(1) Piero Sraffa:A very good work on this issue is Constatinos Repapis, “Hayek’s Business Cycle Theory during the 1930s: A Critical Account of its Development,” History of Political Economy 43 (2011): 699–742.
He was really the first and possibly the most important in these articles:Sraffa, P. 1932. “Dr. Hayek on Money and Capital,” Economic Journal 42: 42–53.See also:
Sraffa, P. 1932. “A Rejoinder,” Economic Journal 42 (June): 249–251.Kurz, H. D. 2000. “Hayek-Keynes-Sraffa Controversy Reconsidered,” in H. D. Kurz (ed.), Critical Essays on Piero Sraffa’s Legacy in Economics. Cambridge University Press, Cambridge. 257-302.(2) Karl Gunnar Myrdal:
Lawlor, M. S. and Horn, B. 1992. “Notes on the Hayek-Sraffa exchange,” Review of Political Economy 4: 317–340.
Lachmann, L. M. 1986. “Austrian Economics under Fire: The Hayek-Sraffa Duel in Retrospect,” in W. Grassl and B. Smith (eds.), Austrian Economics: Historical and Philosophical Background, Croom Helm, London. 225–242.Myrdal, G. 1933. “Der Gleichgewichtsbegriff als Instrument der geld-theoretischen Analyse,” in F. A. Hayek (ed.), Beitrage zur Geldtheorie, Vienna. 361–487.(3) Paul Rosenstein-Rodan:
However, I don’t think his criticisms were ever published (I could be wrong), but were certainly conveyed to Ludwig Lachmann in conversations in the 1930s as reported in this Austrian Economics Newsletter (AEN) (an interview with Lachmann):“AEN: You have talked a number of times about the importance of expectations in business cycle theory. What first drew your interest to expectations as far as the business cycle question was concerned.Rosenstein-Rodan was possibly referring to Gunnar Myrdal’s work listed in (2) above.
Lachmann: Talking to Paul Rosenstein-Rodan, who was then a lecturer at University College, London – not technically in the London School of Economics – but he gave a course on the history of economic thought to which all of us who were research students then went.
It was Rosenstein-Rodan who in discussing Austrian trade cycle theory with me said, ‘Ah yes, but whatever happens in the business cycle is in the first place determined by expectations.’ And then he told me of the work that had been done in Sweden.”
Ludwig Lachmann, “An Interview with Ludwig Lachmann,” The Austrian Economics Newsletter, Volume 1, Number 3 (Fall 1978), Mises.org.
(4) John Maynard Keynes:
Keynes’s criticisms were in a response to Hayek’s review of his earlier work, and mostly in his private correspondence with Hayek:Keynes, J. M. 1931. “The Pure Theory of Money. A Reply to Dr. Hayek,” Economica 34 (November): 387–397.It was in Keynes (1931) that he delivered his rather harsh verdict on Prices and Production:
Ingrao, B. 2005. “When the Abyss Yawns and After. The Correspondence between Keynes and Hayek,” in M. C. Marcuzzo and A. Roselli (eds.), Economists in Cambridge. A Study Through their Correspondence, 1907–1946. Routledge, London. 236-256.
Ingrao, B. and F. Ranchetti. 2005. “Hayek and Cambridge: Dialogue and Contention,” in M. C. Marcuzzo and A. Roselli (eds.), Economists in Cambridge. A Study Through their Correspondence, 1907–1946. Routledge, London. 392-413.
Moggridge, D. (ed.). 1973. The Collected Writings of John Maynard Keynes (vol. 13). Macmillan for the Royal Economic Society, London.“The book, as it stands, seems to me to be one of the most frightful muddles I have ever read, with scarcely a sound proposition in it beginning with page 45 … It is an extraordinary example of how, starting with a mistake, a remorseless logician can end up in Bedlam.” (Keynes 1931: 394).(5) Ludwig M. Lachmann:Lachmann, L. M. 1943. “The Role of Expectations in Economics as a Social Science,” Economica n.s. 10.37: 12–23.(6) Frank H. Knight:Knight, Frank H. 1935. “Professor Hayek and the Theory of Investment,” Economic Journal 45.177 (March): 77-94.Here is one of Hayek’s responses to Knight:Hayek, F. A. von. 1936. “The Mythology of Capital,” Quarterly Journal of Economics 50.2: 199-228.See also:Boettke, P. and K. Vaughn. 2002. “Knight and the Austrians on Capital and the Problem of Socialism,” History of Political Economy 34: 155–176.(7) Nicholas Kaldor:
Cohen, A. J. 2003. “Hayek/Knight Capital Controversy: The Irrelevance of Roundaboutness, or Purging Processes in Time?,” History of Political Economy 35.3: 469-490.Kaldor, N. 1939. “Capital Intensity and the Trade Cycle,” Economica n.s. 6.21: 40–66.(8) George L. S. Shackle:
Kaldor, N. 1940. “The Trade Cycle and Capital Intensity: A Reply,” Economica n.s. 7.25: 16–22.
Kaldor, N. 1942. “Professor Hayek and the Concertina-Effect,” Economica n.s. 9.36: 359–382.Shackle, George L. S. 1981. “F. A. Hayek, 1899– ,” in D. P. O’Brien and J. R. Presley (eds.), Pioneers of Modern Economics in Britain. Macmillan, London. 234–261, at p. 240.(9) Gottfried von Haberler:Haberler, G. 1986. “Reflections on Hayek’s Business Cycle Theory,” Cato Journal 6: 421–435.(10) Gordon Tullock:
Reprinted in Haberler, G. 1991. “Reflections on Hayek’s Business Cycle Theory,” in John Cunningham Wood and Ronald N. Woods (eds.), Friedrich A. Hayek: Critical Assessments (vol. 4). Routledge, London. 249–262.Tullock, G. 1988. “Why the Austrians are Wrong About Depressions,” The Review of Austrian Economics 2: 73–78.(11) David Ramsay Steele
His views (quite insightful) are described in this comment:http://consultingbyrpm.com/blog/2012/05/federal-government-outlays-and-receipts-as-of-nominal-gdp.html#comment-39021I am not certain, but there may be some more discussion of the ABCT in David Ramsay Steele’s book From Marx to Mises: Post-Capitalist Society and the Challenge of Economic Calculation (Open Court, La Salle, Ill., 1992).
(12) Allin Cottrel:Cottrell, A. 1993. “Hayek’s Early Cycle Theory Re-examined,” Cambridge Journal of Economics 18: 197–212.(13) Ulrich Witt:Witt, U. 1997. “The Hayekian Puzzle: Spontaneous Order and the Business Cycle,” Scottish Journal of Political Economy 44: 44–58.(14) Tyler Cowen:Cowen, Tyler. 1997. Risk and Business Cycles: New and Old Austrian Perspectives. Routledge, London.(15) Robert P. Murphy:
Although I suppose Murphy sees himself as a defender of the ABCT, nevertheless his work here is nothing but a critique of the classic Hayekian theory (where Hayek uses the Wicksellian natural rate of interest):Murphy, Robert P. 2003. Unanticipated Intertemporal Change in Theories of Interest, PhD dissert., Department of Economics, New York University.(16) Robert L. Vienneau:
Murphy, Robert P. “Multiple Interest Rates and Austrian Business Cycle Theory.”
http://consultingbyrpm.com/uploads/Multiple%20Interest%20Rates%20and%20ABCT.pdfVienneau, R. L. 2006. “Some Fallacies of Austrian Economics,” September
Vienneau, R. L. 2010. “Some Capital-Theoretic Fallacies in Garrison’s Exposition of Austrian Business Cycle Theory,” September 4
The list above is far from complete. I may update it after further thought.
In addition, here are some criticisms of Mises’s version of the ABCT:
Vasséi, Arash Molavi. 2010. “Ludwig von Mises's Business Cycle Theory: Static Tools for Dynamic Analysis,” in Harald Hagemann, Tamotsu Nishizawa, Yukihiro Ikeda (eds.). Austrian Economics in Transition: From Carl Menger to Friedrich Hayek. Palgrave Macmillan, Basingstoke. 196–217.
Vasséi, Arash Molavi. 2010. “The Foundation of Ludwig von Mises’s Business Cycle Theory: Real Analysis as a Chain of Tautologies,” SSRN paper, June 5, 2012.