Testing Alternative Models of the Quality-quantity Trade-off in Fertilityngrawe/papers/Alternative... · 2003-12-22 · Testing Alternative Models of the Quality-quantity Trade-off

Testing Alternative Models of the Quality-quantity Trade-off in Fertility

Nathan D. Grawe*Carleton College

[email protected] North College St.Northfield, MN 55057

(507) 646-5239

*Thanks to Lars Lefgren, Mark Kanazawa, and Jenny Wahl for helpful comments on this paper. The author is responsible for any remaining errors.

mailto:[email protected]

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AbstractThe dominant explanation for the often observed negative relationship between the size

of an individual’s family of origin and subsequent market achievements (or “quality-quantitytrade-off”) emphasizes the budget constraint; additional children necessarily reduce per childinvestments as parental resources are spread ever more thinly (the Chicago-Columbia model). While this model attributes the trade-off to deleterious effects of siblings, two alternative modelspoint to more positive causes. First, if preferences for children are transmitted from parent tochild, a trade-off may result even if children’s opportunities are independent of family size (thePennsylvania model). Second, if early experiences caring for siblings lower the cost of futurefertility, children in large families choose to have more children and so spend less time on marketrelated activities (the learning by doing model).

Using data from the British National Childhood Development Study, this paper teststhese three alternative models. Consistent with the Chicago-Columbia model, a quality-quantitytrade-off is found in physical, mental, and emotional development as early as age 7. However,consistent with the Pennsylvania model the trade-off evident in adult earnings and fertility isgreatly diminished when preference controls are added. Evidence for the learning by doingmodel was not found; controls for teen and pre-teen experience in child care did not alter theestimated trade-off between family size and adult earnings and younger siblings do not reduceachievement more than siblings in general.

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I. Introduction

Numerous studies document a substantial negative relationship between family of origin

size and future economic and educational achievements. (See Rosenzweig and Wolpin 1980,

Blake 1989, and Hanushek 1992 for examples.) For instance, the probability of college

attendance for a Canadian only child is about one-third as compared to only one-fifth for a first

born in a family of four children (Sweetman and Rama 2000). Because parents appear to choose

between many children or highly achieving children this effect is often termed a “quality-quantity

trade-off”. Economists have convincingly explained a portion of this relationship with a model

of the opportunity costs faced by fertile women. Because child rearing requires considerable

time, it is not surprising that women with lower levels of market ability (and lower forgone

wages associated with fertility) typically have more children. At the same time, the

intergenerational transmission of skills from parent to child creates a positive correlation between

a parent’s market ability and that of her child. These correlations with the mother’s market

ability combine to create a spurious correlation between the number of children in the family of

origin (hereafter “family size”) and market achievements of her children. Recognizing the

importance of the mother’s value of time, all modern studies include controls for the mother’s

human capital.

While these controls reduce the magnitude of the quality-quantity trade-off, the pattern

nevertheless remains. In an attempt to explain this remaining effect, sociologists have pointed to

the potentially important role that birth order plays in family decisions. Historically, birth order

has been an important determinant of parental treatment. Primogeniture (preference for the first

born) naturally leads to a negative relationship between family size and achievement since the

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probability of being a first born is higher the smaller the family size (50% in a family with two

children, 33% in a family with three children, and so forth).

However, even with controls for parental human capital (with emphasis on the mother)

and birth order, a negative relationship between family size and market performance remains.

For example, Ermisch and Francesconi (2001) and Iacovou (2001) find negative impacts of

family size on educational attainment and cognitive test scores in British families. The dominant

theory explaining this remaining quality-quantity trade-off emphasizes the scarcity of parental

resources (see Becker and Lewis 1973 and Willis 1973). Put simply, as children are added to the

family, the per child share of parental resources is reduced. This theory is sometimes referred to

as the Chicago-Columbia model.

Recent developments in other fields of microeconomics suggest two alternative

explanations that warrant consideration. The first, suggested by the work of Easterlin et

al.(1980), emphasizes heterogeneity in preferences and preference formation. In particular, the

authors hypothesize that fertility preferences are transmitted from parent to child. It is easy to see

how this model would lead to a quality-quantity trade-off. Because people who desire and

anticipate high fertility (and thus higher levels of home production time) in the future have less

incentive to invest in education, a simple preference formation model predicts a quality-quantity

trade-off. Hereafter this theory will be termed the Pennsylvania model.

Finally, a model can be derived from the theory of learning by doing. Individuals who

grow up with many siblings learn about child development and child rearing through firsthand

experience, reducing the future costs of their own fertility. Facing lower fertility costs, these

individuals have more children, spend more time in home production, and so, just as in the

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Pennsylvania model, have less incentive to invest in education. Once more a quality-quantity

trade-off is predicted.

After more formally developing the three alternative models, the next section shows that

despite their common prediction concerning a quality-quantity trade-off, the models differ in

their predictions about the effects of increased family size on child welfare. While the Chicago-

Columbia model predicts decreased welfare, the Pennsylvania model predicts no change and the

learning by doing model predicts increased welfare. Unfortunately, because all three of these

models predict a negative relationship between family size and market achievement in adulthood,

it is impossible to differentiate them empirically based solely on observations of a trade-off at

adulthood.

However, data reflecting childhood and teen achievements, tastes for children, and child

care experiences can be used to differentiate the models. In the third section, this paper utilizes

data from the British National Child Development Study to test implications of the models for

how and at what point in the life cycle the trade-off develops. The concluding section

summarizes the results. While the findings do provide support for the dominant explanation that

emphasizes the scarcity of parental resources, there is also evidence that as much as one-quarter

of the effect of family size on adult earnings is explained by heterogeneity in tastes for children.

By contrast, no evidence was found consistent with the learning by doing model.

II. Alternative Theories of the Quality-quantity Trade-off

Given our interest in financial decisions, it is not surprising that the leading economic

theory explaining the trade-off emphasizes the parents’ budget constraint. (Economists typically

couple the constraint with an optimization problem, but Zajonc 1976 demonstrates that the same

1Zajonc only unintentionally makes this point. Briefly, Zajonc models child outcomes asa function of average maturity in the household during childhood. As more children enter thehousehold, the average maturity level falls, thereby hindering child development. Not only doesthis non-rational model predict a negative relationship between family size and later marketachievement, it also predicts a u-shape relationship between birth order and achievement. It isnot clear that the additional assumptions of rational choice provide any additional testablepredictions for the quality-quantity trade-off.

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predictions are obtained in the context of non-rational decision making.1) The household head

maximizes utility, a function of her own consumption c, per capita quality of children q, and

fertility n

(1)

Her decisions are constrained by a budget constraint, the key feature of which is an interaction

between investments in child quality q and family size n:

(2)

where B is the unit cost of child investments, cp is consumption of the parent, and W represents

family resources. As family size n increases, the implicit price of quality q rises (and vice versa);

families with many children cannot afford to make large per child investments and families that

make large per child investments cannot afford to have many children. Thus, families will tend

to be large with small per capita investments in children or small with high per capita

investments in children and a quality-quantity trade-off obtains in education. Because earnings

are a function of human capital investments, the negative relationship is also present in the

fertility-earnings relationship as well.

While this theory clearly provides an explanation for the quality-quantity trade-off, it is

by no means the only model that is capable of producing the effect. Notably, the Pennsylvania

2Easterlin et al. (1980) and this paper focus on preference differences that are correlatedwith fertility. Of course, other unobserved family characteristics correlated with fertility alsoproduce the same patterns. Also note that, technically, “intrafamily preferences” are also presentwhen child preferences are systematically opposed to those of their parents. But, in the presentwork, the interesting case is when parents and children share common values.

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model focuses on the role of preferences. Easterlin et al. (1980) propose a model of “intrafamily

preference formation” in which children learn preferences from their parents.2 Axinn et al.

(1994) provide empirical evidence for this hypothesis, showing that parental preferences for

fertility may directly affect a child’s subsequent attitudes toward fertility. (It may also be that the

actual fertility choices of the parent affect the preferences of the child.) However these

intergenerational correlations in tastes for fertility are transmitted, the combination of these

models of preference formation with models of fertility choice produces a quality-quantity trade-

off.

To see this and to distinguish the effects of limited parental resources from those of

preference formation, I will modify the previous model in three ways. First, the model must be

expanded slightly to allow for heterogeneity in preferences for children. Let " represent a “child

preference” parameter that positively depends on the family of origin size. Next, to remove the

limiting effects of parental resources, suppose each child chooses her own level of human capital

investment q, self-financing this investment out of future earnings. Allowing for self-financing

effectively eliminates the credit market failure that produces the quality-quantity trade-off in the

Chicago-Columbia model. Finally, individuals are given a time allocation choice. By spending

more time at home, the household head can reduce the cost of children. However, less time at

3This time allocation decision is added easily to the Chicago-Columbia model withoutmeaningfully altering the predictions of the model. Because this is not critical to the Chicago-Columbia explanation this decision is not included in equations (1) and (2).

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work results in lower earnings.3 This time allocation decision interacts with the heterogeneity in

tastes for children to produce the apparent quality-quantity trade-off.

More formally, suppose utility is a function of the head’s consumption and fertility

(3)

where " is a heterogeneous preference parameter. Households maximize utility subject to the

budget constraint

(4)

where p is the per child cost of fertility which is a negative function of the share of time spent in

home production t. Actual income is also dependent on the time allocation; actual income is the

product of potential income w and time allocated to work. Individuals can affect their own

potential income w by choosing to invest in their own human capital q. Because human capital

investments are made when young and paid back in adulthood, they must be paid back with

interest r.

An individual facing this maximization problem will notice a connection between the

fertility she desires for the future and the human capital investments she makes for herself earlier

in life. If a large family is desired, it makes sense to plan on spending more time in home

production to reduce the costs of fertility. But if time spent in market production will be small,

the return to human capital investment will be low. So individuals with a large preference for

children will anticipate less time in market production, acquire less human capital, and earn less

4The consumption and wealth opportunities of the two groups are not identical, however. Parents who split their wealth among their children will have to give smaller per capita bequeststhe more children they have. As a result, the consumption of children from larger families willalso be a bit lower than that of children from small families because children from large familiesreceive a smaller bequest.

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both on an hourly and an annual basis. Combined with the intrafamily preference formation

posited by Easterlin et al. (1980), we expect to find that individuals from large families have

larger than average families themselves, acquire less education, and earn less than those from

small families even though the educational and earnings opportunities of the two groups are

identical.4

Finally, a learning by doing model can also produce an apparent quality-quantity trade-

off. Of course, learning by doing is typically associated with market production (see Arrow 1962

for a formal model). But application to household production is quite straightforward; children

who grow up in large families may gain insights into child rearing, child development, and

household management. For example, suppose people maximize utility

(5)

subject to

(6)

where n0 represents family of origin size and all other variables are defined as in the previous

problem. Because opportunities to care for siblings teach valuable child-rearing skills,

individuals who grew up in large families face a lower cost of fertility. This is especially true of

people with many younger siblings since presumably much of the learning comes from taking

care of siblings. Once more, we see that individuals from large families choose large families for

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themselves which in turn provides an incentive to increase home production time and reduces the

incentive to invest in human capital. While the model once more predicts that children from

large families will have less education and lower earnings, it is technically inaccurate to describe

this as a quality-quantity trade-off because children from large families actually have greater

home-production skill than those from small families. It is only due to the fact that economists

typically measure achievement in terms of market outcomes that this result appears as if children

from large families are of lower quality.

While all three models predict the same negative relationship between family size and

subsequent market achievement, the implications for child welfare are obviously strikingly

different. Figure 1 analyzes the problems facing children from large (type A) and small (type B)

families under the three alternative models. Panel A depicts the Chicago-Columbia model.

Child A from a large family has less market ability due to the large number of competing siblings

and so faces fewer opportunities and has relatively lower welfare than child B. In panel B, the

Pennsylvania model depicts the same relationship between family size and market achievement

but explains the difference entirely in terms of preference differences. In this case it is

impossible to compare the relative welfare of the two individuals, although it is reasonable to

conclude that the individuals were neither harmed nor helped by their parents’ fertility choices.

Finally, in panel C, the learning by doing model shows that a decreased cost of fertility among

individuals from large families causes the different consumption choices, with children from

large families actually experiencing a welfare advantage. And so it is unclear whether the

quality-quantity trade-off is a trade-off at all.

5This is not to say the models could not be tested using other predictions of the models. Entire literatures have emerged to examine these other predictions. For instance, Wahl (1992)examines the auto-covariance structure in incomes across three generations; Grawe and Mulligan(2002) survey the connections between credit constraints and intergenerational mobility; andAltonji et al. (1997) examine whether financial bequests fully offset other shifts in income fromthe parent generation to the child generation.

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III. Empirically Differentiating the Models

Because all three models predict that children from large families will have more children

and lower levels of education and market achievement, it is impossible to distinguish them by

simply observing a quality-quantity trade-off in adult achievements.5 Fortunately, early

childhood achievement data and information on preferences for and experiences with children

can be used to examine aspects of the trade-off which do differentiate the models. Commenced

in 1958, the National Child Development Study (NCDS) records information on all children born

in the first full week of March 1958. Subsequent survey waves collected achievement,

experience, and attitudinal data at several points in the life cycle, the latest wave taking place at

age 41. I use these data to examine the apparent cause of the trade-off using several tests. While

each test individually cannot completely differentiate the models, taken as a whole the tests lend

support to the Chicago-Columbia and Pennsylvania models while providing no evidence for the

learning by doing model.

Table 1 establishes a baseline for examination of the quality-quantity trade-off among

men and women separately. The regression results reported reflect a typical regression analysis

of family size effects. Achievement is measured by log income reported at ages 31 and 41 and

age-41 employment status (equal to 1 if the individual is employed full time). The number of

children had by age 41 is also included as a non-market measure of achievement. All three

6Because the NCDS collected father income data by income bracket, it is impossible toknow the exact actual earnings of fathers. Following Dearden et al. (1997) and subsequent usersof the NCDS, the method of Stewart (1983) is used to estimate average income within eachbracket. This average income is then assigned to all fathers whose income was reported to fallwithin the given bracket.

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models predict a negative effect of family size on earnings and employment and a positive effect

on fertility.

In addition to a family size variable, the regressions include several control variables.

(These controls are present in all subsequent regressions, but in later tables regression

coefficients for the controls are suppressed to save space.) Controls for parental human capital

include years of education for both the mother and the father-figure and the father-figure’s log

earnings.6 A dummy variable notes whether the subject was a multiple (i.e. twin or triplet).

Finally, controls for birth order are required. Theory suggests that birth order may enter the

regression non-parametrically. Creating a dummy for each birth order-family size combination

could capture birth order effects non-parametrically, but the effects of family size would not be

easily discernable from the results. Instead, dummies are created to note first-born and last-born

children. Implicitly, this specification assumes middle children share a common expected

achievement level. (Table 2 reports summary statistics for all of the variables used in this and

subsequent regression analyses for men and women separately.)

The results in Table 1 show that incomes are lower by as much as 5 percent per additional

sibling in the family of origin. Among women the effect is stronger in early adulthood than later

in life, consistent with Kessler’s (1991) results using US data. However, among men the trade-

off is found consistently across all measures of economic achievement; men experience an

income loss of roughly 2.5% per additional sibling and are less likely to be employed full-time

7Of course, early childhood family size effects are not inconsistent with either thePennsylvania or learning by doing models.

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the larger their family of origin. Finally, both men and women are likely to have more children

the more siblings they have, though the magnitude of the effect is relatively small. Despite the

modest size of the effect, it is striking to note that for both men and women the only explanatory

variable that is statistically significant in predicting fertility is the family size variable (which is

significant at "=.01). In total, these results using NCDS data appear generally consistent with

other studies reporting a quality-quantity trade-off.

A. Early Childhood Development

But what is the cause of this observed trade-off? Because the three models presented in

the previous section cannot be presented as nested hypotheses, it is not possible to propose a

single test to incontrovertibly separate the wheat from the chaff. However, a closer examination

of the stories behind the models reveals several tests that can evaluate the plausibility of the

theories. First, consider again the Chicago-Columbia model. By emphasizing the constraints of

scarcity, the Chicago-Columbia model suggests that achievement deficiencies should appear

early on in the child’s development (perhaps even before birth). After all, the scarcity of parent

resources likely affects child development at the earliest stages of life. By contrast, the

Pennsylvania and learning by doing models would not predict a quality-quantity trade-off in early

childhood achievement because it seems unlikely that pre-teens would shirk on arithmetic

assignments in anticipation of future fertility choices. Evidence that family size effects are

present early in childhood would be consistent with the relevance of the Chicago-Columbia

model.7

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Tables 3, 4, and 5 report the effect of family size on early child development physically

(low birth weight, walking and talking at appropriate ages, physical coordination at age 7, speech

impediments, and toilet training problems), mentally (reading and math scores at ages 7 and 11

and teacher assessment of general ability scores at age 11), and emotionally (total Bristol Social-

Adjustment Guide syndrome score at ages 7 and 11 and a doctor’s assessment of emotional

maladjustment at age 7). (Note that in this table and all subsequent tables, the dependent

variables are measures of positive achievement. A quality-quantity trade-off is identified when

an increase in family size results in diminished achievement.)

Examining the results, family size does not appear to negatively affect early physical

development at all in the first two years of life; it is not a significant predictor of birth weight,

walking success, or talking success. Later physical developments show some signs of a trade-off

among girls who are slower to toilet train and more likely to suffer speech impediments, but not

among boys. By and large, physical development does not exhibit the quality-quantity trade-off.

By contrast, a strong trade-off emerges in both mental and emotional development.

Among both boys and girls, the more siblings one has, the lower are cognitive test scores and the

more prevalent are social adjustment syndromes. For instance, having one additional sibling

moves an individual 0.1 standard deviations down in the distributions of math, reading, and

general ability. (The magnitude of this finding is consistent with the results of Hanushek 1992

who studies children in Gary, Indiana.) If only cognitive test scores were affected, a case could

be made that this is a byproduct of a variation of the Pennsylvania model in which parents who

place little value on education inculcate this indifference in their children. But the presence of a

clear trade-off in measures of emotional development combined with some weak evidence of a

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trade-off in some physical developments suggests an explanation more in line with the Chicago-

Columbia model.

B. Tests for Taste Heterogeneity

Even if constraints on parental resources do cause a quality-quantity trade-off, a portion

of the trade-off observed at adulthood may yet be explained by heterogeneity in “child tastes” or

child rearing skills. The first of these hypotheses can be examined by seeing whether the trade-

off observed in adulthood is mitigated when controls for tastes for or experiences with children

are added to the regression. This section reports results when measures of child tastes are

investigated. The sixth wave of the NCDS asked respondents (age 41) three taste questions that

may be useful. The respondents were asked to assess how much they agreed with the following

statements: “Unless you have children you will be lonely when you get old,” “People can have a

fulfilling life without having children,” and “People who never have children are missing an

important part of life.” Three dummy variables code the individual’s agreement or disagreement

with these statements. In addition, at age 16 respondents were asked, “What size family would

you like to have?” This is added to the three measure of age-41 attitudes to complete the controls

for “child tastes”.

Table 6 reports the resulting estimates of the family size effects both with and without

these taste controls. The first row repeats the results reported in Table 1 where no taste controls

are included. Rows two through five report regression results once the preference controls are

added. Consistent with Easterlin et al. (1980), preference heterogeneity does prove to be an

important predictor in all but one of the regressions (the exception is male full-time

employment). However, the question at the heart of this paper is not whether preference

8The survey also asks if the respondent had experiences in child care outside the home, atschool, in a playgroup, or in another situation. Because the theory pertains to learning gained bysiblings, I focus on child care experience in the home. However, no significant changes to theresults occur when controls for experiences in other settings are included.

9Qualitatively similar results are found when self-reported levels of child developmentknowledge are used as the learning by doing controls.

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heterogeneity has some effect, but rather whether it explains the quality-quantity trade-off.

Looking at the magnitudes of the family size effects, inclusion of preference controls reduces the

family size effect in each regression except female employment status (which is not statistically

significant in any case). The reduction is relatively minor in the age-31 regressions (roughly 5

percent), but more substantial when age-41 or fertility are used (between 30 and 50 percent). In

total, these results appear to support the Pennsylvania model in that preference heterogeneity

matters and it matters in a way that is correlated with family size. In fact, including controls for

child preferences statistically eliminates the effects of family size on age-41 income.

C. Tests for Learning by Doing

While the previous results point toward the importance of both the Chicago-Columbia

and Pennsylvania models, it still may be that some of the observed trade-off is attributable to the

acquisition of child care skills through interactions with siblings. If learning by doing explains a

portion of the negative family size coefficients, including controls for experiences with child care

should result in smaller family size coefficients. The NCDS asks respondents at age 16 if they

have had experience babysitting at home.8 A dummy variable capturing this experience is added

to the baseline regressions of Table 1; the resulting estimates of family size effects are reported in

Table 8. While experience with child care at home often significantly predicts achievement, the

family size coefficient actually increases when learning by doing controls are present.9 This

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contradicts the prediction of the learning by doing model.

It is possible that this lack of evidence for the learning by doing model is due to the crude

measure of child care skills available. Another approach that does not rely on crude measures of

child care skill notes the difference between older and younger siblings. If the learning by doing

model is correct, younger siblings should have a more negative effect than older siblings (or

siblings in general) because only younger children lead to opportunities to experience child care.

In fact, the older siblings should not have a negative effect if only learning by doing is relevant.

By contrast, in the Chicago-Columbia and Pennsylvania models younger and older siblings have

equal effects. The results reported in Table 7 (rows two and three, specifically) consistently

show a weaker impact of younger siblings on achievement, a result that contradicts the learning

by doing model.

IV. Conclusions

Using data from the British National Child Development Study, this paper confirms the

negative relationship between family of origin size and adult achievement reported in many other

studies. In an attempt to better understand this finding, three possible models are considered.

The dominant theory suggests that increased family size reduces the opportunity set by

diminishing per child parental resources. However, two alternatives emphasize heterogeneity. In

the first model, heterogeneous preferences for children which are transmitted from one

generation to the next creates an incentive for some families to specialize in home production. In

the second alternative model, learning by doing gives children from large families an advantage

in child production.

Because all three models predict the same relationship between adult achievement and

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family of origin size, a more detailed analysis of the family size effect is required to distinguish

the models. The results of this work support the importance of scarcity in parental resources in

that the negative impact of siblings is observed in very early measures of cognitive ability–too

early to credibly be attributable to endogenous choices as required by the alternative models.

However, support for the model of heterogenous preferences is found when adult measures of

achievements are considered. When achievement is measured by log income at ages 31 and 41, a

significant portion (5 to 35 percent) of the family size effect is eliminated when controls for

preferences are included. This finding suggests both scarcity of parental resources and

preference heterogeneity are important determinants of the quality-quantity trade-off. By

contrast, the learning by doing alternative was not supported by the data. The inclusion of crude

measures of child care experience did not diminish the effect of family size on achievement.

Moreover, contrary to the learning by doing model’s predictions, the effect of younger siblings

was weaker than that of siblings in general.

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Table 1The effect of family size on earnings, employment, and fertility

Log income (age 31)

Log income (age 41)

Employment (1 if full-time, age 41)

Number of children(by age 41)

Male Female Male Female Male Female Male Female

Family size -0.025(3.459)

-0.049(3.763)

-0.027(2.475)

-0.020(1.541)

-0.029(2.702)

0.003(0.169)

0.036(3.387)

0.031(3.078)

First born dummy(1 if first born)

-0.051(1.892)

-0.085(3.763)

0.036(0.913)

0.031(0.628)

-0.004(0.044)

0.113(1.740)

0.026(0.627)

-0.003(0.067)

Last born dummy(1 if last born)

0.007(0.230)

-0.040(0.753)

-0.001(0.012)

-0.015(0.282)

-0.022(0.243)

0.034(0.493)

0.039(0.879)

-0.010(0.248)

Multiple birth dummy(1 if a multiple)

-0.0684(0.844)

-0.119(0.895)

-0.054(0.488)

0.010(0.083)

-0.193(0.891)

0.273(1.725)

-0.058(0.503)

-0.050(0.517)

Mother's education(years)

0.015(2.111)

0.051(3.824)

0.007(0.587)

0.032(2.432)

-0.021(0.851)

0.014(0.807)

-0.006(0.529)

-0.005(0.479)

Father's education(years)

0.164(2.900)

0.028(2.548)

0.015(1.769)

0.023(2.090)

0.031(1.480)

0.007(0.514)

0.004(0.422)

-0.008(0.917)

Father's log earnings 0.200(7.140)

0.217(4.076)

0.320(7.481)

0.110(2.109)

0.312(3.531)

-0.067(1.000)

0.051(1.171)

0.066(1.646)

Sample size 2071 1707 2098 2104 2901 2944 2901 2944

R-square 0.065 0.065 0.051 0.021 0.017 0.002 0.002 0.002

Note: Employment fertility regressions estimated by probit and poisson regressions respectively; in these cases reported R-squares are "pseudo R-squares."

Absolute t-statistics in parentheses.

22

Table 2Summary statistics

Male Female

Variable mean(variance)

min/max mean(variance)

min/max

Log income (Age-31) 9.38 (0.47) 5.34/15.42 8.58 (0.78) 5.05/14.08

Log income (Age-41) 9.70 (0.69) 2.48/15.17 8.93 (0.82) 2.48/13.68

Employment (1 if full-time) 0.88 (0.33) 0/1 0.44 (0.50) 0/1

Number of children 1.54 (1.29) 0/8 1.72 (1.29) 0/14

Family size (number ofsiblings+1)

3.39 (1.74) 1/13 3.37 (1.71) 1/15

First born (1 if first born) 0.38 (0.49) 0/1 0.38 (0.49) 0/1

Last born (1 if first born) 0.27 (0.44) 0/1 0.28 (0.45) 0/1

Multiple birth (1 if a multiple) 0.02 (0.15) 0/1 0.02 (0.15) 0/1

Mother’s education (years) 9.91 (1.66) 5/19 9.99 (1.70) 5/19

Father’s education (years) 9.97 (2.07) 5/19 10.02 (2.08) 5/19

Father’s log earnings 7.45 (0.38) 5.22/8.26 7.46 (0.37) 5.23/8.26

Birth weight (1 if >=88 ouncesat birth)

0.93 (0.26) 0/1 0.91 (0.28) 0/1

Walking (1 if walking by age 18months)

0.74 (0.44) 0/1 0.76 (0.43) 0/1

Talking (1 if talking by age 2years)

0.72 (0.45) 0/1 0.75 (0.43) 0/1

Physical Coordination(1if "poor physical coordination"does not apply, age 7)

0.84 (0.37) 0/1 0.89 (0.31) 0/1

Speech Impediment(1 if never stammered and neverhad other speech problem)

0.82 (0.39) 0/1 0.89 (0.32) 0/1

Toilet Training(1 if no toilet training problems)

0.88 (0.32) 0/1 0.90 (0.29) 0/1

23

(table 2 cont.) Male Female

Variable mean(variance)

min/max mean(variance)

min/max

(Reading score (age 7) 22.44 (7.43) 0/30 24.29 (6.70) 0/30

Reading score (age 11) 15.93 (6.55) 0/35 16.03 (6.02) 0/35

Math score (age 7) 5.22 (2.50) 0/10 5.00 (2.48) 0/10

Math score (age 11) 19.81(10.60)

0/40 16.44(10.08)

0/40

General Ability (age 11) 41.81 (16.29 0/79 44.14(15.90)

0/80

Bristol Social-Adjustment Guide(total syndrome score, age 7)

10.14 (9.45) 0/64 7.42 (8.00) 0/63

Bristol Social-Adjustment Guide(total syndrome score, age 11)

9.88 (9.67) 0/70 7.03 (7.95) 0/61

Emotional maladjusted(1 if no emotionalmaladjustment, age 7)

0.72 (0.45) 0/1 0.73 (0.45) 0/1

“Unless you have children youwill be lonely when you get old”(age 41; 1 if agree)

0.23 (0.42) 0/1 0.17 (0.37) 0/1

“People can have a fulfilling lifewithout having children” (age41; 1 if agree)

0.80 (0.40) 0/1 0.83 (0.38) 0/1

“People who never have childrenare missing an important part oflife” (age 41; 1 if agree)

0.37 (0.48) 0/1 0.27 (0.44) 0/1

“What size family would youlike to have?” (age 16)

2.32 (0.93) 0/6 2.57 (1.08) 0/6

Experience caring for children athome (age 16; 1 if yes)

0.28 (0.45) 0/1 0.34 (0.47) 0/1

24

Table 3The effect of family size on early physical development

Proper Birth Weight(1 if $88 ounces)

Walking(1 if walking by 18 months)

Talking(1 if talking by 2 years)

Male Female Male Female Male Female

Family size 0.023(0.826)

0.017(0.683)

0.007(0.388)

-0.022(1.175)

-0.000(0.003)

-0.005(0.288)

Sample size 3872 3642 4038 3795 4038 3795

R-square 0.069 0.090 0.010 0.008 0.010 0.010

Physical Coordination(1if "poor physical coordination"

does not apply, age 7)

Speech Impediment(1 if never stammered and never had

other speech problem)

Toilet Training(1 if no toilet training problems)



0.022(1.075)

-0.024(1.402)

-0.050(2.529)

-0.032(1.798)

-0.054(2.899)

Sample size 3722 3520 3725 3513 4038 3795

R-square 0.003 0.008 0.008 0.014 0.005 0.016

Note: Regressions estimated by probit regression; reported R-squares are "pseudo R-squares." Absolute t-statistics in parentheses.

25

Table 4The effect of family size on early mental development

Reading score(age 7)

Reading score(age 11)

Math score(age 7)



-0.775(10.421)

-0.726(10.076)

-0.909(13.670)

-0.102(3.543)

-0.143(4.882)

Sample size 3726 3517 3617 3439 3712 3506

R-square 0.095 0.094 0.178 0.201 0.060 0.047

Math score(age 11)

General Ability Score(age 11)

Male Female Male Female


-1.221(10.680)

-1.524(8.339)

-2.128(12.056)

Sample size 3616 3439 3617 3440

R-square 0.154 0.161 0.131 0.155

Note: Absolute t-statistics in parentheses.

26

Table 5The effect of family size on early emotional development

Bristol Social-Adjustment Guide*(total syndrome score, age 7)

Bristol Social-Adjustment Guide*(total syndrome score, age 11)

Emotional maladjusted(1 if no emotional maladjustment,

age 7)



-0.635(6.871)

-0.881(7.750)

-0.675(7.287)

-0.017(0.985)

-0.042(2.381)

Sample size 3714 3519 3618 3434 4015 3776

R-square 0.022 0.039 0.041 0.036 0.004 0.010

Note: Emotional maladjustment regressions estimated by probit regression; in this case reported R-squares are "pseudo R-squares." Absolute t-statistics in

parentheses.

*Since the Bristol Social-Adjustm ent Guide (BSAG) total syndrom score measures the degree to which a child suffers from mental syndromes, the regressand in

these regressions is the BSAG score multiplied by -1 so that a negative family size coefficient implies a quality-quantity trade-off.

27

Table 6The effect of family size on earnings, employment, and fertility: Regressions with and without controls for tastes

Log income (age 31)

Log income (age 41)




Family size(no taste controls)

-0.025(3.459)

-0.049(3.763)

-0.027(2.475)

-0.020(1.541)

-0.059(2.702)

0.003(0.169)

0.036(3.387)

0.031(3.078)

Family size (with taste controls)

-0.024(2.939)

-0.047(3.003)

-0.018(1.412)

-0.012(0.849)

-0.056(2.049)

0.014(0.712)

0.025(1.913)

0.016(1.396)

Sample size 1377 1265 1563 1711 2146 2365 2146 2365

R-square 0.091 0.081 0.066 0.036 0.017 0.013 0.008 0.011

p-value (all preferencevariables insignificant)

0.001 0.001 0.003 0.000 0.339 0.000 0.000 0.000


Absolute t-statistics in parentheses. Sample sizes and R-squares for the model with no preference controls can be found in Table 1.

28

Table 7The effect of family size on earnings, employment, and fertility: Regressions with and without controls for learning by doing

Log income (age 31)

Log income (age 41)




Family size(no learning by doing controls)

-0.025(3.459)

-0.049(3.763)

-0.027(2.475)

-0.020(1.541)

-0.059(2.702)

0.003(0.169)

0.036(3.387)

0.031(3.078)

Family size(learning by doing controls)

-0.026(3.517)

-0.056(4.194)

-0.034(3.004)

-0.022(1.433)

-0.068(3.091)

-0.002(0.124)

0.029(2.618)

0.030(2.938)

Sample size 2071 1707 2098 2104 2901 2944 2901 2944

R-square 0.069 0.067 0.050 0.022 0.020 0.003 0.003 0.002

p-value (learning by doingvariable insignificant)

0.502 0.022 0.011 0.158 0.029 0.225 0.002 0.795


Absolute t-statistics in parentheses. Sam ple sizes and R-squares for the model with no preference controls can be found in Table 1.

29

Table 8The effect of family size on earnings, employment, and fertility: Distinguishing the effects of younger siblings from siblings in general

Log income (age 31)

Log income (age 41)




Family size(no learning by doing controls)

-0.024(3.459)

-0.049(3.763)

-0.027(2.475)

-0.020(1.541)

-0.059(2.702)

0.003(0.169)

0.036(3.387)

0.031(3.078)


-0.048(2.119)

-0.033(1.901)

-0.011(0.514)

-0.081(2.551)

-0.004(0.126)

0.023(1.361)

0.024(1.462)

Number of younger siblings -0.002(0.151)

-0.002(0.063)

0.011(0.460)

-0.014(0.543)

0.042(0.969)

0.010(0.295)

0.024(1.108)

0.011(0.573)

Sample size 2071 1707 2098 2104 2901 2944 2901 2944

R-square 0.068 0.065 0.051 0.022 0.018 0.002 0.002 0.002


Absolute t-statistics in parentheses. Sam ple sizes and R-squares for the model with no preference controls can be found in Table 1.

30

Figure 1Alternative explanations for the quality-quantity trade-off

A) Large families reduce the market productivity of children resulting in lower market achievement later in lifeB) Large families produce children with strong taste for fertility resulting in choices which favor home productionC) Large families produce children with experience in child care and lower costs of future fertilityA represents the choice of a typical child from a large family; B represents the choice of a typical child from a small family.

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Testing Alternative Models of the Quality-quantity Trade-off in Fertilityngrawe/papers/Alternative... · 2003-12-22 · Testing Alternative Models of the Quality-quantity Trade-off