Suppose we estimate the following regression equation:
\[
\ln(x_t) = \alpha_0 + \alpha_1 \ln(y_t) + \epsilon_t, \quad \alpha_0, \alpha_1>0
\]
where \(x_t\) and \(y_t\) are some variables, \(\alpha_0\) and \(\alpha_1\) are the intercept and the slope, respectively, and \(\epsilon_t\) is the residual term. What is the interpretation of the coefficient \(\alpha_1\)?