I also come from an Economics background, and am now a software engineer/budding data scientist. As I've delved more into machine learning topics, I'm amazed (though not surprised!) at how both academic and industry economists are still mostly focused on running OLS/logit/probit regressions, and not other classification techniques. My undergraduate thesis did use some computational models that sought convergence for dynamic & stochastic conditions, but that was definitely not the norm.
Macroeconomics and empirical industrial organization are leading the forefront in terms of theoretical and applied technical advances. You ought to look at discrete choice analysis sometime--great stuff.
I can't speak for industry economists, but the reason we academics tend to spend so much time with OLS/Logit/Probit is their flexibility and scalability.
Macro was my favorite subject! I was lucky enough to take the first year PhD sequence during my last year, which was my first taste of coding =D
I think in industry (anti-trust at least), they stick with the older models because their value has legal precedent, and using new methods would require some more legal hand waving by the attorneys.
