6 Robustness check

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6.1 Effects of first birth

One criticism concerning our results in Section 5 is that some women might have given birth once or more before they were first observed in out data, and that the earnings effect associated with the first-born child can be different from that associated with subsequent children, other things being equal. Indeed, first-born children can be different from subsequent children in that they could consume more time from the mother than their future siblings. For example, the first-born child can get sick more easily than subsequent siblings because of the lack of parenting experience. It is also possible that first-time mothers are more sensitive about their children than are experienced mothers.

Admittedly, some of the 3,714 mothers who gave birth once in the 1991-to-1996 period could have had one or more births before they were first observed (in 1983), since some of them were already as old as 29. Therefore, it is desirable to assess whether the first-born child costs more or not than the subsequent children. Since the Longitudinal Worker File does not contain information on birth sequence, a simple way to deal with the problem is to single out a group of mothers who were very young when they were first observed, and were therefore unlikely to have given birth previously. We highlight a group of mothers who gave birth once in the 1991-to-1996 period, were 15- to 19- year olds in 1983 and had not given birth from 1983 to 1990; we then investigate the earnings-gap differences between them and the older mothers.³⁰ The results are contained in Table 7.³¹

The bottom portion of the left side of Table 7 indicates the net effect of the 'first-born' child on the earnings of their mothers. The fixed-effects estimates (not shown in the table) suggest that the first- time mothers did not appear to be different from other mothers, while the estimates under the fixed- trend model indicate that first-time mothers might suffer slightly more earnings drops, but these were not statistically significant, either before, during or after the year of childbirth.

Table 7
Effects of first birth

One problem associated with the above exercise is that the group of mothers we singled out were likely the most low-educated mothers, because under our sampling restrictions they would not have had much chance to obtain an education beyond high school (they were, at most, 19-year olds in 1983 and were in the labour market from then to 2004). Hence, their age–earnings profiles can be quite flat. In light of this argument, we also singled out a group of 'older' mothers who might have had one or more births before they were observed.

In particular, we chose a group of mothers who gave birth in the 1991-to-1996 period and we restricted them to those born in the 1954-to-1958 period (and hence were aged 25 to 29 in 1983), and they did not give birth between 1983 and 1990. Given that the average age of the first-time mothers was around 25 in 1983, these women might have given birth once or more before they were first observed. We investigated if this group of mothers had incurred any additional earnings drops. As the right panel of Table 7 shows, again there was no significant difference between these older and other mothers in the earnings effects of childbirth.

Thus, even though our basic results in Section 5.2 are based on mothers who might have had one or more births before they were observed, these possible and unobserved births were unlikely to have any consequence on our estimation results.

6.2 Two births compared with one birth

The results of Section 5.2 can also be criticised in that mothers in our treated group were restricted to those who gave birth only once in the 1991-to-1996 period. Indeed, Canadian women typically had more than one birth during that period—for example, the number of live births per women (the total fertility rate) was 1.66 in 1995 (Statistics Canada 1995). Hence, our results in the last section may be affected by the one-birth restriction.

In order to address this problem, we modify the empirical model by adding another vector of year- of-childbirth indicators for the second child, born within a four-year window following a previous birth and estimate this model with all of the 7,086 mothers who had one or two births.

where D_it^k is defined in the same way as for D_it^k, except it refers to the years surrounding the birth of the second child. All other aspects of the model remain to be the same as specified for Equation (1).³²

Notice that, because D_it^k and D_it^k are defined relative to the years the two children were born, the number of years for which we can identify the effects of childbirth are limited by both the data and the structure of these two vectors of dummy variables. In the previous section, we identified earnings effects for up to the ninth post-childbirth year for the one-child case. For the earnings effects associated with the second child, we will be able to identify one fewer parameter if the second child was born one year later, two fewer if the second child was born two years later, and so on.

Table 8
Earnings effects due to a second child, fixed-trend model

The results under the fixed-trend model are presented in Table 8.³³ The top portion of the table contains the estimated effects of the first birth (or the only birth for some mothers), while the bottom portion reports the results for the second childbirth. The different columns separate the cases with respect to birth spacing. For example, estimates under the title "2 children, 2 years apart" represent the earnings effects of childbirth for mothers who gave birth twice and the two births were two years apart.³⁴

The earnings effects of the first childbirth were very similar, regardless of how many years the two children were apart. For example, in the second post-childbirth year, the earnings effects were 7% across all groups of mothers, and all of the estimates were significantly different from 0; while in the seventh post-childbirth year, the corresponding estimates were close to 3%, and these were all marginally significant.

With respect to the second child, the earnings drops in the year of childbirth and in the first post- childbirth year were considerably higher than the corresponding estimates for the first birth, possibly because at the second birth the mothers had become older and may have taken a longer time to physically recover from childbirth. In the rest of the post-childbirth years, the earnings effects associated with the second child seemed to be similar to those associated with the first child, particularly when the two children were born within a relatively short time span.

 

³⁰ Out of the 3,714 mothers, 837 fell into this group. We admit that it is still possible that some of them had given birth before 1983 (at age 18 or younger). But it is reasonable to assume that there were very few of them, since the average age of Canadian mothers when they first gave birth was around 25 in 1983 (24.8 in 1981 and 25.5 in 1985, see Statistics Canada [1995]).

³¹ Results under fixed-effects models are similar to those under the fixed-trend specifications for the corresponding groups.

^32. The value of d depends on b and how many years have passed between the first and the second births. Let years between the two children be h, then d=b – h.

³³ Fixed-effects models were also estimated. For the first childbirth, results under both the fixed-effects and the fixed-trend specifications are similar. For the second childbirth, results from the corresponding fixed-effects model also produce similar results as those presented for the year of birth and the first few years thereafter. But for years further away, such as the fifth, sixth or seventh year after the second birth, estimates under the fixed- effects models were almost twice as high as those from the fixed-trend model, highlighting the relevance to allow each woman to have an individual-specific earnings growth path.

³⁴ The number of mothers who had two births one year apart (e.g., one in 1991 and the other in 1992) were 355, and the number of mothers who had two births five years apart were 251. Estimates based on these sub-samples were not reliable because of the small samples. We pooled those "2 children, 1 year apart" with those "2 children, 2 years apart", and those "2 children, 5 years apart" with those "2 children, 4 years apart". The results (not shown but available upon request) were similar to those presented in Table 8 for the corresponding non- pooled cases.