by Imbens and Angrist (1994). The _β_ 1<sup>_IV_</sup> estimate can, then, be interpreted as the average effect of _Fijs_ on _LFPijs_ for those parents whose fertility has been affected by the sex-mix of their previous children. Following the terminology in Angrist and Evans (1996), in order to better understand for which subgroup of parents with two children the average treatment effect can be consistently estimated, it is useful to classify them into the following 3 sub-populations: those who will have a third child even following a son ( _always takers_ ), those who will never have a third child even following two daughters ( _never takers_ ), and those who will have a third child following two daughters but would otherwise stop ( _compliers_ ).

Hence, _β_ 1<sup>_IV_</sup> can consistently estimate the average effect for individuals who have one more child because their first two children are girls (i.e. compliers) provided that the instrument satisfies monotonicity. Basically, what is needed to be assumed is that there are no _defiers_ , those that change their behavior in the opposite direction due to the instrument. In other words, monotonicity requires that having never had a son only makes one more likely to have a third child, a reasonable assumption given the pervasive son preference in Albania.<sup>23</sup> The IV approach fails to identify the effect among two sub-populations: the _always takers_ , who generally have lower costs to childbearing than compliers, and the _never takers_ , who will generally have higher costs to childbearing than compliers.

Therefore, the second-stage regression model that links the endogenous fertility measure _F_<sup>ˆ</sup> _ijs_ with labor supply variables for the parents is the following: where _LFPijs_ measures labor-force participation of the parent _i_ residing in district _j_ and observed in survey year _s_ ; _F_<sup>ˆ</sup> _ijs_ is the endogenous fertility variable measured through the number of children ever born per parent _i_ ; _Xijs′_<sup>isasetofcontrolvariablesthatareplausiblyexogenousto</sup> fertility, such as _parent’s age, parent’s age squared, parent’s age at first birth_ and _parent’s years of education_ ; _b_ 1 and _b_ 2 are indicators for the sex of the first and the second child of parent _i_ , respectively, and _εijs_ is the error term associated with unobserved heterogeneity for the parent. The variables _b_ 1 and _b_ 2 are included to control for potential additive effects of child gender, which might affect labor supply for reasons other than fertility. For example, as mentioned in Angrist and Evans (1998), this effect could arise if parents behave differently towards boys and girls, or whether a father’s commitment to the family is contingent on the sex of the child. For this reason, the sex of the first-born and the second child, _b_ 1 and _b_ 2, are included in the equation to minimize any omitted variable bias caused by additive effects of child sex. I also control for the gender of the first child in order to address potential concerns about the exclusion restriction

> 23However, when relying upon siblings-sex composition as an instrument for fertility, the condition of monotonicity might be violated. Even though son preference is well documented for the case of Albania, a possibly minor fraction of parents might still prefer to have at least two children of the same sex (e.g. three boys), such that monotonicity would not hold. Following De Chaisemartin (2017), in the Appendix B, I show that the 2SLS estimator is still valid, even under the presence of defiers, provided the “compliers-defiers” condition is satisfied.

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