That is, on the whole, influence is zero sum, and the relative pressure of each group (for given values of influence) is inversely related to the other group, scaled by the relative amounts of deadweight loss in _F_ ( _._ ) and _G_ ( _._ ).

Political pressure carries a cost, _mg_ (with the average cost by group being _m_ ̄ _g_ ), and in equilibrium, each group will continue to apply pressure until the marginal change in pressure relative to the marginal increase in this cost ( _∂m_<sup>_∂pg_</sup> _g_<sup>) equals the marginal change in utility (</sup><sup>_U_</sup> _g_<sup>_′_) relative to the change in the average</sup> cost of exerting that pressure _mg_ , as shown in Becker (1985)<sup>2</sup> : Where _Us_<sup>_′≡−_</sup> _∂_<sup>_<u>∂U</u>_</sup> _m_ ̄<sup>_<u>s</u>_</sup> _s_<sup>_/_</sup><sup>_<u>∂U</u>_</sup> _∂s_ ̄<sup>_<u>s</u>_and</sup><sup>_U_</sup> _t_<sup>_′≡−_</sup> _∂_<sup>_<u>∂U</u>_</sup> _m_ ̄<sup>_<u>t</u>_</sup> _t_<sup>_/_</sup><sup>_<u>∂U</u>_</sup> _∂t_<sup><u> ̄</u></sup><sup>_<u>t</u>_.Or,putdifferently,sincetheutilityofboththesubsidized</sup> and taxed groups decreases with the cost of political pressure (i.e., _∂_<sup>_∂U_</sup> _m_ ̄<sup>_<u>g</u>_</sup> _g_<sup>_<_0),groupswillactivelymake</sup> political demands so long as they are beneficial relative to the cost of doing so. The two broader groups ( _s, t_ ) can each easily be extended to include several actors (sub-groups), with the larger budget constraint holding: though no individual actor will necessarily have their transfer offset one-to-one, the whole of the subsidy transfers must equal the whole of taxed transfers.<sup>3</sup> A few specific concepts within this model are worth elaborating further. First, gains by actors receiving subsidies will be mitigated by the political pressure exerted by taxed groups, and that offsetting pressure will scale to the deadweight losses caused by those subsidies. The intuition behind this is that subsidies will generally create deadweight losses, following _G_ ( _._ ), which will increase taxes and, in turn, raise the political demands of the taxed group. The greater the distortion contained in _G_ ( _._ ), the greater the pressure by taxpayers.<sup>4</sup> Extending this analysis to many groups, then, it can be shown that the marginal increase in deadweight losses, _G_<sup>_′_</sup> , will be proportional to the relative influence gained to the costs borne by each group. That is, actors that are more efficient at exerting influence can demand more distortionary payoffs. Showing this relationship for only two actors in the subsidized group, _i, h ∈ s_ , this gives: Intuitively, this means that an actor can receive more as a result of its demands if the marginal increase in deadweight loss is smaller, on one hand, but also if that actor is able to generate more influence relative to the cost of doing so (i.e. _∂_ Θ _/∂m_ ).

Empirically, none of the elements of Eq. 3 (or Eq. 5 by extension), can be directly observed.<sup>5</sup> We are interested in estimating political influence (Θ _i_ ), which is an inherently unobservable—and thus latent— trait. Likewise, but perhaps less intuitively, we consider the transactional costs associated with political

> 2Specifically, for simplicity purposes the model applies a Cournot-Nash equilibrium.

> 3That is<sup>�</sup><sup>_T_</sup> _t_ =1<sup>_ntG_( ̄</sup><sup>_t_) = �</sup><sup>_S_</sup> _s_ =1<sup>_nsG_( ̄</sup><sup>_s_,foralltaxedgroups</sup><sup>_t_= 1</sup><sup>_, ..., T_andsubsidizedgroups</sup><sup>_s_= 1</sup><sup>_, ..., S_.</sup>

> 4Strictly, the taxpayer pressure also depends on the deadweight loss of _F_ ( _._ ).

> 5We limit our discussion to mainly focus on groups receiving subsidies as the primary actors.

3