Analysis of Takaful vs. Conventional insurance firms’ efficiency: Two-stage DEA of Saudi Arabia’s insurance market

Figures & data

Figure 1. Series of two-stage processes.

Table 1. Efficiency measures and their ranks for 33 insurance companies in Saudi Arabia, 2014–2015

	2014						2015
DMU	${\hat{e}}^1$	Rank	${\hat{e}}^2$		${\hat{e}}^0$	Rank	${\hat{e}}^1$	Rank	${\hat{e}}^2$	Rank	${\hat{e}}^0$	Rank
1	0.8976	15	0.4664	27	0.4186	22	0.8914	11	0.6202	18	0.5528	12
2	0.3683	30	0.7292	17	0.2685	30	0.6653	23	0.5555	22	0.3696	23
3	0.3806	29	0.9798	5	0.3729	25	0.507	30	0.8413	9	0.4265	21
4	0.5765	27	0.3292	33	0.1898	32	0.7828	16	0.0966	33	0.0756	33
5	1	1	0.5921	23	0.5921	11	1	1	0.5185	25	0.5185	15
6	0.4229	28	1	1	0.4229	21	0.6267	25	0.5425	23	0.34	25
7	1	1	0.625	21	0.625	10	0.711	20	0.6042	20	0.4296	20
8	0.8332	17	0.5209	25	0.4341	20	0.8048	14	0.8947	7	0.7201	3
9	0.5884	25	0.8381	10	0.4932	14	1	1	0.8836	8	0.8836	2
10	1	1	0.8637	9	0.8637	2	1	1	1	1	1	1
11	0.699	20	0.7215	18	0.5043	13	0.4667	31	0.7412	11	0.3459	24
12	0.9578	12	0.3678	31	0.3523	26	0.7545	17	0.4288	28	0.3235	26
13	0.7603	19	0.4523	28	0.3439	27	0.5879	29	0.4718	26	0.2773	28
14	0.6746	21	0.5575	24	0.3761	24	0.6927	22	0.3599	30	0.2493	31
15	0.6349	23	0.7322	15	0.4649	17	0.7034	21	0.9556	3	0.6721	6
16	1	1	0.381	30	0.381	23	1	1	0.2567	31	0.2567	29
17	1	1	0.6758	19	0.6758	6	1	1	0.7038	14	0.7038	4
18	0.1846	33	0.9983	4	0.1843	33	0.6278	24	0.4006	29	0.2515	30
19	0.9966	10	0.6367	20	0.6345	9	0.8657	13	0.5335	24	0.4619	17
20	0.3006	31	0.9497	6	0.2855	29	0.6096	26	0.6675	15	0.4069	22
21	0.5839	26	0.7912	13	0.462	18	0.5942	28	0.8062	10	0.4791	16
22	0.9032	14	0.7316	16	0.6608	7	0.7515	18	0.908	6	0.6823	5
23	1	1	0.8312	11	0.8312	3	0.8839	12	0.6168	19	0.5452	13
24	0.8598	16	0.6232	22	0.5359	12	0.9017	10	0.5852	21	0.5277	14
25	1	1	0.483	26	0.483	15	1	1	0.6349	16	0.6349	8
26	0.9785	11	0.4488	29	0.4391	19	1	1	0.4341	27	0.4341	18
27	0.8141	18	0.9126	8	0.743	5	0.6065	27	1	1	0.6065	10
28	1	1	0.3373	32	0.3373	28	0.9879	9	0.2399	32	0.237	32
29	0.6559	22	1	1	0.6559	8	0.7161	19	0.9286	4	0.665	7
30	0.6342	24	0.738	14	0.468	16	0.7881	15	0.74	12	0.5832	11
31	1	1	1	1	1	1	1	1	0.6223	17	0.6223	9
32	0.9327	13	0.8041	12	0.7499	4	0.4645	32	0.9257	5	0.43	19
33	0.272	32	0.9395	7	0.2555	31	0.3947	33	0.7284	13	0.2875	27

Note: The rows highlighted in grey refer to Takaful firms.

Table 2. Efficiency measures and their ranks for 33 insurance companies in Saudi Arabia, 2016 and 2017

	2016						2017
DMU	${\hat{e}}^1$	Rank	${\hat{e}}^2$	Rank	${\hat{e}}^0$	Rank	${\hat{e}}^1$	Rank	${\hat{e}}^2$	Rank	${\hat{e}}^0$	Rank
1	0.827	14	0.5245	26	0.4338	19	0.2306	29	0.4318	26	0.0996	26
2	0.2098	32	0.6212	20	0.1303	32	0.1495	30	0.6324	21	0.0945	28
3	0.2845	31	0.6508	18	0.1852	29	0.3129	21	0.7169	16	0.2243	18
4	0.4076	26	0.509	27	0.2075	27	0.2826	26	0.3561	27	0.1006	25
5	0.953	11	0.5488	25	0.523	14	1	1	0.6033	23	0.6033	7
6	0.3515	29	0.9694	3	0.3407	22	0.4116	18	0.9289	5	0.3823	13
7	0.6506	23	0.7015	15	0.4564	17	0.287	24	0.6674	18	0.1915	22
8	0.9899	6	0.5589	24	0.5533	11	0.425	17	0.4971	25	0.2112	20
9	0.7238	21	0.7975	8	0.5772	10	0.5464	14	0.8337	8	0.4556	9
10	0.9715	9	0.9715	2	0.9438	2	0.7032	8	0.9408	4	0.6616	6
11	0.4076	26	0.7253	12	0.2957	24	0.2834	25	0.8456	7	0.2396	17
12	0.6353	24	0.4057	29	0.2577	25	0.2551	27	0.3234	30	0.0825	30
13	0.3654	28	0.49	28	0.179	30	0.3076	22	0.3532	28	0.1086	24
14	1	1	0.3917	30	0.3917	21	0.6674	9	0.3352	29	0.2237	19
15	0.8906	12	0.7839	9	0.6981	6	1	1	0.773	10	0.773	3
16	0.9695	10	0.5961	23	0.5779	9	0.4496	16	0.5885	24	0.2646	14
17	0.6533	22	0.8008	7	0.5232	13	0.5976	11	0.7309	15	0.4368	10
18	0.7305	19	0.6134	21	0.4481	18	0.3233	20	0.6353	20	0.2054	21
19	0.813	15	0.6539	17	0.5316	12	1	1	0.6937	17	0.6937	5
20	0.3242	30	0.6069	22	0.1968	28	0.2327	28	0.7461	14	0.1736	23
21	1	1	0.8293	6	0.8293	3	1	1	0.8673	6	0.8673	1
22	0.7817	16	0.7773	10	0.6077	8	1	1	0.7635	12	0.7635	4
23	0.7252	20	0.7101	14	0.5149	16	0.5582	13	0.7682	11	0.4288	12
24	0.8346	13	0.1015	33	0.0847	33	0.5385	15	0.159	33	0.0856	29
25	0.9742	8	0.6416	19	0.6251	7	0.3927	19	0.6274	22	0.2464	15
26	1	1	0.3383	31	0.3383	23	0.9219	6	0.2602	32	0.2398	16
27	0.7681	17	0.9163	5	0.7038	5	0.8472	7	0.954	3	0.8082	2
28	0.9846	7	0.2396	32	0.2359	26	0.2876	23	0.2846	31	0.0818	32
29	1	1	1	1	1	1	0.0509	33	1	1	0.0509	33
30	0.7462	18	0.6984	16	0.5211	15	0.5748	12	0.7513	13	0.4318	11
31	1	1	0.7451	11	0.7451	4	0.1286	31	0.6414	19	0.0825	30
32	0.5428	25	0.7236	13	0.3928	20	0.6313	10	0.8307	9	0.5244	8
33	0.1784	33	0.9559	4	0.1706	31	0.0986	32	0.996	2	0.0982	27

Note: The rows highlighted in grey refer to Takaful firms.

Table 3. Efficiency of Saudi Arabia’s Takaful and insurance companies, 2014–2017

Code	2014	2015	2016	2017	Average	Rank
	Conventional Companies
1	0.4186	0.5528	0.4338	0.0996	0.3762	18
2	0.2685	0.3696	0.1303	0.0945	0.215,725	31
3	0.3729	0.4265	0.1852	0.2243	0.302,225	25
4	0.1898	0.0756	0.2075	0.1006	0.143,375	33
5	0.5921	0.5185	0.523	0.6033	0.559,225	12
6	0.4229	0.34	0.3407	0.3823	0.371,475	19
7	0.625	0.4296	0.4564	0.1915	0.425,625	17
8	0.4341	0.7201	0.5533	0.2112	0.479,675	16
9	0.4932	0.8836	0.5772	0.4556	0.6024	7
10	0.8637	1	0.9438	0.6616	0.867,275	1
11	0.5043	0.3459	0.2957	0.2396	0.346,375	22
12	0.3523	0.3235	0.2577	0.0825	0.254	28
13	0.3439	0.2773	0.179	0.1086	0.2272	29
14	0.3761	0.2493	0.3917	0.2237	0.3102	23
15	0.4649	0.6721	0.6981	0.773	0.652,025	5
16	0.381	0.2567	0.5779	0.2646	0.37,005	20
17	0.6758	0.7038	0.5232	0.4368	0.5849	9
18	0.1843	0.2515	0.4481	0.2054	0.272,325	26
19	0.6345	0.4619	0.5316	0.6937	0.580,425	10
20	0.2855	0.4069	0.1968	0.1736	0.2657	27
21	0.462	0.4791	0.8293	0.8673	0.659,425	4
22	0.6608	0.6823	0.6077	0.7635	0.678,575	3
23	0.8312	0.5452	0.5149	0.4288	0.580,025	11
24	0.5359	0.5277	0.0847	0.0856	0.308,475	24
25	0.483	0.6349	0.6251	0.2464	0.49,735	15
26	0.4391	0.4341	0.3383	0.2398	0.362,825	21
Average	0.4729	0.48,340	0.44,042	0.34,066	0.43,434
	Takaful Companies
27	0.743	0.6065	0.7038	0.8082	0.715,375	2
28	0.3373	0.237	0.2359	0.0818	0.223	30
29	0.6559	0.665	1	0.0509	0.59,295	8
30	0.468	0.5832	0.5211	0.4318	0.501,025	14
31	1	0.6223	0.7451	0.0825	0.612,475	6
32	0.7499	0.43	0.3928	0.5244	0.524,275	13
33	0.2555	0.2875	0.1706	0.0982	0.20,295	32
Average	0.60,137	0.490,214	0.53,847	0.29,682	0.48,172
Overall Average	0.49,935	0.484,806	0.46,060	0.33,164	0.4441

Table 4. Leader stage identification results for 33 insurance companies in Saudi Arabia, 2014 and 2015

	2014					2015
DMU	${\mathit{e}}^{\mathbf{1}\mathbf{,}\mathit{U}}$	${\mathit{e}}^{\mathbf{1}\mathbf{,}\mathit{L}}$	${\mathit{e}}^{\mathbf{2}\mathbf{,}\mathit{L}}$	${\mathit{e}}^{\mathbf{2}\mathbf{,}\mathit{U}}$	Leader Stage	${\mathit{e}}^{\mathbf{1}\mathbf{,}\mathit{U}}$	${\mathit{e}}^{\mathbf{1}\mathbf{,}\mathit{L}}$	${\mathit{e}}^{\mathbf{2}\mathbf{,}\mathit{L}}$	${\mathit{e}}^{\mathbf{2}\mathbf{,}\mathit{U}}$	Leader Stage
1	0.9247	0.3782	0.857	0.4936	1	0.8939	0.6169	0.8895	0.6227	1
2	0.3693	0.7275	0.3677	0.7302	2	0.699	0.5323	0.6219	0.5892	1
3	0.3858	0.9659	0.3787	0.985	2	0.5263	0.7917	0.4999	0.8605	2
4	0.639	0.2423	0.4904	0.3917	1	0.9068	0	0.3631	0.2205	1
5	1	0.5921	1	0.5921	1	1	0.5185	1	0.5185	1
6	0.4229	1	0.4229	1	2	0.6329	0.5416	0.5867	0.5487	1
7	1	0.625	1	0.625	1	0.7729	0.2609	0.6995	0.6661	1
8	0.8935	0.4529	0.7379	0.5812	1	0.9101	0.2843	0.7838	1	1
9	0.617	0.7999	0.5681	0.8667	2	1	0.8836	1	0.8836	1
10	1	0.8637	1	0.8637	1	1	1	1	1	1
11	0.7071	0.7188	0.673	0.7296	2	0.4817	0.7306	0.443	0.7561	2
12	1	0.3461	0.8353	0.41	1	0.77	0.3196	0.6715	0.4443	1
13	0.8068	0.3054	0.6772	0.4988	1	0.5879	0.4718	0.5879	0.4718	1
14	0.7018	0.4784	0.6204	0.5847	1	0.8624	0	0.5814	0.5296	1
15	0.6598	0.7046	0.5946	0.7571	2	0.7173	0.9088	0.6963	0.9695	2
16	1	0.381	1	0.381	1	1	0.2567	1	0.2567	1
17	1	0.6758	1	0.6758	1	1	0.7038	1	0.7038	1
18	0.1862	0.989	0.1843	1	2	0.6348	0.3688	0.6259	0.4076	1
19	1	0.6365	0.9417	0.6401	1	0.8685	0.5113	0.8654	0.5363	1
20	0.3015	0.9408	0.3005	0.9506	2	0.6205	0.6058	0.6058	0.6784	2
21	0.6014	0.7645	0.5605	0.8087	2	0.6315	0.7769	0.5528	0.8435	2
22	0.9109	0.6821	0.9021	0.7393	1	0.7539	0.8162	0.7511	0.9104	2
23	1	0.8312	1	0.8312	1	1	0.3231	0.8198	0.7329	1
24	0.8847	0.4719	0.8538	0.6481	1	0.9219	0.5303	0.8933	0.6054	1
25	1	0.483	1	0.483	1	1	0.6349	1	0.6349	1
26	1	0.4401	0.9291	0.4702	1	1	0.4341	1	0.4341	1
27	0.8181	0.9104	0.8073	0.9166	2	0.6065	1	0.6065	1	2
28	1	0.3373	1	0.3373	1	1	0.2397	0.5718	0.252	1
29	0.6559	1	0.6559	1	2	0.7875	0.8857	0.5997	1	2
30	0.6489	0.6927	0.6208	0.7527	2	0.8098	0.6877	0.7778	0.7617	1
31	1	1	1	1	1	1	0.6223	1	0.6223	1
32	0.9804	0.7767	0.8598	0.8517	1	0.4843	0.8576	0.4568	0.9455	2
33	0.2797	0.9062	0.2703	0.9471	2	0.4268	0.69	0.3713	0.7605	2

Note: The rows highlighted in grey refer to Takaful firms.

Table 5. Leader stage identification results for 33 insurance companies in Saudi Arabia, 2016 and 2017

	2016					2017
DMU	$e^{1,U}$	$e^{1,L}$	$e^{2,L}$	$e^{2,U}$	Leader Stage	$e^{1,U}$	$e^{1,L}$	$e^{2,L}$	$e^{2,U}$	Leader Stage
1	0.8352	0.5237	0.7471	0.5327	1	0.2651	0.3326	0.2019	0.4663	2
2	0.2486	0.5662	0.1706	0.66	2	0.1566	0.4844	0.1491	0.6395	2
3	0.3593	0.5467	0.2325	0.7256	2	0.3342	0.5467	0.3084	0.7382	2
4	0.4085	0.2567	0.4076	0.51	1	0.3096	0.3075	0.2081	0.3831	2
5	1	0.5083	0.8765	0.5957	1	1	0.6033	1	0.6033	2
6	0.3821	0	0.3505	1	2	0.4827	0.6976	0.3909	1	2
7	0.6571	0.6976	0.6397	0.7081	2	0.2979	0.5745	0.2854	0.6783	2
8	0.9925	0.5549	0.9881	0.5616	1	0.4781	0.3927	0.3707	0.5502	2
9	0.7663	0.6121	0.7085	0.84	1	0.5644	0.6121	0.5445	0.8517	2
10	1	0.939	0.8952	1	2	0.7624	0.6681	0.6763	1	2
11	0.5091	0.6084	0.3395	0.8267	2	0.2958	0.6084	0.2827	0.858	2
12	0.6353	0.402	0.6353	0.4057	1	0.2752	0.2446	0.245	0.3436	2
13	0.3654	0.49	0.3654	0.49	2	0.3746	0	0.2164	0.4202	1
14	1	0.3917	1	0.3917	1	0.7238	0.2946	0.4486	0.3917	1
15	0.8906	0.7839	0.8906	0.7839	1	1	0.773	1	0.773	1
16	0.9897	0.5757	0.9114	0.6164	1	0.4636	0.5163	0.4461	0.6025	2
17	0.6533	0.8008	0.6533	0.8008	2	0.656	0.5948	0.545	0.7894	2
18	0.849	0.506	0.1973	0.7319	2	0.3708	0.429	0.0779	0.6828	2
19	0.8665	0.5543	0.7787	0.7073	1	1	0.6937	1	0.6937	1
20	0.3641	0.5277	0.2818	0.6468	2	0.243	0.6783	0.2312	0.7564	2
21	1	0.8293	1	0.8293	1	1	0.8673	1	0.8673	1
22	0.7859	0.7624	0.7806	0.7815	1	1	0.7635	1	0.7635	1
23	0.7744	0.5846	0.6944	0.7593	1	0.5624	0.5846	0.558	0.7724	2
24	0.9547	0	0.6931	0.2216	1	0.6012	0	0.4054	0.2216	1
25	1	0.6237	0.9395	0.6674	1	0.4133	0.4838	0.3873	0.6481	2
26	1	0.3383	1	0.3383	1	1	0.2296	0.5685	0.3383	1
27	0.8518	0.8784	0.6313	1	2	0.8932	0.8608	0.8262	1	2
28	1	0.2393	0.4508	0.2549	1	0.3258	0.2504	0.0767	0.3229	2
29	1	1	1	1	1	0.0509	1	0.0509	1	2
30	0.812	0.5525	0.6256	0.7642	1	0.6231	0.5525	0.5517	0.7996	2
31	1	0.7451	1	0.7451	1	0.1294	0.5419	0.1286	0.6422	2
32	0.6876	0.6057	0.3448	0.8684	2	0.6742	0.6057	0.6119	0.8736	2
33	0.2225	0.7952	0.1692	1	2	0.1026	0.7952	0.0985	1	2

Note: The rows highlighted in grey refer to Takaful firms.

Table A1. List of Saudi Arabia’s Takaful and conventional insurance Companies in the sample

Number of DMUs	Company Name
	Conventional Insurance Companies
1	Al Alamiya for Cooperative Insurance Company
2	Al Sagr Co-operative Insurance Cooperative
3	Al-Ahlia Insurance Company
4	Alinma Tokio Marine Company
5	Allianz Saudi Fransi Cooperative Insurance Company
6	Amana Cooperative Insurance Company
7	Arabia Insurance Cooperative Company
8	Arabian Shield Cooperative Insurance Company
9	AXA Cooperative Insurance Company
10	Bupa Arabia for Cooperative Insurance
11	Buruj Cooperative Insurance Company
12	Chubb Arabia Cooperative Insurance Company (Chubb)
13	Gulf General Cooperative Insurance Company
14	Gulf Union Cooperative Insurance Company
15	Malath Cooperative Insurance and Reinsurance Company
16	MetLife, American International Group and Arab National Bank Cooperative Insurance Company.
17	Saudi Arabian Cooperative Insurance Company
18	Saudi Enaya Cooperative Insurance Company
19	Saudi Indian Company for Cooperative Insurance
20	Saudi Re for Cooperative Reinsurance Company
21	Company for Cooperative Insurance (Tawuniya)
22	Mediterranean and Gulf Cooperative Insurance and Reinsurance Company
23	Trade Union Cooperative Insurance Company
24	United Cooperative Assurance Company
25	Walaa Cooperative Insurance Company
26	Wataniya Insurance Company
	Takaful Insurance Companies
27	Al-Rajhi Company for Cooperative Insurance
28	AlAhli Takaful Company
29	Aljazira Takaful Taawuni Company
30	Allied Cooperative Insurance Group
31	SABB Takaful Company
32	Salama Cooperative Insurance Company
33	Solidarity Saudi Takaful Company