Interpreting coefficients with Delta ln as independant and dependent variables Imagine we have a DGP such that

$$
\Delta \ln y_{it}=\beta\times\Delta\ln x_{it}
$$

How do you interpret the $\beta$ coefficient, since it is expressed in an approximation of a growth rate?

Thanks for your help
Your equation can be re-written (through the properties of logs) as:

$$
\ln(y_{it} / y_{it-1}) = \beta\ln(x_{it} / x_{it-1})
$$

So it becomes a log-log regression equation.  In this form, it means that if we change the ratio of $x_{it}$ to $x_{it-1}$ by one percent, the ratio of $y_{it}$ to $y_{it-1}$ will change by $\beta$ percent, on average.  In other words, if $x_{i}$ grows by one percent between two periods, $y_{i}$ is expected to grow by $\beta$ percent in that same time span.