Robert Shimer tries to summarize the research of Clark Medalist Daron Acemoglu. One example.
Daron and James [Robinson] explore the transition from autocracy to democracy. What makes the political elites allow the poor to vote? Daron and James argue that the elites enfranchise the poor to ward off revolution. Once the poor can vote, they enact redistributive reforms which make revolution less attractive. The shortcoming of this answer is that the elites could simply enact the redistributive reforms directly, without enfranchising the poor. Daron and James argue that this alternative is infeasible because of a time consistency problem. Once the threat of revolution has passed, an autarchic elite will undo the redistribution. Thus redistribution without enfranchisement is not a credible alternative and does little to alleviate the threat of revolution. In contrast, they argue that it is more difficult to undo the enfranchisement of the poor...Thus extending the franchise solves the time consistency problem and eliminates the threat of revolution. As evidence in support of this mechanism, the authors show that enfranchisement in Britain and other European countries was accompanied by a substantial increase in redistributive taxation and a consequent reduction in inequality.
In describing another example, Shimer writes,
Daron and James examine the nature of redistribution in a democracy, in particular the vexing question of why redistribution often takes an inefficient form such as agricultural price supports rather than transfers to farmers. The authors suggest a theory built on two key assumptions: politicians cannot commit to future policies and political power is increasing in group size, at least over some range of parameters. They develop a two-period model...
Overall, one gets the impression that Acemoglu is very skilled at looking at phenomenon, coming up with a "story" to explain it, and converting it to a formal model. This is the skill set that is most in demand in economics journals. I am afraid that what it leads to in the aggregate is that stories that survive are the ones for which the mathematical models that are developed are fun to play with.
Another skill that Acemoglu has that is popular is that of coming up with empirical exercises that establish important contrasts. For example, Shimer describes this chain of reasoning:
Colonies where settlers had low mortality rates should do more to encourage property rights. Strong property rights should lead to later economic growth. Therefore, we should observe higher economic growth today in places where colonial settlers originally experienced low mortality rates. Acemoglu, Robinson, and Simon Johnson studied this empirically and found it to be the case.
In the field of political economy, I am not convinced of the benefit of formal modeling of stories. First, I think we need to get a broader list of stories, and then we need to sort out the relationships among them.
For example, The Logic of Political Survival, the book I just read, seems to take a different view of democracy and taxation. The authors say (p. 171) that their theory "suggested that tax rates drop as governments become more inclusive and rise as they become more exclusive."
Acemoglu has a story for tax rates rising as governments become more inclusive. The Logic of Political Survival has a story that goes in the other direction. That sort of thing comes up all too often in political economy.
As for evidence, I would like to see empirical studies that have the potential to bear on a number of stories. I find myself highly skeptical of a study aimed at testing one particular story. In the latter case, confirmation bias, both on the part of authors and in the paper selection process ("significant" results increase the odds of acceptance), has an overly strong impact on what gets published.