to the land value data. Even though this higher precision substantially improves the power of our symmetry test, we still fail to reject the null across all specifications. So, proposition 3 is again confirmed. Imposing symmetry, we may now formally address Proposition 2 ( _δ_<sup>_′_</sup> ( _θ_ ) _>_ 0) by testing _H_ 0 : _β_ 1 = 0. As noted, the standard Wald tests are invalid since _γ_ is not identified under _H_ 0. We thus report block-bootstrapped p-values for these hypothesis tests as suggested by Hansen (1999), which yield similar strong rejections of the null.<sup>29</sup> The restricted DPR estimates in Table 3 and the corresponding estimates for land values in Table 4 allow us to quantitatively assess the impact of a relative shift in lobbying influence parameterized by _θ_ = _ιH/ιT_ . Looking across channels, there is near equality of influence between head and tail outlets, with a very slight advantage for the tail (see the log _θ_ histograms in the lower panels of Figure 7, with _G_ as the 98th percentile). Now consider the predicted effect of a shift in log _θ_ by one standard deviation about its mean, as illustrated in the top panels of Figure 7. Our estimates imply that such a shift in favor of the _head_ coalition increases the head-tail differential in DPR from a base of 27.2 (2.3) log points to 39.1 (4.3) log points, whereas the equivalent shift in favor of the _tail_ would bring this differential down to 15.4 (3.1) log points.<sup>30</sup> At the same time, a one standard deviation shift in influence in favor of the head would increase the head-tail land value premium from a base of 11.4 (1.8) log points to 19.8 (3.6), whereas the equivalent shift in favor of the tail would virtually eliminate the premium, bringing it down to 2.9 (2.8).<sup>31</sup><sup>_,_32</sup> Given the primacy of agricultural land in

> 29Indeed, the bootstrapped p-values are smaller than those of the conventional Wald test based on the cluster-robust variance-covariance matrix. Hansen’s statistic essentially uses the likelihood ratio principle and hence cannot be adjusted for clustering. One additional caveat, albeit probably a minor one, is that Hansen assumes a balanced panel, whereas our data are unbalanced due to varying numbers of outlets per channel. It is unknown if Hansen’s results extend to our case.

> 30Standard errors in parentheses. Notice that, as a consequence of Jensen’s inequality, the mean percentage head-tail differential in DPR is larger than the absolute differential as a percentage of mean tail DPR reported in subsection 4.2.

> 31Recall that we are using a different _γ_ for land values than for DPR (i.e., _γ_ = 0 _._ 545 in the former case versus _γ_ = 0 in the latter case), which is why the scales of log _θ_ are different.

> 32That the base head-tail land value differential of 11.4 log points is smaller than the corresponding DPR differential of 27.2 log points is consistent with the diminishing marginal product of water (concavity of ˆ _s_ ( _w_ )). In particular, log( _VH /VT_ ) _≈ P_<sup> ̃</sup> (ˆ _s − b_ ) _/_ (1 _− P_<sup> ̃</sup> ) _s_ 0 and log( _wH /wT_ ) _≈ P_<sup> ̃</sup> _w/_ (1 _− P_<sup> ̃</sup> ) _w_ 0 _._ Now, _s_<sup>_′′_</sup> ( _w_ ) =

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