In Table 4, the results of the one-step GMM method can be found. The coefficient α of the lagged average log GDP per capita zi,s−1 is -0.1322 for the full sample. This is significantly smaller than zero, which indicates that β-convergence of the log GDP per capita is present among the European countries.
This coefficient is also significantly smaller than zero in all subsamples, so β-convergence is observed in all samples. The coefficient of the EU and non-EU countries samples are -0.0712 and -0.0583, respectively. This indicates that convergence seems to occur slower in non-EU countries than in EU countries when we look at the point estimates. However, the 95 per cent confidence intervals of the EU and non-EU samples are [-0.1033,-0.0391] and [-0.0933,-0.0232], respectively.
As the confidence intervals overlap, we can not say with great certainty that convergence occurs faster in EU countries.
When we treat all Schengen countries in our sample as EU countries, we find comparable results. The coefficients then are -0.0768 and -0.0513, and the confidence intervals are [-0.1099,-0.0434] and [-0.0868,-0.0158] for the EU and non-EU countries, respectively. The coefficients in (2) and (4) are quite close to each other, which means that adding the Schengen countries has no large influence on the convergence speed of the EU countries. Moreover, the coefficients in (3) and (5) do not differ a lot, so removing the Schengen countries from the non-EU sample does not heavily change the convergence speed of the non-EU countries as well.
In Table 5, the results of the two-step GMM method can be found. Again, we observe β-convergence in all samples and a larger convergence speed in the EU subsamples than in the non-EU subsamples when we look at the point estimates. However, the confidence intervals are again overlapping.
Table 4: One-step GMM Results
Full sample EU non-EU EU + Schengen non-EU - Schengen
(1) (2) (3) (4) (5)
lagged average log GDP per capita -0.1322(0.0340)*** -0.0712(0.0164)*** -0.0583(0.0179)** -0.0768(0.0169)*** -0.0513(0.0181)**
Spatial average log GDP per capita 0.1133(0.0362)*** 0.0194(0.0089)** 0.0426(0.0290) 0.0141(0.0098) 0.0297(0.0543) Industry -0.0023(0.0027) 0.0010(0.0013) 0.0015(0.0010) 0.0009(0.0013) -0.0007(0.0012) Population growth 0.1057(0.0412)** 0.0336(0.0126)*** -0.0039(0.030) 0.0419(0.0148)*** 0.0292(0.0359)
Hansen test of overid. restrictions 0.062 0.065 0.063 0.069 0.071
Hansen test excluding group 0.307 0.064 0.145 0.094 0.081
Difference (H0 = exogenous) 0.218 0.270 0.280 0.172 0.214
no. instruments 19 19 13 19 13
no. countries 44 28 16 31 13
no. periods 3 3 3 3 3
Note: The table contains the estimated coefficients for each variable. The robust standard errors are given in brackets and ***, **, * denote significance at respectively 1%, 5%, and 10% level. Moreover, the table contains the p-values of the corresponding hypothesis tests.
We observe slightly stronger convergence in both groups when we treat the Schengen coun-tries as non-EU councoun-tries. The coefficient of the lagged average log GDP per capita of the EU and non-EU samples is lower in the two-step method compared to the one-step method. This indi-cates that we observe stronger convergence using the two-step method. However, we also obverse overlapping confidence intervals for these coefficients.
The effects of the control variables are similar in both models, as the sign and significance are equal for all variables. The coefficients of the spatial effects are positive, indicating that when the log GDP per capita of the neighboring countries is higher, it is more likely that the country’s log GDP per capita grows faster. However, the spatial effects are not significant in all subsamples.
More population growth leads to a significantly higher log GDP per capita growth in the full sample and the EU samples, but not in the non-EU samples. The part of the GDP spent on the industry sector does not significantly influence the log GDP per capita growth.
Roodman (2009) argues that a crucial assumption for the validity of GMM estimation is that the instruments must be exogenous. Therefore, the instruments are not allowed to be
over-Table 5: Two-step GMM Results
Full sample EU non-EU EU + Schengen non-EU - Schengen
(1) (2) (3) (4) (5)
Lagged average log GDP per capita -0.1252(0.0373)*** -0.0945(0.0350)*** -0.0615(0.0381)* -0.1111(0.0277)*** -0.0667(0.0215)**
Spatial average log GDP per capita 0.0773(0.0355)** 0.0271(0.0148)* 0.0438(0.0439) 0.0110(0.0216) 0.0502(0.0651) Industry -0.0038(0.0034) 0.0021(0.0031) 0.0015(0.0013) 0.0002(0.0028) -0.0004(0.0014) Population growth 0.0860(0.0219)*** 0.0724(0.0336)** -0.0074(0.0394) 0.0820(0.0253)*** 0.0281(0.0324)
Hansen test of overid. restrictions 0.062 0.068 0.063 0.143 0.120
Hansen test excluding group 0.064 0.080 0.065 0.103 0.087
Difference (H0 = exogenous) 0.218 0.248 0.280 0.310 0.233
no. instruments 19 19 13 19 13
no. countries 44 28 16 31 13
no. periods 3 3 3 3 3
Note: The table contains the estimated coefficients for each variable. The robust standard errors are given in brackets and ***, **, * denote significance at respectively 1%, 5%, and 10% level. Moreover, the table contains the p-values of the corresponding hypothesis tests.
identified, which we can test by the Hansen J test of over-identified restrictions (Hansen, 1982).
The corresponding p-values in Tables 4 and 5 show that the instruments are not over-identified.
Roodman (2009) also mention the importance of the two Difference-in-Hansen tests of exogeneity of instrument subsets, which are the bottom two tests in Tables 4 and 5. The Hansen excluding group test examines the model’s validity without the specified set of instruments, which is satisfied in all our samples. The difference test examines the instrument’s validity by calculating the Hansen J test with and without the set of instruments and taking the difference. From the corresponding p-values, we can conclude that our instruments are exogenous.
4.2.2. FE estimation
The results of the standard FE estimation and the FE estimation with SPJ bias-correction can be found in Tables 6 and 7, respectively. The lagged log GDP coefficients are much lower in the standard FE model than in the SPJ bias-corrected model. This indicates that convergence is overestimated in the standard FE model, which is expected by Hurwicz (1950) and Nickell (1981).
The results of the SPJ bias-corrected model are also much closer to the results of the GMM models.
Therefore, our further analysis is based on the SPJ bias-corrected version of the FE model.
Table 6: Standard FE results
Full sample EU non-EU EU + Schengen non-EU - Schengen
(1) (2) (3) (4) (5)
Lagged log GDP per capita -0.1226(0.0177)*** -0.1628(0.0255)*** -0.1096(0.0142)*** -0.1740(0.0271)*** -0.1001(0.0116)***
Labor Force -0.0004(0.0009) -0.0020(0.0019) 0.0007(0.0011) -0.0020(0.0017) 0.0013(0.0012) Human capital 0.0071(0.0027)** 0.003(0.0045) 0.0082(0.0051) 0.0065(0.0041) 0.0052(0.0055) High-tech -0.0002(0.0003) 0.0002(0.0004) 0.0004(0.0010) 0.0001(0.0004) 0.0010(0.0013) Services -0.0050(0.0016)*** -0.0033(0.0023) -0.0068(0.0024)** -0.0042(0.0022)* -0.0074(0.0027)**
Agriculture -0.0064(0.0017)*** -0.0064(0.0033)* -0.0077(0.0016)*** -0.0076(0.0035)** -0.0076(0.0017)***
Industry 0.0015(0.0014) 0.0018(0.0030) 0.0006(0.0020) 0.0001(0.0030) 0.0011(0.0021) Female unemployment -0.0016(0.0006)** -0.0037(0.0010)*** -0.0006(0.0006) -0.0041(0.0010)*** -0.0005(0.0008) Population growth -0.0012(0.0032) -0.0116(0.0053)** 0.0021(0.0017) -0.0089(0.0053)* 0.0017(0.0016) Population density 0.0003(0.0001)** 0.0004(0.0001)** -0.0005(0.0004) 0.0003(0.0001)** -0.0010(0.0005)*
Trade openness 0.0006(0.0001)*** 0.0008(0.0002)*** 0.0005(0.0002)** 0.0010(0.0002)*** 0.0005(0.0002)**
Inflation -0.0002(0.0002) 0.0014(0.0011) -0.0003(0.0002)* 0.0009(0.0010) -0.0003(0.0001)**
no. countries 44 28 16 31 13
no. years 19 19 19 19 19
Note: The table contains the estimated coefficients for each variable. The robust standard errors are given in brackets and ***, **, * denote significance at respectively 1%, 5%, and 10% level. The standard errors are the square roots of the diagonal elements of the variance-covariance matrix of the variables in θ. This matrix is based on the Hessian of the concentrated log-likelihood, following the method of Sun & Dhaene (2019).
The lagged log GDP per capita coefficient is -0.0695 in the full sample, which is signifi-cantly smaller than zero. This indicates that β−convergence of the log GDP per capita is present among the European countries. The coefficient is also significantly smaller than zero in all sub-samples, so we observe β-convergence in all samples.
The coefficients for the EU and non-EU samples are respectively -0.1028 and -0.0527, which indicates that convergence seems to occur at a faster pace in the EU countries compared to the non-EU countries. However, the 95 per cent confidence intervals for EU and non-EU samples are [-0.1461,-0.0595] and [-0.0978,-0.0074], respectively. We see that the confidence intervals are overlapping, which indicates that we can not say with great certainty that convergence is stronger in the EU countries.
Table 7: FE with SPJ bias-correction results
Full sample EU non-EU EU + Schengen non-EU - Schengen
(1) (2) (3) (4) (5)
Lagged log GDP per capita -0.0695(0.0209)*** -0.1028(0.0221)*** -0.0527(0.0231)** -0.1167(0.0235)*** -0.0484(0.0177)**
Labor Force -0.0007(0.0009) -0.0027(0.0023) 0.0007(0.0015) -0.0027(0.0018) 0.0014(0.0013) Human capital 0.0054(0.0029)* 0.0041(0.0045) 0.0069(0.0074) 0.0046(0.0047) 0.0028(0.0099) High-tech -0.0003(0.0004) 0.0001(0.0004) 0.0006(0.0011) -0.0000(0.0004) 0.0013(0.0016) Services -0.0058(0.0022)*** -0.0038(0.0026) -0.0080(0.0023)*** -0.0045(0.0024)* -0.0085(0.0028)***
Agriculture -0.0052(0.0019)*** -0.0054(0.0043) -0.0067(0.0021)*** -0.0067(0.0042) -0.0069(0.0027)**
Industry 0.0010(0.0017) 0.0013(0.0033) -0.0003(0.0023) 0.0001(0.0028) 0.0003(0.0022) Female unemployment -0.0012(0.0007) -0.0031(0.0011)*** -0.0003(0.0009) -0.0034(0.0010)*** -0.0002(0.0010) Population growth -0.0018(0.0050) -0.0122(0.0059)** 0.0012(0.0067) -0.0091(0.0062) 0.0003(0.0100) Population density 0.0003(0.0003) 0.0004(0.0005) -0.0001(0.0009) 0.0003(0.0005) -0.0013(0.0021) Trade openness 0.0006(0.0002)*** 0.0007(0.0003)*** 0.0006(0.0003)** 0.0007(0.0002)*** 0.0005(0.0004) Inflation -0.0002(0.0003) 0.0017(0.0014) -0.0003(0.0003) 0.0013(0.0011) -0.0003(0.0003)
no. countries 44 28 16 31 13
no. years 19 19 19 19 19
Note: The table contains the estimated coefficients for each variable. The robust standard errors are given in brackets and ***, **, * denote significance at respectively 1%, 5%, and 10% level. The standard errors are the square roots of the diagonal elements of the variance-covariance matrix of the variables in θ. This matrix is obtained from the same Hessian as in the standard FE model but now evaluated at the corresponding SPJ estimate ˜θ, where the uncorrected log-likelihood with respect to the fixed effect parameters is maximized, with θ fixed at ˜θ, following the method of Sun & Dhaene (2019).
When we treat all Schengen countries as EU countries, the coefficients are -0.1167 and -0.0484, and the confidence intervals are [-0.1628,-0.0706] and [-0.0831,-0.0137] for the EU and non-EU countries, respectively. The coefficient of the EU sample is slightly lower, and the non-EU sample’s coefficient is slightly higher, while the standard deviations barely changed. This makes the confidence intervals almost non-overlapping.
We observe quite some differences in the effects of the control variables on the log GDP per capita values in the different samples. A larger part of the GDP spent on services and agri-culture leads to lower log GDP per capita values in all samples. More female unemployment and population growth leads to a lower log GDP per capita in the EU samples, and more inflation leads
to a lower log GDP per capita in the non-EU samples. More trade openness leads to a higher GDP per capita in all samples, but more human capital leads to higher log GDP values in the full sample only. A higher population density leads to a higher log GDP per capita in the full sample and the EU samples, but it leads to a lower log GDP per capita in the non-EU samples. However, this effect is only weakly significant or not significant at all in the non-EU samples.
When we compare the results of GMM and FE models, we observe significant β-convergence in all cases. Moreover, the convergence speed is always larger in the EU countries than in the non-EU countries when we look at the point estimates. However, the convergence of the non-EU countries seems to be slightly stronger in the FE models, and the convergence of the non-EU countries seems to be slightly stronger in the GMM models. This leads to a larger difference in convergence speed between the EU and non-EU countries in the FE models compared to the GMM models. This could be caused by the fact that we used much more control variables in the FE models compared to the GMM models. When we perform an unconditional FE estimation with only the lagged value of log GDP per capita growth as an independent variable, we get opposite results in which EU coun-tries converge slower than non-EU councoun-tries. However, when we start adding control variables, the convergence speed of the EU countries becomes larger compared to the non-EU countries.
So it seems that unconditional β-convergence is stronger in the non-EU countries and conditional β-convergence is stronger in the EU countries.