Principal component analysis interpretation
It is harder to interpret coefficients principal components in terms of original regressors.


Indeed, since you are now dealing with components, you can't. That being said, if your original regressors are highly colinear and all capturing wealth-related phenomena, a possibility is that your first component is still somehow strongly related to wealth, and other components only controling for phenomena that are not related to wealth at all. Put differently, you could reduce the dimensionality of your problem to this unique first component, and maintain your interpretation.

But do not take what i am saying for granted: if you really want to know how abusive maintaining your economic interpretations would be, it's all a matter of visualizing/diagnozing the relative weights of your components, e.g. you need to check the eigen decomposition of your correlation matrix.

I recommend you to read Michael Friendly and Ernest Kwan (2009) "Where's Waldo? Visualizing Collinearity Diagnostics" The American Statistician, Vol. 63, No. 1 (Feb., 2009), pp. 56-65.

Also, Yoel Haitovsky (1966) "A Note on Regression on Principal Components" is very clear and concise.