Alex Tabarrok muses on the "political" part of "political economy":
Furthermore, the petition says that central bank decisions should not be "politicized." Again, this is disingenuous. Why are more independent central banks better at fighting inflation than less independent central banks? There is nothing magical about independence that makes for low-inflation. Suppose we pick someone at random and give them complete power over monetary policy. Such a central banker would be very independent but I wouldn't count on this policy resulting in much in the way of systematically lower inflation.
The primary reason that independent central banks are better at controlling inflation is that absent direct political control the default selection mechanism favors bankers, i.e. lenders, people whose interests make them more favorable towards lower inflation.
Thus, independence is a political decision that favors lenders in the decisions of monetary policy. Now, depending on the alternatives, there may be good reasons for making this choice but we should not fool ourselves into thinking that we have depoliticized money. We should not be surprised, for example, that "independent" central banks tend to make lender of last resort decisions that protect banks and bankers.
This isn't the first time I have been disappointed in Tabarrok's (lack of a) grasp of simple political economic theory. Fortunately for the world, there are a few people who think about the "political" part of "political economy", and they might even have something to say on the topic. For instance, Rosenbluth and Schaap found that electoral rules (i.e. single-member districts vs. proportional representation) play a major role in what types of banking regulations are chosen by governments. In proportional systems governments tend to choose "profit-padding" regulations that are intended to reduce risk-taking by limiting competition, thus guaranteeing higher profits for domestic banks. In other words, political variables can have major effects on banking policy.
Nor is it clear that bankers prefer lower inflation. If the higher inflation comes from lax monetary policy, then banks may prefer easy access to cheap credit over a lower price level*. In fact, Copelovitch and Singer found [pdf] that central banks that have multiple mandates -- i.e. to regulate banks and fight inflation -- choose different policies than those have a single mandate to fight inflation. Interestingly (and contra Tabarrok), Copelovitch and Singer found that central banks that regulate domestic banking sectors have higher inflation rates than those with a single mandate, but that central bank independence has no statistically significant effect on inflation rates. If bankers prefer low inflation, as Tabarrok states, then independent central banks are not acting in the interests of bankers**.
All to say that central banks may be "politicized" in many different ways, and the potential outcomes of that politicization is not predetermined or unidirectional. If these studies are to be believed, a less-independent Fed should lead to higher inflation and more prudential regulation of banks.
More distressing than Tabarrok's specific empirical claims is his attitude. Perhaps there is nothing "magical about independence that makes for low-inflation," but there could be something political about independence that makes for low inflation. In fact, there is a broad and deep literature in both the economic and political science disciplines showing that central bank independence is positively associated with lower rates of inflation. This is unsurprising for students of political economy, since we understand that short-run political incentives often diverge from longer-run economic incentives. "De-politicizing" monetary policy prevents politicians from damaging the macroeconomy in the longer-run in exchange for short-run political gains (at least, it prevents them from using monetary policy as such a tool; fiscal policy is another matter).
In short, there is nothing "magic" about politics, and we don't need "magical" reasons for expecting a link between central bank independence and lower rates of inflation: we have political explanations for these phenomena.
[UPDATE]: McMegan adds comment, and basically gets it right (she's got the story right but loses a few points for saying "magic" rather than "politics"):
Central bank independence works, not because the bankers aren't accountable to Congress (they are, after all, reappointed every so often), but because Congress is only weakly accountable for the actions of the central bank. If Congress were held to account for the actions of the central bank, Congress would appoint bankers who would do populist things that would make us all worse off. Most of the financial policy journalists I know have the sense that Congress actually supported most of what Paulson/Bernanke/Geithner did, but knew they did not dare enact it. They don't want a more accountable central bank.
*In a rational expectations framework lenders shouldn't much care about levels of inflation since they can adjust the interest rates they charge to compensate. In the long-run equilibrium, real profits should be the same no matter what the inflation rate is, so long as the inflation level is mostly stable.
**Or the Copelovitch/Singer results are spurious. For example, they did not test potential interactions between central bank independence and a central bank's mandate, or indeed any interactions including central bank independence. I have a lot of problems with their article, but so far it has not been challenged empirically.