Relationship between elasticity and interpretation of approximate percentage change Let's define elasticity, in a regression setting, as $\frac{\partial \log E(y|u)}{\partial \log x_j }$. How do we relate this definition to the percentage change interpretation, i.e., seeing this elasticity as the approximate change in $E(y|x)$, when $x_j$ increases by 1 percent? I'm reading Wooldridge. 

Any help would be appreciated.
The derivative of $log(x)$ is $1/x$, which implies that $dlog(x)=(dx)/x$. Therefore, $e=dlog(y)/dlog(x)$ is the same as $e=(dy)/y/(dx)/x$. This ratio $e$ is known as the elasticity of $y$ with respect to $x$. We usually express derivatives $f′(x)$ as the change in $f$ when $x$ moves one unit, but $f(x)+1∗f′(x)$ is just an approximation (a Taylor approximation) of $f(x+1)$. Therefore, saying that a 1% change in $x$ will lead to an $e$ change in $y$ is just an approximation. It's a rate of change that is exact only at the $x$ point, but not exact as you move away from it to $x+0.01∗x$.