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Marriage and children I

Quantity, quality, costs

ECON 339 Investments in children

How do economists view the role of children?

Three roles:

1. consumption good: argument of parent(s)’ utility function(s)

2. social insurance: as providers of support for elderly parents

3. household labour: in home, on farm, family business…

Importance of these roles can vary across economic circumstances, including stage of development of economy.

ECON 339 Investments in children

A: Developed economies

In an economy with a well-established social welfare system (employment insurance, pensions…) focus on children as arguments of utility function.

1. Simplest model:

a) preferences: household utility function (unitary model or identical preferences) defined over number of children (n) and all other goods (A)

b) constraints: unit price for A=1,

unit price of child = c,

fixed income = y

ECON 339 Investments in children

All other goods (A)

Assume: fixed income y

y price per child c

unit price A =1

Preferences: identical

optimal choice? (n*,A*)

n* y/c # of children (n)

ECON 339 Investments in children

1. What happens as income increases?

if children and A both normal goods, both increase with income

2. What happens as c goes up?

income and substitution effects

- substitution effect: opportunity cost of children increases; if initial IC still feasible, n↓ and A↑

Income effect: budget set decreases →household moves to lower IC

→both A and n fall, if both normal

Net effect? A ambiguous; n ↓

ECON 339 Investments in children

What might cause these changes?

1. income increase without changing cost of children?

Transfers from government

Inheritances

…..?

2. increase in cost per child without change in income?

- increase in # years of required schooling

- decrease in sports, etc, in school system

- …?

ECON 339 Investments in children

Income and the cost of children

Suppose the cost `c` per child is in time, not money: so each child requires t units of time per period.

Let be wages of male and female, respectively, and let each person have one unit of time per period.

Then: if n =0 (no children), income is .

Suppose couple has one child. What is value of income?

ECON 339

Depends on who takes time to look after the child:

Let be the time spend in childcare by the male and female respectively.

Then and income is

If , income is maximized when , so the female does all the childcare.

With more than one child, if each needs t units of time, the female spends more time out of the market, and income falls more.

ECON 339

How is time different from money?

If view this as a lifetime, once-and-for-all decision, nothing.

In a unitary family model, nothing.

If bargaining period-by-period….

Suppose two periods

First period, childcare for one child (so time = t<1)

Second period: both parents work full time

Bargaining at beginning of period

ECON 339

How is time different from money?

If view this as a lifetime, once-and-for-all decision, nothing.

In a unitary family model, nothing.

If bargaining period-by-period….

Suppose two periods

First period, childcare for one child (so time = t<1)

Second period: both parents work full time

Bargaining at beginning of period

ECON 339

2nd period

2nd period wages increasing in time spent in market in first period

Male:

Female:

Wage difference?

period 1:

period 2:

If first period childcare not split equally between parents, even if initial wages are the same, a gap emerges in 2nd period.

ECON 339

Have: n increases with income, if constant c

Then why do poor people have more children than people with higher income

Why are families larger in developing countriesÉ

Role of children as social insurance and support for old age

In developing countries, financial markets are less complete – fewer avenues for saving for old age

ECON 339

Quality of children

Observations (Becker):

1. over time, income has grown and fertility declined;

2. cross section data: inverse correlation between income and fertility

Why? Are children inferior goods?

Ans: Parents have preferences over both number of children, and quality per child: children are a normal good, but multi-dimensional.

What is "quality"?

-children a durable good;

- quality is increasing in expenditure/child

expenditures on human capital - time, money, level of education

Simple static model:

unitary household

assumption: quality same per child

Problem: max subject to

Variables in utility function?

n = number of children q = quality per child

A = “all other goods” reflecting parents' standard of living; let unit price be 1

Variables in budget constraint?

I = total household income

= price index of goods & services for children

= price index of goods & services for adults

Notice: budget constraint is not linear in n and q.

Variables in budget constraint?

I = total household income

= price index of goods & services for children

= price index of goods & services for adults

Notice: budget constraint is not linear in n and q.

as n , additional quality/child more expensive (marginal cost of child quality increases with number of children, given all children of same quality)

as q , additional child more expensive (marginal cost of child is increasing in child quality – again, given all children of same quality)

optimal choice may lead to n as income 

depending on income and substitution effects - income elasticities

Children, part 2: expenditure on children

parents determine human capital investment in children, and direct transfers

- are parental choices efficient?

how are resources divided between siblings?

Possibilities:

- equally

- to compensate for inequality

- to reinforce inequality

diagram:

- axes: wealth of child 1, child 2

- 45° line: equal concern - parent's IC's symmetric about this

- : earnings levels of children if parents make no investment in human capital

- : earnings if wealth-max'g human capital investment

Can derive a “wealth possibility frontier” for children. Given parents’ preferences over distribution of wealth across children, and (income) benefits to children from human capital investment, can derive parents' choice of investment (in human k) and transfer of financial assets.

With 2 children,

1. with equal concern, and ass'm that child 1 receives higher payoff from human k investment than does child 2, parents invest more in human capital of child 1, and give more transfers to child 2 - to equate wealth

2. if parents are wealthy enough, both receive wealth-max'g human k, and transfers (efficient investment)

Results?

- parents' investments reinforce endowment differences

- investments are socially efficient

- transfers counter earnings differences

3. If parents are not sufficiently wealthy to allow efficient human k investment in both children, then, more educable child has higher wealth

- human capital investments in at least one child too low for efficiency

Cost of children – evidence?

1. Manitoba Agriculture: estimates on raising a child to age 18 (average; not calculated after 2004):

- costs vary by sex:

- daughter $166, 549

- son $166,972 (higher food costs)

- costs non-linear in age:

- first yr most expensive (over $10,000)

- lowest at 12 yrs ($7000)

- increasing through teen age yrs

2. Canada’s federal child support guidelines:

- amount varies with

- income (of payer)

- province of residence

- number of children

Research on family spending shows there is no single fixed cost of raising a child. Families spend more on their children as family income increases, with the proportion of family income devoted to children remaining the same across all levels of income. So the "cost of raising a child" depends on how much income, and how many children the family has. The paying parent's contribution is set in accordance with the average proportion of income that parents at that income level spend on their children.

The receiving parent is presumed to contribute to the children in proportion to own income.

(Canada, Department of Justice, FAQS on child support guidelines)

Moneysense magazine http://www.moneysense.ca/magazine-archive/the-real-cost-of-raising-kids/ http://www.moneysense.ca/save/financial-planning/the-real-cost-of-raising-a-child/

August 2011 issue: “…$243,660 as the total cost of raising a typical child to age 18 (in other words, until the day before his or her 19th birthday). That’s $12,825 per child per year or $1,070 per month.”

Revised, April 2015: “Adjusted for inflation that figure today would be $13,366 pushing the total cost of raising a child past the quarter million mark—a $10,200 increase in four years.”

ECON 339 Investments in children

3. “The Cost of Raising Children” by C. A. Sarlo; The Fraser Institute, Sept. 2013

“Prevailing estimates of the cost of a child for Canada and the United States, currently, tend to be in the range of $10,000 to $15,000 per annum. These cost estimates have a distinct middle class bias and do not reflect the reality of raising children in lower income and newer immigrant households. There is a concern that such estimates send a clear message to lower income families that they really cannot afford children and, perhaps, shouldn’t have any.

“Examining the basic marginal costs necessary for the healthy development of a child, this paper finds that an annual outlay of $3,000 to $4,500 (depending on the community or region and the age of the child) would be sufficient.

“These cost estimates exclude any savings strategies such as home gardens, sewing and knitting clothing, couponing and taking advantage of sales, own repair and maintenance work in the home, etc. This cost range is for Canada in 2010 and is drawn from budget standard estimates by social agencies and experts with experience in this area. It can serve as a useful benchmark for child costs.

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