The effort by economists to ape the scientific methodology of the natural sciences is one of the most intellectually dangerous ideas of the 20th century. Unfortunately, despite the rise in the 1980s and 1990s of serious philosophical challenges to the hegemony of scientism, economists in the 21st century seems to be moving along unaffected by this critique. At least in the 1940s and 1950s, economists sought philosophical justification for their practice of model and measure. Now-a-days, the focus is on conventionalism. The only justification is that economists do what other economists do, and what they do is build models and test for statistical significance.
Gene Callahan and Peter Leeson have an interesting working paper "Scientisim in the Way of Science", where they argue that the collapse of mechanical philosophy demonstrates (a) how scientific convention can serve to limit progress in the social sciences, and (b) that scientific systems can completely collapse. Kuhnian paradigm shifts can and do occur, and economics is long overdue.
F. A. Hayek, of course, addressed this issue of scientism in depth in the 1940s and 1950s. The Counter-Revolution of Science (1952) is made up of the essays that started "the abuse of reason" project. Bruce Caldwell's Hayek's Challenge discusses this work in depth. Steve Horwitz's review essay of Alan Ebenstein's Hayek's Journey and Caldwell's book provides a good discussion of how Hayek's scientific theory of the mind challenges the scientism of mid-20th century. If Hume used reason to whittle down the claims of reason, Hayek used science to challenge the ambitions of scientism. Scientism can indeed get in the way of scientific progress.
The reader should also be alerted to the new Liberty Fund edition of Ludwig von Mises's Theory and History and to the discussion in this great work of the challenges of scientism.