Measuring the costs of children

Journal of Public Economics 22 (1983) 89-102. North-Holland

MEASURING

THE COSTS OF CHILDREN

An alternative approach

Ranjan RAY* University of Manchester, Manchester MI3 9PL, UK

Received May 1982, revised version received May 1983 The ‘cost of a child’ or, the general equivalence scale as it is more commonly known, is a concept of considerable importance in matters relating to public policy and welfare. It has played a crucial part in numerous theoretical and empirical studies relating to poverty, income distribution, dietary needs, income maintenance programs, supplementary and child benefits and other forms of social security payments in a welfare state, and in assessing the horizontal equity of income taxation. In spite of a long tradition of estimating the scale from observed household budget data, there remain severe problems in estimation and interpretation of the scales. This paper proposes a new methodology for calculating the scale using a framework which is consistent with utility theory and which overcomes the identification problem without having to enforce the arbitrary prior assumptions of recent studies. The proposed method allows easy calculation of not only the basic ‘scale’ parameter but also how it varies with price and reference utility. We illustrate the usefulness of the procedure by estimating on U.K. budget data at two different levels of aggregation and employing two sets of quite different functional forms. The results are plausible, compare favourably with one another and, hence, confirm the robustness and usefulness of the proposed procedure.

1. Introduction

The ‘cost of a child’, or the ‘general equivalence scale’ as it is more commonly known, is a concept that is of considerable importance in issues relating to public policy and welfare. Viewed as a True Cost of Living Index (TCLI), the general equivalence scale compares two households with different composition and calculates their relative cost of enjoying the same level of utility - in other words, it seeks to answer questions of the form: ‘What expenditure level would make a family with one child as well off as it would be with no children and ;E2000?’ The equivalence scale, as its name suggests, converts households with differing size and composition into equivalent units in terms of some reference household. The scale, thus, seeks to quantify and represent in one summary measure the changing ‘needs’ of a family as it expands and changes its composition with the passage of time. *I wish to thank anonymous referees including a member of the editorial board for comments on an earlier version. I am also grateful to John Smith for programming assistance. I retain responsibility for all errors that may remain. 0047-2727/83/$3.00

0

1983 Elsevier Science Publishers B.V. (North-Holland)

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R. Ray, Measuring the costs

of children

The importance of the scale in welfare economics in general and public policy discussion in particular stems from the fact that considerations of equity, justice and the like crucially involve an examination of people’s ‘needs’ in relation to, available resources. Such ‘needs’ will obviously vary from household to household depending on, among other things, its size and composition. Larger households will have greater needs than smaller households. Similarly, households with more children in the older category will make greater demands on certain items, less on others, than those with more children in the younger category. Since it is the household rather than the individual that is the unit of consumption, decision-making and beneficiary of; public welfare programs, it seems natural to make welfare comparisons across households in a manner similar to the way the TCLI compares individuals over time. The equivalence scale has figured prominently in the theoretical and empirical literature on poverty, income distribution and income maintenance programs. In the United States, for example, the scale provides the basis for many empirical studies aimed at identifying and counting the poor [see Orshansky (1965), Mahoney (1976), Lazear and Michael (1980), and van der Gaag and Smolensky (1980)]. Atkinson (1969), Stark (1972), Howe (1971) Garganas (1977) and Muellbauer (1974a, 1974b) are examples of numerous U.K. studies that use the scale to investigate issues relating to poverty, income distribution, the distributional impact of price movements [see also Kakwani (1980) and Sen (19Sl)]. In countries like the United Kingdom [Beveridge Report (1942)] and Sweden which have supplementary benefits and an elaborate network of social security payments, the scale acquires added importance. The ‘scale’ also figures prominently in the ‘Living Standards Measurement Study’ (LSMS) launched recently by the World Bank [see Deaton (1981) and Grootaert (1983)]. Besides, household circumstances are also important in issues relating to fertility [Willis (1973)], in incidence of taxation [Senneca and Taussig (1971) and Blundell (1981)] and in female labour supply [Gronau (1973) and Blundell and Walker (1982)]. There has been, broadly, two approaches to the measurement of equivalence sca1e.l The first uses nutritionist requirements of different agesex groups to determine the scales. This method, however, has not found wide favour since ‘needs’ are usually regarded as a social rather than a physiological concept. Also, experts rarely agree on what the ‘correct’ nutritional requirements are [see, for example, Sukhatme (1978) and such requirements are likely to vary Dandekar (1982)], and, moreover, considerably over time and across countries, being relatively large for many ‘For a third approach which relies on using survey questionnaires see Goedhart, Halberstadt, Kapetyn and van Pragg (1977).

and asking

families directly,

R. Ray, Measuring

the costs

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91

poor economies where women and children have a higher work load [Hamilton (1975)]. The second, more widely used approach, consists of calculating the scales from observed expenditure pattern of households, and is the approach followed in this paper. The approach originated with Engel’s (1895) pioneering analysis of Belgian working class budget data, which was generalised by Prais and Houthakker (1955). The Engel procedure uses a household’s budget share for Food as an indicator of welfare. Hence, a comparison of expenditure of households with different family size and composition but identical budget share for Food gives us the equivalence scale. Recent studies using the Engel/Prais-Houthakker framework include Singh and Nagar (1973), McClements (1977) and Muellbauer (1979). An alternative approach, due to Rothbarth (1943) involves comparing expenditure on goods, not consumed by children, between households which differ in the number of children. Applications of this last procedure in one form or another include Nicholson (1949) Henderson (1949) Dublin and Lotka (1947) and Deaton (1981). Unlike earlier work on equivalence scales, Barten (1964) pioneered estimation of scales from pooled budget data using price information within a utility-consistent framework [see also Gorman (1976)]. In spite of the long tradition of estimation of equivalence scales, there remain severe problems in estimating and interpreting the estimated scales. The Prais-Houthakker method leads to a serious identification problem, as noted by Forsyth (1960). McClements’ (1977) suggestion of using TheilGoldberger priors to overcome the problem has been criticised by Muellbauer (1979) on the gounds that the priors largely determine the estimates, as recently confirmed on Australian data by Bardsley and McRae (1982). Muellbauer’s (1979) suggestion of using nutritionist Food priors has been similarly criticised by McClements (1979) for dominating the general scale, which he seeks to estimate, and is inconsistent with Muellbauer’s own approach, generally, of not following the nutritionist method of determining equivalence scales. The Barten method, though overcoming the identification problem of Prais-Houthakker through use of price information, assumes a type of household behaviour that implies excessive quasi-price substitution in response to demographic changes and biases the estimated scales downwards. Recently, Muellbauer and Pashardes (1981) have introduced a ‘demographically flexible’ procedure which involves an ad hoc introduction of demographic variables into a household’s cost function and working out the implied equivalence scales. Their results yield, however, negative estimates for the cost of a child, The present paper proposes an alternative technique for estimating equivalence scales. Although in the Barten-Gorman tradition of using a utility-consistent framework, it has the advantage of overcoming the

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R. Ray, Measuring the costs of children

identification problem by directly specifying and calculating the ‘general’ scale without having to rely on prior calculation of ‘specific’ scales. The proposed method is easy to apply, and the estimated parameters easy to interpret. This is particularly useful in view of our earlier discussion of the relevance of the scales in issues of public policy. We demonstrate the usefulness of our procedure by applying our methodology to pooled time series of U.K. budget data and obtaining plausible results. The robustness of our procedure is established by performing the empirical work under two quite different sets of circumstances involving different functional forms, different commodity and household aggregation and different number of observations but, yet, obtaining results which compare quite favourably with one another. The plan of the paper is as follows. Section 2 introduces the proposed methodology, and the alternative framework under which the procedure is applied. The results are presented in section 3. Section 4 discusses some of the criticisms levelled against the use of estimated equivalence scales in welfare comparisons, and summarises the results.

2. Theoretical

framework

The proposed demographic technique stems from the definition of the general equivalence scale, mOh, as the ratio of costs of obtaining a reference utility level u at a given level p of household, h, with z children and reference household ‘R’ (adult couple with no children):

Ch(% P, 4 = m&,

P, 4CR(U, PI.

(1)

If one specifies a suitable functional form for the cost function of the reference household, cR(n, p),” which satisfies the usual economic theoretic conditions of linear homogeneity in prices, symmetry and concavity, then choice of a suitable functional form for m&z, p, u) gives us the corresponding form for the cost function of household h. Using price information and household budget data, one can then calculate the general scale directly by estimating the parameters entering m, using the estimable demand system of household, h, implied by (1). The direct specification of m,, suggested by this approach, not only simplifies calculation of the general scale, but allows an easier investigation of the variation of the scale with prices and reference utility level. This is, again, particularly useful since the variation of the scale with price, as much as the scale magnitude itself, is of relevance in welfare and income maintenance programs. It is worth pointing out that while the

‘The ‘cost’ or expenditure function shows the ‘minimum’ cost incurred maximising household to obtain a specified level of utility at a given set of prices.

by

the

utility

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the costs of children

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Prais-Houthakker methodology almost guarantees the scale to rise with reference utility, the reverse is the case for the Barten scale, as illustrated by the contradictory relation between m, and u on near-identical data reported by Deaton and Muellbauer (1980, table 8.2). The general scale m, can be split into two multiplicative factors: a ‘basic’ component C,, and a price and utility-varying component, 4, where 4 represents the dependence of the general scale on the structure of relative prices and utility:

where q5(p,z,u) must be non-negative and homogeneous of degree zero in price p. A test of unit C$constitutes a test of the invariance of the scale with price and utility. It is worth noting that in such an event, i.e. if 4 = 1, the cost function of household h would be given by:

4% p,4 = %(z)cR(u, PI. Taking logs, and applying Shepherd’s Lemma, Wi= 6 log c/6 log pi, where Wi is budget share of item i, gives us the following relationship:

W!(% P, 4 = w%4 PI. Eq. (4) says that households, which enjoy the same level of utility, have identical expenditure composition which, as noted above, is the basis of the Engel model. The generalisation of the present procedure over the Engel model thus directly rests on the variation of the scale with prices, as is evident from the following relationship implied by (1) and (2):

dlog4 6logPi

w:(u,p,z)=wy(u,p)+-.

In the empirical exercise which follows, we choose two quite different frameworks, to be referred to, subsequently, as Fl and F2. Both use the same functional form for tie:

mo=i+pz,

(6)

where z indicates the number of children in the household, and the scales are normalised at unity for the childless couple. p is the ‘basic’ equivalence scale, i.e. the ‘cost’ of a child at base year (p= 1). It should be pointed out that we also tried a cubic specification for (6) but found coefficients of the quadratic and cubic terms in z to be insignificant. This seems to suggest that

R. Ray, Measuring the costs of children

94

‘economies’ &functions,

of scale in household size that may exist are well captured rendering quadratic and cubic terms in (6) redundant.

2.1. First framework

by the

(Fl)

A simple multiplicative

form was chosen

for the scale function (7)

where c di = 0. ai measures the effect of a change in the relative price of item i on the general scale, m,. It should be noted that the 6’s would be identified only if there is reasonable relative price variation. This is clear from the fact that if prices move near identically, or are constant over a single budget data, 4 would be close to unity regardless of the &values. The following non-separable generalisation of the LES [see Blundell and Ray (1982)] was chosen as the functional form for the reference household’s cost function:

CR(PY u,=CC yijp!‘2p~‘2 +U n i

k

j

ptk,

Eq. (8) nests where C fli = 1 and Yij =~ji. estimable demand system is, then, given by:

Wi =6iz

+I

yij(pfpj*)+ .i

LES

when

yij =O,

i #j.

The

(%rJP:q

(9) where tie is given by (6), p:( ‘pi/p) is the ‘normalised’ price, and p is aggregate household expenditure. The data base of Fl is provided by the U.K. Family Expenditure Surveys. A total of 160 observations over the period 1968-79 and covering households with 0, 1, 2 and 3 children was considered. A four-item classification was used Food, Clothing and Footwear, Fuel and Light, and Durable Household Goods. The retail price series was normalised at unity in 1968. 2.2. Second framework3 The

specifications

(F2) adopted

in

Fl

imply

restrictive

behaviour

in

two

31 am grateful to Professor John Muellbauer for supplying me with the data used in F2. This data is the same as that used in the Muellbauer and Pashardes (1981) study which, as already reported, found the cost of a child to be enormously negative using their suggested procedure.

R. Ray, Measuring the costs

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95

important respects: utility invariance of the scale and linear Engel curves. To relax these restrictive assumptions, we choose the following functional forms:

where 1 pi =I vi =O. The vi’s allow dependence of the scale on both prices and utility. The direction of variation of I$ with u would depend on the magnitude of the vi’s, namely being positive (i.e. m, rising with u) if I-I k pp > 1, and negative otherwise: CR(p,U)=C(0+CCLi10gPi+3CCYij10gpi10gpj+u~p,BL,

k

(11)

where yij =yji, 1 c(~= 1, and Lpi =ci yij =O. The estimable demand system is, then, given by: wi =

Mi

+I

Yi

j

log

Pj

+

pi*

log [X/tiO(Z)P],

(12)

where j?T= pi + viz, and log I’ = ~10+ 1 Clilog pi + 3 C 1 Yijlog pi log Pj. The data base of F2 is also provided by the U.K. Family Expenditure Surveys (196879). A total of 303 observations covering households with 0 to 4 or more children is considered. The data for 1968-73 are for somewhat finer income brackets than published, but from 1974 to 1979 the published data are used. The following four-item classification is considered: 1. Fuel; 2. Food; 3. Alcohol, Clothing and Durables; 4. Transport, Services and Other Goods. The cross equation restrictions Yij= Yji were enforced for both frameworks, and a non-linear maximum likelihood program written by Wymer (1974) was used for estimation. Both Fl and F2 were initially estimated ignoring children? age differences, and age effects were subsequently introduced. For Fl, child age effects were introduced by generalising (2) and (3) to:

~o(z,,z,)= 1+p1z,

+p2z2,

where z1 =number of young children (Q-5 years), z2 = number children (5518), and &&r =zk 6,, =O. For F2, child age effects were introduced by generalising (6) to: fio(z1,z,,z,)=

1 +Plzl

+P2z2+P3z3,

(13)

of older

(15)

R. Ray, Measuring

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the costs of children

where z1 is the number of very young children aged O-2 years, z2 is the number of young children aged 2-5 years, and z3 is the number of older children aged 5-18 years. 3. Results Table 1 presents the parameter estimates (with asymptotic standard errors) for Fl under the generalised system with and without price dependence of the scale, and that for the LES, assuming the scale to be price invariant (i.e. the Engel model). The parameters principally of interest here are the basic equivalence scale, p, and the 6’s which measure its variation with relative prices. The significance of 6, and 6, suggest rejection of the Engel model and point to our proposed methodology representing a significant improvement over Engel on likelihood-based chi-square criteria. Under price invariance of the scale, a child costs around 12 percent of a childless couple. Allowing the scale to vary with prices opens up the possibility of substitution responses and this leads to a drop in the basic scale estimate to around 7 percent of a childless couple. It should be pointed out, however, that since Housing, which is likely to have a large positive effect on the scale, was excluded in Table Parameter

Parameter

Yl Yz Y3 Y4

Y12 Y13 Y14

Yzs Yz4

Y34

6, 62

63 64 P Log-likelihood No. of free parameters

estimates

under

Fl

1

ignoring children’s parentheses).

Allowing scales to vary with price

Ignoring variation

0.356 (0.010) 0.289 (0.008) 0.035 (0.006) 0.320 (0.012) 3.314 (0.701) 0.605 (0.66) 0.980 (0.475) 0.796 (1.05) - 1.982 (1.416) -0.167 (0.363) -2.663 (1.541) 0.057 (0.268) - 2.621 (1.349) -0.087 (0.202) 0.020 (0.004) -0.002 (0.003) - 0.002 (0.002) -0.017 (0.003) 0.067 (0.023) 2025.61

0.414 0.297 0.018 0.271 2.969 -0.421 0.654 0.339 -0.965 -0.090 - 1.325 0.461 - 0.945 0.156

17

age differences

price of scale (0.009) (0.007) (0.005) (0.010) (0.491) (0.79) (0.449) (0.724) (1.497) (0.351) (1.308) (0.239) ( 1.006) (0.128)

(standard

errors

LES without price variation of scale 0.424 0.295 0.024 0.256 2.418 -0.511 1.198 -0.482

(0.009) (0.006) (0.005) (0.009) (0.149) (0.123) (0.033) (0.112)

_

El85 (0.007) 1987.08 14

0.1065 (0.007) 1974.28 8

in

R. Ray, Measuring

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the costs of children

these calculations, the present scale estimate is likely to be downward biased. The results show that the ‘cost’ of a child is significantly and positively related to the relative price of Food. Since our calculated price indices show that the relative price of Food rose from 1.24 in 1974 to 1.41 in 1978, these results seem to suggest that the scale rose quite significantly over the last 5 years of our sample period. The parameter estimates for Fl, with children’s age differences incorporated, are presented in table 2. The ‘cost’ of a young child is insignificant, while that of an ‘older’ child is around 23 percent of an adult couple. The results decisively reject the hypothesis of identical ‘cost’ of young and older children and confirm the generalisation of the present procedure over Engel via significance of the 6’s. The parameter estimates for F2, ignoring children’s age differences, are presented in table 3. The parameters principally of interest here are the rli’s and p. The significance of qz and n4 estimates confirm improvement of the present procedure over Engel. Under F2, and allowing for price and utility Table 2 Parameter estimates under Fl with children’s differences (standard errors in parentheses). Parameter

2 Yl Y2 Y3 Y4 Y12 Y13 Y14 YZS Y24 Y34 6 11 6 12 6 21 6 22 b 31 6 32 6 41 6 42 Pl

kg-likelihood No. of free parameters

Estimate 0.361 (0.010) 0.284 (0.008) 0.040 (0.006) 0.315 (0.012) 3.047 (0.609) 0.361 (0.814) 0.835 (0.448) 0.709 (0.676) - 1.595 (1.227) -0.058 (0.345) -2.355 (1.335) 0.086 (0.254) -2.218 (1.140) -0.091 (0.193) 0.020 (0.016) 0.003 (0.007) 0.001 (0.011) 0.010 (0.005) -0.010 (0.009) - 0.009 (0.004) -0.010 (0.015) - 0.004 (0.006) 0.011 (0.095) 0.227 (0.059) 2032.04 21

age

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R. Ray, Measuring

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Table 3 Parameter estimates under F2 ignoring children’s differences (standard errors in parentheses). Parameter

Yll ?I2 Y13 Yzz Y23 Y33 ‘II v2 ‘13 )14 P

Log-likelihood No. of free parameters

age

Estimate 0.204 0.679 0.07 1 0.046 -0.058 -0.178 0.080 0.157 0.020 -0.067 0.003 0.021 0.098 0.042 -0.0002 0.009 - 0.001 -0.007 0.0778 4024.5

(0.003) (0.005) (0.008) (0.008) (0.002) (0.002) (0.004) (0.004) (0.013) (0.010) (0.009) (0.016) (0.013) (0.017) (0.0004) (0.0009) (0.0006) (0.0009) (0.017)

16

variation of the scale, a child costs about 7.8 percent of an adult couple. This compares quite favourably with the comparable estimate of 6.7 percent for Fl and establishes the robustness of the proposed procedure. The significant and positive estimate for q2 confirms the result noted above that a rise in the relative price of Food exerts a positive effect on the scale. Table 4 presents the parameter estimates with children’s age differences introduced, but q1 =q3 =0 enforced, as suggested by table 3. Young children have insignificant scales, while an older child costs around 10 percent of an adult couple. The basic scale estimates are generally well determined, which suggest that these data sets do have the necessary price and demographic information to overcome the identification problem, without the necessity of enforcing the arbitrary Theil-Goldberger priors imposed by McClements, or equally arbitrary nutritionist Food priors used by Muellbauer. 4. Summary and conclusion This paper proposes and employs an alternative demographic technique to estimate the ‘cost’ of a child or, as it is more generally known, the ‘general equivalence scale’. The ‘scale’, which performs a function analogous to that of

99

R. Ray, Measuring the costs of children Table 4 Parameter estimates under F2 with children’s differences (standard errors in parentheses). Parameter

Estimate

a1 a2 a3 a4

0.208 (0.003) 0.689 (0.005) 0.065 (0.009) 0.038 (0.008) - 0.060 (0.002) -0.181 io.oozj 0.080 (0.004) 0.161 (0.004) 0.024 (0.013) -0.071 (0.010) 0.006 (0.009) 0.010 (0.016) 0.100 (0.013) 0.038 (0.017) 0.008 (0.0004) - 0.008 (0.0004) 0.003 (0.033) 0.028 (0.030) 0.103 (0.010) 4028.59

j: B: YII Y12 Y13 Y22 Y23 Y33 v2 P4 Pl P2 P3 Log-likelihood No. of free parameters

age

16

the true cost of living index, makes welfare comparisons across households of different size and composition and converts them into equivalent units in terms of some reference household. The equivalence scale has been widely used in numerous theoretical and empirical studies relating to poverty, income distribution, taxation, fertility, dietary needs, and female labour supply. It has proved particularly important in matters relating to supplementary benefit, child benefit, and other forms of social security payments and in assessing the horizontal equity of income taxation. The measurement of the equivalence scale is, therefore, of considerable policy importance. However, in spite of a long tradition of using observed household budget data to calculate the equivalence scale dating back to Engel’s pioneering study in the last century, estimation of the scale is still beset with considerable difficulties. These relate to identification, estimation and interpretation of the calculated scales, and they all stem from lack of a satisfactory theoretical framework. The present work was motivated by the need to overcome these difficulties. This paper uses a new approach to modelling equivalence scales. The general scale is specified directly as a function of prices and/or utility. The implied cost function is used to derive

100

R. Ray, Measuring the costs of children

preference-consistent demand systems which are then used to estimate the general scale. This approach rids the theory of ‘specific’ scales and the necessity of complicated calculation of previous investigators to obtain the ‘general’ scale, and yet allows generality for an objective study of price effects on the scale. The empirical results demonstrate the usefulness of our proposed procedure in giving precise and plausible estimates not only of the equivalence scale itself but also of the effect of changes in the relative price on the ‘cost’ of a child. Such estimates are likely to prove particularly useful in calculating supplementary and child benefits and in revising them to keep in line with inflation. An important implication of the present results is that relating to inequality in a period of rising prices. It is well known that the relative price of inelastic items rise, and since such items also happen to be ‘necessities’ with a greater share of the poorer households consumption basket, the index of real expenditure inequality tends to rise. The present paper suggests an additional reason - the cost of children. Children in poor households make a relatively larger demand on necessities than those in better-off households, and contribute to the inability of the former to substitute in favour of ‘luxuries’ with below average price rises. This study would, however, be incomplete if we did not remind the reader of several issues which remain unresolved and which have been the basis of numerous criticisms of the present tradition of calculating scales from observed consumption data. The most fundamental criticism seems to be that of Pollak and Wales (1979) who argue that the true equivalence scales which we require in welfare analysis are ‘unconditional’ scales which should not only reflect the utility households derive from consumption but also from the presence of children. However, observed consumption data only provides us with ‘conditional’ scales which do not reflect how the family feels about having children. The use of ‘conditional’ scales in welfare comparisons, it is claimed, is hence illegitimate. An alternative way of looking at the problem is to note that the cost functions c(4(u,z),p, z) and c(u,p,z) have identical behavioural consequences while giving quite different equivalence scales leading to a non-unique link between behaviour and welfare. A further criticism is that observed consumption data cannot adequately reflect the ‘cost’ or ‘benefits’ of a child since it ignores such diverse factors as the effects on female labour supply [see Gronau (1973)], a child’s contribution to household earnings which is quite substantial in many poor economies, and the effect of having a child on the life-cycle earning potential of the household earners. The theory of household behaviour is purely static with very little dynamic or intertemporal considerations, and, moreover, there has been hardly any attempt4 at investigating the decision-making process within the household. 4Bojer (1977) is an interesting

exception.

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Further work in this area must address itself to these issues before one can confidently recommend the estimated scales for policy use. However, as McClements (1979, p. 241) quite rightly pointed out in this journal, ‘most policy decisions cannot be deferred until academics are satisfied that they have the right answers’, and until such a time does come, the use of observed consumption data to estimate equivalence scales, however unsatisfactory otherwise, must remain the only practical approach. References Atkinson, A.B., 1969, Poverty in Britain and reform of social security (Cambridge University Press, Cambridge). Bardsley, P. and I. McRae, 1982, A test of McClements’ method for the estimation of equivalence scales, Journal of Public Economics 17, 119-122. Barten, A.P., 1964, Family composition, prices and expenditure patterns, in: P.E. Hart, G. Mills and J.K. Whittaker, eds. Econometric analysis for national economic planning (Butterworth, London). Beveridge Report, 1942, Social insurance and allied services, Cmnd. 6404 (HMSO, London). Blundell, R.W., 1981, Taxation, demographic effects and rationing in a random preference model of female labour supply, Paper presented at European Meeting of the Econometric society (Amsterdam). Blundell, R.W. and R. Ray, 1982, A non-separable generalisation of the linear expenditure system allowing non linear Engel curves, Economics Letters 9, 3499354. Blundell, R.W. and I. Walker, 1982, Modelling the joint determination of household labour supplies and commodity demands, Economic Journal 92, 351-364. Bojer, H., 1977, The effect on consumption of household size and composition, European Economic Review 9, 169-193. Dandekar, V.M., 1982, On measurement of undernutrition, Economic and Political Weekly, February, 203-212. Deaton, A.S., 1981, Measurement of welfare: Theory and practical guidelines, LSMS Working Paper, 7 (World Bank, Washington DC). Deaton, AS. and J. Muellbauer, 1980, Economics and consumer behaviour (Cambridge University Press, Cambridge). Dublin, L.I. and A.J. Lotka, 1947, The money value of a man (Ronald Press Co., New York). Engel, E., 1895, Die Libenskosten Belgischer arbieter - familien fruher and jetzt, International Statistical Institute Bulletin 9, l-74. Forsyth, F.G., 1960, The relationship between family size and family expenditure, Journal of the Royal Statistical Society, Series A 123, 367-397. Garganas, N.C., 1977, Family composition, expenditure patterns and equivalence scales for children, in: G. Fiegehen, S. Lansley and A.D. Smith, eds., Poverty and progress (Cambridge University Press, Cambridge) ch. 7. Goedhart, T., V. Halberstadt, A. Kapetyn and B. van Praag, 1977, The poverty line: Concept and measurement, Journal of Human Resources 12, 503-520. Gorman, W.M., 1976, Tricks with utility function, in: M.J. Artis and A.R. Nobay, eds., Essays in economic analysis (Cambridge University Press, Cambridge). Gronau, R., 1973, The effect of children on the housewife’s value of time, Journal of Political Economy 81, S168-S199. Grootaert, C., 1983, The conceptual basis of measures of household welfare and their implied survey data requirements, Review of Income and Wealth 29, l-23. Hamilton, C., 1975, Increased child labour - An external diseconomy of rural employment creation for adults, Asian Economies, December. Henderson, A.M., 1949, The cost of a family, Review of Economic Studies 17, 1277148. Howe, J.R., 1971, Two parent families: A study of their resources and needs in 1968, 1969 and 1970, Department of Health and Social Security Statistical Report Series no. 14 (HMSO, London).

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source

‘United Kingdom London).

Family

Expenditure

Surveys,

1968-7!$

Department

of Employment

(HMSO,