Elsevier

Economic Modelling

Volume 24, Issue 6, November 2007, Pages 954-968
Economic Modelling

Analyzing a panel of seasonal time series: Does seasonality in industrial production converge across Europe?

https://doi.org/10.1016/j.econmod.2007.03.006Get rights and content

Abstract

In this paper we consider deterministic seasonal variation in quarterly industrial 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 method that 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. Our main empirical finding is that there is no evidence for convergence in seasonality.

Introduction

The increasing integration across European economies may be reflected in basic time-series features becoming more similar over time. Focusing on production series, we are interested in whether deterministic seasonal cycles indicate convergence. We choose industrial production, as this variable is of major economic importance and it also offers reliable data for longer time spans.

Despite some major advances in the study of seasonality from an economic as well as from an econometric perspective (Hylleberg, 1992, Ghysels and Osborn, 2001), we feel that this aspect of economic behavior does not yet catch the attention it would deserve. In many economic variables, the size of the seasonal cycle clearly dwarfs the business cycle. Accordingly, we also find strong evidence for seasonality in production data. The typical pattern is a peak of activity in the fourth quarter and troughs in the first and third quarters. Using statistical tests, we establish that seasonal cycles are mainly deterministic for most European countries.

Several reasons may be named for the existence of seasonal cycles in production. Summer vacations are mainly responsible for the slumps in the third quarter. Pooling of vacations in summer is due to the peak of the climatic cycle, but it also has a cultural component. Conversely, the peak in the fourth quarter is mainly determined by Christmas, when private spending peaks due to a cultural tradition. Cold weather may be an obstacle for economic activity in the first quarter, particularly in the North of Europe. While cultural traditions are comparable across European countries, the direct impact of the climate varies. Neither source of seasonality is carved in stone for centuries. Improving technology may allow spreading economic activity to cold and rainy seasons, and the emphasis on Christmas as the one and only event for the exchange of gifts among consumers may also be subject to taste shifts. Cultural exchange across borders may increase the synchronization of regional tastes.

A main feature of our paper is that we wish to examine if there is evidence of more common deterministic seasonality over the years. We consider 13 European countries, and we wonder whether increased economic coherence is leading to more common patterns over time.

The development of appropriate econometric tools for the study of convergence is still an ongoing research topic. Inspired by Bernard and Durlauf (1996), among others, several researchers investigated convergence in linear vector error-correction models. Findings of unit roots in differences across countries but also of stationary differences with non-zero means are interpreted as indicating non-convergence. A problem with such applications is that they implicitly view convergence as having occurred before the sample at hand, such that a steady state has already been attained. It seems more plausible to assume that convergence is a phenomenon linked to the movement from starting conditions toward an eventual steady state or from one steady state to a different one. Then, a linear time-series model with constant coefficients may be an inadequate tool.

Models with abrupt structural breaks are not adequate either, as slow and gradual change is more typical for economic convergence. Smooth-transition models (for example, Baum et al., 2001) or Markov chains (for example, Aubyn, 1999) that generalize linear time-series models allowing for time-changing coefficients are suggestions that deserve attention. However, we feel that their inherent laws of change are too restrictive to map convergence features in the typical economic environment. Therefore, we loosely assume that traditional autoregressive time-series models are good approximations to the data-generating process for restricted time windows, whereas such approximations become less acceptable for longer time spans. The shortness of the time windows implies that it is important to exploit the cross-section dimension of the panel in order to obtain reliable evidence.

Our approach does not intend to test for a null hypothesis of time-constant seasonal cycles. Rather, we allow for gradual changes of deterministic seasonal cycles as a working hypothesis. Within this framework, we monitor the evolution of seasonal deterministics. A test statistic for the hypothesis of identical seasonality across the panel is used as a measure of distance from a hypothetical common European seasonal cycle. If this distance measure indicates a shrinking tendency, this is interpreted as evidence for convergence.

Our focus is on quarterly time series of industrial production for the following thirteen European countries: Austria, Belgium, Finland, France, Germany, Greece, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, and the United Kingdom. In short, these are all members of the European Union as of 2003, that is, before the Eastern enlargement. We exclude Denmark and Ireland, for which countries data of comparable length are not available. The time range for all series is from 1962 to 2002. Data are taken from the OECD data base. All industrial production series are real indexes.

We consider two versions of the industrial production variable. Firstly, production in total industry excluding construction (TIEC), and secondly, production in manufacturing. For total industrial production in Sweden, only seasonally adjusted series are reported. We used this adjusted series and multiplied it with a seasonal factor that was obtained from production in mining and manufacturing, which is reported in a seasonally adjusted and in an unadjusted version.

The outline of our paper is as follows. In Section 2 we start with a basic analysis of each of the series and in Section 3 we use the familiar HEGY test approach. In Section 4, we describe a model for panels of quarterly time series, in which we allow the autoregressive parameters to be country-specific. We then discuss useful estimation methods. In Section 5, we consider the panel models for two times 13 series, where we consider the full sample as well as moving window samples. Basically, our main finding is that there are no signs of more common deterministic seasonality over the years. In Section 6, we conclude with a discussion of limitations and possible extensions.

Section snippets

Stylized facts

Table 1, Table 2 report the results from regressing first-order differences of the logarithmic series on quarterly dummies for the TIEC data, whereas Table 3 reports corresponding regressions for the manufacturing data. In line with the findings by Miron (1996), we see that R2 values are rather high for most countries. While these high values might be spurious as seasonal unit roots would also deliver such values, see Franses et al. (1995), they at least indicate that seasonal variation

Univariate analysis

This section deals with an analysis of the time series properties of the 26 series under scrutiny. For this purpose, we rely on the HEGY test procedure.

Panels of time series

In this section, we provide details on the representation of the panel data models we use in our empirical work below, and on the relevant estimators and tests.

This paper deals with the analysis of panels of seasonal time series. Such a panel can consist of a number N units (like countries or sectors), and the observations span T = ST data points, where S denotes the seasonal frequency and T the number of years. In the present paper S is 4, T is 41 and N is 13.

If, as in Eq. (1), all countries

Results

In this section we apply the ID panel model that was outlined in the previous section to the two times 13 industrial production series of interest. We aim to answer the question in the title, whether there is any sign of converging seasonal deterministics.

The previous section has motivated why some countries with evidence of seasonal unit roots were excluded. Those excluded cases were four countries for the manufacturing data (Finland, France, Germany, and Portugal) and five countries for the

Conclusion

The celebrated definition of seasonality by Hylleberg (1992) states that seasonal cycles are rooted in various sources, among which the climate, cultural traditions, and technology play a key role. While the climate is unlikely to converge across Europe, regional traditions and technologies may now have come much closer to each other than 40 years ago. The increasing intra-European trade, division of labor and production processes, and integration in various fields would motivate a tendency

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The authors wish to thank two anonymous referees for their helpful comments.

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