The AIDS Framework
Addressing the need for a general but accessible empirical specification for econometric studies, Muellbauer and Deaton made a tremendous contribution to economics in developing their Almost Ideal Demand System.
The AIDS framework is rare in being both well-grounded in economic theory and empirically tractable and flexible for estimating a broad range of consumer behaviour. By drawing on Muellbauer's earlier work on duality theory, aggregation and PIGLOG preferences, building on the 1970s literature on flexible functional forms (see Diewert 1971), and combined with Deaton's econometric insights, the AIDS framework derives demand specifications that can be aggregated across households and estimated using linear techniques. When it was created, it had several features which made it attractive relative to its two main competitors for estimating demand systems—the linear expenditure system of Stone, and the “Rotterdam model” associated with Henri Theil and Anton Barten.From a theoretical perspective, the AIDS framework has four major, desirable properties for a system of demand functions for different types of goods, while assuming that households are rational and specifying a form of heterogeneity enabling aggregation across households. The least technical of these properties (“additivity”) implies that individual demands will add up to satisfy an overall budget constraint. Three technical attributes stemming from maximising behaviour could easily be imposed: homogeneity in prices and income, symmetry in the cross-price responses, and a condition on the matrix of cross-price derivatives.[203] Symmetry implies that the marginal effect of a change in the price of good A on the demand for another good B is the same as the marginal effect of a change in the price of good B on the demand for good A, for a given level of utility.
One implication of the matrix condition is that a higher price of a good should not increase the demand for that good (holding utility constant). These features are shared by Stone's LES, but they follow in the AIDS framework with preferences less restrictive than the Stone- Geary utility form assumed by the LES approach. An advantage over the Rotterdam model is that the AIDS framework can be derived from well- behaved preferences while still having much of the empirical flexibility of the Rotterdam model.The AIDS framework proved especially suited for a wide range of empirical applications. The flexibility and limited restrictions imposed by the AIDS model made it popular for analysing the demand for various goods. As it is nearly linear, the component demands in AIDS can be estimated independently. If used with a well-specified aggregate price index, ordinary least squares suffices to estimate each component or the whole system.
Deaton and Muellbauer (1980a: 312) eloquently summarise their paper's contribution:
Our model, which we call the Almost Ideal Demand System (AIDS), gives an arbitrary first-order approximation to any demand system; it satisfies the axioms of choice exactly; it aggregates perfectly over consumers without invoking parallel linear Engel curves; it has a functional form which is consistent with known household-budget data; it is simple to estimate, largely avoiding the need for non-linear estimation; and it can be used to test the restrictions of homogeneity and symmetry through linear restrictions on fixed parameters.
For all these reasons, the paper has, according to RePEC, been cited in over 1,400 publications.
The extensive application of the AIDS approach rests partly on the ease with which expenditure shares of broad categories of goods and services can be modelled. Moreover, if consumer preferences are weakly separable, then the AIDS, like other demand systems, can model expenditure on goods within a broad expenditure category independently of how spending is allocated across the goods in other expenditure categories.
The separability assumption also makes the AIDS framework useful for empirically modelling portfolio behaviour (see Barr and Cuthbertson 1991; Blake 2004). Separability[204] allows for a hierarchy of decision-making where a household chooses an overall portfolio size, then an allocation across different categories of assets and liabilities, and then particular instruments within each of these categories.As with any framework, there are limitations to the AIDS. In applications that condition on average income without considering distributional shifts, it implicitly assumes that the distribution does not change over time. Another shortcoming in some implementations is the use of a simple approximation of the underlying price index to deflate nominal income (rather than taking further steps in a simple iterative procedure,[205] or implementing a full systems estimation). Thirdly, expenditure shares are not always linear in log income, as noted by Banks et al. (1997), who developed a variant of the AIDS framework allowing for quadratic Engel curves, which they dubbed QUAIDS. The appeal and applicability of the AIDS model, along with the development of variants to address its weaknesses, have made it a widely used framework in empirical analysis. Indeed, three and a half decades after its publication, Besley (2016: 381) described it as a ‘cornerstone of demand estimation'.
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