Early Precursors to the AIDS Model and Economics and Consumer Behaviour
Many of John’s early publications contained the individual building blocks that he and Angus Deaton combined to develop their famous Almost Ideal Demand System (AIDS) model. These include the use of duality theory to formulate indirect utility functions (or cost functions) that are more amenable to generating estimable demand functions than are direct utility functions.
Using the cost function representation of preferences made it possible to discuss the impact of taste and quality change on consumer cost of living indices in a more elegant and compelling way than hitherto (see Muellbauer 1975). It also permitted a translation of the framework for defining household equivalence scales, proposed by Prais and Houthakker (1955) and Barten (1964), into cost functions (see Muellbauer 1974a, 1977, 1980). This allowed welfare comparisons across households of different compositions, the measurement of the “cost of children” (also see Deaton and Muellbauer 1986) and incorporation of the differential impact of relative price movements and of household composition in the measurement of welfare and inequality (see Muellbauer 1974b).A second important application of duality theory was to devise forms of preferences that could be aggregated across households, while being less restrictive than then-prevailing frameworks used by economists. The earlier, seminal contributions of Gorman and Stone had imposed identical linear Engel curves such that the marginal propensities to consume of particular classes of goods and services were invariant to levels of income. This assumption is convenient in permitting aggregation across households into aggregate demand functions but is contrary to empirical evidence.
The research that led to the AIDS model began with a 1974 Birkbeck working paper, triggered by John's concern about the distributional impact of inflation, entitled “The Political Economy of Price Indices”.
John made a remarkable discovery in asking the question: whom does an index such as the retail price index (RPI) represent, or where in the income distribution could one find a household with expenditure patterns similar to the weights used in the RPI? With identical linear Engel curves, such a representative household would have had average income, which is restrictive. John generalised the concept of the representative household, leading to a new class of preferences and a more general representative income level (see Muellbauer 1975, 1976). This research spawned a new literature in demand analysis discussed below. Though not published at the time, the 1974 paper also generated a research on “social cost of living indices”, for example, Jorgenson and Slesnick (1983) (see Muellbauer 2019a, b, for the paper and its historical context).In his 1976 Econometrica paper, John asks what form of preferences, shared by all consumers, would allow budget share equations defined for the aggregate of consumers to be represented simply by budget share equations driven by prices and the income of a single representative consumer. He characterised this income concept—in general—as a function of prices and of the entire income distribution of individual consumers. This characterisation of “community preferences” imposed less restrictive assumptions than used earlier by Gorman. John gave the name “generalised linearity” (GL) to this form of preferences. Under GL preferences, budget share equations are linear, but now in a general (non-linear) function of prices and income common to each budget share equation. In his 1975 article in the Review of Economic Studies, the same problem was studied with the further requirement that the income of the representative consumer be independent of relative prices, depending only on the underlying income distribution across consumers. This “price independent generalized linearity” (which he christened PIGL) meant that the budget share equations are linear in a general power function of income, whose form is the same for all consumers.
A special case arose where the function was logarithmic, which he named “the PIGLOG case”. Subsequent empirical micro-evidence suggested that the PIGLOG case was in fact the best fitting in the PIGL class.PIGLOG imposes the condition that expenditure shares be linear in log income, which allows Engel curves in the level of income to be non-linear. This is more realistic than the assumptions made in the linear expenditure system (LES) of Stone. The PIGLOG specification allows aggregate behaviour across consumers to be modelled as though it emanated from a single maximising agent. Nevertheless, PIGLOG implies that that aggregate behaviour depends not only on average income, but also on its distribution. With reliable time-series data on income distribution, PIGLOG also provides a way of linking aggregate behaviour and the income distribution.
The work described in Muellbauer (1975, 1976) inspired a new literature that extended forms of Engel curves and of preferences, with useful aggregation and other properties. Gorman (1981) introduced the notion of the rank of a system of Engel curves. Rank 1 corresponds to homothetic preferences where budget shares do not depend on the level of total expenditure. Rank 2 includes linear Engel curves and GL, the latter being the necessary and sufficient condition for the representative household concept discussed above. Engel curves of Rank 3 further extend functional forms, and with useful aggregation properties (see Lewbel 1988, 1989, 1991). The “Quadratic Expenditure System” of Howe et al. (1979) is an example of such an extension of GL, while the translog form of demands of Jorgenson et al. (1982) is an application within the GL class.
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