Measuring recent changes of insurance gross premiums distribution using ten inequality measures: case study of Croatia

Figures & data

Figure 1. The number of insurance companies in Croatia in the period 2000–2012, Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Figure 2. Gross written premiums of insurance companies in Croatia in the period 2000–2012, in HRK. Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 1. The review of the concentration measures characteristics.

Index name	Symbol and interval value	Index value interpretation
Concentration ratio of the order r	1/n ≤ Cr ≤ 1	The concentration ratio value (for r insurance companies with the highest gross premiums) is close to 0 when there are many identical insurance companies on the market, and its value is 1 when the sum of insurance gross premiums of r subjects with the highest gross premiums makes the entire insurance industry.
Lorenz curve	0 ≤ FT ≤ 1	Concentration of the insurance gross premiums increases as the curve distances from the line of perfect equality.
Gini coefficient	0 ≤ G ≤ 1	As the concentration of insurance gross premiums increases, the Gini coefficient value increases as well. In the case of total market inequality, its value is 1.
Entropy	0 ≤ H ≤ log2n	A higher entropy (H) value indicates a smaller concentration of insurance gross premiums. In case of a monopoly the value of H is 0.
Herfindhal-Hirschman index	1/n ≤ HHI ≤ 1	A higher HHI value indicates a higher concentration of insurance gross premiums. In case of an insurance market monopoly, its value is 1.
Hall-Tideman index	0 ≤ HTI ≤ 1	When HTI or RI equals 0, a large number of insurance companies of the same size exist, while the value 1 indicates a pure market monopoly.
Rosenbluth index	0 ≤ RI ≤ 1

Source: Authors’ creation.

Table 2. Overview of concentration measures for life insurance gross premiums in Croatia in the period 2000–2012.

Year	Concentration ratios		Herfindhal-Hirschman index	Normalised Gini	Entropy			Hall-Tideman index	Rosenbluth index	Number of insurers
	C2	C5	HHI	G*	H	Hmax	H*	HTI	RI	n
2000	0.388	0.797	0.154	0.662	2.135	2.833	0.754	0.153	0.036	17
2001	0.354	0.729	0.124	0.560	2.301	2.773	0.830	0.132	0.041	16
2002	0.330	0.700	0.102	0.500	2.456	2.833	0.867	0.122	0.042	17
2003	0.317	0.684	0.108	0.525	2.414	2.833	0.852	0.116	0.039	17
2004	0.302	0.664	0.103	0.471	2.443	2.773	0.881	0.112	0.043	16
2005	0.302	0.648	0.102	0.459	2.461	2.773	0.888	0.110	0.044	16
2006	0.301	0.610	0.101	0.383	2.426	2.639	0.919	0.111	0.053	14
2007	0.312	0.611	0.098	0.402	2.479	2.708	0.915	0.108	0.051	15
2008	0.310	0.612	0.120	0.531	2.404	2.833	0.848	0.109	0.040	17
2009	0.278	0.581	0.095	0.438	2.470	2.773	0.891	0.106	0.044	16
2010	0.281	0.573	0.092	0.418	2.505	2.773	0.904	0.103	0.045	16
2011	0.294	0.583	0.094	0.429	2.498	2.773	0.901	0.105	0.045	16
2012	0.314	0.602	0.098	0.481	2.484	2.833	0.877	0.098	0.040	17

Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 3. Overview of concentration measures for non-life insurance gross premiums in Croatia in the period 2000–2012.

Year	Concentration ratios		Herfindhal-Hirschman index	Normalised Gini	Entropy			Hall-Tideman index	Rosenbluth index	Number of insurers
	C2	C5	HHI	G*	H	Hmax	H*	HTI	RI	n
2000	0.687	0.836	0.124	0.662	2.445	3.178	0.769	0.198	0.023	24
2001	0.680	0.853	0.137	0.667	2.279	2.996	0.761	0.222	0.032	20
2002	0.660	0.842	0.132	0.633	2.313	2.944	0.785	0.210	0.032	19
2003	0.647	0.833	0.125	0.618	2.390	2.996	0.798	0.195	0.030	20
2004	0.637	0.841	0.152	0.684	2.231	2.996	0.745	0.199	0.029	20
2005	0.622	0.846	0.162	0.683	2.140	2.890	0.740	0.203	0.032	18
2006	0.594	0.826	0.152	0.627	2.169	2.773	0.782	0.192	0.037	16
2007	0.571	0.809	0.135	0.611	2.257	2.833.	0.797	0.178	0.035	17
2008	0.556	0.793	0.129	0.596	2.337	2.890	0.809	0.164	0.033	18
2009	0.538	0.774	0.114	0.543	2.428	2.890	0.840	0.156	0.036	18
2010	0.524	0.761	0.116	0.584	2.408	2.944	0.818	0.149	0.032	19
2011	0.514	0.755	0.114	0.592	2.433	2.996	0.812	0.143	0.030	20
2012	0.505	0.746	0.120	0.597	2.423	2.996	0.809	0.139	0.031	20

Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Figure 3. Lorenz curve for gross premium for life insurance in Croatia 2000 and 2012. Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Figure 4. Lorenz curve for gross premium for non-life insurance in Croatia 2000 and 2012. Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 4. Forecast measures for trend models for the gross premium entropy by types of insurances in Croatia for the period 2000–2012.

	LIFE		NON-LIFE
FORECASTQUALITYMEASURE	Linear trend	Quadratic trend	Linear trend	Quadratic trend
MAPE	2.147	1.681	3.415	2.405
MAD	0.051	0.040	0.078	0.056
MSD	0.005	0.003	0.009	0.005
R^2	0.513	0.698	0.089	0.554
S.E.	0.074	0.061	0.104	0.077

Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 5. The quadratic trend of entropy for life insurance gross premium in Croatia, annual data in the period 2000–2012.

Y qadratic trend=2.173 + 0.066t - 0.00t^2
	Coefficients	Standard Error	t Stat	P-value
Intercept	2.173	0,060	36.512	0.000
t	0,066	0.020	3.363	0.007
t^2	−0.003	0.001	−2.479	0.033

Source: Author’s calculation.

Figure 5. The quadratic trend of entropy for life insurance gross premium in Croatia in the period 2000–2012 and forecasts for 2013 and 2014. Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 6. The quadratic trend of entropy for non-life insurance gross premium in Croatia, annual data in the period 2000–2012.

Y qadratic trend= 2.465 - 0.069t + 0.006t^2
	Coefficients	Standard Error	t Stat	P-value
Intercept	2.465	0.075	32.841	0.000
t	−0.069	0.025	−2.815	0.018
t^2	0.006	0.002	3.228	0.009

Source: Authors’ calculation.

Figure 6. The quadratic trend of entropy for non-life insurance gross premium in Croatia in the period 2000–2012 and forecasts for 2013 and 2014. Source: Economic reports and statistics (2013), Croatian Insurance Bureau, Authors’ calculations.

Table 7. The descriptive statistics and the tendency for the entropy for life and non-life insurance gross premiums in Croatia in the period 2000–2012 and forecasts for 2014.

Descriptive statistics	Entropy H for gross written premium
	H for Life	H for non-life
Median	2,46	2,34
Average 2000–2012	2,41	2,33
Standard Deviation	0,10	0,11
Coefficient of variation 2000–2012	4,17%	4,50%
The (best fitted) quadratic trend tendency description:	Progressive-digressive	Digressive-progressive
H value in 2000	2.14	2.44
H value in 2012	2.48 (smaller concentration compared to 2000)	2.42(higher concentration compared to 2000)
Quadratic trend forecasted value of H in 2014	2.40(expected higher concentration compared to 2012)	2.60(expected smaller concentration compared to 2012)

Source: Authors’ calculation.

Economic reports and statistics. (2013). Croatian Insurance Bureau. Retreived December 6, 2013, from http//:www.huo.hr

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