During the last decade, economists have shown that the inverse relationship between economic growth and unemployment rate varies over time. Rolling regression has been the main tool used to quantify such a relationship. This methodology suffers from several well-known problems which lead to spurious non-linear patterns in the Okun's coefficient behaviour over time. Here, we take a penalized regression spline approach to estimate the Okun's time-varying effects. As a result, spurious non-linearities are suppressed and hence important time-varying coefficient features revealed. Our empirical results show that the inverse relationship in some Euro area countries is spatially heterogeneous and time-varying. The findings are complemented by the calculation of the rate of output growth needed for a stable unemployment rate, as proposed by Knotek.