# Economic Convergence in EU NUTS 3 Regions: A Spatial Econometric Perspective

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## Abstract

**:**

## 1. Introduction

“In order to promote its overall harmonious development, the Union shall develop and pursue its actions leading to the strengthening of its economic, social and territorial cohesion. In particular, the Union shall aim at reducing disparities between the levels of development of the various regions and the backwardness of the least favoured regions. Among the regions concerned, particular attention shall be paid to rural areas, areas affected by industrial transition, and regions which suffer from severe and permanent natural or demographic handicaps such as the northernmost regions with very low population density and island, cross-border and mountain regions.”

## 2. The Economic Convergence Models

## 3. The Spatial Augmented Model of Conditional β-Convergence

## 4. Some Methodological Issues

#### 4.1. The Bayesian Interpolation Method

#### 4.2. The Heteroscedastic Estimation Approach

**g**is the $N\times 1$ vector of observations on the per-worker GDP growth rate, $i$ is the $N\times 1$ vector of ones associated with the intercept term ${\beta}_{0}$, $\rho $ is the scalar spatial autoregressive coefficient, $Wg$ is the $N\times 1$ vector of the spatially lagged dependent variable, $X$ is the $N\times p$ matrix including $p=3$ explanatory variables defined as in (4), $\mathsf{\theta}$ is the $p\times 1$ vector including the regression coefficients associated with the $p$ explanatory variables, in our case $\mathsf{\theta}={\left({\beta}_{1},{\beta}_{2},{\beta}_{3}\right)}^{t}$, $WX$ is the $N\times p$ matrix of the $p$ spatially lagged explanatory variables, $\mathsf{\psi}={\left({\rho}_{1},{\rho}_{2},{\rho}_{3}\right)}^{t}$ is the $p\times 1$ vector of parameters associated with the $p$ spatially lagged explanatory variables, $\mathsf{\epsilon}$ is a $N\times 1$ vector of error. More compactly, the SDM model given in (10) can be rewritten as:

## 5. The Empirical Analysis of NUTS 3 Regions

## 6. Discussion

## 7. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**$\sigma $-convergence analysis—coefficient of variation (CV) of $\mathrm{ln}{y}_{it}$, NUTS 3 regions.

**Table 1.**Moran’s I statistics for the annual growth rate of GDP per worker in PPS. Connectivity matrix based on $K=7$ nearest neighbors.

Year | Moran’s I | Expectation | Standard Deviation | p−Value |
---|---|---|---|---|

1992 | 0.543 | −0.001 | 0.0002 | 0.000 |

1993 | 0.420 | −0.001 | 0.0002 | 0.000 |

1994 | 0.437 | −0.001 | 0.0002 | 0.000 |

1995 | 0.163 | −0.001 | 0.0002 | 0.000 |

1996 | 0.273 | −0.001 | 0.0002 | 0.000 |

1997 | 0.264 | −0.001 | 0.0002 | 0.000 |

1998 | 0.183 | −0.001 | 0.0002 | 0.000 |

1999 | 0.243 | −0.001 | 0.0003 | 0.000 |

2000 | 0.211 | −0.001 | 0.0002 | 0.000 |

2001 | 0.286 | −0.001 | 0.0002 | 0.000 |

2002 | 0.396 | −0.001 | 0.0002 | 0.000 |

2003 | 0.241 | −0.001 | 0.0002 | 0.000 |

2004 | 0.398 | −0.001 | 0.0002 | 0.000 |

2005 | 0.080 | −0.001 | 0.0002 | 0.000 |

2006 | 0.310 | −0.001 | 0.0002 | 0.000 |

2007 | 0.246 | −0.001 | 0.0002 | 0.000 |

2008 | 0.315 | −0.001 | 0.0002 | 0.000 |

2009 | 0.237 | −0.001 | 0.0002 | 0.000 |

2010 | 0.267 | −0.001 | 0.0002 | 0.000 |

2011 | 0.260 | −0.001 | 0.0002 | 0.000 |

2012 | 0.274 | −0.001 | 0.0002 | 0.000 |

2013 | 0.268 | −0.001 | 0.0002 | 0.000 |

2014 | 0.394 | −0.001 | 0.0002 | 0.000 |

**Table 2.**Estimation results for alternative models for $\beta $ -convergence analysis (1981–2014), using cross-sectional data, 901 NUTS 3 European regions.

Non-Spatial Absolute Model | Non-Spatial Conditional Model | Weights Matrix: 7 Nearest Neighbors | ||
---|---|---|---|---|

SDM Conditional Model ML | SDM Conditional Model GS2SLS-Het. | |||

Coefficient (standard error) | Coefficient (standard error) | Coefficient (standard error) | Coefficient (standard error) | |

Constant | 0.2633 *** (0.0048) | 0.2856 *** (0.0071) | 0.0948 *** (0.0126) | 0.0191 (0.0443) |

$\mathrm{ln}{y}_{1981}$ | −0.0232 *** (0.0005) | −0.0239 *** (0.0005) | −0.0269 *** (0.0005) | −0.0271 *** (0.0009) |

$\mathrm{ln}{s}^{k}$ | 0.0000 (0.0000) | 0.0001 ** (0.0000) | 0.0001 * (0.0000) | |

$\mathrm{ln}v=\mathrm{ln}\left(n+l+k\right)$ | 0.0053 *** (0.0012) | 0.0056 *** (0.0012) | 0.0058 *** (0.0016) | |

$W\mathrm{ln}{y}_{1981}$ | 0.0194 *** (0.0011) | 0.0257 *** (0.0038) | ||

$W\mathrm{ln}{s}^{k}$ | −0.0001 (0.0001) | −0.0001 (0.0001) | ||

$W\mathrm{ln}v$ | −0.0032 * (0.0020) | −0.0049 * (0.0025) | ||

$\rho $ | 0.5973 *** (0.0361) | 0.9067 *** (0.1781) | ||

$\lambda $ (Convergence Rate) | 4.57% | 4.93% | 7.24% | 7.48% |

Moran’s Test | 0.3291 *** | |||

Breusch-Pagan | 46.14 *** | |||

Studentized Breusch-Pagan | 23.77 *** | |||

$AIC$ | −7212.03 | −7226.67 | −7493.94 | |

${R}^{2}$ | 0.7158 | 0.7216 | 0.7485 | 0.7447 |

**Table 3.**Average direct, indirect, and total impacts of the explanatory variables (1981–2014) for the spatial heteroscedastic model estimated with GS2SLS, 901 NUTS 3 European regions.

Model | Variable | Average Direct Impact | Average Indirect Impact | Average Total Impact |
---|---|---|---|---|

Conditional model with heterosc. GS2SLS | $\mathrm{ln}{y}_{1981}$ | −0.0266 *** (0.0010) | 0.0124 (0.0131) | −0.0142 (0.0134) |

$\mathrm{ln}{s}^{k}$ | 0.0001 (0.0001) | 0.0002 (0.0008) | 0.0003 (0.0008) | |

$\mathrm{ln}v$ | 0.0060 *** (0.0018) | 0.0039 (0.0194) | 0.0099 (0.0202) |

**Table 4.**Estimation results for alternative models for $\beta $ -onvergence analysis (1991–2014), using cross-sectional data, 1133 NUTS 3 European regions.

Non-Spatial Absolute Model | Non-Spatial Conditional Model | Weights Matrix: 7 Nearest Neighbors | ||
---|---|---|---|---|

SDM Conditional Model | Conditional Model with Heterosc. GS2SLS | |||

Coefficient (standard error) | Coefficient (standard error) | Coefficient (standard error) | Coefficient (standard error) | |

Constant | 0.2238 *** (0.0047) | 0.2350 *** (0.0077) | 0.1044 *** (0.0129) | 0.0172 (0.0523) |

$\mathrm{ln}{y}_{1991}$ | −0.0193 *** (0.0005) | −0.0199 *** (0.0006) | −0.0216 *** (0.0009) | −0.0211 *** (0.0017) |

$\mathrm{ln}{s}^{k}$ | −0.0001 (0.0001) | 0.0000 (0.0000) | 0.0000 (0.0000) | |

$\mathrm{ln}v=\mathrm{ln}\left(n+l+k\right)$ | 0.0019 * (0.0010) | −0.0021 ** (0.0009) | −0.0027 ** (0.0013) | |

$W\mathrm{ln}{y}_{1991}$ | 0.0135 *** (0.0013) | 0.0198 *** (0.0042) | ||

$W\mathrm{ln}{s}^{k}$ | −0.0001 * (0.0001) | −0.0001 (0.0001) | ||

$W\mathrm{ln}v$ | 0.0072 *** (0.0016) | 0.0037 (0.0029) | ||

$\rho $ | 0.6527 *** (0.0297) | 0.9473 *** (0.1617) | ||

$\lambda $ (Convergence Rate) | 2.60% | 2.71% | 3.04% | 2.94% |

Moran’s $I$ | 0.3946 *** | |||

Breusch-Pagan | 373.45 *** | |||

Studentized Breusch-Pagan | 103.70 *** | |||

$AIC$ | −7973.93 | −7974.20 | −8378.15 | |

${R}^{2}$ | 0.6129 | 0.6143 | 0.6484 | 0.6517 |

**Table 5.**Average direct, indirect, and total impacts of the explanatory variables (1991–2014) for the spatial heteroscedastic model estimated with GS2SLS, 1133 NUTS 3 European regions.

Model | Variable | Average Direct Impact | Average Indirect Impact | Average Total Impact |
---|---|---|---|---|

Conditional model with heterosc. GS2SLS | $\mathrm{ln}{y}_{1991}$ | −0.0212 *** (0.0017) | −0.0038 (0.0142) | −0.0250 * (0.0143) |

$\mathrm{ln}{s}^{k}$ | −0.0001 (0.0001) | −0.0005 (0.0014) | −0.0006 (0.0015) | |

$\mathrm{ln}v$ | −0.0020 (0.0019) | 0.0206 (0.0363) | 0.0186 (0.0372) |

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**MDPI and ACS Style**

Postiglione, P.; Cartone, A.; Panzera, D. Economic Convergence in EU NUTS 3 Regions: A Spatial Econometric Perspective. *Sustainability* **2020**, *12*, 6717.
https://doi.org/10.3390/su12176717

**AMA Style**

Postiglione P, Cartone A, Panzera D. Economic Convergence in EU NUTS 3 Regions: A Spatial Econometric Perspective. *Sustainability*. 2020; 12(17):6717.
https://doi.org/10.3390/su12176717

**Chicago/Turabian Style**

Postiglione, Paolo, Alfredo Cartone, and Domenica Panzera. 2020. "Economic Convergence in EU NUTS 3 Regions: A Spatial Econometric Perspective" *Sustainability* 12, no. 17: 6717.
https://doi.org/10.3390/su12176717