...don't you also have to compare the effects of...

Economic theory suggests there are many factors besides wages... RTFP ;-D

The thing I don't get about regression analysis is, in order for it to work, you have to control for every variable that can affect what you're measuring, but how can you possibly know what every such variable is?

1. You do not have to control for every variable that can affect what you're measuring. The error term picks up all omitted variabls and measurement errors. From a theoretical point of view, errors are often assumed to be normally distrbuted since they represent the combined effect of a myriad of omitted variables with good manners (see Lindeberg-Levy or Lindeberg-Feller Central Limit Theorem). You only run into trouble if those omitted variables are not orthogonal to the regressors. In this case the estimates are biased. But keep in mind that if you include unnecessary regressors, your estimates become inefficient.

2. Runnig a regression is just one stage of a long process. Econometricians do such things as Model Selection, Diagnostic Checking, Specification Testing, Sensitivity Analysis... Sure, omitted variables are a nasty problem because residuals ("estimated errors") are always orthogonal to the regressors (that's what OLS does...). But even here the situation is not entirely hopeless.

3. What you are actually saying is that one cannot make any statements about economic reationships at all because there are too many effects which would have to be taken into account. The Austrian School would probably say that it is logical that wage-increases reduce quit rates. Sure, but by 0.1%, 10%, or 100%? That's what non-ivory-tower people care about. 

Well I like the example a lot, but I think it just illustrates this problem. Before you take other variables into account, you have a correlation. After you think about all the variables you can possibly imagine and control for them, then you still have a correlation.

I don't know much about econometrics but it's almost daily that you see correlational health studies reported (my favorite example is "women who do more housework found to have lower endometrial cancer rate"), with the clear implication that the result is somehow causative. In almost every case, you can think of at least 5, typically 10 variables that could play a role in the observed effect (e.g. age, race, income, job type, family status, other exercise, smoking, drinking, history, culture, etc.). Sometimes some of these variables are accounted for, but I suspect there's a strong bias to include only the most obvious ones, or ones that don't weaken the correlation; in any case, rarely, even for JAMA or NEJM articles like this, do you get the sense that other variables really aren't a problem.

So I guess I'm just taking out my frustration, because it infuriates me almost every time I see a correlational study reported - I feel like these data are typically latched onto because it gives people an excuse to believe what they want to be true.