It's a provocative argument. He's certainly right that the definition of GDP involves some more or less arbitrary choices about what is included in final output. (The New York Fed had a nice piece on this, a couple years ago, which was the subject of the one of the first posts on this humble blog.) However, I can't help thinking that Foley is wrong on a couple key points. Specifically:
While in other industries such as Manufacturing (MFG) there are independent measures of the value added by the industry and the incomes generated by it (value added being measurable as the difference between sales revenue and costs of purchased inputs excluding new investment and labor), there is no independent measure of value added in the FIRE and similar industries mentioned above. The national accounts “impute” value added in these industries to make it equal to the incomes (wages and profits) generated. Thus when Apple Computer or General Electric pay a bonus to their executives, GDP does not change (since value added does not change–the bonus increases compensation of employees and decreases retained earnings), but when Goldman-Sachs pays a bonus to its executives, GDP increases by the same amount.This seems confused on a couple of points. First, unless I'm mistaken, value-added in FIRE is calculated exactly in the way he describes -- sale price of output minus cost of inputs. (The problem arises with government, where there is no sale price.) Second, I'm pretty sure there is no difference in the way wages are treated -- total incomes in a sector always equal the total product of the sector, by definition. There is a question of whether executive bonuses are properly considered labor income or capital income, but that's orthogonal to the issues the paper raises, and is not unique to FIRE. In any case, it is definitely not correct to say that higher compensation implies lower earnings in non-FIRE but not in FIRE.
It seems to me that there is a valid & important point here, but Foley doesn't quite make it. The key thing is that there is no way of measuring price changes in FIRE. That's what he should have said in place of the paragraph quoted above. The convention used in the national accounts is that the price of FIRE services rises at the same rate as the price level as a whole, so changes in nominal FIRE incomes relative total nominal income represent changes in FIRE's share of total output. But you could just as consistently say that FIRE output grows at the same level as output as a whole, and deviations in nominal FIRE expenditure represent relative changes in FIRE prices.  There's no empirical way of distinguishing these cases, it really is a convention. Doing it the second way would imply lower real GDP and higher inflation. I think this is the logically consistent version of Foley's argument. And it would motivate the same empirical points about Okun's Law, etc.
There's another argument, tho, which I don't quite have a handle on. Which is, what are the implications of considering FIRE services intermediate inputs rather than part of final output? If a firm pays more money to a software firm, that's considered investment spending and final output is corresponding higher. If a firm pays more money to a marketing firm, that's considered an intermediate good and final output is no higher, instead measured productivity is lower. I think that FIRE services provided to firms are considered intermediate goods, i.e. are already treated the way Foley thinks they should be. But I'm not sure. And there's still the problem of FIRE services purchased by households. There's no category of intermediate-goods purchases by households in the national accounts; any household expenditure is either consumption or investment, so contributes to GDP. This is a real issue, but again it's not unique to FIRE; e.g. why are costs associated with commuting considered part of final output when if a business provides transportation for its employees, that's an intermediate good?
He raises a third question, about the possibility that measured FIRE outputs includes asset transfers or capital gains. There is serious potential slippage between sale of financial services (part or GDP, conceptually) and sale of financial assets (not part of GDP).
Finally, it would be helpful to distinguish between services where measuring output is practically difficult but conceptually straightforward, and FIRE proper (and maybe insurance goes in the previous category). It seems clear that capital allocation as such should not be considered as part of final output. Whatever contribution it makes to total output (modulo the deep problems with measuring aggregate output at all) must come from higher productivity in the real economy. The problem is, there's no real way to separate the "normal service" component of FIRE from the capital-allocation and representation-of-capitalist-interests (per Dumenil and Levy; or you could say rent-extraction) components.
But whatever the flaws of the paper, it's pointing to a very important & profound set of issues. We can't bypass the conceptual challenges of GDP, as Matt Yglesias (like lots of other people) imagines, with the simple assertion that labor is productive if it produces something that people are willing to pay for. Producing a consistent series for GDP still requires deliberate decisions about how to measure price changes, and how to distinguish intermediate goods from final output. Foley is absolutely right to call attention to these problems, that most social scientists are happy to sweep under the rug ; he's right that they're especially acute in the case of FIRE; and I think he's probably right to say that to solve them we would do well to return to the productive/unproductive distinction of the classical economists.
 I wasn't there, but a comrade who was thought so. And he seems to be right, based on the papers they've got up on the website.
 Or you could say that FIRE output is fixed (perhaps at 0), and all changes in nominal FIRE output represents price changes. Again, this problem can't be resolved empirically, nor does it go away simply because you adopt a utility-based view of value.
 Bob Fitch had some smart things to say about the need to distinguish productive and unproductive labor.