Sustainability assessment of pension systems of new EU member states using data envelopment analysis with sensitivity and cross-efficiency analysis

Figures & data

Table 1. Cross-efficiency matrix.

	Rated DMU
Rating DMU	1	2	3	4	5	6	Averaged appraisal of peers
1	E11	E12	E13	E14	E15	E16
2	E21	E22	E23	E24	E25	E26
3	E31	E32	E33	E34	E35	E36
4	E41	E42	E43	E44	E45	E46
5	E51	E52	E53	E54	E55	E56
6	E61	E62	E63	E64	E65	E66
	Ē1	Ē2	Ē3	Ē4	Ē5	Ē6
	Averaged appraisal by peers (peer appraisal)

Source: Doyle and Green (1994).

Table 2. Descriptive statistics.

	S1 (%)	S2 (%)	S3d (%)	S4 (%)	S5a (%)	S5b (%)	S8 (%)	S3a (yrs)	S3b (yrs)	S3c (%)	S6 (%)
Min	18.7	5.2	1.4	0.0	44.8	3.0	2.8	11.7	14.5	39.4	8.4
Max	100.0	27.3	1.7	7.3	73.9	14.0	4.3	17.0	19.4	52.0	74.8
Mean	63.8	11.3	1.6	4.5	59.3	6.8	3.4	14.0	16.3	44.6	43.9
SD	22.6	6.2	0.1	2.4	10.2	3.2	0.4	1.7	1.4	3.9	20.2

Source: OECD (2019).

Note: Variable S7 is omitted from Table 4 because its values do not vary between the countries.

Table 3. Super-SMB scores and ranks.

No.	DMU	Score	Rank	Alt. rank
1	Bulgaria	1.006381	8	2
2	Croatia	1.06526	2	9
3	Czech Republic	1.011386	6	7
4	Estonia	1.323985	1	1
5	Hungary	1.008692	7	11
6	Latvia	1.04935	3	5
7	Lithuania	1.003278	9	6
8	Poland	1.034523	4	3
9	Romania	1.022784	5	4
10	Slovakia	0.760621	11	10
11	Slovenia	1.00307	10	8

Source: Own.

Table 4. Deviations (in percent) from projections on the production possibilities frontier.

DMU	1/S1	1/S2	1/S3d	1/S4	1/S5a	1/S5b	1/S8	S3a	S3b	S3c	S6
BG	−3	0	−5	−17	−6	−48	0	7	−1	−5	0
HR	−15	61	−9	−17	−39	−79	−18	−5	17	−11	−89
CZ	−21	−34	6	4	0	−31	−6	−17	−8	4	−47
EE	4	35	2	20	14	139	−2	−14	−4	8	165
HU	−75	−41	−4	−98	0	−53	0	3	−5	7	−40
LV	17	−19	8	0	−3	−31	−3	22	12	−8	−77
LT	−23	−49	−2	−50	4	−8	−11	−3	0	−12	−4
PL	−4	0	−11	22	−15	−51	2	0	12	6	−59
RO	−34	−58	2	−5	−26	0	26	−2	−7	0	−8
SK	−57	−24	−9	−29	−20	−65	−3	−16	0	−8	−55
SI	0	−12	0	−74	−22	−17	−4	−5	−10	4	−40

Source: Own.

Note: Variable S7 is omitted from Table 4 because its values do not vary between the countries.

Table 5. Reference sets and peers.

	BG	HR	CZ	EE	HU	LV	LT	PL	RO	SK	SI
BG				0.50		0.38			0.12
HR				1.00
CZ				0.78				0.22
EE	1.00
HU						0.37		0.48	0.14
LV				1.00
LT				0.14		0.86
PL				0.56					0.44
RO				0.27		0.47		0.26
SK				0.51		0.49
SI			0.75		0.25			0.01
count	1	0	1	8	1	5	0	4	3	0	0

Source: Own.

Table 6. Comparison of the Efficiency of Pension Systems of EU Member States.

Rank	Country	Rank	Country
1	Estonia	15	Bulgaria
2	Ireland	16	Austria
3	Netherlands	17	Lithuania
4	Denmark	18	Portugal
5	Finland	19	Czech Republic
6	Latvia	20	Belgium
7	Sweden	21	Croatia
8	Luxembourg	22	Germany
9	Poland	23	Slovakia
10	France	23	Slovenia
11	Malta	23	Spain
12	Romania	23	Italy
13	Hungary
14	Cyprus

Source: Own.

Table 7. Rankings when one indicator is dropped from the analysis (12 columns for each new ranking).

	-S1	-S2	-S3	-S4	-S5	-S6	-S7	-S8	-S9	-S10	-S11	-S12
BG	8	7	8	7	8	8	8	7	10	8	6	10
HR	2	9	2	2	2	2	2	2	2	2	2	2
CZ	6	5	7	8	6	6	6	5	6	6	7	6
EE	1	1	1	1	1	1	1	1	1	1	1	1
HU	7	6	6	6	7	7	7	6	9	7	9	7
LV	3	2	3	3	3	3	3	3	4	3	3	3
LT	9	8	9	9	10	9	9	8	7	10	8	8
PL	4	3	4	5	4	4	4	4	3	4	4	4
RO	5	4	5	4	5	5	5	10	5	5	5	5
SK	11	11	11	11	10	11	11	10	10	11	9	11
SI	10	10	10	10	9	10	10	9	8	9	9	9

Source: Own.

Table 8. The results of the cross-efficiency analysis.

	BG	HR	CZ	EE	HU	LV	LT	PL	RO	SK	SI
BG	1	0.851	0.921	1	1	1	0.913	0.999	1	0.866	0.907
HR	0.960	1	0.833	1	0.742	1	0.887	0.901	0.773	0.904	0.694
CZ	0.966	0.885	1	1	1	1	0.925	0.972	0.994	0.898	1.000
EE	0.980	0.838	0.896	1	0.875	0.941	0.791	1	1	0.906	0.838
HU	0.969	0.897	1	1	1	1	0.916	1	0.995	0.901	0.981
LV	0.976	0.872	0.963	1	1	1	0.912	1	0.957	0.874	0.954
LT	1	1	1	1	1	1	1	1	1	1	1
PL	0.991	0.912	0.930	1	0.916	1	0.876	1	1	0.944	0.880
RO	0.925	0.829	0.932	1	0.887	1	0.937	1	1	0.862	0.857
SK	1	1	1	1	1	1	1	1	1	1	1
SI	0.968	0.896	1	1	0.962	1	0.913	0.997	1	0.890	1
average	0.976	0.907	0.952	1	0.944	0.995	0.915	0.988	0.974	0.913	0.919
rank	4	11	6	1	7	2	9	3	5	10	8
SD	0.021	0.062	0.053	0.000	0.079	0.017	0.054	0.029	0.065	0.046	0.092

Source: Own.

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. https://doi.org/10.1057/jors.1994.84

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OECD. (2019). Funded and private pensions: Pension Markets in Focus. http://www.oecd.org/pensions/private-pensions/pensionmarketsinfocus.htm

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