INTRODUCTION

Youth unemployment has attracted significant attention in recent years, especially in Europe, where it is particularly high relative to adult unemployment (see, eg, Perugini and Signorelli, 2010), and has been affected even more than the latter by financial crises (see Choudhry et al., 2012). Some key factors driving it that have been identified include the relatively low human capital of young people (see OECD, 2005), the ‘youth experience gap’ (see Caroleo and Pastore, 2007) and the mismatch between the skills acquired through education and those required by employers (see, eg, Quintini et al., 2007). Policy recommendations have been put forward both in the academic literature (see, eg, Brunello et al., 2007) and by the European Commission (2008).

This paper investigates the main statistical features and the macroeconomic determinants of youth unemployment in a number of European countries. It is well-known that an important feature of unemployment in Europe is its relatively high degree of persistence, which suggests that a hysteresis model (Blanchard and Summers, 1986; Gordon, 1988) might be appropriate. In fact, many empirical papers have found evidence consistent with this hypothesis, including Alogoskoufis and Manning (1988), Graafland (1991), Lopez et al. (1996), Wilkinson (1997) and so on using standard unit root methods, and Caporale and Gil-Alana (2008) and Cuestas et al. (2011) and others applying fractional integration methods. High persistence appears to be a feature also of European youth unemployment (see, eg, Heckman and Borjas, 1980; Ryan, 2001; Caporale and Gil-Alana, 2013). Therefore, first of all we examine the degree of persistence of the series, which sheds light on whether appropriate policy actions are required in case of high persistence, by estimating both autoregressive AR(1) processes and long memory (fractional integration) models. Second, we investigate the main macroeconomic determinants of youth unemployment in Europe by means of a fractional cointegration model that includes variables such as GDP and inflation as explanatory variables. The organization of the paper is as follows. The next section outlines the econometric framework. The penultimate section presents the data and the empirical results. The final section offers some concluding remarks.

THE ECONOMETRIC FRAMEWORK

As mentioned in the introduction, our main analysis is based on the concept of fractional integration, which allows the differencing parameter d making a series stationary I(0) to be a fraction as well as an integer. Therefore, the series of interest can be represented as

where u t is assumed to be an I(0) process, defined as a covariance stationary process with a bounded positive spectral density function. Note that this approach includes the unit root case as a particular case when d=1.

Given the above parameterization, one can consider different cases depending on the value of d. Specifically, if d=0 and x t =u t , x t is said to be a ‘short memory’ or I(0) process, and in the case of autocorrelated (AR) disturbances the autocorrelation is ‘weak’, that is, the autocorrelation function decays at an exponential rate; if d>0, x t is said to be a ‘long memory’ process, so called because of the strong association between observations far apart in time. In this case, if d belongs to the interval (0, 0.5), x t is still covariance stationary, while d≥0.5 implies non-stationarity. Finally, if d<1, the series is mean-reverting, with the effects of shocks disappearing in the long run, in contrast to the case with d≥1 where these persist forever.

Two methods of estimation of the fractional differencing parameter are employed here: one is a Whittle parametric approach in the frequency domain (Dahlhaus, 1989), while the other is a semiparametric ‘local’ Whittle method (Robinson, 1995; Abadir et al., 2007). In addition, a simple AR(1) model is also considered as an alternative to measure persistence as the autoregressive coefficient. Other more general AR(p) processes could be considered, with persistence than being defined as the sum of the AR coefficients. However, given the relatively small sample size in our case, a simple AR(1) specification is adequate to describe the short-run dynamics of the series.

The fractional integration framework can be extended to the multivariate case by estimating a fractional cointegration model. Specifically, we follow the approach developed in Gil-Alana (2003), which is a natural generalization of Engle and Granger’s (1987) procedure allowing for fractional parameters. In particular, we estimate a linear regression of youth unemployment against its macroeconomic determinants and check the significance of the estimated coefficients as well as the order of integration of the residuals; if this is smaller than for the individual series, then cointegration holds and there exists a long-run equilibrium relationship between the variables that can be interpreted as the steady state in economic terms. In addition, a Hausman test for the null of no cointegration against the alternative of fractional cointegration, as suggested by Marinucci and Robinson (2001), is also carried out.

EMPIRICAL RESULTS

The data used include the total youth unemployment rate in 15 countries, Austria, Belgium, Denmark, Finland, France, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden and the United Kingdom. This variable is defined as the number of unemployed in the 15–24 years age group divided by the labor force for that group, obtained from the International Labor Organisation. For GDP, inflation, output and consumer prices, data from the World Development Indicators are used. All series are annual and span the period from 1980 to 2005.

As a preliminary step we estimate a simple AR(1) process to measure the persistence of the series as its AR(1) coefficient. The results for the three series are displayed in Table 1.

Table 1 Estimated AR coefficients for each series in each country
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It can be seen that the autoregressive coefficients are much higher for youth unemployment and inflation compared with GDP. In the case of youth unemployment, the highest values are found for the peripheral (Northern and Southern) countries: Ireland (0.94), Finland (0.92), the Netherlands (0.89), Spain (0.89), Norway (0.88), Sweden (0.88), Italy (0.87) and Greece (0.86). This high level of persistence is consistent with the empirical evidence on total unemployment in most European countries, suggesting the relevance of hysteresis models in the European case (see, eg, Gordon, 1989; Graafland, 1991; Lopez et al., 1996).

Next, we estimate the fractional differencing parameter d and the corresponding 95% intervals for each of the three series, youth unemployment, inflation and GDP, in each country using the parametric approach based on the Whittle function in the frequency domain. In all cases, an intercept is included in the model and the d-differenced process is assumed to be a white noise process. We report in bold in Table 2 the cases where the unit root null hypothesis, d=1, cannot be rejected.

Table 2 Estimates of d and 95% confidence intervals for the individual series
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This happens in five countries, the United Kingdom, Italy, Norway, Sweden and Ireland, for all three series. In the case of youth unemployment, rejections of the null hypothesis in favor of higher degrees of integration only occur for Finland, the Netherlands, Portugal and Spain, the latter two countries having some of the highest youth unemployment rates in the sample. For inflation, the unit root null cannot be rejected in any case. For GDP, this hypothesis is rejected in favor of explosive behavior (d>1) in Finland, the Netherlands, Portugal and Spain, evidence of mean-reversion (d<1) is found for Austria, Belgium, Denmark, France, Greece and Luxembourg.

Table 3 focuses on the semiparametric results using three different bandwidth parameters. For each series there is at least one case when the unit root null hypothesis cannot be rejected. Given the evidence of non-stationarity, the estimation was carried out using first differences, then adding 1 to the estimated values to obtain the integration orders. Overall, this evidence suggests non-stationarity and the presence of a unit root in all three series in all countries examined.

Table 3 Estimates of d based on a local Whittle semiparametric method
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The step is the estimation of a multivariate cointegration model. We started by including the same set of variables as in previous studies by Jacobsen (1999), Blanchflower and Freeman (2000), Choudhry et al. (2012). In particular, there is a large literature emphasizing the impact of output and its growth on unemployment, the so-called Okun’s law (see, eg, Lee, 2000; Solow, 2000). Moreover, it appears that youth unemployment is even more sensitive to macroeconomic and labor market conditions than is total unemployment (see Choudhry et al., 2013). However, since regressors such as FDI and openness were found not to be significant, the results reported below are those obtained from a model including GDP and inflation only as the macroeconomic determinants of youth unemployment, namely

where y t stands for the youth unemployment rate, x1t for inflation and x2t for GDP. The error term u t is assumed to be a white noise or have an autocorrelated structure in Tables 4 and 5, respectively.

Table 4 Parameter estimates in the cointegrating relationship with uncorrelated errors
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Table 5 Parameter estimates in the cointegrating relationship with autocorrelated errors
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Table 4 shows that for six countries, Italy, Belgium, Denmark, France, Greece and Luxembourg, the estimated value of d is smaller than 1; however, in all these cases the confidence intervals are so wide that the unit root null hypothesis cannot be rejected. In fact, the only rejections of the unit root null occur in the cases of Finland, the Netherlands, Portugal and Spain, but always in favor of higher orders of integration.Footnote 1 Therefore, there is no evidence of cointegration of any degree under the assumption of uncorrelated errors. As for the estimated coefficients, they are all negative and more significant for inflation than GDP.

Next, we analyze the case with autocorrelated disturbances. Specifically, we consider a simple AR(1) process, the reason being that, given the small number of observations, higher orders would lead to overparameterized models. In this case all the estimated values of d are below 1 and close to 0 in many cases, implying mean-reversion and therefore cointegration. The low fractional differencing parameter is now combined with a very large AR coefficient, implying that the errors are still very persistent. Only for Finland is d significantly above 0. As for the estimated coefficients, the inflation coefficient is significant and negative in all countries except Spain, while the GDP coefficient is significant in half of the cases. Given the differences in the results depending on the specification of the error term, we also estimated d in equation (2) using a log-periodogram semiparametric estimator. These additional results, not reported, suggest that the differencing parameter is very sensitive to the bandwidth parameter, although most cases lie in the interval between 0.5 and 1, implying fractional integration, non-stationarity and mean-reverting behavior.

Finally, we perform the Hausman test proposed by Marinucci and Robinson (2001). This is specified as follows:

where i=x, y and z stand for each of the series under examination, youth unemployment, inflation and GDP, in turn, s is the bandwidth parameter (we set s=(T)0.5), are the univariate estimates of the parent series and is a restricted estimate obtained in the multivariate representation under the assumption that d x =d y =d z . The results using this approach are displayed in Table 6.

Table 6 Testing the null of no cointegration with the Hausman test of Marinucci and Robinson (2001)
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The test statistics indicate the presence of fractional cointegration in seven out of the fifteen countries examined, with statistical significance for youth unemployment and inflation in the majority of cases. It is also noteworthy that the estimated order of integration in the cointegrating regression is in the interval (0.5, 1) in all cases, implying non-stationary mean-reverting behavior. The highest degree of cointegration is found in the case of Italy and Portugal, where the estimated d is equal to 0.576 and 0.577, respectively, followed by the United Kingdom (0.634), Luxembourg (0.646), the Netherlands (0.746), Ireland (0.771) and Sweden (0.810). For the remaining countries, this approach provides no evidence of cointegration.

CONCLUSIONS

Both academics and policymakers have recently focused on the challenge represented by European youth unemployment, which has become even higher relative to adult unemployment following the recent financial crisis and appears to be very persistent. This paper has investigated its stochastic properties as well as its macroeconomic determinants by using annual data on total youth unemployment in 15 countries and estimating autoregressive and long memory (fractionally integrated) models as well as fractional cointegration ones. The evidence confirms that youth unemployment is highly persistent in all European countries examined, which suggests the relevance of hysteresis models (Blanchard and Summers, 1986; Gordon, 1988) in a European context and the need for active labor market policies aimed at preventing short-term unemployment from becoming structural or long term. These could include better school-to-work transition institutions as well as educational, placement and training schemes (see Choudhry et al., 2012).

As for the macroeconomic factors driving European youth unemployment, the fractional cointegration results are rather sensitive to the method applied. Specifically, when following the approach of Gil-Alana (2003), the findings are different depending on the underlying assumptions about the error term: if the errors are assumed to be uncorrelated, no evidence of cointegration is found in any case; by contrast, under the assumption of autocorrelated errors, cointegration appears to hold in all cases. When using the semiparametric method of Marinucci and Robinson (2001) some evidence of (fractional) cointegration is obtained in some cases with its estimated order in the interval (0.5, 1). A plausible explanation for the sensitivity of the results to the method employed is the relatively small size of the sample used.

Nevertheless, the analysis provides some useful evidence on the existence of long-run relationships between youth unemployment in Europe and two key macroeconomic determinants, GDP and inflation. It confirms in particular the importance of the linkage between output and unemployment and the sensitivity of youth unemployment to overall macroeconomic conditions (see Choudhry et al., 2013). Of course, a key role is also played by macroeconomic and labor market policies and institutions, as, for instance, stressed by the OECD (2006), but recommending the specific actions required to address the so-called ‘Euro-sclerosis’ or poor employment performance of most European countries is an issue beyond the scope of the present study, whose aim is simply to offer some evidence on the persistence of youth unemployment in Europe and its relationship to output and inflation.