetric (Slutsky symmetry). A key attraction of AIDS is that these appear as linear restrictions on its parameters, so they can be imposed to ensure theory-consistent elasticities or left free and tested as hypotheses. Testing them is also a useful diagnostic, since strong rejection can signal a misspecified model or destination set.