# The Cost of Children and the Distribution of Welfare

## Abstract

This chapter applies the theory developed in Chapter 3. It is concerned with the estimation of the cost of children in Colombia and the use of this to identify the poor correctly by comparing income levels taking into proper account differences in household composition. This is made operational by deflating the distribution of incomes using the estimated household equivalence scales to obtain the distribution of welfare, which is, as shown in Section 3.6, a fully comparable money measure of cardinal utility. The derivation of the distribution of welfare requires that the household information can be separated from utility so that household equivalence scales are independent of the base level of utility or income chosen for comparison.

## Keywords

Capita Expenditure Equivalence Scale Household Type Demand System Food Share## Preview

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## Notes

- 1.From this point on, we will use the term
*IB*in lieu of*ESE*because the acronym*IB*evokes the definition of the property of independence of the base level of income chosen for comparison more closely.Google Scholar - 2.This model of economies of scale and household public goods was initially developed by Lazear and Michael (1980), and then further elaborated by Nelson (1988), Deaton (1997) and Deaton and Paxson (1998). Interestingly, these approaches are all based on Barten’s (1964) theoretical construct.Google Scholar
- 3.For the formal definition of distribution of welfare see Chapter 3, Section 3.6.Google Scholar
- 4.In the non-parametric analysis, the distribution of welfare is the vector of equivalent incomes obtained as
*y/m(p,d)*, where*m(p,d)*is a household equivalence scale being a nonlinear function of both unit values*p*and a vector of demographic characteristics*d*whose estimates are presented in Chapter 4.Google Scholar - 5.This notation is adopted for convenience of exposition considering that, quite implausibly, it rules out the existence of household public goods.Google Scholar
- 6.This is the specification adopted in Caiumi and Perali (2000) to carry out the structural estimation of the sharing rule between husband and wife.Google Scholar
- 7.For reasons of conciseness the estimated parameters are not reported, but are available from the author upon request.Google Scholar
- 8.Deaton and Muellbauer’s prediction that Barten-Gorman estimates should be within the Rothbarth and Engel bounds is not expected to hold exactly. In the present context, the relevance of the result is as a cross-validation tool.Google Scholar
- 9.The interest reader may visit the internet site:(www.iser.essex.ac.uk/bhps/index.php).Google Scholar
- 10.Of course, the normalization of a reference childless couple to 2 does not preclude the change of base to a gender specific adult equivalent member. On the other hand, if we think in terms of the quality of interhousehold comparisons, it would be highly desirable to include information on intra-household allocation of resources in the estimation of household equivalence scales in order to widen the information set about household characteristics and circumstances on which interhousehold comparisons are based.Google Scholar
- 11.The iso-elastic equivalence scales are often used in international comparisons of poverty and inequality levels. Atkinson
*et al.*(1995) and Johnson and Smeeding (1998) adopt the size elasticity of 0.5, that is the square root of household size. This approach is not informative about the cost of a specific household characteristic.Google Scholar - 12.As was shown in Chapter 3, Section 3.9, proxy scales are also based on utility theory, but are based on single equation demand estimates rather than complete demand systems.Google Scholar