What Are The Differences Between Econometrics, Statistics, And Machine Learning?

What are the differences between econometrics, statistics, and machine learning? I discovered this myself a couple years ago, through an analysis of the economics literature that required the research team to classify articles into economics fields (like labor and macro) and research styles (like theory and econometrics). The project was motivated by frustration with complaints lodged against academic economics in the wake of the Great Recession (perhaps you've seen the movie version: Inside Job). I thought: "What's with all the whining? "Economics has never been better!"