As recently discussed in the literature, the conventional unit root tests are inappropriate to test the stationarity of series in the case of presence of cross-sectional dependence in series since they assume cross-sectional independence. Hence, instead of conventional unit root tests, it will be better to conduct second-generation unit root test, which accounts for cross-sectional dependence. Thus, we started our empirical analysis firstly by implementing various cross-sectional dependence tests. Table 2 displays cross-sectional dependence test results for four distinct tests, namely Breusch-Pagan [30] LM test, Pesaran [31] scaled LM test, Baltagi, Feng, and Kao [32] Bias-corrected Scaled LM test, Pesaran [31] CD test. The entire test results depicted in Table 2 strongly rejects the null hypothesis of "No cross-section dependence" at the 1% significance level in the data.
Table 2
Cross-Section Dependence Test (H0: No cross-section dependence (correlation))
INFLATION | Test-statistic | P-value |
Breusch-Pagan [30] LM | 1434.992 | 0.000 |
Pesaran [31] scaled LM | 26.092 | 0.000 |
Baltagi, Feng, and Kao [32] Bias-corrected Scaled LM | 24.676 | 0.000 |
Pesaran [31] CD | 27.964 | 0.000 |
GDPPERCAP | Test-statistic | P-value |
Breusch-Pagan [30] LM | 7130.548 | 0.000 |
Pesaran [31] scaled LM | 189.456 | 0.000 |
Baltagi, Feng, and Kao [32] Bias-corrected Scaled LM | 187.998 | 0.000 |
Pesaran [31] CD | 84.287 | 0.000 |
UNEMPLOYMENT | Test-statistic | P-value |
Breusch-Pagan [30] LM | 1921.121 | 0.000 |
Pesaran [31] scaled LM | 38.442 | 0.000 |
Baltagi, Feng, and Kao [32] Bias-corrected Scaled LM | 36.984 | 0.000 |
Pesaran [31] CD | 16.124 | 0.000 |
SUICIDE | Test-statistic | P-value |
Breusch-Pagan [30] LM | 2801.451 | 0.000 |
Pesaran [31] scaled LM | 63.962 | 0.000 |
Baltagi, Feng, and Kao [32] Bias-corrected Scaled LM | 62.503 | 0.000 |
Pesaran [31] CD | 41.771 | 0.000 |
We also conducted residual cross-section independence test for the error terms of the models in Eqs. 1, 2 and 3. As indicated by the results in Table 3, null hypothesis of cross-section independence is rejected for each equation.
Table 3
Residual Cross-Section Independence Test (H0:Cross-section independence)
Eq. 1 (SUICIDE-INFLATION) | Test-statistic | P-value |
Breusch-Pagan [30] LM | 1932 | 0.000 |
Pesaran, Ullah and Yamagata [34] bias-adjusted LM | 76.590 | 0.000 |
Pesaran [31] CD | 32.500 | 0.000 |
Eq. 2 (SUICIDE-GDPPERCAP) | Test-statistic | P-value |
Breusch-Pagan [30] LM | 1072 | 0.000 |
Pesaran, Ullah and Yamagata [34] bias-adjusted LM | 20.360 | 0.000 |
Pesaran [31] CD | 0.943 | 0.346 |
Eq. 3 (SUICIDE-UNEMPLOYMENT) | Test-statistic | P-value |
Breusch-Pagan [30] LM | 1377 | 0.000 |
Pesaran, Ullah and Yamagata [34] bias-adjusted LM | 40.580 | 0.000 |
Pesaran [31] CD | 19.710 | 0.000 |
Given the detection of cross-sectional dependence in the data suggested by the test results in Tables 2 and 3, we apply the CIPS test for unit roots in heterogeneous panels developed by Pesaran [35] accounting for cross-sectional dependence. The CIPS test results are displayed in Table 4 below. According to the indications of the test, all series are not stationary in levels but they are stationary in first differences at 1% significance level. In other words, the CIPS unit root test findings hint that variables of SUICIDE, INFLATION, GDPPERCAP, and UNEMPLOYMENT are integrated of order one ( i.e. I (1)).
Table 4
CIPS test (H0: homogeneous non-stationary)
| Levels | First Differences |
SUICIDE | -2.502 | -3.446*** |
UNEMPLOYMENT | -1.744 | -3.113*** |
INFLATION | -2.715 | -3.672*** |
GDPPERCAP | -2.053 | -3.180*** |
Notes: *** indicates statistical significance at 1% level. The model used in CIPS unit root test contains a constant term and time trend. |
Upon identifying that our series are I(1), we check the cointegration relation among variables by utilizing two different panel cointegration test paying regard to cross-sectional dependence across panels. First, we apply Persyn and Westerlund [36] error-correction-based panel cointegration tests with robust P-values, which is obtained through bootstrapping. The findings are reported in Table 5 and the last column shows the robust P-values in the sense of cross-sectional dependence. Gτ and Gα, which allow error correction terms to be heterogeneous across panels, stand for group-mean test results while Pτ and Pα, which assume error correction terms to be homogeneous across panels, stand for panel test results. Besides, group-mean test looks for cointegration in some panels whereas panel test seeks for cointegration in all panels. Robust P-values in Table 5 reveals that SUICIDE and GDPPERCAP variables are cointegrated with regard to the both test findings while there is a cointegration association between SUICIDE and INFLATION variables and between SUICIDE and UNEMPLOYMENT variables based on just panel test results not for group-mean test results.
Table 5
Persyn and Westerlund [37] ECM panel cointegration tests (H0: No cointegration)
SUICIDE-INFLATION | Test Statistic | P-value | Robust P-Value |
Gτ | -1.810 | 0.416 | 0.220 |
Gα | -4.763 | 0.995 | 0.400 |
Pτ | -12.361 | 0.000 | 0.010 |
Pα | -5.294 | 0.081 | 0.040 |
SUICIDE-GDPPERCAP | Test Statistic | P-value | Robust P-Value |
Gτ | -2.416 | 0.000 | 0.000 |
Gα | -6.860 | 0.621 | 0.000 |
Pτ | -16.531 | 0.000 | 0.000 |
Pα | -8.522 | 0.000 | 0.000 |
SUICIDE-UNEMPLOYMENT | Test Statistic | P-value | Robust P-Value |
Gτ | -1.922 | 0.171 | 0.120 |
Gα | -5.189 | 0.983 | 0.160 |
Pτ | -12.627 | 0.000 | 0.040 |
Pα | -5.499 | 0.045 | 0.030 |
Next, we carried out heterogeneous ECM panel cointegration test of Gengenbach, Urbain and Westerlund [34] in which cross-sectional dependence is explicitly taken into consideration. Table 6 reports the findings of the test. The results imply that there is no cointegrating relation between SUICIDE and INFLATION variables whereas there exists a cointegrating relation between SUICIDE and GDPPERCAP variables and between SUICIDE and UNEMPLOYMENT variables at 1% significance level. In overall the findings of two distinct cointegration tests in Tables 5 and 6 strongly support the presence of cointegration for the models in Eqs. 2 and 3 while weakly support the existence of cointegration for the model in Eq. 1. Even though there is a weak evidence for the existence of cointegration in the model of Eq. 1, we will assume cointegrating relation for that equation too and therefore we will estimate long-run elasticities for the model in Eq. 1 as well in addition to the models Eqs. 2 and 3.
Table 6
Gengenbach, Urbain and Westerlund [33] heterogeneous ECM panel cointegration test (H0: No cointegration)
| EC-coefficient | T-bar Statistic | Significance |
SUICIDE-INFLATION | -0.834 | -2.399 | not significant at 1% |
SUICIDE-GDPPERCAP | -1.397 | -3.830 | significant at 1% |
SUICIDE-UNEMPLOYMENT | -1.149 | -3.602 | significant at 1% |
Before proceeding to estimations of long-run elasticities we implement Swamy test of parameter constancy to find out whether parameters across panels are heterogeneous. Reported results in Table 7 show that parameters do not remain constant across panels for all three models. Therefore, the estimation model that will be chosen to estimate long-run elasticities should allow for heterogeneous slope coefficients across panel members and also account for correlation across panel members (i.e., cross-section dependence). For that reason, we preferred to use the Augmented Mean Group (AMG) estimator developed in Eberhardt and Teal [37] as an alternative to the Common Correlated Effects Mean Group (CCEMG) estimator.
Table 7
Swamy parameter constancy test
| Test statistic | P-value |
SUICIDE-INFLATION | 18948.090 | 0.000 |
SUICIDE-GDPPERCAP | 25828.270 | 0.000 |
SUICIDE-UNEMPLOYMENT | 35218.480 | 0.000 |
Table 8 below depicts the long-run elasticities for the model in Eq. 1. As seen from the mean group estimation results, coefficient of error correction term, as expected, is negative and statistically significant and hence this guarantees existence of a log-run association between SUICIDE and INFLATION. The long-run coefficient of INFLATION is positive and statistically significant at 10% significance level. This finding hint that an increase in inflation by 1% leads to a rise in suicide rate by 0.088%. Regarding to group specific estimation results, both coefficient of error correction term and long-run coefficient are statistically significant for just Romania, Spain, Switzerland and Czech Republic. Long-run elasticities are positive for Romania, Spain and Switzerland whereas it is negative for Czech Republic. A one percent increase in inflation lead to an increase in suicide rate by 0.090% in Romania, 0.135% in Spain, 0.612% in Switzerland.
Table 8
Long-run Elasticities for Eq. 1
Mean group estimation results |
| EC-coef. | Long-run coef. |
| -1.353 | 0.088 |
| 0.000 | 0.061 |
Group specific estimation results |
| EC-coef. | Long-run coef. |
Austria | -1.160 | 0.004 |
| 0.000 | 0.968 |
Belgium | -1.576 | -0.074 |
| 0.000 | 0.382 |
Bulgaria | -0.248 | 0.175 |
| 0.665 | 0.038 |
Switzerland | -1.798 | 0.612 |
| 0.000 | 0.000 |
Czech Republic | -0.936 | -0.171 |
| 0.051 | 0.080 |
Germany | -1.037 | 0.015 |
| 0.000 | 0.884 |
Denmark | -2.187 | 0.176 |
| 0.052 | 0.411 |
Spain | -1.384 | 0.135 |
| 0.000 | 0.011 |
Estonia | -1.127 | -0.035 |
| 0.207 | 0.881 |
Finland | -1.644 | 0.042 |
| 0.268 | 0.769 |
France | -1.469 | -0.044 |
| 0.215 | 0.814 |
United Kingdom | -2.113 | 0.033 |
| 0.000 | 0.858 |
Greece | -1.196 | 1.270 |
| 0.085 | 0.180 |
Croatia | -2.030 | 0.069 |
| 0.001 | 0.369 |
Hungary | -1.374 | 0.059 |
| 0.000 | 0.297 |
Iceland | -2.088 | 0.317 |
| 0.000 | 0.131 |
Israel | -1.013 | 0.016 |
| 0.030 | 0.912 |
Kazakhstan | -1.052 | 0.209 |
| 0.119 | 0.077 |
Kyrgyz Republic | -0.907 | 0.036 |
| 0.152 | 0.789 |
Lithuania | -1.621 | -0.044 |
| 0.003 | 0.292 |
Luxembourg | -2.118 | 0.600 |
| 0.003 | 0.465 |
Latvia | -3.757 | -0.208 |
| 0.032 | 0.146 |
Moldova | -1.040 | 0.105 |
| 0.692 | 0.408 |
Macedonia, FYR | -0.833 | 0.020 |
| 0.290 | 0.870 |
Malta | -1.808 | -0.092 |
| 0.000 | 0.911 |
Netherlands | -0.875 | -0.006 |
| 0.029 | 0.956 |
Norway | -1.588 | -0.034 |
| 0.016 | 0.816 |
Poland | -1.256 | 0.030 |
| 0.000 | 0.645 |
Romania | -1.541 | 0.090 |
| 0.000 | 0.047 |
Russian Federation | -0.125 | -0.065 |
| 0.897 | 0.691 |
Serbia | -0.464 | -0.092 |
| 0.650 | 0.571 |
Slovenia | -0.629 | -0.100 |
| 0.613 | 0.520 |
Sweden | -0.555 | -0.044 |
| 0.680 | 0.739 |
Turkmenistan | NA | NA |
| NA | NA |
Ukraine | -1.463 | -0.020 |
| 0.010 | 0.544 |
Notes: Coefficient estimations are in bold faces and P-values are in italic forms. We dropped Turkmenistan from the estimation since Turkmenistan has no observation for inflation. |
Table 9 below displays the long-run elasticities for the model in Eq. 2. The coefficient of error correction term is negative and statistically significant as seen from the mean group estimation results, ensuring the existence of a log-run relationship between SUICIDE and GDPPERCAP. The long-run coefficient of GDPPERCAP is negative and statistically significant at 1% significance level. This finding suggests that an increase in GDP per capita by 1% results in a fall in suicide rate by 0.752%. Regarding to group specific estimation results, both coefficient of error correction term and long-run coefficient are statistically significant for Estonia, Finland, France, United Kingdom, Croatia, Kazakhstan, Lithuania, Latvia, Macedonia, Netherlands, Norway, and Ukraine. Long-run elasticities are negative for Estonia, France, United Kingdom, Croatia, Lithuania, Latvia, Netherlands, Norway, and Ukraine while they are positive for Finland, Kazakhstan, and Macedonia. A one percent increase in GDP per capita cause to a decrease in suicide rate by 1.286% in Estonia, 5.265% in France, 1.957% in United Kingdom, 0.636% in Croatia, 1.666% in Lithuania, 1.802% in Latvia, 2.537% in Netherlands, 0.828% in Norway, and 1.114% in Ukraine.
Table 9
Long-run Elasticities for Eq. 2
Mean group estimation results |
| EC-coef. | Long-run coef. |
| -1.722 | -0.752 |
| 0.000 | 0.005 |
Group specific estimation results |
| EC-coef. | Long-run coef. |
Austria | -0.980 | -2.679 |
| 0.426 | 0.248 |
Belgium | -0.680 | -1.865 |
| 0.512 | 0.593 |
Bulgaria | -0.485 | -0.615 |
| 0.588 | 0.439 |
Switzerland | -1.228 | 0.020 |
| 0.000 | 0.951 |
Czech Republic | -1.474 | -2.320 |
| 0.136 | 0.144 |
Germany | -0.286 | 0.333 |
| 0.344 | 0.790 |
Denmark | -1.133 | -1.834 |
| 0.330 | 0.153 |
Spain | -1.976 | -0.457 |
| 0.001 | 0.133 |
Estonia | -1.447 | -1.286 |
| 0.022 | 0.005 |
Finland | -1.399 | 1.191 |
| 0.000 | 0.000 |
France | -7.028 | -5.265 |
| 0.020 | 0.052 |
United Kingdom | -3.009 | -1.957 |
| 0.001 | 0.001 |
Greece | -1.643 | -1.212 |
| 0.056 | 0.183 |
Croatia | -1.834 | -0.636 |
| 0.035 | 0.020 |
Hungary | -1.094 | -1.457 |
| 0.276 | 0.413 |
Iceland | -1.728 | 1.038 |
| 0.000 | 0.420 |
Israel | -0.355 | 0.399 |
| 0.416 | 0.777 |
Kazakhstan | -1.662 | 0.568 |
| 0.009 | 0.053 |
Kyrgyz Republic | -0.631 | -2.415 |
| 0.212 | 0.161 |
Lithuania | -1.907 | -1.666 |
| 0.020 | 0.054 |
Luxembourg | -1.898 | 0.492 |
| 0.028 | 0.824 |
Latvia | -2.844 | -1.802 |
| 0.007 | 0.011 |
Moldova | -1.638 | 0.729 |
| 0.152 | 0.184 |
Macedonia, FYR | -3.543 | 2.435 |
| 0.000 | 0.056 |
Malta | -1.849 | 2.364 |
| 0.001 | 0.771 |
Netherlands | -1.695 | -2.537 |
| 0.017 | 0.004 |
Norway | -1.799 | -0.828 |
| 0.003 | 0.098 |
Poland | -0.933 | 0.596 |
| 0.017 | 0.529 |
Romania | -1.339 | -0.151 |
| 0.000 | 0.536 |
Russian Federation | -1.316 | 0.156 |
| 0.013 | 0.347 |
Serbia | -1.577 | 0.045 |
| 0.011 | 0.918 |
Slovenia | -2.729 | -1.583 |
| 0.154 | 0.011 |
Sweden | -1.396 | 0.011 |
| 0.024 | 0.983 |
Turkmenistan | -0.872 | -3.022 |
| 0.042 | 0.148 |
Ukraine | -2.873 | -1.114 |
| 0.006 | 0.003 |
Notes: Coefficient estimations are in bold faces and P-values are in italic forms. |
The long-run elasticities for the model in Eq. 3 are provided in Table 10. The coefficient of error correction term is negative and statistically significant which ensures the existence of a log-run correlation between SUICIDE and UNEMPLOYMENT. The long-run coefficient of UNEMPLOYMENT is positive and statistically significant at 1% significance level which indicates that a rise in UNEMPLOYMENT by 1% causes suicide rate to increase by 0.238%. Regarding to group specific estimation results, both coefficient of error correction term and long-run coefficient are statistically significant for Belgium, Denmark, Estonia, Finland, United Kingdom, Greece, Hungary, Lithuania, Latvia, Poland, Serbia, and Slovenia. Long-run elasticities are positive for Denmark, Estonia, United Kingdom, Greece, Hungary, Lithuania, Latvia, Poland, Serbia, and Slovenia whereas they are negative for Belgium and Finland. A one percent increase in unemployment rate causes to an increase in suicide rate by 0.222% in Denmark, 0.489% in Estonia, 0.407% in the United Kingdom, 0.563% in Greece, 0.558% in Hungary, 0.249% in Lithuania, 0.378% in Latvia, 0.257% in Poland, 0.265% in Serbia, and 0.514% in Slovenia.
Table 10
Long-run Elasticities for Eq. 3
Mean group estimation results |
| EC-coef. | Long-run coef. |
| -1.501 | 0.238 |
| 0.000 | 0.011 |
Group specific estimation results |
| EC-coef. | Long-run coef. |
Austria | -0.326 | -0.365 |
| 0.515 | 0.119 |
Belgium | -1.246 | -0.630 |
| 0.008 | 0.044 |
Bulgaria | -0.872 | 0.063 |
| 0.294 | 0.701 |
Switzerland | -0.604 | -0.049 |
| 0.000 | 0.568 |
Czech Republic | -1.134 | 0.419 |
| 0.571 | 0.665 |
Germany | -0.890 | -0.111 |
| 0.000 | 0.407 |
Denmark | -1.649 | 0.222 |
| 0.073 | 0.051 |
Spain | -1.443 | 0.051 |
| 0.004 | 0.259 |
Estonia | -2.563 | 0.489 |
| 0.001 | 0.002 |
Finland | -1.391 | -0.425 |
| 0.006 | 0.000 |
France | -1.020 | -0.226 |
| 0.342 | 0.463 |
United Kingdom | -2.521 | 0.407 |
| 0.000 | 0.020 |
Greece | -2.649 | 0.563 |
| 0.000 | 0.010 |
Croatia | -2.119 | 0.116 |
| 0.002 | 0.472 |
Hungary | -1.396 | 0.558 |
| 0.000 | 0.000 |
Iceland | -1.480 | -0.285 |
| 0.002 | 0.176 |
Israel | -0.785 | 0.540 |
| 0.059 | 0.380 |
Kazakhstan | -0.656 | 0.395 |
| 0.317 | 0.697 |
Kyrgyz Republic | -1.197 | 0.939 |
| 0.247 | 0.448 |
Lithuania | -1.599 | 0.249 |
| 0.056 | 0.009 |
Luxembourg | -1.511 | -0.532 |
| 0.073 | 0.371 |
Latvia | -2.504 | 0.378 |
| 0.000 | 0.001 |
Moldova | -1.183 | -0.385 |
| 0.332 | 0.152 |
Macedonia, FYR | -1.735 | 0.228 |
| 0.018 | 0.863 |
Malta | -1.630 | 1.131 |
| 0.001 | 0.576 |
Netherlands | -1.093 | 0.208 |
| 0.090 | 0.381 |
Norway | -2.234 | 0.094 |
| 0.000 | 0.589 |
Poland | -3.256 | 0.257 |
| 0.002 | 0.018 |
Romania | -0.852 | -0.122 |
| 0.152 | 0.827 |
Russian Federation | -0.991 | -0.101 |
| 0.121 | 0.322 |
Serbia | -1.415 | 0.265 |
| 0.008 | 0.051 |
Slovenia | -2.948 | 0.514 |
| 0.002 | 0.002 |
Sweden | -0.330 | 0.634 |
| 0.596 | 0.020 |
Turkmenistan | -1.341 | 2.405 |
| 0.066 | 0.269 |
Ukraine | -1.991 | 0.434 |
| 0.150 | 0.179 |
Notes: Coefficient estimations are in bold faces and P-values are in italic forms. |