Very short question. What exactly is the difference between an instrumental variable and a proxy variable when building a regression model?
An instrumental variable is used to help estimate a causal effect (or to alleviate measurement error). The instrumental variable must affect the independent variable of interest, and only affect the dependent variable through the independent variable of interest. The second part (only effecting the dependent variable through the independent variable) is called an exclusion restriction.
A proxy variable is a variable you use because you think it is correlated with the variable you are really interested in, but have no (or poor) measurement of.
One way to think about what an instrumental variable is doing is to say you are first regressing X on the instrument Z. What you then have are the predicted values for X - say, X*. So intuitively this is sort of the part of X that you get from Z. Then you take Y and regress it on those X* (and correct for standard errors). This is different from deciding to use Z as a proxy directly and regressing Y on Z. Intuitively, you then have all of Z in the regression instead of Z's relationship to X.