Abstract
This paper looks at unemployment rate convergence among the EU Member States. In particular, it examines whether the unemployment rate differences diminished between 1991 and 2014 among the old EU countries, among the new EU countries, among the euro countries and among the no-euro countries, and whether the new EU countries were converging in this sense to the group of old EU countries. Three alternative concepts of convergence are considered and tested for on each group of countries: σ-convergence, stochastic convergence and time-series β-convergence. The results provide strong support for EU unemployment rate convergence, although within each group there are large differences between the countries and during the recent economic downturn, there were clear signs of temporary divergence as well.
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Notes
http://ec.europa.eu/eurostat/statistics-explained/index.php/Unemployment_statistics, accessed 06 December 2016.
Euro countries are meant to be the Eurozone countries at the end of 2014.
This issue was pointed out by Perron and Yabu (2009, p. 369) who designed an alternative, but similarly asymptotic, test for shifts in trend based on two sets of critical values that are much closer to each other.
In the literature cross-sectional β-convergence and time-series β-convergence are both known as β-convergence as they are both related to the slope parameter of some regressions. Still, to avoid any confusion, in this paper we are going to refer to them as cross-sectional β-convergence and time-series β-convergence, respectively, unless the context makes this distinction unnecessary.
In the first case xi,t and \( x_{i,t}^{*} \) are both integrated of order zero, I(0), while in the second case they are integrated of order one, I(1), and cointegrated of order one and one, CI(1,1). This definition of stochastic convergence has been generalised by Bernard and Durlauf (1995): xi,t and \( x_{i,t}^{*} \) converge to each other in a stochastic sense if their long-term forecasts are equal at a fixed time (Definition 2.1); and they have a common trend if their long-term forecasts are proportional at a fixed time (Definition 2.2). Consequently, xi,t and \( x_{i,t}^{*} \) are either stationary with zero (or at least equal) means, or are cointegrated with cointegrating vector [1,-1] (Definition 2.1) and [1,-α] (Definition 2.2), respectively.
Both requirements of time-series β-convergence are satisfied when \( 0 < t \le \; - \mu_{i} /\beta_{i} \).
About bootstrap tests see e.g. Godfrey (2009).
A useful review and comparison of these tests are provided by Palm et al. (2008).
In principle the break dates could be considered known and the same for all series, but we prefer considering them unknown and estimating them with a grid-search for every group of countries and for every country within each country group individually prior to testing for unit roots for the following reasons. (i) Common exogenous break dates would impose some kind of uniformity for all countries and if these strong but untested restrictions are false they can potentially falsify the convergence test results. (ii) Even if a particular event, like the introduction of the euro or the latest recession, triggered a structural break in every EU country, it is still questionable whether the actual breaks occurred instantaneously and simultaneously in all data series. (iii) If there were common break dates in the data series, we would expect the grid-search procedures to pick them up. However, as the results in Tables 2, 3, 4, 5, 6 and 7 indicate, the revealed break dates vary by countries and groups of countries.
Following Hayashi (2000, p. 594), we set the maximal lag as \( pmax = \text{int} \left( {\hbox{min} \left( {\frac{T}{3},12} \right) \times \sqrt[4]{{\frac{T}{100}}}} \right) \).
The ILO unemployment rate indicates the proportion of the labour force that does not have a job and is actively looking and available for work. It is harmonised to account for differences in national data collection and tabulation methodologies, but for the sake of brevity, we are going to refer to it as unemployment rate. The unemployment rate (UR) and labour force (LF) data were extracted from the ILO database by the 9th Edition of the KILM (Key Indicators of the Labour Market, 2015) software.
These country groups are shown in Table A in the Appendix.
See e.g. http://ec.europa.eu/economy_finance/euro/adoption/who_can_join/index_en.htm about the euro convergence criteria, also known as the Maastricht criteria..
This way we also manage to take into consideration the huge differences between EU countries in terms of labour force. The most striking difference is between Germany and Malta. During our sample period the labour force of Germany was about 225 to 270 times larger than that of Malta.
To save space, we do not present these trend regressions here, but they are available on request.
These dates coincide with the 1997 Asian financial crisis and the 2007-2008 global financial crisis, but whether the potential structural changes are indeed linked to these events is a different issue.
To save space we focus on these two groups. As mentioned above, the EURO and NONEORO average unemployment rate series appear to be mainly driven by the OEU group and the NEU group, respectively.
For the sake of simplicity, we refer to NEU2 too as a weighted cross-sectional standard deviation.
It does not matter whether these deviations are calculated from the group mean or from the mean of the other group members. Suppose that \( y_{i,t} = x_{i,t} - \bar{x}_{t} \), where \( \bar{x}_{t} = \frac{1}{n}\sum\nolimits_{j = 1}^{n} {x_{j,t} } \) is the mean of all n group members in period t, and \( y_{i,t}^{*} = x_{i,t} - \bar{x}^{*}_{t} \), where \( \bar{x}^{*}_{t} = \frac{1}{n - 1}\sum\nolimits_{j = 1,j \ne i}^{n} {x_{j,t} } \) is the mean of all group members but i in period t In this case \( \bar{x}_{t} = \frac{n - 1}{n}\bar{x}^{*}_{t} + \frac{1}{n}x_{i} \) and \( y_{i,t} = \frac{n - 1}{n}y_{i,t}^{*} \), so up to a constant factor the \( \left\{ {y_{i,t} } \right\} \) and \( \left\{ {y_{i,t}^{*} } \right\} \) time series are equivalent.
To save space, the URD time-series plots are not shown here, but they are available on request.
The relevant t-ratio and p value are 0.4355 and 0.6677, respectively.
In fact, the EURO group has the largest sample mean and the smallest sample standard deviation out of all groups.
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Kónya, L. Did the unemployment rates converge in the EU?. Empir Econ 59, 627–657 (2020). https://doi.org/10.1007/s00181-019-01678-5
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DOI: https://doi.org/10.1007/s00181-019-01678-5