Allocating Spending

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Allocating Spending

• Afternoon Session
• Part I

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Topics

• Allocating Spending to Children
• Direct methods Per Capita and USDA
• Indirect methods Engel and Rothbarth
• Break
• Data -- Consumer Expenditure Survey
• Choosing values for an Economic Table

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Big Questions

• What proportion of the familys spending can be
  attributed to spending on the children?
• How does the proportion of spending devoted to
  the children change as total spending increases?
• How does the number of children in the family
  affect the proportion devoted to the children?

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Allocating Spending

• A family of three (two parents and a child)
  spends during the year, 40,000 -- how much did
  they spend on the child?
• Types of Spending
• Personal Spending Categories
• Shared or Joint Spending Categories
• Equal Sharing of all Spending -- Per Capita
• Childrens Share K/(KA)
• K is the number of Children and A is the number
  of Adults

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USDA Approach

• Personal Spending -- Direct allocation to
  children and adults
• Adults (7) clothing, alcohol, tobacco,personal
  insurance, miscellaneous, cash contributions
• Children (6) clothing, child care
• Allocations based upon research or assumptions
  (43)
• Food (allocation based upon nutritional
  requirements)
• Transportation (based upon DOT research)
• Medical Spending (based upon DHHS research)
• Other Shared Consumption (44) -- Per Capita
  Allocation

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Special Allocations

• Food (adult equivalent needs -- each adult is 1)
• Age 0-2 3-5 6-12 13-15 16-17
• .511 .570 .802 .943 .969
• Sum the adult equivalent needs for the children
  (sum F) then the amount of food spending on the
  children would equal F/(FA)
• Transportation
• Allocate non-work related expenses on a per
  capita basis. If youngest child is 0 to 5 then
  work expenses is 40, otherwise work related
  expenses is 38.
• Medical Spending (adult equivalent needs)
• Age is 0 to 5, the scale is .696. If age is 6
  to 17, the scale is .786

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Smith Family of Four

• Family Spending by Category
• Food 9,200
• Shelter 12,700
• Utilities 4,200
• Household O,F, and S 3,000
• Transportation 12,200
• Child Clothing 1,000
• Adult Clothing 2,000
• Child Care 2,000
• Tobacco and Alcohol 800
• Entertainment 4,000
• Personal Care 700
• Reading 200
• Education 1,700
• Medical Spending 3,000
• Personal Insurance 700
• Miscellaneous,Cash Contributions 3,000

Allocation to Children
Survey
USDA 3,740 3,962 4,800 6,350 1,814 2,100 890
1,500 2,623 3,600 1,000 1,000 0 0 2,000 2,000
0 0 2,040 2,000 282 350 72 100 1,620 1,700
1,544 1,277 76 0 70 0 Total 22,571 25,939
37.4 42.9
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Two Children -- CEX
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Average Percentage Spent on Children by Number of
Children and Total Spending of Family
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Average vs Marginal

• 44 of the budget is based upon a per capita
  allocation of the family spending to the children
• Should the amount of spending on a child reflect
  the average (per capita) spending or the marginal
  spending on a spending category?
• Housing Assume that a family with one child
  spends 12,000 on housing. Was spending on the
  child equal to 4,000 or the additional spending
  on housing that the couple made when they had the
  child?

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Predicting Spending

• Marginal Housing Costs
• Housing Expenditures with one children
• - Housing Expenditure if no children
• To predict the couples housing spending if they
  didnt have children, you would want to hold
  constant the level of total spending
• Housing Spending f(A,K, Total Spending)
• Problem Couples with the same level of total
  spending but with no children are better off than
  the family with children. Better off families
  spend more on housing hence the above procedure
  would understate the marginal spending on
  children.

12
Mark Rogers

• Uses a modified USDA approach to estimate
  spending on children
• The modification reflects his attempt to compute
  the marginal spending amounts to spending
  categories that the USDA employs a per capita
  allocation -- predominately housing.

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Indirect Methods

• If we had an empirical measure or indicator of
  the well being of the family that systematically
  varied with the level of total spending and
  across different types of family types, we could
  determine the marginal economic cost of a child
  by
• Estimate the relationship between the measure of
  well being and the total spending for different
  family sizes and compositions
• For a family with a given number of children,
  determine their level of well being given their
  total spending, TSC, using the estimated
  relationship
• Determine the level of total spending, TSo, that
  a couple without children would need so that
  their level of well being was identical to the
  family with C children
• The amount of spending on the children would
  equal TSC-TSo

14
Engel

• As families become wealthier, they spend a
  smaller share of their spending on food.
• Families with children are poorer than families
  without children hence families with children
  will spend more on food holding total spending
  constant.
• If the food share is a reasonable indicator of
  family well being then we can estimate the
  marginal cost of children by comparing the level
  of total spending between families with and
  without children needed to maintain the same food
  share.

FS
One Child
Spending on Child
No Children
TS1
TSo
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Comments

• Gorman showed that for the Engel approach to be
  correct, the economies of scale in consumption in
  all goods had to be the same as scale economies
  as in food consumption.
• Deaton and Paxson provided both theoretical and
  empirical evidence against the Engel approach.
• From my analysis (2000 Report) of CEX data
  (1996-8)
• Number of children 1 2 3
• Engel 30.1 43.9 52.0
• USDA 30.4 44.9 53.5

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Rothbarth

• As families become wealthier, the adults spend
  more on themselves.
• Families with children are poorer than couples
  without children even if they have the same level
  of total spending they will spend less on adult
  goods.
• If spending on themselves indicates the level of
  well being of the adults, the Rothbarth approach
  asks what level of total spending would yield the
  same level of spending on adults if the couple
  didnt have children.

No Children
One Child
AG
Spending on Child
TS1
TSo
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Spending on Adult Clothing
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Rothbarth Estimates
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Other Approaches

• My 1990 Report examine other approaches ISO-Prop
  (a bundle of necessities more than just food) and
  Gorman-Barten (specific utility function is
  assumed)
• The hope would be the method by which we estimate
  the cost of children would not affect the
  estimate. This hope was not realized.
• The precision by which we can estimate the
  proportion of total spending devoted to the
  children is roughly 3 percentage points for the
  average family.

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Critiques of Rothbarth

• Mark Rogers for the Rothbarth estimate to be an
  underestimate, it must be assumed
• Parents dont like sharing with their children
• Parents get no sense of well-being from their
  children
• Income and Substitution Effects of Children
• As the number of children rises, child goods and
  shared goods become more expensive relative to
  adult goods

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Barnow and BassiJPAM (1993)
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Under or Over Estimate?
Adult Goods
No Children
Complements
With Children
Substitutes
TS1
Total Spending
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Changes over Time

• If we replicate the same methodologies on data
  collected at different points in time, will we
  get the same answer each time?
• We would expect the estimates to differ because
  of
• Sampling Error or variation
• Spending patterns change over time

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Comparison -- One Child
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Comparison -- Two Children
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Comparison -- Three Children
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Has Spending Changed?

• Over time, I have detected that
• Rothbarth estimates of spending on children have
  risen for the average family
• The relationship between spending on children and
  the total spending by family has grown flatter
• I havent been able to determine whether this
  change is reflective of actual changes in
  behavior or is a statistical artifact of the data

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Next Session

• Data Consumer Expenditure Survey
• How do we choose an Economic Table?