How does the interpretation of a log-log model differ from a level-level model?

Answer 1

In one sense, the interpretation doesn't change. You're still finding the association between a dependent/criterion variable and one or more independent variables. What does change is the interpretation of the parameters that result from the model fitting process. When you take the log of both the dependent variable and any given independent variable, your estimated parameter (߈) is now an elasticity, meaning that a percent change in X is associated with a percent change in Y. It's called an elasticity because you might get a result like, a 1% change in X leads to a 50% change in Y, so Y is highly elastic with regard to X.

And in the level-level model it's the old, "a one-unit increase in X is associated with a ß increase in Y, holding other regressors constant."