For development practitioners, the main problem is a lack of data on lobbyists' contributions. Thankfully there is a way around this since trade protectionism is most obviously against the general public interest and heavily favors one particular group. So trade protectionism = evil government, right? Of course right. Oh, and that whole correlation thing between low average tariffs and high levels of development implies that highly developed countries are very benevolent and less-developed are ... not. Oh dear. So is development caused by benevolence or trade? Or by the same institutional set ups that lead to both (or to all three!)? The whole thing muddies the waters quite heavily.
In the 2006 paper, they put the problem thusly, "The main implication from the estimates of the preference parameter ... is that ... the US government is approximately a welfare maximizer. But welfare maximization would lead to free trade and trade in agriculture is by no means free! The deadweight losses from protection are considerable. ... The distortion in agricultural prices is substantial." So there are some significant kinks still to work out in GH94.
Gawande and Hoekman (2006) [ungated World Bank version] and Gawande, Krishna, and Olarreaga (2009) [ungated WTO version] both apply and expand on the framework by looking at trade policy. Both are published in International Organization.In some ways the second paper really ought to have come first in that it largely ignores the insights from the first and sets at the problem in a much more naive way, so I'll talk about it first.
"What Governments Maximize and Why: The View of Trade" (2009) is a straightforward application of GH94. Here are a bunch of countries with 54 industrial sectors, their trade openness, and estimates of their benevolence. They then ask what institutional arrangements lead to more benevolent governments. Literacy and urbanisation lead to informed* voters --> more informed voters reduce the power of media to sway votes --> this reduces demand for lobbyists' funds --> this leads to more benevolent governments. Executive checks and balances make the legislature more benevolent (in part by assumption that the executive represents the median voter), but hotly contested executive elections increase the demand for lobbyist contributions, decreasing benevolence. They also come down in favor of proportional election systems over majoritarian, ideologically differentiable parties (the greater the difference, the less contributions matter), and though they don't state this, shouldn't weak media be on the list?
In "Lobbying and Agricultural Trade Policy in the United States," (2006) Gawande and Hoekman show that assuming a unitary government gives estimates of benevolence that are way out of line.The GH94 version posits that governments provide lobbyists with a menu: this much in contributions for this much protection/subsidy. Lobbyists choose a combination that suits them. In reality, lobbyists pay first and get something that is somewhat out of the control of the person they are paying for the goods. This uncertainty dramatically lowers the value of contributions (to the lobbyist), reducing contributions relative to the amount of protection actually given. They look only at the US, whether lobbyists compete with importers or exporters, and the effective size of non-tariff barriers to trade.
To some extent, the 2006 highlights that it doesn't matter much for agricultural policy whether Republicans or Democrats are elected from the big farm states: "Agriculture is distinguished among committees for the stability of their coalitions as issues move from committee to the floor" - that is, legislators don't change their votes once the bill hits the floor. Logrolling implies that lobbyists don't have to pay "the government" just influence a few key people whose political survival depends on it.
* - Informed voters do not get that way by having signals of the way things really are and information does not change anyone's vote. Informed voters are merely obstinate and cannot be swayed by their historical/ideological/etc. party preferences by mere propaganda.