"Children and their Mother's Labour Supply"

Understanding the relationship between fertility and labour supply is important for a number of reasons. First, the link between childbearing and labour supply might partly explain the post-war increase in women's labour-force participation rates if having fewer children causes an increase in labour-force attachment. Second, fertility-induced changes in female labour supply has important implications for many other phenomena, including marriage, fertility, divorce, child care, the distribution of family earnings and male-female wage differentials.

Not surprisingly, given the wide and long-standing interest in the link between child bearing and labour supply, hundreds of empirical studies report estimates of this relationship. The vast majority of these studies find a negative correlation between fertility (or family size) and female labour supply. As noted by many researchers, however, the interpretation of these correlations remain unclear.

In a survey of the 'Economics of the Family', Willis (1987)2 writes "... it has proven difficult to find enough well-measured exogenous variables to permit cause and effect relationships to be extracted from correlations among factors such as the delay of marriage, decline of childbearing, growth of divorce, and increased female labour force participation.” Browning (1992)3 expresses similar views: "... although we have a number of robust correlations, there are very few credible inferences that can be drawn from them."

Scepticism regarding the causal interpretation of associations between fertility and labour supply arises in part from the fact that there are strong theoretical reasons to believe that fertility and labour supply are jointly determined. In fact, labour economists often consider the relationship between work hours and fertility, while demographers and others aim to characterise the impact of wages on fertility. Since fertility variables cannot be both dependent and exogenous at the same time, it seems unlikely that either sort of regression has a causal interpretation.

To investigate the link between fertility and labour supply, we will consider data on American women in 1990, containing detailed information about their labour and family characteristics.

Documentation of the data

The data set consists of 337,500 observations from a representative sample of US women aged in 1990 21-35 who have at least two children. For each individual, we observe selected information related to their family and work situation. The following variables are available:

Table 1: List of variables

Questions

All questions are compulsory.

1. Describe the variables listed in Table 1. Provide one or more tables that present relevant characteristics for each variable. Include a discussion of the table(s). (5 marks)

2. Provide a table that compares mothers with SAMESEX = 1 to mothers with SAMESEX

= 0, in terms of relevant characteristics. Comment on the table. (5 marks)

3. Consider the regression in Model (1):

�_� = �₀ + �₁��������_� + �₂���1�����_� + �₃���2�����_� + �₄����_�

+ �₅����1�����_� + �₆�����_� + �₇ℎ���_� + �₈��ℎ��_� + �_�

where �_� = {�����_�, �����_�, ℎ����_�, �����_�, log (������_�)} and �_� is an unobserved error term.

a. What is the interpretation of �₁? What is the expected sign of �₁?

b. What is the interpretation of �₄ and �₅? (5 marks)

4. Estimate the parameters of Model (1) by OLS using work status (�����), weeks worked (�����), hours worked (ℎ����), labour income (�����) and log family income (log (������)) as dependent variables (i.e. run five separate regressions). Report your estimates in a table with your preferred choice of standard errors or t- statistics. Please clearly indicate whether you are using standard errors or t-statistics. Based on your OLS estimation results, comment on the relationship between having more kids and mothers' labour market outcomes. (10 marks)

5. Does the order of children's gender matter for the labour market outcomes of mothers with two children of opposite sex? That is, do mothers with a firstborn girl and second born boy have different labour market outcomes compared to mothers with a firstborn boy and a second born girl? Explain how this hypothesis can be tested using on the basis of Model (1) and OLS estimation. Write up the null hypothesis and specify the alternative hypothesis that you are testing against. Explain what test statistic is used and why. What is your conclusion? (5 marks)

6. Empirically assess the degree of multicollinearity in model (1). Clearly state your conclusions.

7. Briefly discuss whether heteroskedasticity is a problem in model (1).

(5 marks)

(5 marks)