Several Austrian schools criticized Milton Friedman.
F. A. Hayek pointed out that Milton Friedman was basically a Keynesian because he considered monetary and fiscal issues primarily from the perspective of aggregates. According to Karl Menger's heirs, this was a major mistake. It is a form of scientism. Aggregation is not important. The fusion of human interactions that produce easy-to-observe categorical results is what matters most. Not those results. That is, the outcome of the Keynesian "macro" level has always depended on individual behavior and the tendency toward and away from theoretical price equilibrium among millions of economic participants. Treating them holistically with the magnitude obtained from statistics (or worse, merely hypothesized, formally) misunderstands the fluidity of equipoise and de-equilibrium. Put economists on the wrong path.
Ludwig von Mises, for example, is a proponent of quantitative theory of money, but fears that it may (and is often) too literal. Money is trickier than familiar equations developed by Simon Newcomb and popularized (and extended) by Irving Fisher. The theory makes sense as a simplified view of the problem, but does not properly explain changes in the value of currencies, in part because of unstable demand.
In a sense, these are expressions of the fundamental differences in methods. Austrians have always been more "subjective" than mainstream economists. This has led to skepticism about mathematical modeling and constant thinking on a holistic level.
Keynes also lacked a realistic theory of capital, while Friedman—perhaps following the early figure of the Chicago School, Frank Knight—ran a simplified theory of capital that, while arguably more realistic than the Keynesian "k," was still less powerful and nuanced as various Austrian versions. But it is important to note that the Austrian School and the economists influenced by the Austrian School have been struggling with the complexity of capital from the beginning, and there are many differences between them, from Menger to Wiesel to Eugen von Böhm-Baweek, from Mises to Hayek, from Rahman to Kirzner to Rothbard. From all this to Sir John Hicks, who came up with the "New Austrian Theory" of capital a generation ago.
The theory of capital is not unrelated to monetary theory, for example the differences between the methods of the American marginalist Clarke to the Austrian version are profound. by Austrians.
Another aspect of monetary theory that separates the Austrian School from Friedman and his company is that Mises and Hayek developed a theory of business cycles that emphasized that inflationary booms led to deflationary depressions and saw depressions as natural consequences of "man-made" prosperity. Friedman's famous monetary history (co-authored with Anna Schwartz) highlights the deflationary aspects of the Great Depression and defines deflation as an appropriate response to tragedy, describing the Fed's failures of this period as being too arbitrary (inadequate, really) in dealing with deflation. Austrians, such as the authors of the 1937 analysis of the banking and business cycle (Phillips, McManus, and Nelson) and later Murray N. Rothbard, blamed the problem primarily on the early days of inflation. A completely different focus. (The 1937 analysis, though, is more reliable than Rothbard's history because it extends the theory to the Great Depression for longer and combines three aspects.) See my retweet of the laissez-faire book eBook version. ）
This long-standing disagreement over the business cycle has become quite complicated. Two interesting developments have emerged (at least!). :(1) Among the Austrians, after the excellent research of Hayek's student Vera Smith, a strong field of study has developed, namely the free banking option; (2) over time, both Friedman and Schwartz have become more "Austrian" in monetary theory. and the business cycle. For the former, Friedman began to realize how difficult it was to define money. A major Austrian theme.
But I'm pretty sure I remember Hayek expressing his strongest concerns in Friedman's famous essay on positivism as a foundation of economics. A huge mistake, he wondered. Remember that Hayek's mentor Mises was a notorious "behaviorist" in his understanding of the foundations of economic science, so he stepped out of the mainstream. Friedman, in his famous green cover book, belongs to the mainstream of economic thought. Although Hayek did not follow Mises in his methodology, he still regarded Friedman's simple "positivist" basis of economics as a kind of scientism, which is a very serious mistake.
While the mainstream of economics has long scoffed at transcendentalism (the behavioral approach) as phi rational and unscientific, Hayek's criticism is that positivism in economics is inherently unscientific, because treating certain methods of the physical science as blueprints for all fields—in effect turning programs into dogmas—allows theorists and researchers to take on the cloak of science and superficially apply their complex social realities. As far as I know, Hayek was opposed to the actological approach because it was too simple. He rejected the positivist approach because it was simpler, if in a different direction.
In addition, the Economists of the Chicago School of the Austrian School and the Friedman School agreed on many aspects.
Oh, and I should mention David S. Early in The Hidden Order, David D. Friedman defended his father's positivist approach very skillfully in a common-sense manner. I highly recommend reading that book. Especially as a balance against over-reading austrian methodology.
My own skepticism about economists' approach to economics: they often misunderstand what they are doing when they do economics. I think that's true of both Mises and Friedman. Both men's views are too far from the center of the critique. Sir John Hicks' humble approach made it easier for me to defend. But that's just an outsider's opinion.