I know this is a old post, but since I found it and I know the answer I might as well share it.
I would go further than the first component, but it also depends on how much of the variance is actually explained within the component. There is two approaches that I use when determining which components I am using.
- The rule of thumb is to use and component with a eigen value greater than one.
- Keep an eye on the cumulative variance, for example I have a data set of 150 macro indicators and the first ten can explain 96% of the variance for a particular problem I was attempting to forecast, if I extend the components out to 20 it explains 96.7% of the variance. Is the ten additional factors really relevant? In this case I would stick to the first 10, but again it all depends on your individual analysis.
To answer your second question, yes..
PCA is process commonly used in Factor Investing, or smart beta.. Google Smart beta and see how many firms are approaching it. As far as strait economics, the answer is still yes. I have seen many working papers published by the Fed that references PCA. It certainly does not hurt to include other methods for reducing high dimensional data. Generalized boosted models comes to mind, it uses a tree based approach. Another would be the minimum redundancy maximum relevance model. Probably the best method would be a combination of models using different machine learning and ensemble modeling.
Either way, I hope this helps even if I am answering the question 3 years after it was posted. Good luck solving the worlds problems with econometrics.