between cells. However, this implies we are over-stating the real effect of spraying on overall cultivation, and does not rule out our conclusion that farmers respond rationally to the increase in enforcement; it simply suggests another margin of response. However, one additional piece of evidence suggests that reallocation may not be that pervasive. When we estimate the effect of the discontinuity in enforcement on the likelihood of cultivation (the extensive margin, rather than the intensive margin), we find no effects (not reported to save space). This suggests that cultivation in the exclusion region increases within cells, and not because farmers move to new cells in this area. In any case, we cannot entirely rule out the extent of reallocation of coca crops, and our point estimates remain an upper bound of the effects of spraying on coca cultivation.

# 4 CONDITIONAL DIFFERENCES IN DIFFERENCES ESTIMATES

ˆ Let _Ti_  1{ _Di_  0} and<sup>_Y_</sup> _i_<sup>be the average cultivation in grid</sup><sup>_i_from 2000 to 2005. We are</sup> interested in estimating the treatment effect of<sup>_T_</sup> _i_<sup>on</sup> _Yit_  _Yi_ , for _t_  2006 (or _t_  2008 —when Colombia effectively stopped spraying in the exclusion area). This effect informs us about changes in cultivation brought about by the differences in enforcement induced by the diplomatic friction.

In the previous section we exploited the geographical discontinuity in enforcement around the 10 km cutoff to identify this effect. We relied on comparing cells near the cutoff and controlling for potential differences using a smooth function of their geographic location.

In this section, we present complementary estimates exploiting within-cell variation and use the data from 2000 to 2005 to construct counterfactuals for cultivation and spraying in a given cell. In particular, we exploit the following conditional independence assumption (CIA): where _Yitd_ is the potential cultivation in cell _i_ and year _t_ for cells in the sprayed area, _d_  1 , and cells in the exclusion area, _d_  0 . The assumption states that once we condition on the whole history of cultivation and spraying in a cell ({ _Yit_  , _Sit_  } _t_   2005 ), and cell characteristics,<sup>_Z_</sup> _i_ (including a polynomial in altitude— determining yields— and municipality fixed effects), the _change_ in potential cultivation from 2006 onward would be equal for cells in the sprayed and exclusion areas (in the absence of changes in spraying).<sup>9</sup> In other words, the assumption requires that all differences between cells in the exclusion and sprayed areas are captured by their history of spraying and cultivation and the observed geographic characteristics. Any change in cultivation not predicted by these observables is attributed to changes in aerial spraying since 2006.

We believe this is a plausible assumption. Including lags of cultivation and spraying takes into account the fact that, before 2006, there was a differential behavior of cultivation in both areas (see figure 10, which plots the difference in spraying and cultivation between the sprayed and exclusion areas for each year). This implies a violation of traditional difference in difference estimates and requires us to condition on the observed paths of cultivation and spraying, as we do here.

9 We use the change in potential cultivation instead of its level to remove any permanent difference between cells not captured by the conditioning set. In theory, we do not need to remove the average cultivation, as this is already in the conditioning set. In practice, this helps to control for potential sources of misspecification in the model for the propensity score used below.