You correctly argue that Friedman's contribution was based on theory and not on evidence. His impact however, was clearly based on evidence. Here I stress as always Krugman's recollection of a lunchtime conversation. Note the lunchers are students of Samuelson and of Solow http://krugman.blogs.nytimes.com/2013/12/16/more-paleo-keynesianism-slightly-wonkish
The relatinship between the evidence and Friedman's influence is made clear in many popular discussions of the recent history of economic thought. Two good places to start are the Wiki on the Phillips curve http://en.wikipedia.org/wiki/Phillips_curve and "Zombie Economics " http://www.amazon.com/Zombie-Economics-Ideas-Still-among/dp/0691154546
The occurance of stagflation in the 1970s was considered proof that Friedman had been right and his intellectual opponents wrong. Without presenting proof, I note that I think that exactly this episode convinced most macroeconomists that macroeconomics needed a methodological revolution. However, the episode provided no useful information relevant to the debate at all. Friedman had no prominent opponents who asserted that stagflation was impossible. It is perfectly consistent with an expectations augmented Phillips curve in which expected inflation is a constant less than one times lagged inflation.
One might say (and I have so written) that the very simple constant times lagged CPI inflation (which was conventional pre 1973) failed because over time the estimated constant increased significatnly (rejecting the null , if such rejection were needed which it never was, that it i a structural parameter). However, I now discover that I was wrong. I finally decided to test the null that the relationship between US wage growth and US lagged CPI inflation as estimated with pre Friedman Presidential address data (pre 1968) is inconsistent with post 1968 data. This is a very crude simple test -- I just look at the coefficient on lagged cpi inflation times a post 1968 dummy.
Regression with Newey-West standard errors Number of obs = 259
maximum lag: 3 F( 3, 255) = 27.63
Prob > F = 0.0000
ldqwinf | Coef. Std. Err. t
unem | -.3776157 .1145142 -3.30
infcpi | .5516583 .2054788 2.68
infcpia68 | .0089793 .1800448 0.05
_cons | .0527488 .008214 6.42
I think this is the main evidence that the old methodology was not ideal. The null that messing around with data and leaving theory last (or never) is rejected at the 96% level (that is the probability that the old approach would do at least this badly if it were valid is 96%).
The empirical success of the assumption that expected inflation is a constant times lagged inflation is surprising and would be surprising even if it were 100% true (not a useful model but the pure essential truth about human psychology). Note however, that the paleo Keynesians never bet their reputations on the constant times lagged inflation model. They were perfectly prepared to use Friedman's adaptive expectations model and used both well before the oil shocks.
Now the revolution was based on evidence at the time and not data up till now. I ran a few regressions with quarterly data always Newey-West standard errors (because I am using overlapping year long periods). I didn't find an interval such that the old pre-Friedman formula is rejected by the data. By 1985 the rational expectations revolution had definitely occurred (it's when I started grad school).
Data through t-statistic on lagged inflation times the post Friedman dummy
This is what you expect when testing a null which happens to be true. I don't think any prominent paleo Keynesian bet his or her reputation on the failure to reject that null. The informal impression that the data showed the null was no good is, I think, the storming of the Bastille of the rational expectations revolution.
I believe there was no good reason at the time to consider the new approach promising (and I recall that Brad DeLong said in 1982 or 1983 that he thought macroeconomics had taken a wrong turn and would be sterile for at least a decade). I think that subsequent evidence strongly supports the view that the then new approach is not promising.
Now note that I think the actual methodology which actually influenced macroeconomic thought is the straw man rhetorical trick. I am quite sure that macroeconomists were generally convinced that neglect of micro foundations had caused someone prominent to be sure that stagflation was impossible and so macroeconomists should base macroeconomics on microfoundations to avoid such errors in the future. I think that this was a completely unsound method of attempting to find a good method based on the use of fictional intellectual history.
I am moving this to the end of my comment, as I think it will irritate readers. You will note that I have repeatedly deleted rudeness. I can't manage to discuss the topic in a way which is both diplomatic and honest. I hope the stuff above won't be ignored because of the stuff below.
I sincerely doubt that methodology is discussed little because mainstream macroeconomists think it is unproblematic. I am quite confident that it is discussed little, because the methodology of mainstream economics is indefensible. I have certainly never heard anything which I consider to be a argument that there is any reason to think it is a valid approach (I am thinking of what I've heard from Thomas Sargent and Robert Barro). The argument, as well as I can understand it, is that the approach might someday yield useful insights. This is a special case of the fact that "might" makes right. On disarray -- if only. [more rudeness deleted]. I think that mainstream macroeconomics has the relationship with evidence typical of totally false theories. That doesn't mean that it is totally false ( and not a useful approximation). I think this is what the available evidence suggests, but it isn't proof (as it is always impossible to prove that a research program is sterile -- something might turn up).