Pares de convergencia estocástica regional en Colombia: 2000-2016.

Domingo Rodríguez Benavides, Owen Eli Ceballos Mina


Se evalúa la hipótesis de convergencia estocástica por pares usando el PIB per cápita de los departamentos colombianos en el periodo 2000-2020 y se aproxima al grado de convergencia regional conjunta. Una ventaja del enfoque usado es que considera los diferenciales en el PIB per cápita que se forman entre todas las regiones incluidas en el análisis y no sólo las que resultan con respecto a una economía líder o un promedio. Los resultados muestran que aunque existe el cierre de brechas del producto entre unas pocas regiones del país el grado de convergencia del conjunto nacional es bastante bajo.


The problem of whether per capita output gaps between different countries or regions tend to decrease or will do so in the future has played a central role in the empirical growth literature; the convergence concept has long been used in many contexts (Mendoza, German-Soto, Monfort, and Ordóñez, 2020; Moncayo, 2004). In developing countries, the pressing need to improve living standards places the analysis of growth differentials at the top of research programs. In Colombia, various techniques have been used to test the hypothesis of convergence in the living standards of its regions; for instance, -convergence, -convergence, among others, but some of these strategies, with their respective scopes and limitations, are more used than others (Galvis, Hahn, and Galvis, 2017; Leon, 2013). One of the most often employed approaches in the literature is -convergence, which considers the speed with which a country's or region's per capita output converges over time to its steady state. This approach assumes a deterministic growth process that may be inappropriate if technological progress linked to growth is stochastic (Pesaran, 2007; Binder and Pesaran, 1999). Based on Bernard and Durlauf (1995), Pesaran, Smith, Yamagata and Hvozdyck (2009) proposed a probabilistic or stochastic version of the concept of convergence in which the possibility of closing the gaps is completely independent of the initial income levels of economies, in contrast with the -convergence. Stochastic convergence between two economies is supposed to exist if their differential is a stationary process around a constant or a trend over time. In this definition, per capita output gaps are only a transitory phenomenon that tends to disappear in the future. Applying unit root or stationarity tests to the GDP per capita differential has been the common way to test this hypothesis. The presence of a unitary root is sufficient to reject the convergence hypothesis or that the differential does not contain a deterministic tendency shall be proof to the contrary. Panel unit root tests offer the possibility of testing convergence for several countries or regions at the same time but have the disadvantage that they require a leading economy or an average comparison, which is not in all cases the best reference (Le Pen and Sévi, 2010). Recent literature has proposed to test the notion of stochastic convergence under a strategy whose central idea is to consider all possible pairs of countries or regions and apply unit root tests or other stationarity tests on each differential of the product. One of the advantages of this new pairs-wise approach is that unlike cross-sectional testing and panel data models most commonly used in the literature, it is based on a definition related to the concept of convergence clubs such as those developed by Durlauf and Johnson (1995), Quah (1995, 1996, 1997) and Galor (1996), who recognize that economies can converge to different steady states and that they add great flexibility to the hypothesis contrast. Most studies on convergence in Colombia have focused on associating economic and social factors with changes in gaps and very few works on the subject in the country have used methodologies related to time series econometrics (Galvis et al., 2017). Convergence studies in the country have documented many methodological strategies to measure the behavior over time of regional gaps. The set of results on the hypothesis of regional convergence arguments in different directions with a slight inclination in the recent towards persistence of the gaps between Colombian departments. The few works that compare GDP per capita between pairs of regions in Colombia have used the average of the country or the capital city as the reference region. Their results describe a process of regional polarization and highlight Bogotá's position as the capital with a per capita income that doubles the national average and a position that has been consolidating over time compared to peripheral regions. The literature affirms that most of the regions have maintained the same relationship with respect to Bogotá for several years and that only some departments such as Meta and Santander improved their relative position, explained by the behavior of their wealth from oil and its refining. The literature on regional convergence in Colombia under the approach of time series has a space for analysis to explore. Instead of focusing the unit root tests exclusively on the differential of the GDP per capita of the regions with respect to a leading economy, this paper employs an alternative methodology that tests the stochastic convergence hypothesis for all possible pairs that are formed between all Colombian departments and those that result from excluding the main mining regions of the country. The paired stochastic convergence test is performed under the approach proposed by Pesaran (2007) and Pesaran et al. (2009) using the departmental gross domestic product (GDP) per capita at constant 2005 prices between 2000 and 2020. The panel data was constructed from the information provided by the Departmental Accounts of the Board of Synthesis and National Accounts of the National Administrative Department of Statistics (DANE) from Colombian Government. Unit root tests were applied on the gaps of all pairs of per capita income for the 32 departments and Bogotá D.C. in natural logarithms. The econometric analysis refers to the degree of national convergence by identifying the proportion of output gaps that converge among all possible pairs that are formed with the regions of analysis. The paper is divided in six sections. The first is the introduction. Section two provides a brief review of works that have addressed the issue of convergence in Colombia and its methodological strategies. Section three presents a descriptive exercise based on sigma-convergence calculations and the GDP per capita gap of the Colombian departments with respect to Bogotá D.C. as a benchmark economy. The fourth section on the methodology and problem of identification provides the definition of convergence and the econometric tests of the proposal of Pesaran. Data and empirical results are discussed in section five. The sixth and last section presents the conclusions. The calculation based on sigma-convergence and departmental GDP per capita gap with respect to Bogota in the period 2000-2010 provide evidence that there is a closing of regional gaps, but with low intensity. The convergence process is most strength in the first decade of the analysis period; it is a process guided by the variability of income of a few regional economies linked mostly with mining economies. Another side, most departments show little variability and a slow closing of the gap with respect to the leading economy. Econometric analysis supported by unit root tests show that considering all departments of the 528 possible pairs, there are between 14% and 36% of pairs of regions converging in mean or trend respectively, while using KPSS stationarity tests the proportion of convergence pairs on average increases to 62% of the set. Although the estimates are evidence of the closing of gaps between several regions of the country, the low proportion of pairs that close their output differentials against the whole refers to a low degree of convergence in the Colombian aggregate as suggested by sigma-convergence calculations and gap analysis with respect to the leading economy in descriptive analysis. The results were confirmed by unit root and stationarity tests, both for all the departments, and when the main mining regions of the country are excluded from the analysis. This suggests that the inclusion of these regions does not generate any bias in the convergence analysis under this pairwise stochastic strategy. Although the scope of stochastic convergence tests is limited by the series and the availability of the data, in this paper the accompanying descriptive and complementary sensitivity tests and the test flexibility enhance their interpretation.

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