Indexes of Characteristics: Income and Substitution Effects

  • Federico Perali


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.


Income Effect Family Type White Collar Demand System Demographic Effect 
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  1. 1.
    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.Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Note that the same formal procedure used to define a quantity index of characteristics can be used to construct either price or expenditure indexes.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    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.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Federico Perali
    • 1
    • 2
  1. 1.University of VeronaItaly
  2. 2.CHILD (Center for Household, Income, Labour, and Demographics)Italy

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