A time-series examination of convergence in social protection across EU countries* por José A. Herce* Simón Sosvilla-Rivero* Juan José de Lucio** DOCUMENTO DE TRABAJO 98-10

April 1998

* The authors are very grateful to Daniele Franco and Teresa Bento for providing the data used in this paper, and to Pierre Perron for kindly making available the RATS programmes for unit root test with breaks.

** FEDEA and Universidad Complutense de Madrid.

*** FEDEA and Universidad de Alcalá de Henares

ABSTRACT

This paper examines the degree of convergence in social protection registered in the European Union during the 1970-94 period. To that end, we use EUROSTAT and OECD data and study the long-run properties of the data set using time series analysis. Our results indicate that there is not evidence of long-run convergence in social protection/GDP ratios with respect to Germany. However, we do find evidence of catching up with respect to Germany for all countries, except for Greece.

JEL Codes: F42, H53, O52.

Key words: Social Protection Benefits, Convergence, European Union.

1.- INTRODUCTION

The issue of social policy co-ordination has regularly been present in the agenda of the current European Union (EU), although it has never been granted the high profile that economic policy co-ordination has forcedly enjoyed. One powerful reason for such interest has been to ease higher labour mobility across countries, since the safety net system is considered to be an important disincentive to job mobility (see, e. g. OECD, 1990). Also the idea of a social Europe has been present since the founding Treaties were signed. On the other hand, Member States have always claimed that social policies, that involve enormous economic resources, are not to be harmonised given the present real economic difference among countries, letting apart other arguments about the proper jurisdictional level from which to conduct social policy.

Yet, beyond actual moves towards social policy co-ordination at a EU scale, every country looks at the rest, more or less informally, as a reference and given global resources (for instance GDP), similar population structures, lifestyles or welfare programmes would progressively lead towards similar standards in benefits.

This paper examines the degree of convergence in social protection across the EU countries. To that end, we apply time-series unit root-based tests to EUROSTAT social protection data covering the 1970-1994 period. The rest of the paper is organised as follows. In section 2, we outline the econometric methodology. Section 3 reports the empirical results, while some concluding remarks are offered in Section 4.

2.- TIME-SERIES CONVERGENCE

Consider two countries A and B, and denote their Social Protection Benefits (SPB)/GDP ratios as and . Following Bernard and Durlauf (1995 and 1996) and Oxley and Greasley (1995), we can distinguish between catching-up and long-run convergence.

Catching-up implies that the difference between the two series is a stochastic variable with a mean different from zero, suggesting that the deviation between the series is expected to decrease, but not to disappear. Formally, assuming two dates, t and , and that , the definition of catching up implies that

\[\mathrm{E} \left\{s p ^ {A _ {t + T}} - s p ^ {B _ {t + T}} / I _ {\mathrm{t}} \right\} < s p ^ {A _ {t}} - s p ^ {B _ {t}}\tag{1}\]

where denotes all the information available at t. Therefore, a stochastic trend in the difference between the two time series would violate the definition (1), although the presence of a deterministic trend, in itself, would not. A sufficient condition for catching-up would be the existence of stochastic cointegration between both variables. Note that this concept of "weak convergence" or "catching-up" could be appropriate in our context, since convergence in SPB/GDP ratios could be an ongoing process.

Conversely, long-run convergence is a more demanding level of convergence, since it implies both the absence of a unit root in the difference between the two series and a time trend in the deterministic process (i.e., the absence of both stochastic and deterministic trend). Long-run convergence can be formally defined as follows:

\[\lim _ {t \to \infty} \mathrm{E} \{\mathrm{sp} ^ {\mathrm{A}} _ {\mathrm{t+T}} - \mathrm{sp} ^ {\mathrm{B}} _ {\mathrm{t+T}} / \mathrm{I} _ {\mathrm{t}} \} = 0\tag{2}\]

In this case, a sufficient condition for convergence would imply both stochastic and deterministic cointegration between the two series.

As can be seen, statistical tests of catching-up and long-run convergence hinge on the time-series properties of . These properties are characterised by the order of integration of the deviation from their deterministic paths (Nelson and Plosser, 1982). To that end, we make use of the widely used Augmented Dickey Fuller tests (see Said and Dickey, 1984):

\[\Delta (s p _ {t} ^ {A} - s p _ {t} ^ {B}) = \mu + \alpha (s p _ {t - 1} ^ {A} - s p _ {t - 1} ^ {B}) + \beta t + \sum_ {i = 1} ^ {k} c _ {i} \Delta (s p _ {t - i} ^ {A} - s p _ {t - i} ^ {B}) + \varepsilon_ {t}\tag{3}\]

If the difference contains a unit root ( ), SPB/GDP ratios in the two countries will diverge. The absence of a unit root ( ), indicates either unit root (if ) or long-run convergence (if ).

In addition, we consider the existence of a structural break over the period when testing for a unit root. Following Perron (1989, 1997), we allow for the possibility of a one-time structural change in the trend function occurring at time . Three situations are considered: a change in the intercept, a change in both the intercept and the slope, and a change in the slope. Regarding the transition to the new trend path, and following Perron (1989), two models are evaluated: the "additive outlier model" (AOM) and the "innovational outlier model" (IOM). While the AOM specifies that the change to the new trend function occurs instantaneously (with no further effect on future observations), in the IOM that change takes place gradually (feeding back into the process dynamics).

In the case of the IOM, the unit-root test is performed using the t-statistic for testing in the following regressions:

\[I O M - 1 \quad s p _ {t} ^ {A} - s p _ {t} ^ {B} = \mu + \beta t + \gamma D U _ {t} + \delta D (T _ {b}) _ {t} + \alpha (s p _ {t - 1} ^ {A} - s p _ {t - 1} ^ {B}) + \sum_ {i = 1} ^ {k} c _ {i} \Delta (s p _ {t - i} ^ {A} - s p _ {t - i} ^ {B}) + \varepsilon_ {t}\tag{4}\]

\[\begin{array}{l} I O M - 2 \quad s p _ {t} ^ {A} - s p _ {t} ^ {B} = \mu + \beta t + \theta D U _ {t} + \gamma D T _ {t} + \delta D (T _ {b}) + \\ \qquad + \alpha (s p _ {t - 1} ^ {A} - s p _ {t - 1} ^ {B}) + \sum_ {i = 1} ^ {k} c _ {i} \Delta (s p _ {t - i} ^ {A} - s p _ {t - i} ^ {B}) + \varepsilon_ {t} \end{array}\tag{5}\]

where if (0 otherwise); if (0 otherwise); and if (0 otherwise). In equation (4) we allow for a one-time change in the intercept of the trend function, while in equation (5) we allow both a change and the slope of the trend function to take place simultaneously.

Regarding the AOM, the following two-step procedure is used. First, the series is detrended using the following regressions:

\[A O M - 1 \quad s p _ {t} ^ {A} - s p _ {t} ^ {B} = \mu + \beta t + \gamma D U _ {t} + \left(s \tilde {p} _ {t} ^ {A} - s \tilde {p} _ {t} ^ {B}\right)\tag{6}\]

\[A O M - 2 \quad s p _ {t} ^ {A} - s p _ {t} ^ {B} = \mu + \beta t + \theta D U _ {t} + \gamma D T _ {t} + \left(s \tilde {p} _ {t} ^ {A} - s \tilde {p} _ {t} ^ {B}\right)\tag{7}\]

\[A O M - 3 \quad s p _ {t} ^ {A} - s p _ {t} ^ {B} = \mu + \beta t + \gamma D T _ {t} + (s \tilde {p} _ {t} ^ {A} - s \tilde {p} _ {t} ^ {B})\tag{8}\]

where is accordingly defined as the detrended series. As can be seen, in equation (6) we allow for a one-time change in the intercept of the trend function, in equation (7) we allow both a change and the slope of the trend function to take place simultaneously, and in equation (8) we allow for a change in the slope of the trend function. For models AOM-1 and AOM-2, the test is then performed using the t-statistic for testing a=1 in the regression:

\[s \widetilde {p} _ {t} ^ {A} - s \widetilde {p} _ {t} ^ {B} = \alpha (s \widetilde {p} _ {t - 1} ^ {A} - s \widetilde {p} _ {t} ^ {B}) + \sum_ {j = 0} ^ {k} d _ {j} D (T _ {b}) _ {t - j} + \sum_ {i = 1} ^ {k} c _ {i} (s \widetilde {p} _ {t} ^ {A} - s \widetilde {p} _ {t} ^ {B}) + \varepsilon_ {t}\tag{9}\]

while for model AOM-3, the second step is of the form:

\[s \widetilde {p} _ {t} ^ {A} - s \widetilde {p} _ {t} ^ {B} = \alpha (s \widetilde {p} _ {t - 1} ^ {A} - s \widetilde {p} _ {t} ^ {B}) + \sum_ {i = 1} ^ {k} c _ {i} \Delta (s \widetilde {p} _ {t - i} ^ {A} - s \widetilde {p} _ {t - i} ^ {B}) + \varepsilon_ {t}\tag{10}\]

Note that in regressions (4) to (10), the break date ( ) and the truncation lag (k) are treated as unknown. Therefore, to carry out the test procedure, we need to consider a method to choose and k. In order to select the break date endogenously, we consider the procedure whereby is selected as the value, for all possible break points, which minimises the test statistic for testing in the appropriate autocorrelation specification [see Zivot and Andrews (1992)]. Regarding the truncation lag parameter (k), we use a general-to-specific recursive approach based on the value of the t-statistic on the coefficient associated with the last lag in the estimated autocorrelation (see Perron, 1989)

(1) That is, start with a large and then estimate the model with lags. If the coefficient of the last included lag is significant at the 10 percent level, select . Otherwise, reduce the order of lags by one until the coefficient on the last included lag is significant.

3.- EMPIRICAL RESULTS

As it has been mentioned above, in this paper we have used harmonised data on social protection benefits collected by EUROSTAT (SP) and Gross Domestic Product (GDP) collected by the Organisation for Economic Co-operation and Development (OECD). We then look at the SP/GDP ratio. Our sample covers the period 1970-94 (the latest available), and the countries under study are the EUR12 countries (i. e., Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain and the United Kingdom) that formed the Union before the last enlargement.

As mentioned above, to test for unit roots we apply the Augmented Dickey-Fuller tests to the difference of Social Protection/GDP ratios with respect to Germany. In Table 1 the statistics are reported for the levels and first differences, where the lag length (k) is optimally chosen using the sequential procedure suggested by Perron (1989), with the maximum lag length ( ) set to . As one can see, for all the series the null hypothesis of a unit root cannot be rejected at conventional significance level. These results suggest that there has not been (long-run or strong) convergence between these countries and Germany.

Next, the test by Perron (1997) and Vogelsang and Perron (1994) is applied to the difference of Social Protection/GDP ratio between these countries and Germany. This test allows us to distinguish between series that are I(1) and series that are stationary around a trend with a structural change. In the former case there will not be convergence, while in the latter case we will find catching up or weak convergence.

(2) Test results remain qualitatively the same when the maximum lag length ( ) is set to 10. They are not reported to economize on space.

After visual inspection of the data, it was decided to apply the following models to each country: Innovational Outlier Model 1 (IOM-1) (i. e., a gradual change in the intercept of the trend function) for Denmark and the Netherlands; Innovational Outlier Model 2 (IOM-2) (i. e., a gradual change in both the intercept and the slope of the trend function) for Belgium, France, Greece, Ireland, Spain and the United Kingdom; and Additive Outlier Model 3 (AOM-3) (i. e., a change in the slope of the trend function without any sudden change in the level at the time of the break) for Italy, Luxembourg and Portugal.

Table 2 presents the empirical results of these tests for each country with the corresponding model of the selected trend function. Columns 1 and 2 give, respectively, the date of break in the trend function and the value of the truncation lag parameter k in the autoregression. Columns 3, 4 and 5 present key estimated parameters of the autoregressions along with their t-statistics in parentheses: is the estimated of the initial (pre-break) slope of the trend function, is the estimate of the change in the intercept of the trend function in the case of model IOM-2, and is the estimate of the change in the slope of the trend function in models IOM-2 and AOM-3. For model IOM-1, it is the estimate of the change in the intercept of the trend function. Columns 6 and 7 present the key estimated parameters related to the estimate of the sum of the autoregressive coefficient ( ) and its associated t-statistics for testing .

As can be seen in Table 2, we reject the null hypothesis of the unit root for all countries considered, except for Greece. Therefore, we find evidence of weak convergence or catching up with respect to Germany for 10 of our 11 countries.

Since the time-series version of catching-up captures a version of cross-sectional test of convergence (see Oxley and Greasley, 1995), our results are in line with those presented in Alonso et al. (1998), where the traditional indicators ( -convergence and -convergence) suggest a certain degree of convergence in social protection benefits for a panel of 11 EU countries during the 1966-94 period.

4.- CONCLUDING REMARKS

This paper has examined the degree of convergence in social protection registered in the EU during the 1970-94 period. To that end, we have studied the long-run properties of time series of social protection benefits using data from EUROSTAT and OECD for the 12 member countries that formed the European Union before the last enlargement to Austria, Finland and Sweden. Our results suggest that there is no evidence of long-run or strong convergence (with respect to Germany) in Social Protection/GDP ratios, that would imply equalisation of the latter. However, we do find evidence of catching up or weak convergence with respect to Germany for all countries, except for Greece.

These results, in turn, suggest that some countries have been carrying out a stronger effort, as far as social protection is concerned, in order to make their situation converge with that of other countries where the expenditure was much more significant. This effort can contribute to facilitate factor mobility within Europe and can have important implications for the speed of growth in each European country and the EU at large (see, Herce, Sosvilla-Rivero and de Lucio, 1998)

REFERENCES:

Alonso, Javier, Miguel A Galindo,. and Simón Sosvilla-Rivero, (1998), "Convergence in social protection benefits across EU countries", Applied Economics Letters, Vol. 5, pp. 153-155.

Bernard, Andrew B. and Steven N. Durlauf, (1995), “Convergence in international output”, Journal of Applied Econometrics, Vol. 10, pp. 97-108.

Bernard, Andrew B. and Steven N. Durlauf, (1996), “Interpreting tests of convergence hypothesis”, Journal of Econometrics, Vol. 71, pp. 161-173.

Herce, José A., Simón Sosvilla-Rivero and Juan J. de Lucio. (1998), “Growth and the Welfare State in the EU: A causality analysis”, forthcoming in Applied Economics Letters.

Mackinnon, James G. (1991), “Critical values for cointegration test”, in Robert F. Engle and Clise W.J. Granger (Eds.). Long-run economic relationships (Oxford University Press, Oxford, UK).

Nelson, Charles R. and Charles I. Plosser, (1982), “Trends and random walks in macroeconomic time series”, Journal of Monetary Economics, Vol. 10, pp. 139-162.

OECD (1990) Employment Outlook, (Paris: OECD).

1. Oxley, Les and David Greasley, (1995), “A time-series perspective on convergence: Australia, UK and USA since 1870”, The Economic Record, Vol. 71, pp. 259-270.

Perron, Pierre, (1989), “The Great Crash, the oil price shock and the unit root hypothesis”, Econometrica, Vol. 57, pp. 1361-1401.

Perron, Pierre, (1994), “Trend, unit root and structural change in macroeconomic time series” in B. Bhaskara Rao (Ed.) Cointegration for the applied economist (London:, St. Martin's Press), pp. 113-146.

Perron, Pierre, (1997), “Further evidence on breaking trend functions in macroeconomic variables”, Journal of Econometrics, Vol. 80, pp. 355-385.

1. Said, Said D. and David A. Dickey, (1984), “Testing for Unit Root in Autoregressive-Moving Average Models with Unknown Order”, Biometrica, Vol. 71, pp. 599-607.
2. Zivot, Eric and Donald W. K. Andrews, (1992), “Further evidence on Great Crash, the oil price shock and the unit root hypothesis”, Journal of Business and Economic Statistics, Vol. 10, pp. 251-270.

Table 1: Augmented Dickey-Fuller unit root tests Difference of social protection/GDP ratios with respect to Germany (1970-1994)

NOTES: a. The optimum lag length is selected as suggested by Perron (1989). b. (1), (2) and (3) denote the Augmented Dickey-Fuller statistics with drift and trend, with drift, and without drift, respectively. c. * and ** denote significance at the 5% and 1% levels, respectively, using Mackinnon's (1991) extended tabulations of critical values.

Table 2: Perron unit root test Difference in social protection/GDP ratio with respect to Germany (1967-1994)

NOTES: a. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively (see Perron 1994). b. t-ratios in parentheses. c. Estimate of the change in the slope of the trend function in models IOM-2 and AOM-3. For model IOM-1, it is the estimate of the change in the intercept of the trend function. d. Estimated parameters related to the estimate of the sum of the autoregressive coefficient and its associated -statistics of the above estimates for testing .

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