How would you test a hypothesis that an independent variable has a greater effect on a dependent variable in one country than it does in another? For example, the value of education is greater (in terms of relative wages) in country A than in country B. The independent variable is years of education and the dependent variable is the relative wage.

This could be a place for a regression with an interaction between education and country.
$$
y=\beta_0+\beta_1x_{country}+\beta_2x_{education}+\beta_3x_{country}x_{education}
$$
The $\beta_3$ parameter tells you the difference in slope between the two countries. Since you know the type of difference of interest, a one-sided test would be appropriate.
