First, I agree with Mark Thoma that Mr. Posner apparently has little understanding of macroeconomics, either of old-style Keynesian type, or the new(er) real business cycle type, or certainly New Keynesian approaches. His charge that her current pronouncements are at sharp variance with her earlier academic work really makes me wonder if he's read any of Dr. Romer's previous work. I suspect that he's taken at face value the conservative mis-apprehension that her tax cut paper contradicts the view that government expenditures can have an impact on growth. As I've explained in my responses to reader comments here, Romer and Romer (2008) provided estimates of tax cut multipliers, but no spending multipliers. Hence, a comparison of instrument efficacy is not feasible (comparing multipliers across methodologies can be done, but would be inappropriate).

Second, I would not pass a student out of intermediate macro who wrote in an exam:

The impact of the public-works program on investment is more complicated. But suppose, plausibly in a serious economic downturn such as the one that we're in at present (and that was even more serious back when the stimulus bill was enacted), that a great deal of investment is in the form of passive savings, such as demand deposits and Treasury securities, because people and companies are anxious about their economic prospects, and they want safe savings, rather than savings that would be at risk because invested in entrepreneurial projects.

As Mark Thoma points out, this is confusing a financial investment with physical investment in a NIPA sense.

This confusion tells me that anybody writing far outside their area of expertise should think twice, consult a textbook or two, before committing virtual pen to virtual paper. (I'm not saying one shouldn't write outside of one's area of research expertise on a weblog -- just one has to be careful).

Third, before he pontificates on what economists who work in the government should or should not be doing, I think Mr. Posner should read Martin Feldstein's discussion of how the CEA works ("The Council of Economic Advisers and Economic Advising in the United States," The Economic Journal, Vol. 102, No. 414 (Sep., 1992), pp. 1223-1234 [JSTORE pdf]; excerpt here). Here's a quote:

Although the CEA is physically as well as operationally part of the White House complex (CEA offices are in the Old Executive Office Building adjacent to the White House and within the same security cordon), the economic staff functions in a completely professional and nonpartisan way. My very able and distinguished staff included Larry Summers, who was prominent as chief economic adviser to presidential candidate Michael Dukakis.

The tradition of professionalist is so strong that even in a presidential election year the CEA chairman appoints members of the staff for the coming academic year with the clear understanding that they will continue to serve even if the party in power loses the presidential election. ...

My limited observations, having been a staff economist in the situation mentioned in the last paragraph, is that CEA members (nominated by the President and confirmed by the Senate) do not "leave behind their academic scruples" when they move from academia to government service. That doesn't mean that I think they're correct in their analyses -- just that what they believed when they came in is pretty close to what they say in public. (After all, silence is also an option.)

Fourth, I think any blog post (let alone paper) should be internally consistent. Consider Mr. Posner's (approving) statement:

Most economists, however, believe that it is unrealistic to suppose that people have enough information about the future to adjust their current behavior to expectations of higher taxes, inflation, devaluation, or other possible consequences of an increase in the national debt. There is too much uncertainty.

Then, he says two paragraphs later:

But Romer actually gives some credence to the unrealistic picture of the far-sighted consumer or businessman by arguing that recipients of tax credits authorized by the stimulus bill will spend rather than save the tax-credit money because they will assume that the credits are permanent.

But if in fact consumers do not look forward (as Mr. Posner argues, not as Dr. Romer argues), they will only respond to current changes in disposable income, and in fact the multiplier will look pretty big.

(Actually, I find the biggest problem with Mr. Posner's argument here is that the failure of consumers to respond in a fashion consistent with unencumbered intertemporal optimization w/perfect certainty is not due only to uncertainty, but also liquidity constraints, as well as possibly more exotic utility functions.)

Fifth, Mr. Posner should read a bit more widely. He states:

Romer argues in her talk that by the end of the second quarter of this year, $100 billion of stimulus money had been spent. That is a suspiciously round number, and it is unclear how it was arrived at; but let us assume it is accurate. She then argues that this small expenditure--about two-thirds of one percent of the Gross Domestic Product--is responsible for the fact that the decline in GDP fell (on an annualized basis) from 6.2 percent in the first quarter of the year to 1 percent in the second quarter (though the latter figure is likely to be readjusted upwards).

This assertion is groundless. No one has the faintest idea what effect the stimulus has had.

As someone who had to "fact-check" numbers going into White House policy documents and speeches on occassion, I can say that the numbers are verifiable regardless of Administration (whether they are interpreted in an appropriate fashion is a fair question).

But the more substantive question is whether the math is so nonsensical. As I showed quite clearly in this post, the number Dr. Romer obtained was easily calculated and plausible.

Sixth, my impression is that former CEA staffers and members that have become bloggers are pretty careful with the numbers and analytics -- certainly more so than Mr. Posner. These include Jeff Frankel, Paul Krugman (notwithstanding Mr. Posner's barbs), Andy Samwick, Diane Lim Rogers, and Nouriel Roubini. (see this post for former gov't/Fed economists who became bloggers.)