Interpretation of change in log in regression

Question

I have build a time series regression with the formula: $$\Delta\log A = \alpha+\beta\Delta\log B $$ I have found $\beta= -0.05$. I can't seem to figure out how to interpret this number. I know that in a log-log regression the coefficient denotes a procentual effect. But I can't figure out how to inpret it for a $\Delta\log-\Delta\log$ regression. Could someone help me out?

Answer 1

The value $\beta= -0.05$ represents the slope for the linear regression in the plane $\Delta\log-\Delta\log$ and $\alpha$ is the $y$ value assumed for $B=1$.

For the exponential representation we have

$$\Delta\log A = \alpha+\beta\Delta\log B \iff e^\frac A{A_0}=e^{\alpha}e^{\left(\frac B{B_0}\right)^{\beta}}$$