Almost Ideal Demand System
Also known as: AIDS, Deaton-Muellbauer Demand System, LA-AIDS, Almost Ideal Demand Model
The Almost Ideal Demand System (AIDS), introduced by Angus Deaton and John Muellbauer in 1980, is the workhorse flexible demand system in applied microeconomics. It models each good's budget share as a linear function of the logarithms of all prices and of log real total expenditure, derived from a flexible (PIGLOG) cost function. The form is 'almost ideal' because it satisfies the axioms of choice exactly, aggregates consistently over heterogeneous consumers, has a functional form that is a first-order approximation to any demand system, and can be estimated and tested for homogeneity and symmetry with linear regression once a price index is specified.
Key highlights
- Flexible: a first-order approximation to any demand system, so it does not force restrictive a priori substitution patterns like the LES does.
- Parameters map directly into closed-form expenditure and price elasticities evaluated at observed budget shares.
- Homogeneity and Slutsky symmetry enter as simple linear cross-equation restrictions that are easy to impose or test.
- Consistent with exact aggregation over heterogeneous consumers (PIGLOG preferences) and yields exact welfare and cost-of-living measures.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use AIDS when you want a flexible, theory-consistent demand system for a moderate number of broad commodity groups and you have price and budget-share data across households or over time. It is the default choice for computing own-, cross-price, and expenditure elasticities for welfare analysis, tax incidence, food and nutrition policy, and cost-of-living measurement, and it makes homogeneity and symmetry directly testable. Prefer the full nonlinear AIDS when prices vary substantially (so the translog index matters) and the Linear-Approximate AIDS when computational simplicity is paramount and price variation is modest. Consider the Quadratic AIDS (QUAIDS) when Engel curves are nonlinear, and censored-system variants when microdata contain many zero purchases. AIDS is less suitable for highly disaggregated, differentiated products with frequent zeros, where discrete-choice demand models are more appropriate.
Strengths & limitations
- Flexible: a first-order approximation to any demand system, so it does not force restrictive a priori substitution patterns like the LES does.
- Parameters map directly into closed-form expenditure and price elasticities evaluated at observed budget shares.
- Homogeneity and Slutsky symmetry enter as simple linear cross-equation restrictions that are easy to impose or test.
- Consistent with exact aggregation over heterogeneous consumers (PIGLOG preferences) and yields exact welfare and cost-of-living measures.
- The exact form requires a nonlinear translog price index; the popular Linear-Approximate (Stone-index) version introduces approximation bias when prices vary widely.
- Engel curves are linear in log expenditure, which can misfit goods whose budget shares are nonlinear in income (motivating QUAIDS).
- Like all share systems it assumes interior solutions, so frequent zero purchases in microdata require censored-system extensions.
- Homogeneity and symmetry are often statistically rejected in real data, raising questions about the maintained theoretical structure.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What is the difference between exact AIDS and Linear-Approximate AIDS (LA-AIDS)?
Exact AIDS uses the model's own nonlinear translog price index, making estimation nonlinear in the parameters. LA-AIDS replaces that index with a simpler Stone (share-weighted log) price index, which makes the system linear and easy to estimate with SUR, at the cost of an approximation error. When relative prices vary little, LA-AIDS is close to exact AIDS; when prices vary widely, the Stone-index approximation can bias estimates, so the full nonlinear AIDS is preferred.
How do I get income and price elasticities from AIDS?
They are closed-form functions of the estimated parameters and the budget shares. The expenditure elasticity of good i is 1 + β_i / w_i, so β_i < 0 marks a necessity and β_i > 0 a luxury. The uncompensated own- and cross-price elasticities use the formula −δ_ij + (γ_ij − β_i w_j)/w_i, where δ_ij is one for own price and zero otherwise; compensated elasticities and the Slutsky matrix follow by adding the income effect. Elasticities are typically reported at sample-mean shares.
When should I use QUAIDS instead of AIDS?
Use the Quadratic AIDS when the relationship between budget shares and log expenditure is nonlinear — that is, when some goods are necessities at low incomes but luxuries at higher incomes (or vice versa), producing curved Engel curves. QUAIDS adds a quadratic term in log real expenditure to capture this curvature while retaining AIDS's flexibility, aggregation, and testability. If Engel curves are approximately linear in log expenditure over your data range, standard AIDS is adequate and simpler.
Sources
- 1.Deaton, A., & Muellbauer, J. (1980). An almost ideal demand system. The American Economic Review, 70(3), 312–326.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 22). Almost Ideal Demand System. ScholarGate. https://scholargate.app/economics/almost-ideal-demand-system