Noah Smith and Jason Smith have been writing a series of blog posts focusing on three main ideas: Empiricism, paradigm shifts, and 'negative empiricism' (which is, as far as I'm concerned, equivalent to Postpositivism, which would basically be synonymous with 'whatever Karl Popper said,' but whatever).
Regarding empiricism, I'm not sure why this is getting any attention from people discussing philosophy of science in the 21st century. Empiricism is most closely associated with David Hume -- i.e. an enlightenment philosopher -- and, while it serves as the backdrop for newer philosophy of science, is neither new nor worthy of attention when considering a new philosophy of economics. It seems that people have confused empiricism with caring about empirical evidence when in reality empiricism is an epistemology that elevates experience over a priori deductions (which are characteristic of rationalism). For a more in-depth look into this, see "Rationalism vs. Empiricism" in the Stanford Encyclopedia of Philosophy. Needless to say empiricism alone does not qualify as a philosophy of science.
Jason somewhat repairs this by arguing for "negative empiricism" which he defines as "theory rejection." Here my only issue is that Jason has almost literally argued for Postpositivism, which is exactly that: hypothesis rejection. Basically think Popper; what really matters for a theory is falsifiability. Interestingly, Popper essentially solves the empiricist (Humean) problem of induction by arguing that empirical evidence in favor of a hypothesis is irrelevant and falsification is all that matters. In this sense, Jason is basically a Postpositivist by arguing for "theory rejection" based on empirical evidence. Noah Smith also weighs in, suggesting that economics was in "an age of great theoryderp" before the IT revolution which (according to him, not me) allowed for theories to be invalidated. To his credit, Noah acknowledges that "you can be a pure theorist and still subscribe to empiricism - you just don't believe in theories until they've been successfully tested against data," which is, in my opinion, the way most of economics currently is and will remain forever.
Both Smith's talk about paradigm shifts (further solidifying my suspicion that neither of them are empiricists and that they did not just come forward in time from 1748), which are attributed to Thomas Kuhn (another 20th century philosopher of science). In Kuhn's view, science operates in a single paradigm until the usefulness of said paradigm is exhausted at which point there will be a revolution. Both of the Smith's seem to be arguing for such a regime change, whether it is Jason's Information Transfer Framework or Noah suggesting that economics is experiencing a wave of "new empiricism" (OK, every time I read the word empiricism in this topic I shudder, please stop calling it that). Either way, each of them sees economics as being on the verge of or currently undergoing a revolution which begs the question of whether or not the current paradigm is really exhausted. I'll leave this to others to determine, but I personally don't see the field as being in a dead-end right now.
So, really, this post all comes down to two requests: please stop calling Postpositivism Empiricism and please stop trying to get economists to accept an 18th century epistemology instead of actually arguing for a new philosophy of economics (or, at least, coming clean and saying you are a Postpositivist).