Testing for converging deterministic seasonal variation in European industrial production

In this paper we consider deterministic seasonal variation in quarterly production for several European countries, and we address the question whether this variation has become more similar across countries over time. Due to economic and institutional factors, one may expect convergence across business cycles. When these have similar characteristics as seasonal cycles, one may perhaps also find convergence in seasonality. To this aim, we propose a new method, which is based on treating the set of production series as a panel. By testing for the relevant parameter restrictions for moving window samples, we examine the hypothesis of convergence in deterministic seasonality while allowing for seasonal unit roots. We derive the estimation bias, and show that it is very small for samples of more than three years of quarterly observations. Our main empirical finding is that there is almost no evidence for convergence in seasonality.