Abstract
This paper studies regional income convergence and its conditioning factors across 81 provinces of Turkey over the 2007–2019 period. Through the lens of a nonlinear dynamic factor model, we first test the hypothesis that all provinces would eventually converge to a common longrun equilibrium. We reject this hypothesis and find that the provincial dynamics of income per capita are characterized by 6 convergence clubs. Next, we evaluate the conditioning factors behind club formation. Our results suggest that spatial dependence across provinces plays an essential role in the formation of convergence clubs. The spatial distribution of the convergence clubs has a clear spatial pattern, and the dynamics of the provincial income distribution are spatially integrated. We also find that geographical neighbors are more important for middle and highincome provinces. Finally, we show that the performance of geographical neighbors affects the probability of club membership through spillovers in capital accumulation and structural change.
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Notes
The club convergence methodology has been used in different concepts beyond per capita income, such as convergence in carbon dioxide emissions (Panopoulou and Pantelidis 2009), ecological footprint (Apaydin et al. 2021), labor productivity (Mendez 2020), happiness (Apergis and Georgellis 2015), house prices (Churchill et al. 2018), patents (Barrios et al. 2019a), institutional quality (Glawe and Wagner 2021), etc.
Appendix 3 presents the equations for measuring global and local spatial dependence.
More specifically, we estimate a SLX spatial model. See Elhorst (2014) for further details.
Specifically, Phillips and Sul (2009, p. 1171) argue that the third step of their clustering algorithm is highly conservative when setting the sieve criterion to zero for short time series. However, one negative consequence of this setting is that it increases the probability of finding more convergent clubs than the actual true number. Thus, they recommend implementing a sequential club merging procedure as the fifth step of their clustering algorithm. From a computational implementation standpoint, Du (2017) and Schnurbus et al. (2017) have supported this argument and included this fifth step in their Stata and R routines, respectively.
As explain by Gunawan et al. (2021), having large clubs is methodologically desirable for the next stage of the analysis in which the conditioning factors of club membership will be evaluated.
This matrix indicates that the neighbors of a region are those who share a common border or vertex.
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Appendices
Appendix
1. Clustering algorithm for club identification

1.
Crosssectional ordering: Sort the economies in decreasing order based on their last observation.

2.
Core group formation: Select the first k highest economies in the panel to form the subgroup \(G_{k}\) for some \(2 \le k<N\) and apply the logt regression to obtain the convergence test statistic \(t_{k}=t\left( G_{k}\right)\) for this subgroup. Then, choose the core group size \(k^{*}\) by maximizing \(t_{k}\) over k according to the criterion \(k^{*}={\text {argmax}}_{\mathrm {k}}\left\{ t_{k}\right\}\) subject to min \(\left. \left\{ t_{k}\right\} \right\rangle 1.65\). \(t_{k}\) indicates the oneside tstatistic that is needed to evaluate the statistical significance of the convergence test. If \(t_{k}>1.65\) is not valid for \(k=2\), then the highest economy is dropped from the core group and the algorithm can be repeated again for the rest of the sample.

3.
Sieving economies for club membership: The remaining economies are added to the core group \(G_{k}\) one by one and the logt test is executed again Eq. (5). When the economy is added, a new group is formed if the tstatistic is greater than − 1,65.

4.
Recursion and stopping: Form the new group consisting of all economies that could not be selected in Step 3, and apply logt test for this subgroup. If \(t_{k}>1.65\), it indicates that two convergence subgroups exist. Otherwise, if the null hypothesis of convergence is rejected, Step 1 to 3 are repeated. If no core group is found, then the remaining economies are labeled as divergent and the algorithm stops.

5.
Club merging: Run the logt test for all pairs of initial clubs. The merging procedure is iterative. That is, the logt test is applied for the initial clubs 1 and 2, and if they fulfill the convergence test jointly, they should be merged into a new. Repeat this merging procedure for the remaining clubs until the convergence test is rejected.
2. List of convergence clubs
See Table 8
3 Measurement of global and local spatial dependence
3.1 Global spatial dependence
For any period t, the global Moran’s I statistic is defined as follows:
where N is the number of regions, \(w_{i j}\) is an element of a spatial weight matrix (W) that defines the neighborhood structure between each pair of regions, \(X_{i}\) and \(X_{j}\) indicate the income values of regions i and j, respectively; and \(\bar{X}\) is the average value of income.
3.2 Local spatial dependence
For any period t, the local Moran’s I statistic is defined for each region i as follows:
where the notation follows that of Eq. 7.
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Ursavaş, U., Mendez, C. Regional income convergence and conditioning factors in Turkey: revisiting the role of spatial dependence and neighbor effects. Ann Reg Sci (2022). https://doi.org/10.1007/s00168022011680
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DOI: https://doi.org/10.1007/s00168022011680
JEL Classification
 O47
 R10
 R11