Econometrics: Is elasticity meaningful in my, or any, regression? A few months ago I interned at this organization; and, as a going away present, I decided to spend my last week, with whatever off time I had, to investigate the factors that affect teacher salaries. One problem that I ran into with teacher salaries was that the distribution for the given state was skewed. I had a lot of observations that clung to the lower end of the wage spectrum. I tried resolving this by incorporating a Comparable Wage Index into my dependent variable (teacher wages), but the results I found were completely out of date for the scope of my project. I instead decided to log my dependent variable. This was nice because now my wages had a normal distribution and it just looked perfect in the histogram. When I started testing down, I got to the point where I was left with one last independent variable, property tax returns. The problem with my normative wages was also apparent in my property tax return observations. I had a huge skew of property tax return numbers towards the lower end of the spectrum. So, I logged this variable as well and it still passed the null hypothesis test just fine.

I am not sure if this is precisely correct, but by comparing the change of one logged variable to another logged variable gave me the elasticity. Assuming that this is correct, my regression equation (something like LogWages = B0 + B1(LogPropertyTaxReturns)) shows the elasticity between the two variables. Is this meaningful though? If my goal was to see which variable most affected teacher salaries in any given county of my state, then is showing the elasticity between the two variables helpful? We want to raise the counties with the lowest teacher salaries up higher to increase their living standards, but I fear that I've extrapolated so far away from the real observations that my concluding regression equation is meaningless. 

Edit: One of my bigger fears is that I should have used a non-linear model to show the relationship. I feel that forcing both the dependent and independent variable to cooperate in a this linear regression is misleading in some way.
The answer to the question is yes, it is indeed meaningful (at least mathematically speaking). If you estimate the linear equation

$$ W = \beta_0 + \beta_1 PTR, $$

then $\beta_1=\frac{\partial W }{\partial PTR}$, meaning that $\beta_1$ represents the marginal change of $PTR$ over $W$. Now, if you estimate

$$ log(W) = \beta_0 + \beta_1 log(PTR), $$

then $\beta_1=\frac{\partial W}{\partial PTR}\cdot\frac{PTR}{W}$, which is the very definition of elasticity.

Generally speaking, linear transformations only affect the interpretation given to the coefficients, but the validity of the regression itself (in broad economic terms) is given by the model's assumptions and the economic phenomena being analyzed.