The beauty of a Tobin tax is that it would discourage short-term speculation without having much adverse effect on long-term international investment decisions. Consider, for example, a tax of 0.25% applied to all cross-border financial transactions. Such a tax would instantaneously kill the intra-day trading that takes place in pursuit of profit margins much smaller than this, as well as the longer-term trades designed to exploit minute differentials across markets.
Economic activity of this kind is of doubtful social value, yet it eats up real resources in terms of human talent, computing power, and debt. So we should not mourn the demise of such trading practices.
He says that the tax will raise much-needed revenue for all kinds of socially-beneficial programs. But if the tax is successful in limiting cross-national transactions ("throwing some sand in the wheels of international finance"), then the revenue from the tax will be less significant. Only if large, frequent, cross-national flows persist will the revenue come in, and if that happens then the other goal of the Tobin tax (protection from "hot money" flows) will be betrayed. It's like raising cigarette taxes to pay for education: if people do what you want them to do -- stop smoking -- then you don't have any money to fund the new education program.
But even if that weren't true, Rodrik is in effect arguing that markets should be less efficient. The "intra-day trading that takes place in pursuit of profit margins" is done by arbitrageurs, and arbitrageurs serve a very valuable function: they bring financial markets into equilibrium in quick and relatively painless ways. Without them inefficiencies will persist for longer, potentially leading to harsher corrections down the road. Moreover, financial instability is not caused by arbitrageurs trading for tenths or hundredths of a percent; it comes from quick reversals of the "long-term international investment decisions" that Rodrik hopes to keep, and argues that the Tobin tax won't affect. It may be possible to argue that some short-term efficiency should be sacrificed for long-term stability, but that isn't what Rodrik is really saying. In fact, he acknowledges a Tobin tax will have no effect on stability:
What the Tobin tax does not do is help with longer-term misalignments in financial markets. Such a tax would not have prevented the US-China trade imbalance. Neither would it have stopped the global saving glut from turning into a ticking time bomb for the world economy. It would not have protected European and other nations from becoming awash in toxic mortgage assets exported from the US. And it would not dissuade governments intent on pursuing unsustainable monetary and fiscal policies financed by external borrowing.
So what we're left with is the new revenue. Rodrik says that a small Tobin tax would raise "hundreds of billions" worldwide. Presumably these will used on all sorts of really great projects that everyone loves (he lists "foreign aid, vaccines, green technologies, you name it"). But the vast majority of these taxes will be recouped by the countries with the biggest financial sectors (who receive the most inflows): the U.S., U.K., Germany, Japan. In essence, then, we would be taxing investors from poorer countries in order to redistribute to citizens of richer countries. How is this a net global benefit? Does it make sense for the Chinese to fund the health care system in the U.K. or retirement pensions in the U.S.? Should Indians have to pay for the privilege of investing in the U.S. or Japan?
I don't see how a Tobin tax would improve the system.