Structure of the population or economic conditions? Determinants of spending on social protection in the European Union

Figures & data

Figure 1. Left panel: real GDP in million EUR (r_gdp) and real spending on social protection benefits (r_spb) in million EUR; Right panel: age dependency ratio (adr) and real spending on social protection benefits (r_spb) in million EUR; all data for 28 EU-average.

Source: own work based on Eurostat data

Table 1. Results of the regressions, baseline PCSE technique and robustness checks, specifications with the age dependency ratio.

	PCSE		FGLS		SCC		FE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{adr}}_{i,t}$	0.114* (0.065)	0.059 (0.059)	0.064 (0.052)	0.021 (0.047)	0.146* (0.077)	0.092 (0.062)	0.146* (0.078)	0.092 (0.069)
${d\_un\_r}_{i,t}$	0.060** (0.026)	0.098*** (0.024)	0.056*** (0.021)	0.079*** (0.017)	0.064** (0.028)	0.110*** (0.026)	0.064** (0.031)	0.110*** (0.030)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.051*** (0.012)	−0.037*** (0.011)	−0.049*** (0.010)	−0.032*** (0.009)	−0.049** (0.019)	−0.036 (0.022)	−0.049** (0.022)	−0.036* (0.020)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−10.840*** (1.507)	−7.567*** (1.350)	−11.058*** (1.230)	−8.782*** (1.091)	−12.065*** (3.100)	−8.274*** (2.309)	−12.065*** (3.069)	−8.274*** (2.449)
${d\_ln\_av\_\mathit{pop}}_{i,t}$	−3.803 (3.921)	−2.580 (3.810)	−2.208 (3.222)	−3.996 (3.049)	13.193* (7.476)	10.430* (5.978)	13.193*** (6.410)	10.430 (8.414)
${d\_fr}_{i,t}$	0.893 (0.706)	0.813 (0.595)	0.491 (0.575)	0.632 (0.490)	1.367** (0.654)	1.279** (0.559)	1.366 (0.966)	1.279* (0.688)
${\mathit{ele}}_{i,t}$	0.084 (0.052)	0.037 (0.043)	0.096** (0.041)	0.049 (0.032)	0.108* (0.057)	0.036 (0.041)	0.108** (0.046)	0.036 (0.042)
const.	0.728*** (0.111)	0.409*** (0.093)	0.633*** (0.085)	0.342*** (0.072)	0.243* (0.119)	0.107 (0.128)	0.679*** (0.136)	0.407*** (0.121)
No	416	416	416	416	416	416	416	416
$R^2$	0.7484	0.7308	x	x	0.7235	0.7114	0.7235	0.7114

Note: PCSE – Beck and Katz (1995) panel-corrected standard errors procedure (with panel-specific autocorrelation structure and heteroscedasticity across panels), FGLS – Parks (1967) feasible generalised least squares estimator (with panel-specific autocorrelation structure and heteroscedasticity across panels), SCC – fixed effects incorporating the Driscoll and Kraay (1998) standard errors, FE – fixed effects model with cluster option. *, **, *** - denote significance at 10%, 5% and 1%, respectively; errors in parentheses; time-effects not reported.

Source: own elaboration.

Table 2. Results of the regressions, baseline PCSE technique and robustness checks, specifications with the old-age dependency ratio and the young-age dependency ratio.

	PCSE		FGLS		SCC		FE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{odr}}_{i,t}$	0.162 (0.098)	0.116 (0.093)	0.042 (0.079)	0.048 (0.072)	0.150 (0.144)	0.185 (0.121)	0.150 (0.169)	0.185 (0.123)
${d\_\mathit{ydr}}_{i,t}$	0.079 (0.090)	0.035 (0.089)	0.087 (0.074)	0.021 (0.071)	0.142 (0.082)	0.027 (0.069)	0.142* (0.080)	0.027 (0.080)
${d\_un\_r}_{i,t}$	0.061** (0.026)	0.099*** (0.024)	0.056*** (0.021)	0.078*** (0.018)	0.064** (0.028)	0.109*** (0.026)	0.064** (0.031)	0.109*** (0.030)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.050*** (0.012)	−0.036*** (0.011)	−0.050*** (0.010)	−0.031*** (0.009)	−0.049** (0.019)	−0.034 (0.020)	−0.049** (0.022)	−0.034 (0.021)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−11.030*** (1.550)	−7.663*** (1.390)	−10.910*** (1.282)	−8.826*** (1.128)	−12.058*** (3.183)	−8.704*** (2.185)	−12.058*** (3.249)	−8.704*** (2.555)
${d\_ln\_av\_\mathit{pop}}_{i,t}$	−3.462 (3.945)	−1.995 (3.837)	−2.384 (3.275)	−3.680 (3.136)	13.212 (8.698)	12.159* (6.760)	13.212* (7.388)	12.159 (8.899)
${d\_fr}_{i,t}$	0.950 (0.710)	0.829 (0.597)	0.470 (0.583)	0.649 (0.491)	1.379** (0.651)	1.348** (0.539)	1.379 (0.978)	1.348* (0.682)
${\mathit{ele}}_{i,t}$	0.085* (0.051)	0.038 (0.043)	0.095** (0.041)	0.049 (0.032)	0.110* (0.057)	0.036 (0.041)	0.110** (0.046)	0.036 (0.043)
const.	0.709*** (0.116)	0.388*** (0.101)	0.648*** (0.090)	0.340*** (0.077)	1.353*** (0.143)	1.000*** (0.106)	0.676*** (0.143)	0.368*** (0.120)
No	416	416	416	416	416	416	416	416
$R^2$	0.7487	0.7309	x	x	0.7235	0.7126	0.7235	0.7126

Note: Description as below Table 1.

Source: own elaboration.

Table A1. Descriptive statistics and data sources.

Variable	Description	Obs.	Mean	Std. dv.	Min	Max	Source
${\mathit{adr}}_{i,t}$	age dependency ratio, population aged 0-14 and 65 and more to population aged 15-64	468	48.84	4.18	38.60	60.20	Eurostat
${\mathit{ydr}}_{i,t}$	young-age dependency ratio, (population aged 0-14 to population 15-64 years)	468	24.52	3.07	19.90	34.50	Eurostat
${\mathit{odr}}_{i,t}$	old-age dependency ratio, population 65 and over to population 15 to 64 years	468	24.32	4.13	15.60	34.80	Eurostat
${\mathit{spb}}_{i,t}$	social protection benefits (of general government) % of GDP	468	21.99	5.47	10.33	33.09	Eurostat
${sp}_{i,t}$	COFOG’s spending on social protection (of general government) % of GDP	468	16.29	4.00	7.90	25.50	Eurostat
${\mathit{trade}}_{i,t}$	trade openness (% of GDP)	468	116.68	66.24	45.42	408.36	WB WDI
${\mathit{debt}}_{i,t}$	debt of general government (% of GDP)	468	58.50	33.68	3.775	178.91	AMECO
${pb}_{i,t}$	primary balance (% of GDP)	468	−0.28	3.35	−29.23	9.56	AMECO
${\mathit{capb}}_{i,t}$	cyclically-adjusted primary balance (% of trend GDP)	468	−0.36	3.32	−26.12	7.71	AMECO
${\mathit{vturn}}_{i,t}$	voter turnout	468	70.53	13.60	39.20	96.90	Based on Armingeon et al. (2020)
${\mathit{max}14}_{i,t}$	proportion of population aged 0-14 years (%)	468	16.36	1.91	13.22	22.40	Eurostat
${65\mathit{more}}_{i,t}$	proportion of population aged 65 years and more (%)	468	16.37	2.59	10.23	22.50	Eurostat
${un\_r}_{i,t}$	unemployment rate (%)	468	8.63	4.34	1.81	27.47	WB WDI
${r\_\mathit{gdp}\_pc\_gr}_{i,t}$	growth rate of real GDP (constant 2010 prices, euro) per capita (%)	468	2.01	3.75	−14.27	24.00	calculation based on Eurostat data
${ln\_r\_\mathit{gdp}\_pc}_{i,t}$	ln of real GDP (constant 2010 prices, euro) per capita	468	9.94	0.64	8.21	11.34	calculation based on Eurostat data
${av\_\mathit{pop}\_r}_{i,t}$	growth rate of average population (%)	468	0.30	0.80	−2.26	2.89	calculation based on Eurostat data
${ln\_av\_\mathit{pop}}_{i,t}$	ln of average population	468	15.89	1.46	12.87	18.23	calculation based on Eurostat data
${\mathit{cbr}}_{i,t}$	crude birth rate	468	10.60	1.50	7.60	16.70	Eurostat
${fr}_{i,t}$	fertility rate	468	1.54	0.22	1.15	2.06	Eurostat

Table A2. Im-Pesaran-Shin unit root test (with a trend, p-value in parentheses).

	${\mathit{adr}}_{i,t}$	${\mathit{odr}}_{i,t}$	${\mathit{ydr}}_{i,t}$	${\mathit{spb}}_{i,t}$	${sp}_{i,t}$	${65m\mathit{ore}}_{i,t}$	${\mathit{max}14}_{i,t}$	15-64	${av\_\mathit{pop}\_r}_{i,t}$
Level	1.0000	1.0000	1.0000	0.6127	0.5569	1.0000	1.0000	1.0000	0.0338
First difference	0.0002	0.0002	0.0001	0.0000	0.0000	0.9988	0.1376	0.6020	0.0000
	${un\_r}_{i,t}$	${\mathit{trade}}_{i,t}$	${\mathit{cbr}}_{i,t}$	${r\_\mathit{gdp}\_pc\_gr}_{i,t}$	${fr}_{i,t}$	${\mathit{debt}}_{i,t}$	${\mathit{capb}}_{i,t}$	${pb}_{i,t}$	${ln\_av\_\mathit{pop}}_{i,t}$
Level	0.5207	0.0000	0.7967	0.0000	0.8609	0.6915	0.0006	0.0002	0.9999
First difference	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0338

Table A3. Correlation matrix for variables in baseline specification.

Obs. = 416	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{adr}}_{i,t}$	${d\_un\_r}_{i,t}$	${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	$d\_{ln\_r\_\mathit{gdp}\_pc}_{i,t}$	${d\_ln\_av\_\mathit{pop}}_{i,t}$	$d\_{fr}_{i,t}$
${d\_sp}_{i,t}$	1.0000
${d\_\mathit{spb}}_{i,t}$	x	1.0000
${d\_\mathit{adr}}_{i,t}$	−0.0637	−0.0775	1.0000
${d\_un\_r}_{i,t}$	0.6065	0.5614	−0.0211	1.0000
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.5621	−0.5850	0.0955	−0.2066	1.0000
$d\_{ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−0.7001	−0.6998	−0.1252	−0.6847	0.5208	1.0000
${d\_ln\_av\_\mathit{pop}}_{i,t}$	0.0839	0.0878	−0.2276	0.1003	−0.0839	−0.2326	1.0000
$d\_{fr}_{i,t}$	−0.0172	−0.0074	−0.1371	−0.2225	−0.0801	0.2345	−0.1648	1.0000

Table A4. Descriptive statistics – first differenced variables in baseline specification.

Variable	Obs.	Mean	Std. dev.	Min	Max
${d\_sp}_{i,t}$	442	0.0794	0.8112	−3.4000	4.9000
${d\_\mathit{spb}}_{i,t}$	442	0.1322	0.9954	−4.9154	4.9091
${d\_\mathit{adr}}_{i,t}$	442	0.2271	0.6161	−1.3000	2.1000
${d\_un\_r}_{i,t}$	442	−0.066	1.5441	−4.3790	9.7760
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	416	0.0379	3.9362	−23.1504	17.4959
$\mathrm{d}\_{ln\_r\_\mathit{gdp}\_pc}_{i,t}$	442	0.0192	0.0370	−0.1540	0.2151
${d\_ln\_av\_\mathit{pop}}_{i,t}$	442	0.0030	0.0083	−0.0226	0.0288
$\mathrm{d}\_{fr}_{i,t}$	442	0.0042	0.0468	−0.2000	0.1500

Table A5. Diagnostic tests.

	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
Modified Wald test for groupwise heteroskedasticity in fixed effect regression model	${{\chi }^2}_{(26)}= 825.55$ $\mathit{Prob}>{\chi }^2 = 0.0000$	${{\chi }^2}_{\left(26\right)}=442.91$ $\mathit{Prob}>{\chi }^2 = 0.0000$
Wooldridge test for autocorrelation in panel data	F(1, 25) = 9.601 Prob > F = 0.0048	F(1, 25) = 9.297 Prob > F = 0.0054
Breusch and Pagan Lagrangian multiplier test for random effects	Wald ${\chi }^2$ (22) = 16701.44 Prob > ${\chi }^2\mathrm{ }$= 0.0000	Wald ${\chi }^2$ (22) = 10605.66 Prob > ${\chi }^2\mathrm{ }$= 0.0000
Test of overidentifying restrictions: fixed vs random effects	${\chi }^2$ (7) = 87.18 Prob>${\chi }^2$ = 0.0000	${\chi }^2$ (7) = 57.97 Prob>${\chi }^2$ = 0.0000

Note: Diagnostic tests for FE vs. RE model, baseline specification.

Table A6.1. Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the age dependency ratio, N = 468.

	FE		PCSE		FE		PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{adr}}_{i,t}$	0.117 (0.070)	0.078 (0.075)	0.124** (0.061)	0.064 (0.054)	0.113 (0.073)	0.083 (0.073)	0.128** (0.061)	0.070 (0.054)
${d\_un\_r}_{i,t}$	0.057** (0.026)	0.110*** (0.028)	0.060** (0.025)	0.104*** (0.024)	0.061** (0.026)	0.114*** (0.026)	0.055** (0.026)	0.106*** (0.025)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.052** (0.019)	−0.035** (0.016)	−0.054*** (0.012)	−0.036*** (0.011)	−0.048** (0.019)	−0.033* (0.017)	−0.050*** (0.012)	−0.035*** (0.010)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−12.061*** (2.864)	−8.370*** (2.229)	−10.242*** (1.489)	−7.238*** (1.290)	−10.980*** (2.713)	−8.120*** (2.497)	−9.567*** (1.510)	−7.121*** (1.309)
$d\_{av\_\mathit{pop}\_r}_{i,t}$	−0.236 (0.143)	−0.120 (0.100)	−0.173* (0.089)	−0.065 (0.077)
${d\_\mathit{trade}}_{i,t}$	−0.009** (0.004)	−0.012*** (0.004)	−0.007* (0.003)	−0.011*** (0.003)	−0.009** (0.004)	−0.011** (0.004)	−0.007* (0.004)	−0.011*** (0.003)
${d\_\mathit{debt}}_{i,t}$					0.018* (0.009)	0.004 (0.007)	0.016** (0.007)	0.002 (0.007)
${d\_\mathit{cbr}}_{i,t}$	0.289* (0.165)	0.277 (0.112)	0.172* (0.100)	0.185** (0.087)	0.268* (0.155)	0.267** (0.111)	0.167* (0.100)	0.176** (0.087)
const.	0.736*** (0.124)	0.423*** (0.108)	0.728*** (0.107)	0.399*** (0.089)	0.704*** (0.116)	0.416*** (0.112)	0.711*** (0.107)	0.396*** (0.090)
${\mathrm{R}}^2$	0.7270	0.7219	0.7510	0.7362	0.7282	0.7211	0.7527	0.7376

Note: PCSE – Beck and Katz (1995) panel-corrected standard errors procedure (with panel-specific autocorrelation structure and heteroscedasticity across panels), FE – fixed effect model with cluster option. *, **, *** – denotes significance at 10%, 5% and 1%, respectively; errors in parentheses; time-effects not reported.

Table A6.2. (continuation) Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the age dependency ratio, N = 468.

	FE		PCSE		FE		PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{adr}}_{i,t}$	0.127* (0.069)	0.080 (0.070)	0.135** (0.061)	0.062 (0.052)	0.134* (0.070)	0.086 (0.071)	0.140** (0.062)	0.066 (0.052)
${d\_un\_r}_{i,t}$	0.058** (0.027)	0.105*** (0.026)	0.061** (0.025)	0.100*** (0.023)	0.060** (0.028)	0.107*** (0.027)	0.064** (0.025)	0.104*** (0.024)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.047** (0.019)	−0.032** (0.016)	−0.052*** (0.012)	−0.036*** (0.010)	−0.048** (0.019)	−0.033* (0.016)	−0.058*** (0.012)	−0.039*** (0.010)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−12.433*** (2.904)	−8.710*** (2.205)	−10.342*** (1.474)	−7.281*** (1.244)	−13.998*** (3.020)	−10.323*** (2.266)	−10.923*** (1.545)	−8.054*** (1.284)
${d\_\mathit{trade}}_{i,t}$	−0.010** (0.004)	−0.012*** (0.004)	−0.007** (0.003)	−0.011*** (0.003)	−0.009** (0.004)	−0.012*** (0.004)	−0.007* (0.004)	−0.011*** (0.003)
$d\_{pb}_{i,t}$	−0.052*** (0.016)	−0.051*** (0.014)	−0.039*** (0.012)	−0.045*** (0.011)
${d\_\mathit{capb}}_{i,t}$					−0.045*** (0.015)	−0.046*** (0.014)	−0.026** (0.012)	−0.035*** (0.010)
${d\_\mathit{cbr}}_{i,t}$	0.229 (0.163)	0.226 (0.109)	0.147 (0.098)	0.164** (0.083)	0.233 (0.162)	0.228** (0.109)	0.148 (0.099)	0.166** (0.084)
const.	0.689*** (0.124)	0.377*** (0.087)	0.678*** (0.107)	0.346*** (0.087)	0.752*** (0.126)	0.439*** (0.104)	0.722*** (0.107)	0.392*** (0.088)
${\mathrm{R}}^2$	0.7359	0.7381	0.7594	0.7559	0.7333	0.7354	0.7544	0.7500

Note: Description as below Table A6.1.

Table A7.1. Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the old-age dependency ratio and the young-age dependency ratio, N = 468.

	FE		PCSE		FE		PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{odr}}_{i,t}$	0.091 (0.133)	0.146 (0.113)	0.174* (0.092)	0.126 (0.086)	0.071 (0.141)	0.148 (0.114)	0.165* (0.096)	0.135 (0.088)
${d\_\mathit{ydr}}_{i,t}$	0.137* (0.078)	0.030 (0.077)	0.090 (0.087)	0.033 (0.087)	0.143* (0.080)	(0.035) (0.077)	0.100 (0.090)	0.036 (0.086)
${d\_un\_r}_{i,t}$	0.058** (0.028)	0.110*** (0.029)	0.060** (0.025)	0.105*** (0.024)	0.062** (0.026)	0.114*** (0.026)	0.056** (0.026)	0.106*** (0.025)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.053*** (0.018)	−0.034** (0.016)	−0.053*** (0.012)	−0.035*** (0.011)	−0.049** (0.019)	−0.032* (0.017)	−0.049*** (0.012)	−0.034*** (0.011)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−11.897*** (2.909)	−8.685*** (2.212)	−10.445*** (1.534)	−7.430*** (1.340)	−10.733*** (2.817)	−8.458*** (2.523)	−9.719*** (1.558)	−7.337*** (1.363)
${d\_av\_\mathit{pop}\_r}_{i,t}$	−0.238 (0.142)	−0.118 (0.100)	−0.176** (0.089)	−0.063 (0.076)
${d\_\mathit{trade}}_{i,t}$	−0.009** (0.004)	−0.012*** (0.004)	−0.007* (0.003)	−0.011*** (0.003)	−0.009** (0.004)	−0.012** (0.004)	−0.007** (0.003)	−0.011*** (0.003)
${d\_\mathit{cbr}}_{i,t}$	0.287* (0.166)	0.284** (0.113)	0.177* (0.100)	0.185** (0.087)	0.264 (0.156)	0.274** (0.113)	0.170* (0.100)	0.177** (0.087)
${d\_\mathit{debt}}_{i,t}$					0.018* (0.009)	0.004 (0.007)	0.016** (0.007)	0.002 (0.007)
const.	0.747*** (0.138)	0.397*** (0.115)	0.712*** (0.111)	0.377*** (0.096)	0.720*** (0.128)	0.391*** (0.117)	0.698*** (0.112)	0.374*** (0.096)
${\mathrm{R}}^2$	0.7271	0.7227	0.7514	0.7364	0.7283	0.7219	0.7529	0.7377

Note: Description as below Table A6.1.

Table A7.2. (continuation) Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the old-age dependency ratio and the young-age dependency ratio, N = 468.

	FE		PCSE		FE		PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{odr}}_{i,t}$	0.118 (0.136)	0.162 (0.107)	0.204** (0.093)	0.138* (0.083)	0.129 (0.140)	0.174 (0.110)	0.213** (0.095)	0.146* (0.084)
${d\_\mathit{ydr}}_{i,t}$	0.134* (0.074)	0.018 (0.079)	0.086 (0.089)	0.015 (0.086)	0.136* (0.074)	0.020 (0.079)	0.088** (0.090)	0.018 (0.087)
${d\_un\_r}_{i,t}$	0.058** (0.027)	0.104*** (0.026)	0.061** (0.025)	0.100*** (0.023)	0.060** (0.028)	0.106*** (0.026)	0.065** (0.025)	0.105*** (0.024)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.047** (0.019)	−0.030* (0.016)	−0.051*** (0.012)	−0.035*** (0.010)	−0.048** (0.019)	−0.031* (0.016)	−0.052*** (0.012)	−0.038*** (0.010)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−12.356*** (2.998)	−9.109*** (2.219)	−10.594*** (1.515)	−7.495*** (1.296)	−13.944*** (3.117)	−10.780*** (2.314)	−11.208*** (1.587)	−8.289*** (1.338)
${d\_\mathit{trade}}_{i,t}$	−0.010** (0.004)	−0.012*** (0.004)	−0.008** (0.004)	−0.011*** (0.003)	−0.009** (0.004)	−0.012*** (0.004)	−0.007** (0.003)	−0.011*** (0.003)
${d\_\mathit{cbr}}_{i,t}$	0.228 (0.164)	0.234 (0.111)	0.152 (0.098)	0.164** (0.083)	0.232 (0.163)	0.237** (0.110)	0.153 (0.099)	0.166** (0.084)
$d\_{pb}_{i,t}$	−0.052*** (0.016)	−0.051*** (0.014)	−0.039*** (0.012)	−0.045*** (0.011)
$d\_{\mathit{capb}}_{i,t}$					−0.045*** (0.015)	−0.047*** (0.014)	−0.027** (0.012)	−0.034*** (0.010)
const.	0.693*** (0.133)	0.343*** (0.108)	0.655*** (0.112)	0.317*** (0.095)	0.753*** (0.135)	0.404*** (0.107)	0.698*** (0.112)	0.361*** (0.095)
${\mathrm{R}}^2$	0.7358	0.7392	0.7600	0.7559	0.7332	0.7366	0.7552	0.7501

Note: Description as below Table A6.1.

Table A8. Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the age dependency ratio and institutional controls, N = 468.

	FE			PCSE			FE			PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{adr}}_{i,t}$	0.157* (0.076)	0.156* (0.076)	0.162* (0.079)	0.119* (0.065)	0.117* (0.065)	0.123* (0.065)	0.101 (0.066)	0.100 (0.066)	0.103 (0.066)	0.055 (0.059)	0.057 (0.059)	0.058 (0.059)
${d\_un\_r}_{i,t}$	0.068** (0.030)	0.066** (0.029)	0.069** (0.031)	0.065** (0.026)	0.062** (0.026)	0.065** (0.026)	0.116*** (0.029)	0.114*** (0.028)	0.116*** (0.030)	0.105*** (0.024)	0.105*** (0.024)	0.106*** (0.024)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.046** (0.020)	−0.047** (0.019)	−0.047** (0.019)	−0.049*** (0.012)	−0.050*** (0.012)	−0.048*** (0.012)	−0.032* (0.017)	−0.032* (0.017)	−0.033* (0.017)	−0.034*** (0.010)	−0.035*** (0.011)	−0.032*** (0.010)
${d\_ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−12.161*** (2.932)	−12.074*** (2.961)	−12.007*** ( 2.966)	−10.871*** (1.541)	−10.797*** (1.543)	−10.991*** (1.551)	−8.395*** (2.245)	−8.385*** (2.248)	−8.322*** (2.303)	−7.633*** (1.367)	−7.544*** (1.370)	−7.849*** (1.372)
${d\_ln\_av\_\mathit{pop}}_{i,t}$	8.796 (6.203)	8.435 (6.462)	9.497 (7.097)	−4.647 (3.943)	−4.482 (3.979)	−1.467 (4.666)	4.959 (8.072)	4.717 (8.203)	5.401 (8.752)	−2.752 (3.777)	−2.823 (3.787)	−0.192 (4.313)
${d\_\mathit{trade}}_{i,t}$	−0.007* (0.004)	−0.008* (0.004)	−0.008* (0.004)	−0.007* (0.004)	−0.007* (0.004)	−0.007* (0.004)	−0.011** (0.004)	−0.011** (0.004)	−0.011** (0.004)	−0.010*** (0.003)	−0.010*** (0.003)	−0.010*** (0.003)
${d\_\mathit{cbr}}_{i,t}$	0.250 (0.157)	0.252 (0.160)	0.251 (0.162)	0.151 (0.100)	0.147 (0.100)	0.142 (0.101)	0.257** (0.104)	0.257** (0.105)	0.256** (0.106)	0.171** (0.087)	0.172** (0.087)	0.173** (0.086)
${\mathit{ele}}_{i,t}$	0.104** (0.048)			0.080 (0.052)			0.031 (0.040)			0.036 (0.042)
${\mathit{left}}_{i,t}$		0.039 (0.079)			0.031 (0.069)			0.020 (0.060)			−0.005 (0.057)
${\mathit{vturn}}_{i,t}$			−0.002 (0.011)			−0.003 (0.003)			−0.001 (0.008)			−0.003 (0.002)
const.	0.681*** (0.136)	0.712*** (0.136)	0.832 (0.783)	0.720*** (0.111)	0.740*** (0.108)	1.003*** (0.216)	0.403*** (0.115)	0.410*** (0.114)	0.514 (0.532)	0.396*** (0.093)	0.408*** (0.092)	0.635*** (0.188)
${\mathrm{R}}^2$	0.7274	0.7260	0.7255	0.7501	0.7514	0.7497	0.7216	0.7214	0.7214	0.7386	0.7379	0.7384

Note: Description as below Table A6.1.

Table A9. Robustness checks, results for ${d\_\mathit{spb}}_{i,t}$ and ${d\_sp}_{i,t},$ specifications with the old-age dependency ratio and the young-age dependency ratio and institutional controls, N = 468.

	FE			PCSE			FE			PCSE
	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_\mathit{spb}}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$	${d\_sp}_{i,t}$
${d\_\mathit{odr}}_{i,t}$	0.158 (0.162)	0.159 (0.163)	0.163 (0.159)	0.167* (0.099)	0.173* (0.099)	0.194* (0.100)	0.192 (0.116)	0.192 (0.116)	0.194 (0.115)	0.116 (0.092)	0.121 (0.093)	0.130 (0.092)
${d\_\mathit{ydr}}_{i,t}$	0.156* (0.078)	0.152* (0.081)	0.158* (0.089)	0.088 (0.090)	0.082 (0.090)	0.077 (0.091)	0.039 (0.075)	0.038 (0.076)	0.041 (0.072)	0.031 (0.088)	0.029 (0.088)	0.025 (0.088)
${d\_un\_r}_{i,t}$	0.068** (0.031)	0.066** (0.030)	0.069** (0.032)	0.066** (0.026)	0.063** (0.026)	0.066** (0.026)	0.115*** (0.029)	0.113*** (0.028)	0.115*** (0.030)	0.106*** (0.024)	0.105*** (0.024)	0.107*** (0.024)
${d\_r\_\mathit{gdp}\_pc\_gr}_{i,t}$	−0.046** (0.020)	−0.047** (0.019)	−0.047** (0.019)	−0.048*** (0.012)	−0.049*** (0.012)	−0.046*** (0.012)	−0.030 (0.018)	−0.030* (0.017)	−0.030* (0.017)	−0.033*** (0.011)	−0.034*** (0.011)	−0.031*** (0.011)
$d\_{ln\_r\_\mathit{gdp}\_pc}_{i,t}$	−12.128*** (3.061)	−12.053*** (3.093)	−11.981*** (3.115)	−11.030*** (1.578)	−10.986*** (1.582)	−11.257*** (1.591)	−8.799*** (2.287)	−8.791*** (2.286)	−8.730*** (2.331)	−7.725*** (1.403)	−7.649*** (1.406)	−8.021*** (1.410)
${d\_ln\_av\_\mathit{pop}}_{i,t}$	8.725 (6.951)	8.379 (7.100)	9.440 (7.491)	−4.283 (3.978)	−4.059 (4.012)	−0.629 (0.747)	6.599 (8.384)	6.329 (8.498)	6.996 (8.973)	−2.119 (3.812)	−2.167 (3.828)	0.575 (4.370)
${d\_\mathit{trade}}_{i,t}$	−0.007* (0.004)	−0.008* (0.004)	−0.008* (0.004)	−0.007* (0.004)	−0.007* (0.004)	−0.007* (0.004)	−0.011** (0.004)	−0.011** (0.004)	−0.011** (0.004)	−0.010*** (0.003)	−0.010*** (0.003)	−0.010*** (0.003)
${d\_\mathit{cbr}}_{i,t}$	0.251 (0.157)	0.253 (0.161)	0.251 (0.163)	0.155 (0.100)	0.152 (0.101)	0.146 (0.101)	0.263** (0.105)	0.263** (0.106)	0.262** (0.108)	0.173** (0.086)	0.174** (0.087)	0.176** (0.086)
${\mathit{ele}}_{i,t}$	0.107** (0.048)			0.081 (0.052)			0.031 (0.041)			0.036 (0.042)
${\mathit{left}}_{i,t}$		0.039 (0.080)			0.034 (0.069)			0.022 (0.063)			−0.003 (0.057)
${\mathit{vturn}}_{i,t}$			−0.002 (0.011)			−0.004 (0.003)			−0.001 (0.007)			−0.003 (0.002)
const.	0.680*** (0.145)	0.710*** (0.151)	0.838 (0.809)	0.702*** (0.117)	0.720*** (0.114)	1.005*** (0.216)	0.365*** (0.118)	0.372*** (0.120)	0.466 (0.517)	0.374*** (0.101)	0.384*** (0.100)	0.623*** (0.190)
${\mathrm{R}}^2$	0.7274	0.7260	0.7253	0.7505	0.7518	0.7502	0.7229	0.7227	0.7226	0.7386	0.7379	0.7383

Note: Description as below Table A6.1.

Beck, N. L., & Katz, J. N. (1995). What to do (and not to do) with time-series cross-section data. American Political Science Review, 89(3), 634–647. https://doi.org/10.2307/2082979

 Web of Science ®Google Scholar

Parks, R. W. (1967). Efficient estimation of a system of regression equations when disturbances are both serially and contemporaneously correlated. Journal of the American Statistical Association, 62(318), 500–509. https://doi.org/10.1080/01621459.1967.10482923

 Web of Science ®Google Scholar

Driscoll, J., & Kraay, A. (1998). Consistent covariance matrix estimation with spatial dependent data. Review of Economics and Statistics, 80(4), 549–560. https://doi.org/10.1162/003465398557825

 Web of Science ®Google Scholar

Armingeon, K., Wenger, V., Wiedemeier, F., Isler, C., Knöpfel, L., Weisstanner, D., & Engler, S. (2020). Comparative political data set 1960–2018. Institute of Political Science, University of Zurich.

 Google Scholar