Given that we are analyzing a natural experiment, our
main specifications are very simple. First, we compare
men who have a sister as the next-youngest sibling to
men who have a brother as the next-youngest sibling.
Likewise, we compare women who have a younger
sister to women who have a younger brother. Since
we are interested in estimating the overall effect of
growing up in an environment with more female
siblings, we consider two possibilities that reasonably
bracket the effect that siblings have on respondents’
attitudes.
Assumption 1: All siblings have the same impact on
attitudes.
Assumption 2: Any impact that siblings have on attitudes
happens entirely through the immediately younger
sibling with all other siblings having no effect.
Although we might expect the immediately younger
sibling to be somewhat more important than other
siblings who are much younger or much older, the
sociological literature has posited that parents structure
gender roles within the household based on the
overall gender composition of children, not singling
out adjacent children (see online Appendix 3 for
complete details). Therefore, we think that the former
assumption is more likely than the latter, but the
important point for our purposes is that the truth is
likely somewhere in the middle.
The estimate that we obtain under Assumption 1
(all siblings are equally important) represents the
upper bound of the effect of growing up with sisters
on political attitudes since it implicitly assumes that
any sibling will have the same impact as the immediately
younger one. The estimate of the effect of
having sisters that we obtain under Assumption 2
(younger sibling is all that matters) represents a lower
bound since it assigns an effect of zero to all siblings
but the next-youngest one. By estimating specifications
under each assumption, we thus bracket the true effect
of growing up with sisters. As we show below, under
both assumptions the estimated effects are statistically
significant and substantively meaningful.
We first consider the model specification under
Assumption 1. Define Si to be the share of a respondent’s
siblings who are female.Where Pi is the respondent’s
gender role attitude or partisanship and Xi
represents controls for family size (explained below),
our specification is:
Pi ผ b0
b1Si aXi ui: ๐1
Here, the regression is not identified by ordinary least
squares (OLS) since the share of a respondent’s
siblings who are sisters is endogenous for the reasons
described earlier (e.g., stopping rules). However,
under Assumption 1, all siblings have an impact only
through the overall gender makeup of the household.
Therefore, we have an ideal instrumental variable for
Si, namely a dummy variable indicating whether the
younger sibling is female. This variable, which we call
Zi, is both randomly assigned and strongly correlated
with the endogenous variable of interest in equation
(1). It also satisfies the other requirements for a valid
instrumental variable, as we describe in detail in
online Appendix 3. Therefore, we estimate equation
(1) using two-stage least squares (2SLS) as the
estimation method.