Pension expenditure determinants: the case of Portugal

Medeiros Garcia, Maria Teresa; Rocha da Silva, André Fernando Rodrigues

doi:10.3326/pse.47.2.2.

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Pension expenditure determinants: the case of Portugal

Maria Teresa Medeiros Garcia*

André Fernando Rodrigues Rocha da Silva*

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https://doi.org/10.3326/pse.47.2.2

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Table 1
VECM estimation results

Cointegrating Eq	CointEq1	Sample (adjusted): 1978 to 2014 Included observations: 37 after adjustments Standard errors in ( ) & t-statistics in [ ] Determinant residual covariance (dof adj.) 9.01E-11 Determinant residual covariance 9.35E-12 Log likelihood 259.8113 Akaike information criterion -10.36818 Schwarz criterion -7.407571
Pensions to gross domestic product ratio (-1)	1.000000
Log unemployment (-1)	-0.934243
	(0.08485)
	[-11.0107]
Log apparent labuor productivity (-1)	-3.450917
	(0.61569)
	[-5.60500]
Old age dependency ratio (-1)	-0.114074
	(0.07355)
	[-1.55089]
@TREND(75)	0.024757
C	18.19483
Error Correction:	D(Pensions to gross domestic product ratio)	D(Log unemployment)	D(Log apparent labor productivity)	D(Old age dependency ratio)
CointEq1	-0.823727	0.355044	-0.085035	-0.229154
	(0.25145)	(0.27994)	(0.02454)	(0.19648)
	[-3.27589]	[1.26830]	[-3.46495]	[-1.16627]
D(Pensions to gross domestic product ratio (-1))	0.048722	-0.134046	0.037997	0.216371
	(0.23937)	(0.26649)	(0.02336)	(0.18705)
	[0.20354]	[-0.50301]	[1.62640]	[1.15678]
D(Pensions to gross domestic product ratio (-2))	-0.023504	-0.327028	0.023747	0.140985
	(0.19428)	(0.21629)	(0.01896)	(0.15181)
	[-0.12098]	[-1.51196]	[1.25233]	[0.92867]
D(Log unemployment (-1))	0.402031	0.652833	-0.002592	0.147807
	(0.24351)	(0.27110)	(0.02377)	(0.19028)
	[1.65098]	[2.40812]	[-0.10904]	[0.77679]
D(Log unemployment (-2))	-0.006098	0.136222	-0.054351	-0.148583
	(0.24210)	(0.26952)	(0.02363)	(0.18918)
	[-0.02519]	[0.50542]	[-2.30024]	[-0.78542]
D(Log apparent labour productivity (-1))	-0.221389	3.246082	-0.463845	-1.234411
	(2.35803)	(2.62517)	(0.23014)	(1.84257)
	[-0.09389]	[1.23652]	[-2.01547]	[-0.66994]
D(Log apparent labour productivity (-2))	0.580083	0.776474	-0.055980	-0.496768
	(1.60695)	(1.78900)	(0.15684)	(1.25567)
	[0.36098]	[0.43403]	[-0.35693]	[-0.39562]
D(Old age dependency ratio (-1))	0.170345	-0.345219	0.035069	0.468223
	(0.26139)	(0.29100)	(0.02551)	(0.20425)
	[0.65169]	[-1.18632]	[.37463]	[2.29241]
D(Old age dependency ratio (-2))	0.371367	-0.035296	0.046423	0.150022
	(0.20938)	(0.23310)	(0.02044)	(0.16361)
	[1.77363]	[-0.15142]	[2.27169]	[0.91694]
C	-0.066069	-0.010129	0.001324	-0.066055
	(0.13892)	(0.15466)	(0.01356)	(0.10855)
	[-0.47559]	[-0.06550]	[0.09766]	[-0.60851]
@TREND(75)	0.007064	0.012654	-0.001357	0.003988
	(0.01497)	(0.01667)	(0.00146)	(0.01170)
	[0.47172]	[0.75905]	[-0.92828]	[0.34082]
REV1974	-0.268243	-0.002228	0.053747	0.162941
	(0.13658)	(0.15206)	(0.01333)	(0.10673)
	[-1.96393]	[-0.01465]	[4.03186]	[1.52670]
R1984	0.077589	-0.199898	0.054140	0.244170
	(0.11939)	(0.13292)	(0.01165)	(0.09329)
	[0.64988]	[-1.50395]	[4.64628]	[2.61728]
R1993	-0.383299	0.032310	-0.040317	-0.117924
	(0.17433)	(0.19408)	(0.01701)	(0.13622)
	[-2.19869]	[0.16648]	[-2.36955]	[-0.86567]
R2002	-0.099864	-0.004149	0.002105	-0.144916
	(0.16839)	(0.18746)	(0.01643)	(0.13158)
	[-0.59306]	[-0.02213]	[0.12808]	[-1.10136]
R2007	0.169199	-0.040558	0.000708	0.179928
	(0.10280)	(0.11445)	(0.01003)	(0.08033)
	[1.64589]	[-0.35438]	[0.07054]	[2.23988]
R-squared	0.685045	0.413290	0.802777	0.842369
Adj. R-squared	0.460078	-0.005789	0.661903	0.729776
Sum sq. resids	0.304910	0.377908	0.002904	0.186175
S.E. equation	0.120497	0.134148	0.011760	0.094157
F-statistic	3.045086	0.986188	5.698563	7.481515
Log likelihood	36.27442	32.30368	122.3691	45.40105
Akaike AIC	-1.095914	-0.881280	-5.749681	-1.589246
Schwarz SC	-0.399301	-0.184667	-5.053068	-0.892633
Mean dependent	0.124324	0.023130	0.020237	0.367568
S.D. dependent	0.163987	0.133761	0.020226	0.181129

Source: Authors’ computation.

Table 2
VECM model with p-values

	Coefficient	Std. error	t-Statistic	Prob.
C(1)	-0.8237	0.2515	-3.2759	0.0036
C(2)	0.0487	0.2394	0.2035	0.8407
C(3)	-0.0235	0.1943	-0.1210	0.9049
C(4)	0.4020	0.2435	1.6510	0.1136
C(5)	-0.0061	0.2421	-0.0252	0.9801
C(6)	-0.2214	2.3580	-0.0939	0.9261
C(7)	0.5801	1.6070	0.3610	0.7217
C(8)	0.1703	0.2614	0.6517	0.5217
C(9)	0.3714	0.2094	1.7736	0.0906
C(10)	-0.0661	0.1389	-0.4756	0.6393
C(11)	0.0071	0.0150	0.4717	0.6420
C(12)	-0.2682	0.1366	-1.9639	0.0629
C(13)	0.0776	0.1194	0.6497	0.5228
C(14)	-0.3833	0.1743	-2.1987	0.0392
C(15)	-0.0999	0.1684	-0.5931	0.5595
C(16)	0.1692	0.1028	1.6459	0.1147
R-squared	0.6850	Mean dependent var		0.1243
Adjusted R-squared	0.4601	S.D. dependent var		0.1640
S.E. of regression	0.1205	Akaike info criterion		-1.0959
Sum squared resid	0.3049	Schwarz criterion		-0.3993
Log likelihood	36.274	Hannan-Quinn criter.		-0.8503
F-statistic	3.0451	Durbin-Watson stat		2.3277
Prob(F-statistic)	0.0097

Table A4
Johansen co-integration test summary

Data Trend:	None	None	Linear	Linear	Quadratic
Test Type	No Intercept	Intercept	Intercept	Intercept	Intercept
	No Trend	No Trend	No Trend	Trend	Trend
Trace	0	1	1	1	1
Max-Eig	0	1	1	1	1
*Critical values based on MacKinnon-Haug-Michelis (1999)
Information Criteria by Rank and Model
Data Trend:	None	None	Linear	Linear	Quadratic
Rank or	No Intercept	Intercept	Intercept	Intercept	Intercept
No. of CEs	No Trend	No Trend	No Trend	Trend	Trend
Log Likelihood by Rank (rows) and Model (columns)
0	192.5650	192.5650	195.6342	195.6342	199.7912
1	199.4257	208.0199	210.6990	212.6689	216.0536
2	204.8373	214.6224	217.2509	223.7600	226.8486
3	207.8471	218.6760	220.1204	228.7651	229.9657
4	210.2947	221.3637	221.3637	231.0177	231.0177
Akaike Information Criteria by Rank (rows) and Model (columns)
0	-8.679192	-8.679192	-8.628876	-8.628876	-8.637363
1	-8.617606	-9.028103	-9.010758	-9.063185	-9.083981
2	-8.477689	-8.898507	-8.932482	-9.176216	-9.235057*
3	-8.207949	-8.631136	-8.655158	-8.960277	-8.971121
4	-7.907822	-8.289927	-8.289927	-8.595552	-8.595552
Schwarz Criteria by Rank (rows) and Model (columns)
0	-7.285965*	-7.285965*	-7.061496	-7.061496	-6.895830
1	-6.876073	-7.243032	-7.095072	-7.103961	-6.994141
2	-6.387850	-6.721591	-6.668490	-6.825147	-6.796911
3	-5.769803	-6.062375	-6.042859	-6.217363	-6.184668
4	-5.121369	-5.329322	-5.329322	-5.460793	-5.460793

Sample: 1975 2014

Included observations: 37

Series: Pensions in percentage of gross domestic product Log unemployment Log apparent labour productivity Old age dependency ratio

Lags interval: 1 to 2

Selected (0.05 level*) Number of Co-integrating Relations by Model

Table A10
Johansen Co-integration Test without Dummy Variables

Unrestricted Co-integration Rank Test (Trace)
Hypothesized No. of CE(s)	Eigenvalue	Trace Statistic	0.05 Critical Value	Prob.**
None *	0.5848	62.453	55.2458	0.0102
At most 1	0.4421	29.923	35.0109	0.1580
At most 2	0.1551	8.338	18.3977	0.6481
At most 3	0.0553	2.1040	3.84147	0.1469
Trace test indicates 1 co-integrating eqn(s) at the 0.05 level * Denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Co-integration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s)	Eigenvalue	Max-Eigen	0.05
		Statistic	Critical Value	Prob.**
None *	0.5848	32.5249	30.8151	0.0306
At most 1	0.4421	21.5898	24.2520	0.1082
At most 2	0.1551	6.2343	17.1477	0.7936
At most 3	0.0553	2.1040	3.84145	0.1469
Max-eigenvalue test indicates 1 co-integrating eqn(s) at the 0.05 level * Denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
*Unrestricted Co-integrating Coefficients (normalised by b'S11b=I):*
Pensions in percentage of GDP	Log unemployment	Log apparent labor productivity	Old age dependency ratio
6.4595	-8.5289	-11.7489	1.4318
1.6370	-6.7668	-37.7933	-1.0975
6.4758	-3.6887	-25.9967	-0.8533
-1.8548	3.5122	20.2981	-2.5845
Unrestricted Adjustment Coefficients (alpha):
D(Pensions in percentage of GDP)	-0.0493	0.00881	-0.0167	-0.0274
D(Log unemployment)	0.0496	0.03077	-0.0121	-0.0156
D(Log apparent labor productivity)	-0.0074	0.00668	0.0009	0.0012
D(Old age dependency ratio)	-0.0291	0.0144	0.0329	-0.0019
1 Co-integrating Equation(s): Log likelihood 216.0536
Normalized co-integrating coefficients (standard error in brackets)
Pensions in percentage of GDP	Log unemployment	Log apparent labor productivity	Old age dependency ratio
1.000000	-1.3204 (0.163)	-1.8189 (0.936)	0.2217 (0.082)
Adjustment coefficients (standard error in brackets)
D(Pensions in percentage of GDP)	-0.3182 (0.16656)
D(Log unemployment)	0.3206 (0.12175)
D(Log apparent labor productivity)	-0.0477 (0.01652)
D(Old age dependency ratio)	-0.1883 (0.11411)

Source: Authors’ computation.

Sample (adjusted): 1978 2014

Included observations: 37 after adjustments

Trend assumption: Quadratic deterministic trend

Series: Pensions in percentage of gross domestic product Log unemployment Log apparent labour productivity Old age dependency ratio

Lags interval (in first differences): 1 to 2

Table A11
Variance for the Pensions in percentage of gross domestic product residuals

Years ahead	Pensions in percentage of GDP	Log unemployment	Log apparent labour productivity	Old age dependency ratio	St. errors
1	39.76	57.39	0.00	2.86	0.12
2	14.09	81.98	1.80	2.13	0.21
3	6.51	86.96	4.92	1.61	0.30
4	4.12	87.13	5.94	2.81	0.39
5	3.15	86.15	6.97	3.73	0.45
6	2.68	85.39	7.33	4.59	0.49
7	2.41	85.04	7.55	5.00	0.52
8	2.19	85.06	7.56	5.18	0.54
9	2.02	85.24	7.58	5.15	0.57
10	1.84	85.49	7.57	5.10	0.60
11	1.67	85.65	7.61	5.07	0.63
12	1.52	85.73	7.66	5.09	0.66
13	1.40	85.72	7.72	5.15	0.69
14	1.31	85.71	7.77	5.22	0.71
15	1.23	85.70	7.80	5.27	0.73
16	1.16	85.72	7.82	5.30	0.76
17	1.09	85.75	7.83	5.32	0.78
18	1.04	85.79	7.85	5.33	0.80
19	0.98	85.81	7.87	5.34	0.82
20	0.93	85.83	7.88	5.35	0.84

Table A12
Johansen Co-integration Test with Dummy Variables

Hypothesized no. of CE(s)	Eigenvalue	Trace Statistic	0.05 Critical value	Prob.**
None *	0.7395	84.7403	55.2458	0.0000
At most 1	0.4658	34.9636	35.0109	0.0506
At most 2	0.2490	11.7627	18.3977	0.3270
At most 3	0.0311	1.1681	3.8415	0.2798
Trace test indicates 1 co-integrating eqn(s) at the 0.05 level
* Denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Co-integration Rank Test (Maximum Eigenvalue)
Hypothesised no. of CE(s)	Eigenvalue	Max-Eigen Statistic	0.05 Critical value	Prob.**
None *	0.7395	49.7768	30.8151	0.0001
At most 1	0.4658	23.2009	24.2520	0.0684
At most 2	0.2490	10.5945	17.1477	0.3447
At most 3	0.0311	1.1681	3.84147	0.2798
Max-eigenvalue test indicates 1 co-integrating eqn(s) at the 0.05 level
* Denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Co-integrating Coefficients (normalised by b'S11b=I):
Pensions in percentage of GDP	Log unemployment	Log apparent labour productivity	Old age dependency ratio
12.69343	-11.8587	-43.8040	-1.4480
-1.652246	-4.79285	1.2328	-0.8655
6.893543	-12.1842	-77.0428	3.6249
-2.640094	3.0243	51.6066	6.0229
Unrestricted Adjustment Co-efficients (alpha):
D(Pensions in percentage of GDP)	-0.0649	0.0490	0.0171	0.0036
D(Log unemployment)	0.0280	0.0668	0.0094	0.0001
D(Log apparent labour productivity L)	-0.0067	-0.0010	-0.0013	-0.0013
D(OAD)	-0.0181	-0.0224	0.0240	-0.0069
1 Co-integrating Equation(s):		Log likelihood	259.8113
Normalised co-integrating coefficients (standard error in brackets)
Pensions in percentage of GDP	Log unemployment	Log apparent labour productivity	Old age dependency ratio
1.000000	-0.9342	-3.4509	-0.1141
	(0.0849)	(0.6157)	(0.0736)
Adjustment coefficients (standard error in brackets)
D(Pensions in percentage of gross domestic product)	-0.8237
D(Pensions in percentage of gross domestic product)	(0.2515)
D(Log unemployment)	0.3550
D(Log unemployment)	(0.2799)
D(Log apparent labour productivity)	-0.0850
D(Log apparent labour productivity)	(0.0245)
D(Old age dependency ratio)	-0.2292
D(Old age dependency ratio)	(0.1965)

Sample (adjusted): 1978 2014

Included observations: 37 after adjustments

Trend assumption: Quadratic deterministic trend

Series: Pensions in percentage of gross domestic product Log unemployment Log apparent labour productivity Old age dependency ratio

Exogenous series: REV1974 R1984 R1993 R2002 R2007

Warning: Critical values assume no exogenous series

Lags interval (in first differences): 1 to 2

Unrestricted Co-integration Rank Test (Trace)

Table 1

VECM estimation results

DISPLAY Table

Figure 1

Pensions to gross domestic product ratio response to Cholesky one standard deviation impulse

DISPLAY Figure

Table 2

VECM model with p-values

DISPLAY Table

Table A1

Descriptive statistics

DISPLAY Table

Table A2

Unit root augmented Dickey-Fuller and Phillips-Perron tests

DISPLAY Table

Table A3

Var lag order selection criteria procedure

DISPLAY Table

Table A4

Johansen co-integration test summary

DISPLAY Table

Table A5

Descriptive statistics - Residuals

DISPLAY Table

Table A6

White heteroscedasticity test (no cross terms)

DISPLAY Table

Table A7

Covariance matrix between variables and residuals

DISPLAY Table

Table A8

Residual normality test

DISPLAY Table

Table A9

Residual serial correlation LM test

DISPLAY Table

Table A10

Johansen Co-integration Test without Dummy Variables

DISPLAY Table

Table A11

Variance for the Pensions in percentage of gross domestic product residuals

DISPLAY Table

Table A12

Johansen Co-integration Test with Dummy Variables

DISPLAY Table

Table A13

Wald test for the VECM short-run coefficients

DISPLAY Table

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