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Sensitivity of the convergence clubs

3.3 Convergence

4.1.2 Sensitivity of the convergence clubs

The outcome of the convergence club algorithm depends on some parameters that we must choose. The threshold value c determines the number of countries added to the core groups, and the HAC estimator depends on the chosen kernel and bandwidth. Moreover, not using all available data but using an alternative starting and ending year can also lead to different results.

We use threshold value c=0 in the algorithm, which is the suggested value by Phillips &

Sul (2009). Using a lower value of c leads to more countries in each convergence club and fewer convergence clubs in total. However, the merging algorithm merges fewer convergence clubs, such that the results after the merging algorithm are still quite similar to the results when c=0. When

c is slightly below zero, we still have three convergence clubs with the same or almost the same countries in each club. When c is very low, but still high enough to not reject convergence in all converge clubs, only the rich and medium convergence clubs are left, with Moldova in the medium convergence club and Ukraine as a diverging country. When c gets larger than zero, more conver-gence clubs are initially be formed, but we always end up with three or four converconver-gence clubs after applying the merging algorithm. Ukraine is sometimes a member of the poorest convergence club and sometimes a diverging country. When c is very high, no additional countries are added to the core group, such that only countries with a similar log GDP per capita value in the last year are in the same convergence club. For all values of c, EU countries are more likely to end up in one of the richest converge clubs, and non-EU countries are more likely to end up in one of the poorest converge clubs.

We estimate the t-statistics using the HAC variance-covariance estimator. The kernel func-tion and the bandwidth characterize the HAC estimator. We use the Bartlett kernel funcfunc-tion in our calculations, following the research of Newey & West (1987). A different kernel function can lead to quite different results. For example, when we use a uniform kernel, Iceland belongs to the sec-ond instead of the first convergence club, and Slovak Republic belongs to the third instead of the second convergence club. All other countries still belong to the same convergence club, stated in Table 2. After performing the merging algorithm, these changes lead to 4 instead of 3 convergence clubs, as clubs 1 and 2, clubs 3 and 4, club 5, and club 6 form a convergence club. Although the convergence clubs are different, it is still the case that EU countries are more likely to belong to the richest convergence club than the second richest convergence club. The two poorest convergence clubs only contain non-EU countries. The bandwidth equals three in our calculations. Using dif-ferent bandwidths lead to slightly difdif-ferent t-statistics but not to difdif-ferent convergence clubs. Only when we use an extremely high or low bandwidth, the convergence club results change.

Den Haan & Levin (1998) propose a vector autoregressive (VAR) model to construct a pre-whitened HAC estimator. They show that their VARHAC estimator converges faster than the kernel-based estimator. We determine the order of VAR using the Akaike Information Criterion

(AIC). This method does not influence the estimated coefficients, but it reduces the standard errors compared to the kernel-based method. This makes the positive t-statistics more positive and the negative t-statistics more negative. Therefore, the countries we add to the core do not change when c=0, as negative t-statistics always stay negative, and positive t-statistics always stay positive. Also, the cores themselves do not change, as the number of countries with the highest t-statistic does not change, following step 2 of the 4-step algorithm of Phillips & Sul (2007). However, it can be the case that the t-statistic of the core is negative but larger than -1.65 if we use the kernel HAC estimator, but smaller than -1.65 if we use the VARHAC estimator, such that convergence is rejected then. This can potentially lead to slightly different convergence clubs and more diverging countries. However, the t-statistics of our cores are always positive, so the cores never change.

Therefore, the kernel HAC estimator and VARHAC pre-whitening estimator provide the same convergence clubs in our case.

Step 1 of the 4-step algorithm of Phillips & Sul (2007) only depends on the last year of the data. Therefore, it is interesting to see how the results change if we use an earlier ending year.

Moreover, the financial structure of countries can change heavily over time. For example, some countries were not a member of the EU in 1994 but joined the EU in a later year. Moreover, financial events like the dot-com bubble affected the GDP of countries (Arnold & Dagher, 2015).

Therefore, we also investigate the changes in the convergence clubs if we use a later starting year.

The corresponding convergence clubs and diverging countries can be found in Appendix A.9.

When we use an early ending year, Luxembourg is often a diverging country, as it is too rich to belong to one of the convergence clubs. When we use a late ending year, Ukraine is often a diverging country, as it is too poor to belong to one of the convergence clubs. Bosnia and Herze-govina, Moldova, and Sweden are diverging counties in only one or two cases. All other countries are never diverging.

The number of convergence clubs stays the same in almost all cases when we change the ending year. However, some countries move to a neighboring convergence club, but no countries move from a very rich to a very poor convergence club, or the other way around.

The number of convergence clubs increases when we use a later starting year. Most coun-tries, which are in one of the richest convergence clubs, stay in one of the richest convergence clubs, but that is not always the case for relatively poor countries. For example, with 1994 as start-ing year, Azerbaijan is always in the first convergence club. However, Azerbaijan is always in the fourth convergence club when we use 2000 as starting year. We observe similar patterns, for ex-ample, for Belarus, Croatia, and Lithuania. In this way, the log GDP per capita values of countries inside a particular convergence club are closer to each other when we use a later starting year.

A possible explanation is that a large part of the growth of poor but quickly improving countries occurs in the first years of the data, which we no longer consider. It is questionable whether these strong improvements continue in the future, such that relatively poor countries as Azerbaijan should belong to the richest convergence club. Therefore, the convergence clubs with a later starting year seem more realistic.

However, not too many years should be removed from the dataset, as the Monte Carlo anal-ysis of Phillips & Sul (2007) shows that the algorithm works best with as many years as possible included. They assume that the t-statistics of the log t test are standard normally distributed, which is only true for the limiting distribution. However, their Monte Carlo simulations show that the results are already quite accurate for T=20. Therefore, we base our further analysis on the years 1999-2018, such that T=20. We visualize the convergence clubs for these years in Figure 5.

In Figure 5, we see that five convergence clubs are present, with Ukraine as the only di-verging country. When we treat all Schengen countries as EU countries, the five convergence clubs consist of 4, 9, 16, 2, and 0 EU countries, and 0, 0, 1, 9, and 2 non-EU countries, respectively. The first three convergence clubs almost consist of only EU countries, and the last two convergence clubs almost consist of only non-EU countries. Turkey is the only non-EU country in convergence club 3, and Bulgaria and Croatia are the only EU countries in convergence club 4. So we see that the EU and non-EU countries almost form separate convergence clubs when we use the algorithm for the years 1999-2018.

Figure 5: Convergence clubs for the years 1999-2018