Result and Discussion
To test the effect of the market structure and domestic economy in the efficiency score, we must first choose which is the best model suited to our data. Since our data are based on an unbalanced panel of seven countries, with data averaged over a period of seven year, we therefore use a panel regression. Hence, it is necessary to use the specification test to identify the existence/inexistence of the individual effect. The result is shown in
Table 3.
The “p-value” of this test is equal to 1.23%, which is lower than 5%. If we focus on Fisher’s test, we conclude that the calculated F is equal to 3.18, which is greater than 2.34, the theoretical value for the degree of freedom (6 and 39) at the 5% level. Thus, the null hypothesis is rejected at the level of five percent. Since the null hypothesis of this test is only a common intercept, there is no individual effect on the regression. The null hypothesis is rejected, so we must include individual effects in the model.
The origin of this heterogeneity can be explained by the independent variable. This heterogeneity can be explained by the individual characteristics of the market and domestic economy in each country.
The specification test shows that our theoretical model can be formalized as a panel with individual effects. These effects can be fixed or random. For that, we use the Hausman test, which is a test for determining whether the coefficients of the two estimates (fixed and random) are statistically different. The result of the Hausman test is shown in
Table 4. If the theoretical value of chi-squared is greater than the value calculated at α% with freedom degree
n we reject the null hypothesis. In this case, the regression is considered as the model with individual fixed effects.
In our regression model the “
p-value” is equal to 24.4% that is higher than ten percent. Additionally, the theoretical chi-squared at the 10% level for three degrees of freedom is equal to 0.584, which is lower than the chi-squared calculated value. Thus, we cannot reject the null hypothesis so the best model suited to our data is the model with individual random effect presented in
Table 5. The result in this table represents the estimated coefficient value of market characteristics and domestic economic variables that can affect the efficiency score.
The result in this table represents the panel regression of the efficiency scores on non-life European insurance over the period between 2002 and 2008.
Focusing on the econometric analysis, we find that the model is globally significant at the 10% level because the probability of the Fischer statistic of this model is equal to 8.83%, which is less than 10%. Only one variable is significant at the level of 5%. The concentration ratio is positive and significant at the 5% level. Indeed, an increase of the concentration ratio by one percent causes an augmentation of the cost efficiency by 4.67%.
Our result reveals a positive correlation between concentration and efficiency. This result is in accordance with SCP theory, which states that the firms become more efficient and more profitable with a higher concentration ratio [
23].
Due to the inverse relationship between higher market concentration and competition, the cost efficiency would decrease if the competition increases. We can explain this negative relation between cost efficiency and competition by the fact that the existence of scale economies on a market means that an increase in the number of competitors results in higher average costs for each incumbent firm.
- b.
Result of second regression
In the second regression model, the efficiency is calculated by the integration of the power of the CEO in the Fourier flexible cost function.
First, to test the existence/inexistence of the individual effect, we use the specification test. The result of this specification test is shown in
Table 6.
The value of fisher calculated was equal to 31.403 that is greater than 3.30 which is the theoretical F-value for the degree of freedom (6 and 39) at the level of 1%. Thus, the null hypothesis is rejected at the level of one percent. Since the null hypothesis of this test consists of the existence of only one common intercept, there is no individual effect in the regression. The null hypothesis is rejected, so we must include individual effects in the model.
Since the market characteristic represented by the concentration ratio and the penetration and the domestic economic characteristic represented by the LnGDP represent the dependent variables that explain the efficiency, we can explain the heterogeneity by these variables.
Our model can be formalized as a panel with individual effects. To identify if these effects are fixed or random, we use the Hausman test which is a test specifically for determining whether the coefficients of the two estimates (fixed and random) are statistically different. The result of the Hausman test is shown in
Table 7.
The regression model shows that the calculated “
p-value” is equal to 10.28%, which is higher than ten percent. Additionally, the theoretical chi-squared at the 10% level for three degrees of freedom is equal to 0.584, which is lower than the chi-squared calculated value, which is equal to 6.187. Thus, we cannot reject the null hypothesis, and so the best model suited to our data is the model with individual random effects presented in
Table 8. The result from this table represents the estimated coefficient value of market characteristics and domestic economic variables that affect the efficiency score.
The result in this table also represents the panel regression of the efficiency scores estimated by the second model on European non-life insurance over the period between 2002 and 2008.
The econometric analysis of the regression shows that the model is generally significant at the level of 5%. Two variables in this regression are significant at the 5% level. The first significant variable in this regression is the concentration ratio, which is positive and significant at the 5% level. In fact, an increase of concentration ratio by one percent causes an augmentation of the cost efficiency by 4%. The second significant variable in this regression is the LnGDP. The gross domestic product is also positive and significant at the 5% level, so the efficiency increases by 5% if the natural logarithm of GDP increases by 1%.
As in the case of the first regression model, the panel regression of the efficiency is estimated by the Fourier flexible cost function including the power of the CEO. The two significant variables are the concentration and the LnGDP. The penetration in this regression has a negative relation with the efficiency and this relation is not significant like in the first regression model. In this regression as it is the case in the first regression, the relation between concentration and efficiency is in accordance with SCP theory. This states that firms become more efficient and more profitable with a higher concentration ratio.
Additionally, the decrease in GDP causes a decrease in efficiency. We can explain this relation by the fact that the diminution in the GDP may reduce efficiency of the non-life insurance segment due to the reduction of value of durable assets, which has an impact on the values of the gross written premium and insurers’ earnings. Finally, we note that the relation between efficiency and penetration is not significant.