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Pension expenditure determinants: the case of Portugal
Maria Teresa Medeiros Garcia* 
André Fernando Rodrigues Rocha da Silva*
André Fernando Rodrigues Rocha da Silva
Affiliation: Lisbon School of Economics and Management, Universidade de Lisboa, Lisboa, Portugal
 0000-0001-8123-6557
Article | Year: 2023 | Pages: 177 - 203 | Volume: 47 | Issue: 2 Received: April 21, 2022 | Accepted: January 23, 2023 | Published online: June 12, 2023
|
FULL ARTICLE
FIGURES & DATA
REFERENCES
CROSSMARK POLICY
METRICS
LICENCING
PDF
|
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.
Source: Authors’ computation.
|
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
|
|
|
|
|
Variables
|
Mean
|
Median
|
Max
|
Min
|
Std. dev.
|
Skewness
|
Kurtosis
|
Jarque-Bera
|
|
Dependent variable
|
|
Pensions in %
of GDP
|
5.05
|
5.15
|
7.70
|
2.20
|
1.28
|
0.16
|
2.82
|
0.28
(0.89)
|
|
Independent variables
|
|
Log
unemployment
|
12.75
|
12.72
|
13.66
|
12.09
|
0.38
|
0.65
|
3.14
|
2.82
(0.24)
|
|
Log apparent
labour productivity
|
2.69
|
2.77
|
3.01
|
2.18
|
0.28
|
-0.53
|
2.03
|
3.43
(0.18)
|
|
Old age
dependency ratio
|
22.35
|
22.00
|
30.70
|
16.30
|
4.09
|
0.33
|
1.94
|
2.61
(0.27)
|
|
No. of
observations
|
40
|
Source: authors’ computation.
|
|
Dickey-Fuller
test
|
Phillips-Perron
test
|
|
|
Deterministic
component
|
P-Value
|
T-Stat
|
Deterministic
component
|
P-Value
|
Adj.
T-Stat
|
|
Dependent
variable
|
|
Pensions in %
of GDP
|
constant
and trend
|
0.44
|
-2.27
|
constant
and trend
|
0.29
|
-2.59
|
|
First
difference
|
constant
|
0
|
-6.23
|
constant
|
0
|
-6.24
|
|
Independent
variables
|
|
Old age
dependency ratio
|
constant
and trend
|
0.98
|
-0.45
|
constant
and trend
|
0.99
|
0.41
|
|
First
difference
|
constant
and trend
|
0.005
|
-4.53
|
constant
and trend
|
0.004
|
-4.58
|
|
Log unemployment
|
constant
and trend
|
0.39
|
-2.36
|
constant
and trend
|
0.69
|
-1.78
|
|
First
difference
|
none
|
0.000
|
-3.97
|
none
|
0.00
|
-3.97
|
|
Log apparent
labour productivity
|
constant
and trend
|
0.86
|
-1.33
|
constant
and trend
|
0.83
|
-1.46
|
|
First
difference
|
constant
and trend
|
0.017
|
-4.01
|
constant
and trend
|
0.017
|
-4.01
|
|
Lag
|
LogL
|
LR
|
FPE
|
AIC
|
SC
|
HQ
|
|
0
|
-86.6845
|
NA
|
0.0044
|
5.9269
|
6.8066
|
6.2340
|
|
1
|
212.3587
|
448.5649
|
6.82e-10
|
-9.7977
|
-8.2142*
|
-9.2450
|
|
2
|
240.9137
|
36.4869*
|
3.73e-10*
|
-10.495
|
-8.2079
|
-9.6969*
|
|
3
|
257.5250
|
17.5341
|
4.35e-10
|
-10.529
|
-7.5381
|
-9.4852
|
|
4
|
278.0591
|
17.1118
|
4.79e-10
|
-10.781*
|
-7.0861
|
-9.4915
|
Endogenous variables: Pensions in percentage of gross domestic product Log unemployment Log apparent labour productivity Old age dependency ratio Exogenous variables: REV1974 R1984 R1993 R2002 R2007 Sample: 1975 2014; Included observations: 36 AIC: Akaike information criterion; SC: Schwarz information criterion; LR: sequential modified; LR test statistic (each test at 5% level); FPE: Final prediction error; HQ: Hannan-Quinn information criterion.
|
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
|
Variables
|
Mean
|
Median
|
Max
|
Min
|
Std. dev.
|
Skewness
|
Kurtosis
|
Jarque-Bera
|
|
Resid01
|
2.25E-17
|
-0.007
|
0.236
|
-0.191
|
0.092
|
0.399
|
3.113
|
1.006
(0.605)
|
|
Resid02
|
-3.00E-18
|
0.015
|
0.245
|
-0.220
|
0.102
|
0.198
|
2.897
|
0.259
(0.879)
|
|
Resid03
|
5.06E-18
|
-0.001
|
0.018
|
-0.021
|
0.010
|
-0.065
|
3.14
|
0.042
(0.979)
|
|
Resid04
|
2.69
|
2.77
|
3.01
|
2.18
|
0.28
|
2.90
|
2.32
|
0.775
(0.679)
|
|
No. of
observations
|
37
|
Note: In parenthesis the probability.
|
Chi-sq
|
df
|
Prob.
|
|
257.1420
|
250
|
0.3646
|
Sample: 1975 2014 Included observations: 37
|
Variables
|
Resid01
|
Resid02
|
Resid03
|
Resid04
|
|
Pensions in %
of GDP
|
0.0022
|
-0.0009
|
-6.561464E-05
|
0.0004
|
|
Old age
dependency ratio
|
-0.0026
|
-0.0062
|
8.657489E-05
|
0.0079
|
|
Log
unemployment
|
-0.0007
|
-0.0002
|
-6.941109E-05
|
0.0010
|
|
Log apparent
labor productivity
|
0.0020
|
0.0004
|
6.809052E-05
|
-0.0003
|
|
Component
|
Skewness
|
Chi-sq
|
df
|
Prob.
|
|
1
|
0.399830
|
0.985828
|
1
|
0.3208
|
|
2
|
-0.039593
|
0.009667
|
1
|
0.9217
|
|
3
|
0.267474
|
0.441177
|
1
|
0.5066
|
|
4
|
-0.430280
|
1.141701
|
1
|
0.2853
|
|
Joint
|
|
2.578373
|
4
|
0.6307
|
|
Component
|
Kurtosis
|
Chi-sq
|
df
|
Prob.
|
|
1
|
3.113281
|
0.019784
|
1
|
0.8881
|
|
2
|
2.672602
|
0.165250
|
1
|
0.6844
|
|
3
|
2.471544
|
0.430535
|
1
|
0.5117
|
|
4
|
2.776496
|
0.077013
|
1
|
0.7814
|
|
Joint
|
|
0.692582
|
4
|
0.9522
|
|
Component
|
Jarque-Bera
|
df
|
Prob.
|
|
|
1
|
1.005611
|
2
|
0.6048
|
|
|
2
|
0.174917
|
2
|
0.9163
|
|
|
3
|
0.871713
|
2
|
0.6467
|
|
|
4
|
1.218713
|
2
|
0.5437
|
|
|
Joint
|
3.270955
|
8
|
0.9162
|
|
Orthogonalisation: Cholesky (Lutkepohl) Null Hypothesis: residuals are multivariate normal Sample: 1975 to 2014 Included observations: 37
|
Lags
|
LM-Stat
|
Prob
|
|
1
|
26.53845
|
0.0469
|
|
2
|
23.67038
|
0.0970
|
|
3
|
14.33662
|
0.5737
|
|
4
|
12.13793
|
0.7344
|
|
5
|
17.84991
|
0.3328
|
|
6
|
15.06970
|
0.5195
|
|
Probs from chi-square with 16 df.
|
|
Null Hypothesis: no serial correlation at lag order h Sample: 1975 2014 Included observations: 37
|
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'*S11*b=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
|
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
|
|
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'*S11*b=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
|
|
|
|
|
(0.2515)
|
|
|
|
|
D(Log unemployment)
|
0.3550
|
|
|
|
|
(0.2799)
|
|
|
|
|
D(Log apparent labour productivity)
|
-0.0850
|
|
|
|
|
(0.0245)
|
|
|
|
|
D(Old age dependency ratio)
|
-0.2292
|
|
|
|
|
(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)
|
Test Statistic
|
Value
|
df
|
Probability
|
|
F-statistic
|
1.3647
|
(2, 21)
|
0.2772
|
|
Chi-square
|
2.7294
|
2
|
0.2555
|
|
Null Hypothesis: C(4)=C(5)=0
|
|
|
|
Null Hypothesis Summary:
|
|
|
|
Normalised Restriction (= 0)
|
|
Value
|
Std. Err.
|
|
C(4)
|
|
0.4020
|
0.2435
|
|
C(5)
|
|
-0.0061
|
0.2421
|
|
All restrictions are linear in
coefficients.
|
|
|
Test Statistic
|
Value
|
df
|
Probability
|
|
F-statistic
|
0.0660
|
(2, 21)
|
0.9363
|
|
Chi-square
|
0.1320
|
2
|
0.9361
|
|
Null Hypothesis: C(6)=C(7)=0
|
|
|
|
Null Hypothesis Summary:
|
|
|
|
Normalised Restriction (= 0)
|
|
Value
|
Std. Err.
|
|
C(6)
|
|
-0.2214
|
2.3580
|
|
C(7)
|
|
0.5801
|
1.6070
|
|
Test Statistic
|
Value
|
df
|
Probability
|
|
F-statistic
|
1.8520
|
(2, 21)
|
0.1817
|
|
Chi-square
|
3.7040
|
2
|
0.1569
|
|
Null Hypothesis: C(8)=C(9)=0
|
|
|
|
Null Hypothesis Summary:
|
|
|
|
Normalised Restriction (= 0)
|
|
Value
|
Std. Err.
|
|
C(8)
|
|
0.1703
|
0.2614
|
|
C(9)
|
|
0.3714
|
0.2094
|
|
|
June, 2023
II/2023
|
