Abstract
This chapter addresses the positive question asking how children affect the expenditure pattern of a household. Traditionally this question has been examined by estimating the impact of demographic variables on quantity consumed. In this research, the objects of interest are the demographic functions per se and the demographically modified quantities.
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Notes
It is relevant to stress that the derived normalization does not apply to demand systems derived in quantity space since no summability is required. Further, the identification of the demographic parameters is always subordinated to sufficient information in the data.
Note that the Barten-Gorman demographic transformation corresponds to a “reverse Gorman” specification in Pollak and Wales terminology (1981) which is obtained by first scaling and then translating the quantities as clarified in Chapter 1.
Note that the same formal procedure used to define a quantity index of characteristics can be used to construct either price or expenditure indexes.
The strict relationship between consumption shares and demographic functions is expressed with great clarity by an example illustrated by Lewbel (1989d). He specifies a Cobb-Douglas sub-group utility function whose coefficients are the demographic functions. In this special case, the shares are the demographic functions.
Note that in the two-good example described in the theorem the first stage budgeting allocation is total expenditure, while the second stage budget allocation is, in our example, the subgroup rice and Italian imported pasta. The latter is the same for all households as it was previously in the case for the consumption of cereals.
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© 2003 Springer Science+Business Media Dordrecht
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Perali, F. (2003). Indexes of Characteristics: Income and Substitution Effects. In: The Behavioral and Welfare Analysis of Consumption. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3729-5_5
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DOI: https://doi.org/10.1007/978-1-4757-3729-5_5
Publisher Name: Springer, Boston, MA
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