Do Spanish regions converge? A time-series approach using fractional cointegration

Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=raec20 Applied Economics ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/raec20 Do Spanish regions converge? A time-series approach using fractional cointegration Mariam Kamal & Josu Arteche To cite this article: Mariam Kamal & Josu Arteche (02 Jan 2024): Do Spanish regions converge? A time-series approach using fractional cointegration, Applied Economics, DOI: 10.1080/00036846.2023.2293089 To link to this article: https://doi.org/10.1080/00036846.2023.2293089 © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. View supplementary material Published online: 02 Jan 2024. Submit your article to this journal View related articles View Crossmark data Do Spanish regions converge? A time-series approach using fractional cointegration Mariam Kamal and Josu Arteche Department of Quantitative Methods, University of the Basque Country, Bilbao, Spain ABSTRACT This article investigates economic convergence in terms of real income per capita between the autonomous regions of Spain over the period 1955–2020. In order to converge, the series should be cointegrated. This necessary condition is checked using two testing strategies recently proposed for fractional cointegration, finding no evidence of cointegration, which rules out the possibility of convergence between all or some of the Spanish regions. As an additional contribution, an extension of the critical values of Nielsen’s (2010) test of fractional cointegration is provided for a different number of variables and sample sizes from those originally provided by the author, fitting those considered in this article. KEYWORDS Fractional integration; fractional cointegration; long memory; persistence JEL CLASSIFICATION C12; C22; C32 I. Introduction Economic convergence has been one of the main focal points of the empirical literature on economic growth. It implies that income gaps between countries/regions tend to disappear, hence involving convergence to a single steady state (equilibrium). The European economy has become more integrated in recent decades, with the states following a converging path due to economic, political, and institutional factors, such as, for example, the exchange rate mechanism in 1979, and the introduction of the euro in 2001. Numerous empirical studies have provided evidence of this integration in the European Union (Beckfield 2006; Caporaso and Pelowski 1971; Martin and Ross 2004). However, this integration among states can come together with economic disparities between the different regions, which may cause non-convergence within a country. This article analyses this possibility in Spain. Several countries have typically employed regional policies to address structural disparities among their geographical areas. Spain, for example, began implementing regional policies in the early 1960s. However, since 1986, Spanish regional policies have undergone significant changes due to its inclusion in the European Union (EU), which has been particularly important in providing regional governments with opportunities to engage in European networks, facilitating the exchange of interests, knowledge, and values. As argued by Arregui (2020), Spain is likely to be one of the members where some state restructuring has taken place, both at national and regional level. This transformation has been influenced by both European integration and the decentralization of political power. These two processes have mutually reinforced each other, and Spain’s EU membership has solidified the role of Spanish Autonomous Communities in shaping and implementing policies in crucial areas such as environment, agriculture, or fishing policies (Arregui 2020). Spanish regions are divided into 17 Autonomous Communities. Some of these regions are richer than others due to their economic or sector specialization and disaggregation according to branches of activity. The income of each Autonomous Community depends on the economic specialization of that region, with some specializations generating low incomes, while others generate significantly higher incomes. Table 1 shows the high-sector heterogeneity presented by the different Spanish regional economies. These regions span from those experiencing substantial growth driven by tourism-related CONTACT Mariam Kamal [email protected] Department of Quantitative Methods at the University of the Basque Country, Bilbao 48015, Spain Supplemental data for this article can be accessed online at https://doi.org/10.1080/00036846.2023.2293089 APPLIED ECONOMICS https://doi.org/10.1080/00036846.2023.2293089 © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-ncnd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. activities (e.g. Balearic Islands, Canary Islands) to those where economic activity is still largely dependent on primary sectors (e.g. Galicia, La Rioja, Murcia, Andalucía). This heterogeneity in the regional economic structures and sources of income generates regional disparities that may prevent convergence, as each region’s growth may be driven by different factors and industries. The different ways of generating income among different regions have produced the current regional differences in productivity and income. Hence, it might be unsurprising to find disparities between the 17 Autonomous Communities. This prompts us to question whether economic convergence among the 17 Autonomous Communities could not occur, which is a question that drives the current research. In addition, we also aim to determine whether some converging subgroups can be identified, for example, among developed or less developed regions, which may be used to define more efficient regional policies delimiting their geographical impact. As a first example of this heterogeneity across the Spanish regions, Figure 1 shows the evolution of the cross-sectional standard deviations for all the logs of per capita income in the 17 Autonomous Communities in Spain from 1955 to 2020. The dispersion begins in 1955 at around 0.91 and rises and declines over time ending at around 0.94 in 2020, confirming the absence of sigma convergence. The large dispersion shown in the graph confirms our previous suspicion of possible heterogeneity and non-convergence. Note that the dispersions in the decade of 1970 and 2010 are the highest. However, the heterogeneity in Spain remains in the sample before and after these peaks, which may hinder regional convergence. In the literature on economic growth, there are three main definitions of convergence: (i) beta convergence, (ii) sigma convergence and (iii) stochastic convergence based on time-series analysis. As the first two have several statistical problems (see Durlauf 2000; Friedman 1992; Quah 1993), we will focus on the time-series approach on cointegration, as suggested by Bernard and Durlauf (1995). The use of different techniques has usually led to different conclusions about the existence of convergence (see, for example, Durlauf 2000). We follow a time-series approach to test for output Table 1. Characteristics and productive structures of the Spanish regions. Andalucia Agri-food sector Transport and logistics sector Extremadura Agri-food sector. Livestock farming Food Industry Aragón Automotive industry Transport and logistics sector Galicia Textile and automotive sector Agri-food sector Asturias Metal and mining sector Madrid Biomedical and pharmaceutical companies Information and Communication Technology sector (ICT) Logistics and transportation Aerospace industry Balearic Islands Tourism sector Food and catering industry Fashion industry Murcia Agricultural sector Plastic sector Canary Islands Tourism Sector Cultural industries Logistics sector Navarre Automotive sector Biomedical cluster ICT sector Cantabria Agri-food sector Automotive components Biotechnology and health Basque Country Energy sector Automotive and aeronautic sector Maritime industry ICT sector Bio-health sector Service sector Catalonia Biotechnology Petrochemical sector Automotive sector Agricultural sector La Rioja Agri-food sector Footwear sector Automotive sector Service sector Castilla-La Mancha Agri-food sector Wine production Valencia Automotive and capital goods sector Agri-food sector ICT and services sector Chemical and pharmaceutical sector Plastic sector Castilla-León Agri-food sector Chemical-Pharmaceutical sector 2M. KAMAL AND J. ARTECHE convergence, paying particular attention to the analysis of cointegration, which provides a natural setting for testing relations between variables (see Bernard and Durlauf 1995, 1996; Durlauf 2000; Evans 1996; Quah 1993). According to the time-series approach of Bernard and Durlauf, 1995, 1996), two series converge if the following conditions are satisfied: (i) The variables are cointegrated, (ii) the cointegrating vector is (1, −1), and (iii) the difference between the series is a stochastic variable with zero mean. Based on these conditions, the notion of convergence can be divided into strong and weak convergence (defined as catching-up in the convergence literature). If conditions (i) and (ii) are fulfilled, the series are cointegrated with cointegrating vector ½1;1], but the difference between them is a stochastic variable with a mean different from zero, which suggests that the deviation between the series is expected to decrease, but not to disappear. This is weak convergence, i.e. catching up, which refers to the situation in which narrowing of the differences between the variables is observed over time, but the convergence process has yet to be complete. If all conditions (i), (ii), and (iii) are fulfilled there is strong convergence because the difference between the variables vanishes. Therefore, if there is no cointegration, convergence does not occur, neither weak nor strong. The rest of the article is organized as follows. Section II provides a literature review on convergence in Spain. Section III explains the methodologies used in our analysis. Section IV contains the data and presents the results, and finally, Section 5 presents the conclusions. II. Literature review There are few studies that specifically examine output convergence between Spanish regions. The majority of them use cross-regional analysis approaches to estimate beta convergence. Meanwhile, those using a time-series approach opt for unit root test as the Augmented Dickey Fuller test in a non-fractionally integrated context, which lacks the power and flexibility needed for a comprehensive analysis. Some authors have found results indicating non-convergence in the Spanish regions in agreement with our results. Martínez-Argüelles and Rubiera-Morollón (1998), focusing solely on the service sector, identify distinct regional growth patterns within this sector using integer cointegration techniques. Cuadrado-Roura et al. (1999) investigate the evolution of regional differences in Spain and use an analysis of beta and sigma convergence to conclude that the primary source of convergence in observed productivity is the alignment of regional sectorial structures. Lamo (2000) examines output convergence across Spanish regions using cross-sectional distribution dynamics. She finds no evidence of income convergence. Maza (2006) examines the phenomenon of regional convergence in per capita income in Spain and studies what factors influence migration patterns within these regions. Using a beta convergence analysis, he Figure 1. Cross sectional standard deviation of the log of per capita income. APPLIED ECONOMICS 3 concludes that there is no convergence among Spanish regions because migrants tend to move towards regions with higher per capita income, inducing a slower pace of regional convergence in Spain. Arroyo et al. (2013) examine the pairwise convergence hypothesis among the 17 Spanish regions using the Augmented Dickey and Fuller (1979) test for unit roots. The findings reveal incomplete catching-up in many instances, with only four converging regions (Andalucia, Extremadura, Castilla-La Mancha, and Galicia) and just one (Baleares) converging with the European Union. Puente (2017) uses traditional growth regressions to analyse the existence of beta-convergence. The results indicate that labour productivity convergence stands out as the primary driver in narrowing regional income disparities. On the contrary, labour market variables such as employment and unemployment, as well as total factor productivity, do not have a substantial impact on diminishing regional disparities during the period under analysis. Other studies have focused on the convergence among provinces rather than Autonomous Communities. Dolado et al. (1994) examine the growth and disparities across Spanish provinces. They use traditional cross-regional analysis to estimate beta convergence, and find evidence of provincial convergence, although with some signs of instability in the speed of convergence during specific subperiods. Gardeazábal (1996) analyses the dynamic evolution of income distribution among Spanish provinces. Using Markov processes, he concludes that per capita incomes among Spanish provinces converge towards equilibrium. Villaverde (2005) examines the existence of beta convergence in labour productivity in the provinces of Spain. He concludes that Spanish provinces with low (high) relative productivity tend to be geographically close to each other, indicating a concentration of productivity. The convergence process does occur, but at a slightly slower pace than in the classical model, and there is a gap that separates the provinces from their steady state. Hierro and Maza (2010) investigate the role played by internal migration of foreign individuals in the income convergence of provinces in Spain between 1996 and 2005. Their results refute the hypothesis that internal migration of the foreign-born influences income convergence. Montañés et al. (2018) investigate convergence between Spanish provinces, with a particular focus on the impact of the recent international crisis. Their results indicate the formation of several convergence clubs, the patterns of which were altered by the 2007 crisis. Tapia and Galarraga (2020) investigate the empirical connection between economic growth and inequality, quantifying the disparities between Spanish provinces for various reference years spanning from 1860 to 1930 and concluding that the growth of income did not directly lead to a reduction in inequality. This article analyses convergence in annual real output per capita of the 17 Autonomous Communities in Spain from 1955 to 2020. We contribute to the existing empirical literature in three main dimensions: ●We test cointegration in an economic framework of convergence that follows the Bernard and Durlauf (1995, 1996) definition of time-series convergence. ●We use semiparametric and nonparametric techniques, which have never been used before to analyse regional convergence, to test for fractional cointegration: the strategies proposed by Robinson (2008), Hualde (2012) and Nielsen (2010). These fractional integration and cointegration techniques are used to avoid the low power of traditional unit root and cointegration tests against fractional alternatives and are more reliable to explore economic convergence. ●We complement Nielsen (2010) test with a new set of critical values of independent interest for practitioners. In particular, we provide critical values for up to 17 variables and three different sample sizes T = 66, T = 150 and T = 1000 for two different values of the memory parameter of the original series: d = 1 and d = 1.4. The latter corresponds to the values found in the series analysed here, while the former (in the supplementary material) corresponds to the traditional unit root case. 4M. KAMAL AND J. ARTECHE III. Methodology The methodology used in this article is based on the concepts of fractional integration and fractional cointegration. Fractional integration and cointegration The idea of fractional integration was introduced by Granger and Joyeux (1980), Granger (1980, 1981) and Hosking (1981) allowing a continuous transition from non-unit to unit root behaviours, offering a more flexible context for the modelling of long-run persistence. A time-series {yt;t¼1;2;3;. . .gis (fractionally) integrated of order d, I dð Þ, if it satisfies: 1Lð Þdyt¼ut;t¼0;�1;. . . ;(1) where d is the memory parameter and uteI0ð Þ, meaning that uthas a finite variance and a spectral density function f wð Þ, satisfying 0<f wð Þ<1. Ifd¼0;yt¼ut and yt is short memory; if 0<d<1 2, yt is said to be long memory. Finally, if 1 2<d<0;ytpresents anti-persistence. Also, if d<0:5;yt is covariance stationary. However, a value d�0:5 implies non-stationarity, but if d<1;the series is mean reverting. In addition, if d¼1, the series has a unit root. If d<1 the effects of the shocks disappear in the long-run and if d�1 the shocks persist indefinitely. Note that ut in (1) may include some type of weak dependence in the form of, for example, a stationary and invertible autoregressive moving average (ARMA) process: Φ Lð Þut¼θ Lð Þεt;t¼0;�1;...;(2) where εt is an independent and identically distributed (iid) sequence. In this case;yt in (1) is an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) process: Φ Lð Þ 1Lð Þdyt¼θ Lð Þεt;t¼0;�1;(3) Engle and Granger (1987) defined cointegration as follows: “A vector yt is said to be co-integrated of order d, b, denoted yt~ CI d;bð Þ, if the components of yt are I dð Þand there exists a vector α �0ð Þsuch that zt¼α0yt~ I d bð Þ;b>0:The vector α is called the co-integrating vector and b denotes the degree of cointegration’’. The original testing strategies proposed for cointegration were only suitable for bivariate settings, and they thus could only identify one cointegration vector. Johansen (1988, 1991, 1995) developed a maximum likelihood approach for testing cointegration in a multivariate setting, allowing for several relations and determining the rank of cointegration. Following these pioneering authors, other standard techniques were developed by Phillips and Ouliaris (1990), Harris (1997), Bierens (1997), and Breitung (2002), among others. The generalization of the traditional Johansen test to a fractional context was proposed by Johansen (2008) and Johansen and Nielsen (2010, 2012, 2014) with the fractionally cointegrated vector autoregressive (FCVAR) model. Standard traditional cointegration is just one particular case of fractional cointegration where the memory parameters d and the degree of cointegration b are restricted to be integer values. Fractional values of d and b allow more flexibility and are good alternatives because many economic series are known to exhibit non-stationary behaviours that may not be exactly I(1), and there is also no need to assume that the equilibrium relation is exactly I(0). Testing for fractional cointegration The strategy we follow is based on the estimation of the cointegration rank in a fractional setting using two different and flexible techniques with good asymptotic properties under mild conditions. First, the methodology proposed by Nielsen (2010) has the following advantages over other cointegration tests: (i) The test statistic is computed without prior knowledge of the order of integration of the series. (ii) Since the test is nonparametric, it does not require specification of a particular model and is invariant to short-run dynamics. This is important because mis-specified short-run dynamics may lead to inconsistent estimation and hence to erroneous inference regarding the cointegration rank in other parametric techniques. (iii) The proposed test has good power for large and small samples. APPLIED ECONOMICS 5 Second, the methodology offered by Hualde (2012), together with the testing strategy used by Robinson (2008), is characterized by the following benefits: (i) The testing strategies in Robinson (2008) do not require estimation of any cointegrating relations or prior selection of any tuning numbers beyond one bandwidth parameter. (ii) Hualde (2012) proposes a procedure to estimate the rank of cointegration in multivariate fractional series, and therefore this can be implemented together with the procedure in Robinson (2008) to infer the dimension of the possible cointegrating subspaces. (iii) The combination of both techniques allows for precise detection of the common trends. Robinson (2008) and Hualde’s (2012) approaches We first consider the test proposed by Robinson (2008) combined with the strategy in Hualde (2012). Hualde’s procedure has the advantage over other fractional cointegration approaches of providing an automatic method for inferring cointegrating relationships without any prior information about the variables. He defines the possibility of cointegration as a situation in which a linear combination of fractional processes is integrated of a strictly smaller order than the maximum order of the elements of the linear combination. For example, if one of the variables has an integration order that is strictly greater than the rest of the variables, then any linear combination with zero weight on this particular variable is considered to be a trivial cointegrating relation. Under this definition, the variables can have different integration orders. However, when all the variables have the same integration order, this definition coincides with that originally provided by Engle and Granger (1987). The proposal by Hualde (2012) is based on an estimator of the cointegrating rank, r, obtained by applying sequentially the procedure discussed in his Theorem 1, which we rewrite here: Theorem 1 (Hualde 2012). yt has cointegrating rank r 21;...;p1f g where p is the number of variables in the vector yt, if (i) and (ii) are satisfied, where: (i) There exists a p rð Þ dimensional subvector of yt, denoted as ybð Þt, whose individual components are common trends, denoted as CT. (ii) All subvectors of yt of dimension larger than pr containing y bð Þt cointegrate. The procedure to estimate the rank of cointegration r is based on the following steps. First, the estimates of the integration orders (memory parameters), ^ di;i¼1;...;p are obtained to define the CT as the series with the highest order of integration. Then, the following hypothesis is tested: Hj1;...;jk ð Þ :yj1t;yj2t;...;yjktare not cointegrated � �; against � Hj1;...;jk ð Þ :Hj1;...;jk ð Þ is not true; where j1. . . ;jk21;. . . ;pf g;k�p;is sequentially tested. In order to estimate the memory parameters, the univariate local Whittle estimator ^ di, proposed by Robinson (1995a) is used. Next, the hypotheses are tested using the statistic X* proposed by Robinson (2008), defined as: X�¼ms�ð~ dÞ2=p2tr ^ R�A^ R�A � �p n o (4) where m is the bandwidth s�~ d ��¼tr ^ G�~ d ��1^ H�~ d �� � � ^ G�dð Þ ¼ 1 mX m j¼1 Iyλj  �λ2d j ^ H�dð Þ ¼ 1 mX m j¼1 vjIyλj  �λ2d j vj¼log j1 mX m i¼1 log i ^ R�¼^ D1=2^ G�~ d ��^ D1=2 ^ D¼diag ^ g11;...;^ gpp n o, where ^ gii is the ith diagonal element of ^ G�~ d �� A¼diag a1;...;ap � � 6M. KAMAL AND J. ARTECHE where Iyλj  �is the periodogram matrix of y al frequency λj, ~ d¼P p i¼1 ai^ di and the ai are arbitrarily chosen weights satisfying that P p i¼1 ai¼1:For instance, Robinson (2008) takes ai;1=p, so the arithmetic mean of the ^ di is used. Another option is using aj¼1;ai¼0;i�j some j. In our case, we use the first option as recommended by Robinson (2008). Under the null hypothesis of non-cointegration and stationarity of the series, which implies that all the memory parameters are smaller than 0.5, X�! dX2 1as T! 1:(5) The methodology to estimate the cointegration rank r is characterized by the following steps: Step 1. Estimate the individual integration orders, di, by ^ di;i¼1;...;p. Then choose a possible CT yc1t as the variable with the highest estimated order, such that c121;. . . ;pf g. Next, reorder the variables in yt so that ypt ¼yc1t in the new ordering. Finally, given the possible CT i.e. ypt, we test the following hypotheses: H1ð Þ :[ p1 i¼1Hp;iversus � H1ð Þ :\ p1 i¼1 � Hp;i Note that H 1ð Þ means non-cointegration in pairs of each variable with the CT, and � H(1) means that H 1ð Þ is not true. The process ends if H1ð Þis rejected, and so it is concluded that ^ r¼p1. Otherwise, it is not rejected, and the process continues to Step 2. Consequently, following Theorem 1, the hypotheses are equivalent to r<p1 and r¼p1 respectively. Step 2. If H1ð Þ is not rejected, choose a second possible CT as the variable with the smallest statistic X* i.e. yc2t;c221;. . . ;p1f g. There will be two possible CTs altogether. These CTs are denoted as yptand yc2t respectively. Then, we reorder again the variables so that ypt ¼yc1t and yp1;t¼yc2t in the new ordering. Finally, given the possible CTs, i.e. ypt;yp1;t, we test the following hypotheses: H2ð Þ :[ p2 i¼1Hp;p1;iversus � H2ð Þ :\ p2 i¼1 � Hp;p1;i. Note that H 2ð Þ means non-cointegration for any set of three variables containing the CTs ypt;yp1;t, and � Hð2) means that H 2ð Þis not true. Then, the hypotheses are equivalent to r<p2 and r¼p2 respectively and the process ends if H 2ð Þis rejected. Step k (for k ¼2;. . . ;p1). If H k 1ð Þ is not rejected, chooseck. Sort the variables so that ypt ¼yc1t;...;ypkþ2;t¼yck1;t and choose the possible CTs, as previously. Finally, test the following hypothesis: H(k): ∪ p-k i-1 H p,p-1,. . .,p-k+1,i versus — H(k): ∩ p-k i-1 — H p, p-1,. . .,p-k,i and if there is cointegration, the estimation will be ^ r¼pk. However, if we reach the last step k¼p1 this means that ^ r¼0 and H ið Þ;i¼1;2;3;...;p1;are not rejected: The testing procedure based on the statistic X* has low power with small sample sizes, which can significantly influence the results obtained when analysing the possibility of cointegration in the Spanish regions. To complement the results obtained we also consider the test proposed by Nielsen (2010), which has higher power for small samples (see Nielsen’s Monte Carlo). Nielsen’s (2010) approach and critical values extension The test statistic is defined as follows: Λp;rd1 ð Þ ¼ T2d1Xpr j¼1#j;r¼0;. . . ;p1 (6) where #j;j¼1;...;p;are the eigenvalues of #BTAT j j ¼ 0, for AT¼P T t¼1 ZtZt0;BT¼P T t¼1 ~ Zt~ Zt0, BT¼PT t¼1~ Zt~ Z0 t, ~ Zt¼Δd1 1Zt with d1>0;t¼1;2;...;T;and Zt is the p-vector of time series under analysis (perhaps after extracting deterministic terms), which is fractionally integrated of order d, where d is a vector containing the individual orders of integration of the elements in Zt;which possibly differ from each other. Note that (6) defines a family of tests indexed by the fractional integration parameter, d1. Nielsen (2010) argues in favour of using d1 = 0.1 based on an asymptotic local power analysis and on simulations. For this reason, we use this value in the empirical application. Large values of Λp;r0d1 ð Þ are associated with the rejection of the null hypothesis H0:r¼r0 versusH1:r>r0: APPLIED ECONOMICS 7 Nielsen’s procedure has the advantage of not requiring knowledge of the fractional integration and cointegration orders d and b as long as the series are non-stationary, implying memory parameters greater than 0.5. However, its asymptotic distribution is non-standard, but Nielsen (2010) simulated critical values for p < 8 variables with a sample size of 1000 observations to facilitate its application. We complement Nielsen’s (2010) tables by providing more critical values to cover up to 17 variables for all models and three different sample sizes. The observed time series Yt f gT t¼1considered by Nielsen (2010) are generated by Yt¼α0δtþZt;t¼1;2;. . . (7) where δt may contain deterministic terms. Three different cases are analysed: δt¼0 when there are no deterministic terms, δt¼1 when there is a nonzero mean, and δt¼1;t½ �0when there is a deterministic trend. The critical values in Nielsen (2010) are here extended for these three cases up to 17 variables, sample sizes T = 1000, 150 and 66, and two different values of the memory parameter of the original series d = 1 and d = 1.4, the latter corresponding to the values found in the series here analysed. All tables are based on 100,000 replications. Tables 2, 3 and 4 show these new critical values for a memory parameter equal to d = 1.4. Tables 24, 25 and 26 in the Supplementary Material show the same set of critical values for d = 1, which are of independent interest for practitioners. IV. Empirical analysis Preliminary analysis of the variables The data analysed are the logarithms of the annual real GDP per capita (constant 2010 €) of the 17 Autonomous Communities in Spain (omitting the autonomous cities) in thousands of euros from 1955 to 2020 for a total of T = 66 observations. In order to apply the semiparametric cointegration analysis by Robinson (2008), the series are differenced to obtain growth rates that are stationary, whereas for the nonparametric cointegration analysis by Nielsen (2010), the series are raw series (non-stationary). The variables in logarithms are denoted by the name of the Autonomous Community, and the growth rates are denoted by the abbreviation of these Autonomous Communities (in parenthesis the notation of the growth rates): Andalucia (andal), Aragon (ara), Asturias (ast), Balearic Islands (bal), Canary Islands (can), Cantabria (cant), Catalonia (cat), CastillaLaMancha (clm), Castilla-Leon (cyl), Extremadura (ext), Galicia (gal), Madrid (mad), Murcia (mur), Navarre (nav), Basque Country (pv), Rioja (rio) and Valencia (val). All data were provided by FEDEA (Foundation for the Study of Applied Economics) and INE (Spanish National Statistics Institute). Figures 2 and 3 show these series. To shed more light on the persistence of the series, the Exact Local Whittle (ELW) estimator proposed by Shimotsu, et al., 2005, which is consistent and asymptotically normal for any value of d, was applied. The ELW estimates and their 95% confidence intervals are shown in Table 5. They confirm the non-stationarity of the series, which is a requirement for the applicability of Nielsen’s procedure. Note also that a value of d = 1.4 is not rejected for any of the series, falling within all the confidence intervals, which justifies the use of this value in the construction of the statistic for Nielsen’s test. The estimation of the memory parameter of the growth rates, required for the application of Robinson’s (2008) test is, however, obtained using the Local Whittle (LW) estimator of Robinson (Robinson 1995) as suggested in Robinson (2008), which is consistent for d < 1 and asymptotically normal for d < 0.75. All the LW estimates, shown in Table 6, are between 0.2 and 0.5, indicating that the growth rate series can be considered stationary (d<0:5Þ. Robinson (2008) and Hualde (2012) cointegration results In order to analyse the robustness of the results to the selection of the bandwidth, the entire analysis has been implemented using three different bandwidths, m = 18, m = 23 and m = 28. According to the results of the LW estimated memory parameters, the possible CT in Step 1 (variable with the largest estimated d) is Murcia (mur) for all 8M. KAMAL AND J. ARTECHE