A missing variable is a problem IF there is, in fact, a variable missing from a statistical model. The problem is that often only theory can tell you if it is missing or not -- not anything in your model itself. This means that you'll never know if it's missing if you haven't thought sufficiently about your problem.
That is why you make control experiments.
This is the real problem that most economists, as well as many other social scientists, and even medical researchers, struggle to answer: "What WOULD have happened if X were true instead of Y?" -- a counterfactual, in other words. That's how causality is best inferred and how statistics is used to find the answer, but doing so is really hard work because counterfactuals are, by definition, unobservable, which means that a better theory makes all the difference.
And this is why you do double-blind placebo-controlled clinical trials.
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.