noted before, the slope estimates are consistent with no parental bias because returns to education are higher for girls (see Table T4.I for the evidence on returns to education in rural India).<sup>29</sup> In contrast, if the conclusion is that there is no strong evidence of difference in the marginal effect of father’s education across gender of children, then we have _θ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_.</sup> This, in turn, implies _δ_<sup> ̃</sup> 2<sup>_dσdRcd_=</sup><sup>_δ_ ̃</sup> 2<sup>_sσsRcs_.Since</sup><sup>_Rcd>Rcs_,wemusthave</sup><sup>_δ_ ̃</sup> 2<sup>_dσd<δ_ ̃</sup> 2<sup>_sσs_.</sup> Observe that if parents underestimate a girls ability, we have _δ_<sup> ̃</sup> 2<sup>_d>δ_ ̃</sup> 2<sup>_s_,andwecanhave</sup> ̃ _δ_ 2<sup>_dσd<δ_ ̃</sup> 2<sup>_sσs_onlyifthereispuresonpreference,i.e.,</sup><sup>_σd<σs_.Wediscussbelowthatthe</sup> evidence on the intercepts is consistent with parents underestimating a daughter’s academic ability.

_R_<sup>_cd_</sup> _> R_<sup>_cs_</sup> when combined with _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_provideevidenceconsistentwithparentsun-</sup> derestimating ability of a daughter, and girls facing constraints in the school. This case is depicted in Figure F1.IR in section 2.3 above. An inspection of the graph makes it clear that it is not possible have _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_with</sup><sup>_Rcd>Rcs_,iftheuppercurveinFigureF1.IR</sup> refers to the daughters. The evidence is consistent with only the case where the upper curve refers to sons, implying gender bias against girls in the form of lower ability estimate and/or unfavorable school environment.<sup>30</sup>

# **Implications of the Intergenerational Mobility Estimates**

With _δ_ 5 = 0 _,_ the evidence that _ψ_ ˆ2 _d > ψ_ ˆ2 _s_ implies the following inequality: _δ_ 2 _d θ_ ˆ1<sup>_d_</sup> 2 + ��� ��� ��� ��� � � ˆ 2 _δ_ 4<sup>_d>δ_</sup> 2<sup>_s_</sup> _θ_ 1<sup>_s_</sup> + _δ_ 4<sup>_s_.Fromtheestimatesoftheinvestmentequationandthediscussion</sup> � � above, we know that _δ_ 2<sup>_d>δ_</sup> 2<sup>_s_becauseoftheconstraintsgirlsfaceintheschool.Sincethe</sup> case with _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_wasdiscussedatlengthforurbanIndia,herewefocusonthecasewhen</sup> _θ_ ˆ1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_.Inthiscase,theinequalityaboveissatisfiedwithoutimposinganyrestrictionson</sup> the relative magnitudes of the parameters _δ_ 4<sup>_d_and</sup><sup>_δ_</sup> 4<sup>_s_.Similarly,itiseasytocheckthatthe</sup> inequality _ψ_<sup>ˆ</sup> 1<sup>_d>ψ_ˆ</sup> 1<sup>_s_alsoisnotusefultosortouttheroleofdifferentmechanismsofgender</sup> bias.<sup>31</sup> Since _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_and</sup><sup>_δ_</sup> 2<sup>_d> δ_</sup> 2<sup>_s_,asufficientconditionfor</sup><sup>_ψ_ˆ</sup> 0<sup>_d<ψ_ˆ</sup> 0<sup>_s_toholdisthat</sup><sup>_δ_</sup> 1<sup>_s> δ_</sup> 1<sup>_d_</sup>

> 29Again, if we assume that the parents are not aware of the fact that returns are higher for girls, and believe the opposite, then the evidence from the investment equation implies implausible conclusions such as parents have pure daughter preference in rural India.

> 30If the parents believe that the returns to education are in fact lower for girls, then it implies that the parents underestimate the ability of boys, and also that boys face gender-based constraints in the school.

> 31This follows from the observation that _θ_ 0 _d_<sup>_θ_</sup> 1<sup>_d< θ_</sup> 0<sup>_sθ_</sup> 1<sup>_s_but</sup><sup>_δ_</sup> 2<sup>_d> δ_</sup> 2<sup>_s._</sup>

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