Gille 18

**Table 6.** Coefficient of Proportionality

|**Group**|**(1)**|**(2)**|**(3)**|**(4)**|
|---|---|---|---|---|
|**No excluded variable**|||||
|Caste|1.34|1.27|0.92|0.79|
|Caste & occup|0.84|0.83|0.81|0.71|
|Jati & occup|0.82|0.79|0.89|0.74|
|Caste & occup, WHEAT|7.76|7.47|2.27|2.88|
|**Excluded var: Head educ and Othe**|**r group mean educ**||||
|Caste|2.05|1.93|1.35|1.14|
|Caste & occup|3.07|3.00|2.90|2.39|
|Jati & occup|1.87|1.80|2.04|1.65|
|Caste & occup, WHEAT|17.93|16.64|3.34|4.36|
|Household controls|Yes|Yes|Yes|Yes|
|Agr. controls|Yes|Yes|Yes|Yes|
|Group controls|No|Yes|Yes|Yes|
|Controls for other group|No|No|Yes|Yes|
|Add. controls|No|No|No|Yes|

_Source_ : Author’s analysis based on the 2006 round of the Additional Rural Incomes Survey and Rural Economic & Demographic Survey (ARIS-REDS) from the National Council of Applied Economic Research. _Note_ : This table reports coefficients of proportionality calculated following the methodology in Oster (2017). Coefficients of proportionality represent the relative degree of selection on unobservables to selection on observables that would imply a true effect of the education of the group of 0. The first set of coefficients has been estimated using all the control variables in the set of observables; the second set of coefficients exludes the education of the head of household and the mean education level of the other group.

household and of the other group) are excluded, as it is unlikely that unobserved factors would be as correlated with the education of members from the same group as these variables, so they do not contain useful information about the relationship of unobservables to the treatment. In both sets of results the maximum possible _R_<sup>2</sup> is assumed to be 1, which renders the results conservative. What the table shows is that the relationship between unobserved factors and education of the group needs to be quite high— between 0.71 and 22.71 times the relation between observed factors and education of the group—to fully drive the correlation between education of the group and productivity. Most of the coefficients are higher than 1, which, as suggested by Oster (2017), can be interpreted as an indication that the true effect is nonzero. All the coefficients that are lower than 1 are estimated using the education variables in the set of controls, which, as argued earlier is very conservative as the unobserved characteristics are unlikely to be as correlated with the education of the group as these two variables. Moreover, the coefficients have been computed under the assumption that the variance in the productivity can be fully explained if the unobservables could be controlled for ( _R_<sup>2</sup> = 1), which is an upper bound, as productivity may be measured with error or some of the variance in productivity may be idiosyncratic. If this assumption is relaxed, all the coefficients are higher than 1 for a _R_<sup>2</sup> higher or equal to 0.94. Finally, a large set of unobservables has been ruled out as potential confounders such that the pool of potential unobservables is quite small. Together, these findings corroborate that the positive effect of neigbors education is indeed likely to be a spillover effect.

# **6. Conclusion**

This paper takes advantage of the social structure in India to study spillovers of education in farm productivity. The results show that the mean education level of members from the same caste is positively related to agricultural productivity. On the contrary, there is no cross-caste effect. The results also show that within castes, only households that have agriculture as their main activity have a positive impact on