Gille 6 of members from the same caste may be correlated with unobserved caste characteristics that also have an impact on productivity. If this is the case, the coefficient on the education of members from the same caste will be biased. The identification strategy that is used to partially deal with this issue is taken from Munshi and Myaux (2006). In their paper, they study the impact of the use of contraception of women from the same community on own use of contraception. They find that the coefficient on the use of contraceptives of women from the same community is positive and significant, whereas the use of contraceptives of women from the other community in the village has no impact. They argue that this result could only reflect a spurious correlation between contraceptive behavior at the community level and contraceptive behavior that is in fact driven by unobservables if unobservables are fully uncorrelated across communities in the same village. This section reproduces their argumentation and applies it to the specification of this paper. It therefore closely follows the wording of their paper.

Equation (5), which is derived from equations (3) and (4), illustrates the problem of omitted variables: ln _yi_ is the agricultural production of household _i_ , _θ_ is a constant, _Ec_ is the average education of caste members in the same village (which excludes the education of household _i_ ), _Xi_ are individual characteristics, _Fi_ represents the factors of production (land, labor and physical capital) and _Uc_ the castelevel characteristics that cannot be controlled for in the estimation because _Uc_ is unobserved. _vi_ is the error term. Cross-caste effects are introduced through _Eo_ , which is the mean education level of village members from other castes. Because interactions are happening within castes, the education level of households from the same caste is expected to have a positive and significant impact, whereas the education level of households from other castes in the village should have no impact. In other words, we expect _δ c >_ 0 and _δ o_ = 0.

It is easy to see that if there is no impact of neighbors’ education on agricultural productivity, the true specification is: In this case, _Ec_ in equation (5) proxies for the unobserved _Uc_ if _Ec_ and _Uc_ are correlated. Put differently, a positive estimate of _δ c_ when the true value is zero could be obtained if the education level of individuals from the same caste in the village is correlated with unobserved caste characteristics that have an impact on agricultural productivity. As _Ec_ cannot by itself perfectly proxy for _Uc_ , in a model where there is no education spillovers _Eo_ is an additional proxy for _Uc_ .

Can we get _δ_<sup>ˆ</sup> _c >_ 0 and _δ_<sup>ˆ</sup> _o_ ≈ 0, the expected result from a model with education spillovers, in a model without education spillovers? Yes, but only if _Eo_ does not provide any information on _Uc_ . This could only be the case if the unobserved characteristics of members from the same caste and members from other castes in the village, respectively _Uc_ and _Uo_ , are orthogonal. Therefore, to explain the pattern where _δ_<sup>ˆ</sup> _c >_ 0 and _δ_<sup>ˆ</sup> _o_ ≈ 0 _without education spillovers_ , _Uc_ and _Uo_ must be totally uncorrelated within villages. When estimating equation (5), getting _δ_<sup>ˆ</sup> _c >_ 0 and _δ_<sup>ˆ</sup> _o_ ≈ 0 consequently rules out that _Ec_ , the education level of households from the same caste, captures caste-level omitted variables _correlated across castes_ in the village.

However, it does not rule out the case where _Ec_ captures omitted variables which are uncorrelated across caste groups. To take that into account, the impact of households from the same caste that have agriculture as their main activity, whose education level is _EAGRc_ , is now estimated. The other group is members from the same caste that do not have agriculture as their main activity, and their education level is noted _EnonAGRc_ . The equation to estimate is: The same reasoning applies here. If _δ_<sup>ˆ</sup> _AGRc >_ 0 and _δ_<sup>ˆ</sup> _nonAGRc_ ≈ 0, it can be ruled out that _EAGRc_ captures the unobserved characteristics _UAGRc_ , as long as _UAGRc_ is not totally uncorrelated with the unobserved