Occasional Paper No. 18

Contents

• Foreword
• Updated costs of children using Australian budget standards
• The estimated costs of children in Australian families 2005-06
• Costs of children and equivalence scales: a review of methodological issues and Australian estimates
• List of tables
• List of figures

Costs of children and equivalence scales: a review of methodological issues and Australian estimates

Matthew Gray¹

Deputy Director (Research), Australian Institute of Family Studies

• 1. Introduction
• 2. Defining the costs of children
    2.1 Needs question
    2.2 Expenditure questions
    2.3 Equivalent living standards (iso-welfare) question
    2.4 Which is the most defensible method for estimating the cost of children?
• 3. Australian estimates of the costs of children
    3.1 Introduction
    3.2 Sensitivity of the costs of children to estimation method
    3.3 The average of Australian estimates of the costs of children
• 4. The costs of children by income and age of children
• 5. Relating the costs of children research to expenditures on children
• 6. Concluding comments
• Appendix-Detailed equivalence scales
• Endnotes
• References

1. Introduction

Economists have long attempted to define and estimate the costs of children. There have also been attempts to estimate how these costs vary by family income and the age of the child. Estimates have been used for a range of purposes, including to measure poverty, design income support systems and design of child support schemes.

While it may seem simple to define the costs of children, the reality is that several different approaches have been used and there is no agreement as to the most appropriate definition. Even where there is agreement as to the concept being used, there is no consensus as to the appropriate method for estimating costs. This presents a problem from a policy perspective since varying approaches and methods for estimating costs can lead to very different results.

Empirically, the fundamental problem that must be solved to measure expenditures made on behalf of children is that a method is needed to divide a family's expenditure on shared goods into two components: the portion that should be attributed to the family's children; and the portion that should be attributed to the family's adults. A further difficulty is that existing data sets for Australia (and many other countries) do not identify the consumption of individual members of a household and so a similar method is also needed to divide a family's expenditure on privately consumed goods (such as food).

Goods and services jointly used lead to economies of scale in consumption. For example, the addition of a child to a family involves extra food consumption but due to sharing of housing services, little extra spending on housing may be required to maintain the previous standard of living of the household.² Economies of scale in consumption may also be generated from purchasing produce in bulk, which might be cheaper. An important feature of estimates of the costs of children is the extent to which they exhibit economies of scale.

A clear definition of the costs of children is provided by Bradbury (2004, p. 1):

… a measure of the actual resources committed to child-raising. Ignoring public goods and household public goods, we can think of this as the expenditure of time and money on children. Taking household public goods into account, the cost to the parents can be defined as the additional income needed by a household in order to maintain parental living standards when they have an additional child.

This report gives an overview of the ways in which the costs of children have been conceptualised and defined in the literature and discusses the methodological issues involved in estimating these costs. The scope of this report is limited to the direct financial costs of children to their parents.³ The main conclusion, which many other authors have also reached, is that there are no 'true costs' of a child and that, in the end, it is a matter for judgement. This judgement, however, needs to be informed by existing empirical estimates (for example, Citro & Michael 1995; Nelson 1993; Stanton 1973; and Whiteford 1985).

The costs of children can also be expressed as equivalence scales. For example, an equivalence scale may show how much income a household with two adults and one child needs, in relation to a childless couple, to enjoy the same level of welfare as the childless couple.

The National Academy of Sciences Panel on Poverty and Family Assistance in the United States undertook a major study on how to measure poverty (Citro & Michael 1995). David Betson (2004, p. 1), a member of the panel undertaking the study, concludes that:

… their estimation require assumptions that can never be independently verified. … equivalence scales are inherently arbitrary and as such are in reality subjective judgements masquerading as science.

The main report of the National Academy of Sciences panel expresses a similar view, albeit in more considered language: 'Although the empirical evidence helps determine the limits of what makes sense, there is no objective procedure for measuring the different needs for different family types' (Citro & Michael 1995).

Australian estimates of the costs of children use a wide range of methods. This report discusses the majority of Australian studies published in the last twenty years. The estimates exhibit considerable variation, and given that no single method is entirely satisfactory, one approach to produce estimates of the costs of children that can be used for policy purposes is to take the average of a range of studies. This approach, used by Whiteford (1985), is used in this report. The average of the majority of post-1985 Australian studies is calculated and thus this paper updates the work of Whiteford (1985). This approach provides one method of combining different estimates of the costs of children into a single consensus estimate.⁴

The remainder of this report is structured as follows: Section 2 discusses the approaches taken to define and estimate the costs of children; Section 3 summarises the Australian estimates of the costs of children; Section 4 discusses the evidence on the extent to which the costs of children vary with family income and the age of children, and the results of selected international studies; Section 5 discusses how the costs of children research can be related to expenditures on children; Section 6 concludes the report.

2. Defining the costs of children

This section gives an overview of the different concepts used to define the costs of children. The methods used to estimate these concepts are summarised and their strengths and weaknesses discussed.

A useful way to summarise the literature on the costs of children is in terms of the questions that it is attempting to answer. Browning (1992, p. 1440) identifies four questions the literature has sought to address. Of these, the following three are relevant to the design of child support schemes⁵:

(i) The needs question: how much income does a family with children need compared to a childless family, to attain a specific standard of living (for example, to be above a poverty line, or to attain a modest but adequate standard of living)?

(ii) The expenditure question: how much do parents spend on their children?

(iii) The iso-welfare (or equivalent living standards) question: how much income does a family with children require to be as well off as a family with no children?

The question most appropriate for designing a child support scheme depends on the rationale behind the scheme. If the conceptual basis is that parents should contribute what they would have pre-separation to the costs of their children, then the expenditure question is most directly relevant. Alternatively, if the conceptual basis of the child support scheme is that children should have their minimum needs met then the needs question is most relevant.

The literature identifies two equivalence scales: conditional and unconditional (Pollak & Wales 1979). Conditional equivalence scales measure the costs of children but not their benefits and so ignore the direct effects of household composition on household welfare. They compare preferences over consumption bundles holding household demographic composition fixed. Unconditional equivalence scales fully account for choice of household composition by defining preferences over demographic composition and consumption bundles.

In a critique of the equivalence scale (and implicitly the costs of children) literature, Pollak and Wales (1979) argue that conditional equivalence scales may be used to analyse patterns of consumer demand, but not for welfare comparisons (for which they argue unconditional equivalence scales are needed). Other researchers argue that conditional equivalence scales are valid for many policy applications such as the level of assistance provided by governments to families with children (for example, Deaton & Muellbauer 1986; Nelson 1993). Conditional equivalence scales are also relevant for the design of child support schemes in which both parents are required to contribute to the costs of children since the standard of living, rather than subjective happiness, is the more relevant concept.

2.1 Needs question

The needs question dominated most of the pre-1940 debate concerning the costs of children (Browning 2002; Nelson 1993; Whiteford 1985). Discussion of needs leads to prescriptive judgements on how much children cost. In this approach a basket of goods deemed necessary for the maintenance of a child is defined and costed. This is taken to be the costs of that child. This approach is commonly known as the 'budgetary approach' or the 'budget standards approach'.⁶ Its origins can be traced back to the work of Rowntree (1901) who attempted to identify the minimum costs of maintaining a family at a subsistence standard of living in York, United Kingdom. Rowntree also conducted a follow up study in 1935-36 (Rowntree 1942).⁷

Approaches to defining a needs estimate of the costs of children fall along a continuum. They range from expertdefined budgets for one or a few categories of expenditure (such as food) with a large multiple to allow for other needed expenditure⁸ to expert estimates of a comprehensive, detailed list of budget items.

There is a long history of the use of budget standards to provide estimates of the costs of children in Australia. A very early example is by Justice Higgins in determining a basic wage in his 'Harvester Judgement' of 1907.

This decision influenced the determination of wage rates until the basic wage was abandoned in 1967. Further work was completed in the 1920s by the Royal Commission on the Basic Wage Chaired by AB Piddington. Professor Wilfred Prest at the University of Melbourne also completed work on budget standards during the Second World War (Saunders 1998).

The first detailed survey of poverty in Australia was undertaken by Professor Henderson and his team at the Institute of Applied Economic and Social Research at the University of Melbourne in 1966. It used costs of children derived from the 1954 'Family Budget Standard', prepared for the Community Council of Great New York to adjust their poverty line for differing family structures. In the absence of an Australian equivalence scale, the subsequent Henderson Commission of Inquiry into Poverty in Australia also used the equivalence scale relativities provided by the 1954 New York Family Budget Standards (Saunders 1998). The cost equivalence scale embodied in the Henderson poverty line makes allowance for the need to vary costs with the number of adults and children in the family, their age, gender and workforce status as well as the number of others residing in the household. While the Henderson Poverty line has been widely used to estimate the costs of children it has also been subject to substantial criticism (for example, Stanton 1980).

In the early 1980s the Institute of Family Studies (now the Australian Institute of Family Studies) developed a budget standards estimate of the costs of children (Lovering 1984).⁹ In 1995 the Minister for Social Security commissioned the Social Policy Research Centre (SPRC) at the University of New South Wales to develop a set of indicative budget standards for a range of households that would, among other things, 'examine the costs of children in different family circumstances'. The SPRC estimates provide the basis of the most recent and comprehensive set of budget standards for Australia. The SPRC developed two separate budget standards for different households-a modest but adequate standard, and a low cost standard (Saunders et al. 1998). The SPRC estimates were restricted to Sydney. Henman (2001, 2005) updated and expanded these for additional household types and for each Australian State and Territory capital city.

In their recent work on budget standards, the SPRC defines a budget standard as:

… what is needed, in terms of material goods and services, by a particular type of family in order to achieve a particular standard of living in a particular place at a particular time. (Saunders 1998, p. 2)

This definition emphasises:

• the material dimensions of wellbeing rather than psychological or subjective determinants
• that a specific list of items which a family needs to attain the standard of living must be defined
• that in theory it is possible to develop a budget standard that corresponds to any standard of living.

If a budget standard is derived for households with no children, and households with children, it is possible to use these standards as a basis for estimating the cost of children.¹⁰ While this may seem simple, in reality it is a complex exercise. Saunders (1999) identified three main approaches which differ in the way they allocate the costs of items consumed by the household as a whole, rather than by individuals within it. Examples of items are housing, transport, consumer durables, and furniture.

Saunders' first approach is the 'individualised method'. This ignores shared household costs when calculating the costs of children and only includes expenditures which can clearly be attributed to children (for example, food, clothing, health, and personal care). The second approach involves calculating the costs which can be clearly attributed to children and adds an estimate of the portion of the cost of each shared item that can be assigned to children. This is termed the 'normative method' because it requires normative judgement to be made when allocating shared costs to individuals. The third approach is the 'difference method'. This estimates the costs of children by taking the difference in the budget standards for households with and without children, or households with different numbers of children.

Each method has strengths and weaknesses. The main limitation of the individualised method is that it excludes shared household costs and therefore produces only a partial estimate of the costs of children. The normative method takes account of fixed costs, but is time-consuming to apply. Further, judgements made as to how to allocate shared costs may be legitimately contested. The main attraction of the difference method is that it is simple to apply and does not include costs that would have been incurred in a childless household. Its main weakness is that some of the cost differences between households with and without children may reflect changes in the behaviour of adult household members in response to the presence of children.

There are several limitations to the budget standards approach. It inevitably requires that normative judgements be made about the goods and services that need to be consumed to achieve a particular living standard. For some goods and services there are official or quasi-official guidelines which provide guidance to the developers of budget standards. For example, many countries have nutritional guidelines.¹¹ In other areas there are no established social norms available and so budget standards are based on expert recommendations which have no official status. This can lead to criticism.

Inevitably normative standards of the goods and services that should or ought to be consumed to achieve a living standard must, to some extent, reflect the customs, habits and social expectations which determine behaviour.¹² The difficulty is how the normative standards can be defined without undermining the ability of a budget standard to reflect normative judgements about needs, as opposed to the resource constraints that also influence actual patterns of behaviour. Since one main use for a budget standard is to provide an independent benchmark for assessing the adequacy of incomes and standards of living, it is important that the standards do not mirror the effects of the constraints under which different families operate.

Whiteford (1985, p. 17) notes that:

The claim that the budgetary approach is objective arose initially from the belief that it is possible to specify 'scientifically' the necessities of life in terms of biological and physiological requirements.

The Social Welfare Policy Secretariat's (SWPS) Report on Poverty Measurement published in 1981 also notes that budgetary standards have an element of arbitrariness. The SWPS report argues that budgets can be constructed to show almost anything.

2.2 Expenditure question

The question of how much parents spend on their children seems the most straightforward. In principle this question can be answered by asking, in a large-scale survey, 'who gets what' in the household. However, available data sets do not contain information on intra-household expenditure, only on total household expenditure on different areas. From expenditure data it is possible to estimate how expenditure patterns vary across families with different numbers and ages of children. Consumption on each good is divided (deflated) by the number of equivalent adults in the household.

An alternative approach is to use information on expenditures on goods that can be attributed to parents-the 'adult goods' approach. This method is usually attributed to Rothbarth (1943), although Rothbarth used this method to address the equivalent living standards question (discussed in Section 2.3). To infer expenditures on children from expenditures on adult goods requires various assumptions. Common assumptions in the literature are that the ratio of expenditure on adult goods to total expenditure on adults is independent of total expenditure and that childless couples have the same consumption preferences as couples with children. These assumptions are not plausible. Other assumptions also used in the literature are not entirely plausible.

2.3 Equivalent living standards (iso-welfare) question

All methods for calculating the costs of children require estimating the effects of adding children to a family on the cost function of the family. Unfortunately, when using data on observed expenditure patterns, the impact of children on this function is not directly measured in the data. Therefore, it is necessary to make assumptions about the way in which children affect the cost function. Different methods of calculating the costs of children vary in the assumptions they make about the impact of children on the cost function. These are described in this section.

Engel and iso-prop methods

The question of how much additional income is required so parents can obtain the same living standard they had before there were children in the household is often termed the iso-welfare question. The cost to parents is a function of the social norms for the raising of children and the extent of support received from outside the household.¹³

Several approaches have been developed to make estimates of the costs of children using this concept. One dates back to the work of Engel (1895) and uses the share of the family budget devoted to food as an indicator of living standards. Engel argued that the share of food in the budget correctly indicates the standard of living across families of different types. Using this assumption, all that is needed to calculate the costs of a child is to calculate how much must be added to the budget to restore the family's food share to its original value.¹⁴ The Engel method is sometimes extended beyond the share of food to the share of other necessities. This method has been called the iso-prop approach and was introduced by Watts (1967).

The Engel and iso-prop methods are only valid if the assumption that the proportion of the budget spent on food (or other necessities) correctly indicates family welfare. A major limitation of the Engel method is that since a child consumes mostly food and clothing, providing an income which will allow the share of the family budget spent on food to return to the pre-child level will overcompensate the family for the addition of a child (see Nicholson 1976).

Rothbarth method

An alternative measure of the standard of living of a family is expenditure on goods that are consumed only by adults. This is termed the Rothbarth or adult goods approach and, as discussed in Section 2.2, a variant of this method has been used to estimate how much parents spend on their children. The logic underlying this method is that children bring needs but no resources to a family, needs that can only be met by making cuts elsewhere in the budget.¹⁵ Expenditure on adult goods (for example, alcohol, tobacco and adult clothing) should decline when a child is added to the family since resources are diverted from adult goods to meeting the needs of the child. The Rothbarth method imputes the same welfare level to households with the same level of consumption of adult goods. It defines the costs of children as the reduction in income which leads to the same reduction in expenditure on adult goods that the addition of a child to a family generates.

The Rothbarth method has been criticised. Perhaps the most telling criticism is that although children do not consume adult goods, their presence may alter their parents' tastes for adult goods. Similarly, the presence of a child is likely to change the way parents spend leisure time and surplus cash. This makes it difficult, if not impossible, to find adult goods for which family consumption is not directly affected by the presence of children. In practice, tobacco and alcohol are often used as adult only goods and it seems rather strange to equate welfare with consumption of these goods. Both the Engel and Rothbarth methods ignore the impact of the addition of a child to a household's preference between items.

Complete demand system methods

Many economists are dissatisfied with the single equation Engel, iso-prop and Rothbarth methods because they are not directly derived from utility theory.¹⁶ Other limitations are that they do not explicitly consider prices or the fact that changes in household composition may lead to changes in the implicit prices a family pays for various items. For example, the birth of a child will increase the price of outside entertainment for a couple if babysitting services are required.

This has resulted in the conceptualisation of the costs of children using consumer demand theory in which the costs of children are estimated directly from the cost function of the household to which they belong. This approach was pioneered by Barten (1964) and developed by, among others, Gorman (1976), Muellbauer (1977), Ray (1983), Jorgenson and Slesnick (1987), and Nelson (1988). Examples of prominent studies which estimate equivalence scales using demand equations are Deaton and Muellbauer (1986) and Blundell and Lewbel (1991).

These methods assume a mathematical relationship between the consumption of each category of goods (also termed demand), the number and age of family members and the level of wellbeing within the family. Once this mathematical relationship is specified, it is possible to determine how much expenditure would have to increase to hold wellbeing constant after the addition of a child. Procedures of this type encompass a broad class of utility maximisation models that could be used for the purpose of estimating the expenditures on children. The parameters of these demand equations are estimated using information on household expenditure. Assumptions which have been used to identify equivalence scales include assumptions about savings and the assumption that the equivalence sale is the same at all income levels.¹⁷

Subjective method

A final method for estimating the costs of children is to collect information through surveys on peoples' subjective evaluations of the relationship between income, family composition and living standards.¹⁸ This subjective method has been widely used overseas, particularly in Europe, but not in Australia. Its main advantage is that it avoids reliance on experts and is based on the prevailing opinion of society. However, the method poses several difficulties. First, results differ substantially for even subtle changes in question wording (for example, Flik & Van Praag 1991). Second, subjective responses may reveal more about underlying differences in expectations and current circumstances rather than relative income needs. When answering questions people may compare their living standards to those in similar families and not to other family types. Bradbury (1989) argues that this may be the reason for the low estimate of the additional costs of children often obtained when using the subjective method. Third, if respondents know or suspect survey results will be used to determine the level of government payments they might give different answers.

2.4 Which is the most defensible method for estimating the costs of children?

If the question is 'How much income does a family with children need compared to a childless family?' then some form of budget standards approach is needed. However, which method is the most defensible, given that each has strengths and weaknesses?

For the expenditure or equivalent living standards questions there is little consensus on the best method to use. The robustness of the complete demand system models is yet to be fully established. Furthermore, the assumptions involved in estimating these models of the costs of children are complex, require a large amount of data and are often unclear. It is often difficult to determine the extent to which the assumptions drive results. For this reason, estimates using these methods often lack transparency.

On balance, the Rothbarth method is the most defensible but there is little to choose from between the Rothbarth and iso-prop methods. The Engel method (food only) is difficult to justify. The National Academy of Sciences study on the measurement of poverty and equivalence scales also concludes that the Rothbarth method is the most defensible (Citro & Michael 1995) although they also conclude that none of the published methods for calculating poverty thresholds provide a fully defensible rationale for calculating the kind of equivalence scale needed for different family types (Citro & Michael 1995, p. 175).

3. Australian estimates of the costs of children

3.1 Introduction

In this section Australian estimates of the costs of children are presented and summarised. Australian research has largely focused either on the needs question or the equivalent living standards approach. There is a large amount of international literature on the costs of children which is not considered in detail in this report, although Table A3 provides equivalence scales of several important international studies, including the estimates of the US Department of Agriculture's guidelines used by many child support schemes.

Studies of the costs of children generally present costs in one of two ways-as a dollar cost (usually at a family or household income level) or as equivalence scales. Equivalence scales show how much additional income is needed to maintain living standards as the number of children increases. For example, if the reference family is a childless couple then they have an equivalence scale of 1.00. If the equivalence scale for a couple with one child is 1.20 then this implies that a couple with one child needs 120 per cent of the income of the childless couple to enjoy the same standard of living. For example if a childless couple needs $100 to achieve a certain standard of living and the equivalence scale for a couple with one child is 1.20, then the couple with one child would need $120 to maintain the living standard of the childless couple. This implies expenditure on children of $20 at an income of $120.

In this report the costs of children are presented as a percentage of income. This allows comparisons between estimates of the costs of children and the results of different studies to be readily compared and averaged. It is also consistent with the Child Support Formula and the way in which the majority of child support formulae around the world are presented. It is a simple exercise to convert percentages to dollar figures for any given income level.

While it is conventional to compare estimates of the costs of children using equivalence scales, caution needs to be exercised in interpreting results. For example, converting budget standards estimates of the costs of children to achieve a certain standard of living to an equivalence scale requires converting dollar costs to a percentage of income. The level of income relative to which the costs of children are expressed will affect the percentage costs of children.

3.2 Sensitivity of the costs of children to estimation method

Before summarising the results of the Australian studies, the sensitivity of the costs of children to the estimation method used is illustrated using Lancaster and Ray (1998) and van de Ven (2003) who use single Australian data sets to estimate the costs of children using different methods. Lancaster and Ray (1998) illustrate the sensitivity of estimates of the costs of children to the estimation method by applying eight methods to the pooled 1984 and 1988-89 HES.¹⁹ Table 1 summarises these estimates. The main point is that they are highly variable. For example, the equivalence scale estimate of the costs of one child varies from 1.08 when estimated using the Barten Almost Ideal Demand System (AIDS) to 1.33 when estimated using the Rothbarth method.

Van de Ven (2004) similarly uses different methods of estimating the costs of children using a more recent HES and finds a similar degree of variability in the estimated costs of children (Table 2) as do Lancaster and Ray (1998). Furthermore, there is no clear pattern to the estimates. For example, van de Ven finds that the Engel method produces higher cost estimates than the Rothbarth method. While this is consistent with the findings of international research, Lancaster and Ray (1998) demonstrate that the Rothbarth method can produce higher cost estimates than the Engel method.

3.3 The average of Australian estimates of the costs of children

In a detailed survey of the literature on equivalence scales twenty years ago Whiteford (1985, p. 130) concluded that:

While there are therefore many good reasons for rejecting nearly all available equivalence scales, the problem remains that equivalence scales are unavoidable in many important areas of social research and social policy, and some sort of choice must therefore be made … Rather than choosing one discredited approach, I would opt for the average of all the discredited approaches!

That there is no objective procedure for measuring the costs of children, and that taking the average of all approaches is a valid approach to estimating the costs of children for policy purposes, still holds despite the large number of studies undertaken in the two decades since Whiteford's original study. In this section the results of the majority of Australian studies since 1985 (when Whiteford conducted his review) are averaged. This type of analysis is sometimes described as meta-analysis and in this report is used as a benchmark for individual studies and for providing a way to obtain consensus estimates of the costs of children in Australia.

Table 3 presents the average of all post-1985 Australian equivalence scale estimates²⁰ and the average of the pre-1985 studies (from Whiteford 1985). It also presents the average of post-1985 studies which use the iso-prop and Rothbarth methods. The Taskforce also commissioned two new studies of the costs of children by Henman (2005) and Percival and Harding (2005) which use the latest available data. The results of these studies are also presented in Table 3 to facilitate comparison with the findings of other Australian studies.

Several points can be made about the average costs of children presented in Table 3. First, estimates from the post-1985 Australian studies are higher than the pre-1985 Australian studies. This is true for couple families with one, two and three children. Second, the average of studies which used the iso-prop and Rothbarth methods is higher than the average of all post-1985 studies. Third, for the post-1985 studies there are no economies of scale evident between the first and second child, and for the third child there are diseconomies of scale. There are strong economies of scale for the fourth child. This is consistent with the pre-1985 average which shows very slight economies of scale for the second child and diseconomies of scale for the third child.²¹

While, on average, there are no economies of scale shown it is probable that the marginal expenditure on children decreases as the number of children increases because of budget constraint. That is, families do not have enough income to keep increasing total expenditures on children as the number of children increases. Most Australian studies address the equivalent living standards (iso-welfare) question and therefore ask how much income is needed to maintain living standards rather than what families actually spend.

Given the general similarity of the average of the iso-prop and Rothbarth studies and the average of all post-1985 studies, the average of the post-1985 studies can be used as the best estimate of the costs of children derived from the recent Australian research. The equivalence scale is normalised to 1.00 for a childless couple and is 1.19 for a couple with one child, 1.38 for two children, 1.59 for three children, and 1.66 for four children. It must be stressed that the average is affected by the addition or exclusion of particular studies. In addition, for some studies, different assumptions about the income level and age and gender of children result in equivalence scale estimates which differ to those used in this report.

The most recent estimates are those produced for the Taskforce by Henman (2005) and Percival and Harding (2005). Consistent with the expectation that the budget standard estimates tend to produce higher estimates of the costs of children than other methods, Henman's (2005) estimates are higher than the average of all Australian studies. Percival and Harding's (2005) results suggest that for an average income couple with one child, the equivalence scale estimate is 1.15. For two children it is 1.26, for three children it is 1.35 and for four children it is 1.42. This estimate for one child is lower than the average for post-1985 studies of 1.19. The Percival and Harding estimates for two, three and four children are also lower than the average of other Australian studies.

4. The costs of children by income and age of children

Income

Australian studies find that in absolute dollar terms the costs of children increase with income. However, there are relatively few Australian estimates of how the costs of children (in percentage terms) vary with income. Using a demand systems approach, Tran Nam and Whiteford (1990) and Valenzuela (1999) find virtually no variation in the costs of children across income ranges. In contrast, Percival and Harding find that the equivalence scale costs of children decreases as income increases (Table 4). Henman (2005) finds a similar pattern with the proportion of income needed to meet the low cost standard higher than the proportion needed to meet the modest but adequate standard (Table 5).

Child age

A number of Australian studies estimate how the costs of children vary with the age of the child. Almost without exception these find that the costs increase with age. There is more difference between studies as to the extent to which costs increase with the age of the child.

Australian studies that find the costs of children increase with the age of the child include Lee (1989)²², Lovering (1984), Henman (2001, 2005), Percival and Harding (2000, 2005), Tran Nam and Whiteford (1990) and Saunders et al. (1998). A number of international studies also find that the costs of children increase with age (for example, Betson 1990; Lino 2004; Turchi 1983).

5. Relating the costs of children research to expenditures on children

Although equivalence scales provide a means of comparing estimates of the costs of children, the percentage costs of children they imply cannot be interpreted as the percentage of family income spent on children. Equivalence scales show how much additional income is needed to maintain living standards as the number of children increases. This can be illustrated by returning to the example of an equivalence scale of 1.00 for a childless couple and 1.20 for a couple with one child. If the childless couple has an income of $100 then the equivalence scale implies that the couple with one child needs $120 to achieve the same living standard as the childless couple. This implies an expenditure on children of $20. But the family would not spend $20 on children if they had an income of $100-they would spend less. They only spend $20 on children at an income of $120. Therefore the proportion of family income spent on the child is $20/$120=16.7 per cent. For the purposes of expenditure costs of children the proportion of budget spent on children is perhaps the most intuitive presentation.

Table 6 presents the average equivalence scale estimates for Australia as the percentage of family income spent on children (derived from the equivalence scales presented in Table 3). The average Percival and Harding (2005) and Henman (2005) estimates are also shown in Table 6. The post-1985 Australian studies conclude that on average couples with one child spend 16 per cent of their income on that child. Couples with two children spend 28 per cent of their income on their children, couples with three children 37 per cent and couples with four children 40 per cent. These averages exhibit economies of scale with the first child requiring an additional 16 per cent of income, the second an additional 12 per cent, the third an additional 9 per cent and the fourth an additional 3 per cent.

6. Concluding comments

This report reviews the approaches that have been used to define the costs of a child and the methods used to estimate these costs. An overview of the strengths and weaknesses of these approaches is provided. The most important conclusion is there is no unambiguous 'true cost' of a child and that, in the end it is a matter for judgement, but that this judgement needs to be informed by available empirical estimates.

No single method for estimating the costs of children is entirely satisfactory. This report produces a consensus figure for the costs by taking the average of all available credible estimates of the costs of children. When calculating the costs of children as a proportion of family income spent on children for the average of Australian studies published in the last twenty years, it is estimated that couples with one child spend 16 per cent of their income on that child, couples with two children 28 per cent, couples with three children 37 per cent, and four children 40 per cent.

Recent Australian research finds that, while in dollar terms the costs of children increase with income, as a proportion of income expenditure on children decreases as income increases. Evidence also suggests that the costs of children increase with the age of the child. This report focuses on the costs of children in intact couple families. It is clear that total costs of children are higher for separated families because of duplicated fixed living costs and the costs associated with contact. There appears to be few estimates of the additional costs of children in separated families as compared to intact families. In US states, where the child support system is based upon a cost share model, the costs of children in couple families are increased by 150 per cent to arrive at a cost of children in separated families. Henman produced estimates of the costs of contact for Australian families and duplicated infrastructure costs in separated families and these are discussed in Henman and Mitchell (2001) and Henman (2005).

The bottom line is that divorce increases living costs and is sometimes associated with a reduction in labour market earnings of fathers. The combination of these factors means that on average there is less money available to separated parents to spend on their children than there would be if they never separated. This means continuity of expenditure on children will be unaffordable for many low and medium income families.

Appendix: Detailed equivalence scales

Endnotes

1. This report was prepared for the Ministerial Taskforce on Child Support. It has benefited from helpful discussions with Bruce Bradbury, Ann Harding and Paul Henman and comments from Boyd Hunter, David Stanton and Peter Whiteford. The views expressed in the report are those of the author.

2. Joint consumption occurs where two or more individuals in a household can share a good or service without reducing the satisfaction derived by any other person.

3. The additional money needed to raise children is only one of the costs of children. Children require time inputs (usually substantial) from their parents and the value of these inputs are large. For a discussion of this see Apps and Rees (2001). In addition, governments make substantial contributions to the costs of children through public education and health care.

4. This type of analysis is sometimes described as a meta-analysis and has been widely used in a range of disciplines, particularly psychology, sociology and medical science (Durlak 1995).

5. Browning (1992, p. 1440) identifies a fourth question which the costs of children literature has addressed: 'How do children affect the expenditure patterns of a household?' This question is concerned with the effects of children on the allocation of a given budget and is not directly relevant to the design of child support schemes.

6. This method is also known as the 'basket-of-goods method', 'expert budget' or 'standard budget' method.

7. The summary in this section of the history of Australian budget standards research draws heavily upon Saunders (1998, 1999) and Whiteford (1985).

8. This is the approach adopted by Orshansky (1965, 1969) in the development of poverty lines in the United States. Orshansky's estimates are essentially based on expenditure on food.

9. Lovering's study was carried out in response to a request from the Family Law Court.

10. This discussion of the budget standards approach is based on Saunders (1999).

11. The National Health and Medical Research Council (NH&MRC) provide nutritional guidelines for Australia.

12. Saunders (1998, p. 7) makes the point compellingly when he writes: 'In the area of food, for example, a diet consisting mainly of lentils and brown rice may meet the NH&MRC dietary guidelines, but be of little relevance to the actual eating habits of the vast majority of Australians'.

13. This differs from the needs approach in which the money required to provide some expert determined bundle of goods and services which are required to have a particular living standard.

14. In practice the Engel method is implemented by fitting an Engel curve in which the share of expenditures on food is linked to income and family characteristics. The estimated equation is then used to calculate what increase in income is equivalent to an additional family member.

15. In Australia (and most other developed countries) many families with children receive government child related income supplements to assist with the costs of bearing and raising children. In reality, therefore, children bring additional resources to a family. This reduces the costs of the children to the parents (the 'private cost').

16. Although on the surface the utility based methods and proxy methods such as the Engel, iso-prop and Rothbarth appear to be very different, it is possible to provide a utility basis for proxy methods. However, this requires strong assumptions to be made.

17. This is termed the Independence of Base (IB) assumption (Lewbel 1989) or Equivalence Scale Exactness (Blackorby & Donaldson 1993).

18. For discussion of the subjective method see Bradbury (1997) and Citro and Michael (1995).

19. Lancaster and Ray (1998) estimate two variants of the Engel method, two variants of the Rothbarth method and four variants of demand system methods using the 1984 and 1988-89 Household Expenditure Surveys for Australia.

20. The average for the post-1985 studies include the equivalence scales presented in Table A1. For the budget standards estimates for Australia made post-1985 the results of Henman (2005) are included and Saunders et al. (1998) are not included because the Henman (2005) estimates update and extend the estimates by the Budget Standards Unit at the SPRC. The underlying budget standards in the Henman (2005) and Saunders et al. (1998) studies are essentially the same. Table A2 shows equivalence scale estimates for Australia made using the budget standards method. Table A3 shows various international equivalence scales.

21. Australian studies which find economies of scale are Percival and Harding (2000, 2004), Bradbury (1994), Henman (2005) (finds economies of scale for the third and fourth children but not for the second, possibly related to assumptions about age and gender of children), and Valenzuela (1999) (economies of scale for second child but not for third child).

22. In Lee's study the only exception is that for ages 0 and 1 years the costs of children are higher than for some of the older age groups.

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