I stumbled across this video.
Cosma Shalizi, a stats professor at Carnegie Mellon, argues that economists should stop "fitting large complex models to a small set of highly correlated time series data. Once you add enough variables, parameters, bells and whistles, your model can fit past data very well, and yet fail miserably in the future."
I think there's a bit of a conflation of problems here. Not all economic data sets are small. An economist friend of mine pointed out that he's been working with datasets that have millions of observations. I am told this is common in microeconomics.
Nevertheless, my experience is that "acceptable" econometric methods are overly-conservative. As stated in the video, an economist saying someone is "data mining" is tantamount to an accusation of academic dishonesty. I was indoctrinated early in the ways of David Hendry's general to specific modeling, which is basically data mining (but doing it intelligently). This, I think, made machine learning an intuitive move for me, and I've always thought that economics research would benefit greatly from machine learning methods.
There are some important caveats to all this. First, I don't see anyone beating out economics the same way computer science is sticking it to statistics. For "big data analytics" to live up to its hype, data scientists have to think a lot like economists, not the other way around. A big part of an economics education is economic thinking; this goes above and beyond statistical methods. Second, (and more importantly) you should take anything I say here with a grain of salt. Though I have a background in (and profound love for) economics, I never held a graduate degree in econ and I've been out of the field (and professional network) for several years. My knowledge may be dated.
Even so, I'm happy to hear voices like Dr. Shalizi's. It adds to Hal Varian's paper on "big data" tricks for econometrics. Maybe instead of worrying about the AI singularity, we should be worrying about economists using machine learning and then taking all of our jobs. ;-)