Psicología cognitiva
3.7. Aspectos éticos
This section describes the empirical approach employed to examine the discussed hypotheses. The partial adjustment model that is employed to test the impact on capital structure is first described. Then, three key competition indicators are discussed, and the definitions of both explanatory and control variables follow. The database used in this chapter is built on information from financial statements of individual insurers, which included balance sheet and income statement, collected from Orbis, Fame and ISIS (or Insurance Focus), and provided by Bureau van Dijk. The World Bank database is the main source for those macro-economic data. The sample covers at least 90% of the market capacity in the UK market from 1998 to 2017. There is no required data for all years;
therefore, unbalanced panel data is accepted. To ensure all monetary values are directly comparable, we deflate each year’s value by the consumer price index to the base year 2015.
3.3.1 Data: Capital structure variable and Competition indicators
One of the critical contributions of this chapter is to test the impact of competition on the insurer’s capital structure, and it is represented by Hypotheses 2 and 5. The choices/definitions of these two key measurements, capital structure and competition degree, are discussed here.
Capital structure variable
Two popular proxies are widely used to represent the insurer’s capital structure. One is measured by the ratio of premium written to surplus, indicating insurer’s leverage (e.g.
Cummins and Lamm-Tennant, 1994; Shiu, 2011; Cheng and Mary A Weiss, 2012; Liu, Shiu and Liu, 2016). Another represents insurer’s equity; it is measured by the ratio of surplus to the total asset (e.g. Cummins and Sommer, 1996; Baranoff, Papadopoulos and Sager, 2007; Mankaï and Belgacem, 2016). Because most of the U.K. insurers are not
publicly traded, it is not available to use market value to define these measurements.
Dhaene et al. (2017) pointed out that studies, which tested the logic of the trade-off and pecking order theories, are most likely to use leverage ratio to represent the insurer’s capital structure. Following Dhaene et al. (2017) and Shiu (2011), the leverage ratio is adopted to test the discussed hypotheses. In line with Cheng and Mary A Weiss (2012) and Mankaï and Belgacem (2016), the traditional leverage ratio is calculated as the ratio of Net Premium to Surplus.
Market Structure indicators
Market structure (competition) can be measured by two approaches, named as a structural and non-structural approach.1 By investigating the connection between structural method (HHI) and the non-structural one (Boone indicator) in container liner shipping industry, Sys (2000) find a conflicting result on the direction of change in competition between two methods. Creusen, Minne and Wiel (2006) achieve a similar conclusion by using four indicators from these two approaches to measure competition in the Netherlands. Among different non-structural models, on the one hand, Doan and Stevens (2012) and Clerides, Delis and Kokas (2015) show that a consistent result could be achieved from different non-structural indexes on measuring the degree of competition.
On the other hand, Degryse, Kim and Ongena (2009) suggest that different models would carry different information on competition in the banking industry from various aspects.
By comparing P-R H statistic and Boone indicator, Schaeck and Cihák (2014) also find that two measures are far from perfect negative correlation,2 it may indicates different methods measure the competition concept in various ways.
As discussed in Appendix 3, all approaches have their own feaures, and face pros and cons. Similar to many previous studies (e.g. Mrabti, 2010; Delis, 2012; Kasman and Kasman, 2015; Leon, 2015; Tan, 2016), three different indicators, which are HHI, Lerner index and Boone indicator, are adopted to measure competition/concertation in the present study. By using multiple methods allows us to capture different concepts of market structure and to achieve a more robust result.
1 Appendix 3 presents a discussion on various approaches to measure market structure.
2 If two measures represent the same thing, it can be assumed that the correlation between them should be perfectly negative (at least, nearly). Because, the higher H statistic values in the range between negative infinity and one indicates that the more intense competition in the market, while, a more negative value signals more competition if the Boone indicators located between negative infinity and zero.
First, the Herfindahl-Hirschman Index (HHI) is used to proxy the structure of the U.K.
insurance market. This HHI calculates as the sum of squares of the individual insurer’s market share in the industry, thus
𝐻𝐻𝐼𝑡 = ∑ 𝑚𝑠𝑖𝑡2
𝑛 𝑖=1
× 10000
where 𝑚𝑠𝑖𝑡 is the market share of an insurer at time t, it is proxied as the ratio of an insurer’s gross premium written to gross market premium. The index tells us that the higher the index, the more concentrated the market is. As a benchmark, an index that overs 1800 represents a highly concentrated market.
Secondly, the Lerner index is determined by adopting Kumbhakar, Baardsen and Lien's (2012) approach, which is based on stochastic frontier analysis, so-called “Stochastic”
Lerner index. Coccorese (2014) also summaries some advantages concerning the usage of this approach, two of them are vital in this study. First, it provides a simple estimation, which originates from efficiency theory, avoids outside manipulation arose from the conventional two-step procedure1; second, non-negative Lerner index can be achieved.
To be more specific, the SFA-Lerner index is defined as 𝑆𝐹𝐴 − 𝐿𝑒𝑟𝑛𝑒𝑟𝑖𝑡 = 𝜃𝑖𝑡
1 + 𝜃𝑖𝑡
Equation (3.1) where 𝜃𝑖𝑡 is another definition of mark-up that can be expressed as
𝜃𝑖𝑡 =𝑃𝑖𝑡 − 𝑀𝐶𝑖𝑡 𝑀𝐶𝑖𝑡
Equation (3.2) in the fraction, the denominator is equal to 𝜕𝑇𝐶𝑖𝑡
𝜕𝑄𝑖𝑡; and the numerator decribes the degree of mark-up, which can be estimated as the inefficiency term (𝑢𝑖𝑡 in “composed error term”) by the stochastic frontier approach, as discussed below.
1 In the conventional Lerner index approach, it contains two componets, which are prices and marginal cost.
The first step is estimating the price and marginal costs separately. Then, to find the Lerner index calculated as the ratio of the mark-up (the difference between price and marginal cost) to price. By using the stochastic frontier approach to estimate Lerner index, the information on output prices is not required as the mark-ups is gathered from the stochastic frontier analysis.
According to Kumbhakar, Baardsen and Lien (2012) and Coccorese (2014), the strategy level 𝑅𝐶𝑖𝑡 can achieve, it is the frontier. Of which, 𝜈𝑖𝑡 represents a noise term that catches unobserved factors (e.g., optimization error) and ∑ 𝜕 ln 𝑇𝐶𝑖𝑡
𝜕 ln 𝑄𝑖𝑔𝑡
2𝑔 is referred as cost elasticity (𝐸𝑇𝐶,𝑄) with respect to output, and it can be computued from an estimated translog cost function2 as Equation 3.5 now looks like the stochastic frontier model, then maximum likelihood estimation techniques and related distributional assumption of both 𝜈𝑖𝑡 and 𝑢𝑖𝑡
1 Coccorese (2014) exhibited a transformation from the mark-up relationship (i.e., 𝑃𝑖𝑡 ≥ 𝑀𝐶𝑖𝑡) to revenue-cost relationship (i.e.,𝑇𝑅𝑖𝑡⁄𝑇𝐶𝑖𝑡≥ 𝜕 ln 𝑇𝐶𝑖𝑡⁄𝜕 ln 𝑄𝑖𝑡 ), and explained why the mark-up can be derived from revenune-cost relationship by using stochastic frontier approach.
2 The cost function with three input prices and two outputs takes the following the translog form:
ln 𝑇𝐶𝑖𝑡= α0+ ∑ 𝛼𝑔ln 𝑄𝑖𝑔𝑡
where, TCit represents insurer’s total cost at time t. Consistence with value-added approach and insurance litertures (e.g. Cummins, Rubio-Misas and Zi, 2004; Hao and Chou, 2005; Cummins and Rubio-Misas, 2006; Yaisawarng, Asavadachanukorn and Yaisawarng, 2014), the outputs, 𝑄𝑖𝑔𝑡, is defined as net claims paid (claims incurred net of reinsurance) and total investment; and 𝑃𝑖𝑗𝑡 measures the three input prices, i.e.
labor, capital and technical reserves. The time trend variable (T) captures the changes over time in technology and underwriting cycle. In the function, the symmetry property requires that 𝛼𝑔𝑘 = 𝛼𝑘𝑔, 𝛽𝑗ℎ = 𝛽ℎ𝑗 and 𝛿𝑔𝑗= 𝛿𝑗𝑔. Also, the linear homogeneity conditions are satisfied by imposing the restrictions as:∑𝛽𝑗= 1, ∑ ∑ 𝛽𝑗ℎ= 0, ∑ ∑ 𝛿𝑔𝑗= 0, ∑ ∑ 𝜉𝑗= 0. The procedure amounts to using one of the input prices (e.g., 𝑃3𝑖𝑡) to normalized total cost and other input price.
(i.e.,𝑢𝑖𝑡~𝑁+(0, 𝜎𝑢2), 𝑣𝑖𝑡~𝑁+(0, 𝜎𝑣2), ) are used to estimate the equation. 𝑢𝑖𝑡 is estimated by using Jondrow et al.'s (1982) approach and it is able to capute the mark-up (and market power) of insurer i at time t, rather than cost inefficiency. A smaller estimated value of 𝑢𝑖𝑡 indicates a lower amount of mark-up. Next, the resulting parameters from Equation 3.5 are substituted back to Equation 3.4 to generate 𝐸̂ . Then both 𝐸𝑇𝐶,𝑄 ̂ and 𝑢𝑇𝐶,𝑄 𝑖𝑡 are used to calculate 𝜃̂ that can be used to find the SFA-Lerner index shown in Equation 3.1. 𝑖𝑡 The last, in line with the theoretical work developed by (Boone, 2008) and the other empirical studies from Schaeck and Cihák (2010), (2014), Bikker and Popescu (2014), Liu, Mirzaei and Vandoros (2014) and Cummins, Rubio-Misas and Vencappa (2017), the indicator is constructed from the following basic form as:
ln 𝜋𝑖𝑡 𝑜𝑟 ln 𝑀𝑆𝑖𝑡 = 𝛼 + 𝛽 ln 𝑀𝐶𝑖𝑡+ 𝜀𝑖𝑡
Equation (3.6) where 𝑀𝐶𝑖𝑡 is the mariginal cost of an insurer i at time t. The coefficienct of 𝑀𝐶𝑖𝑡, which is expected to be negative1, that is 𝛽, so-called Boone indicator; it indicates a relationship that an insurer with higher marginal cost will have less potentical ability to gain benefit relative to its counterparties, in a compeititve envirment. A larger 𝛽 in absolute terms indicates a stronger competitive effect. The paramenter 𝛽, which is estimated by using a dynamic GMM panel model, is then used as one of the key regressors in the empirical investigation. The adoption of the GMM-style estimator is due to the fact that insurer’s performance and cost are jointly determined; and one-year lags of explanatory variables and the GDP per capital are selected as instruments, see a similar adoption from Schaeck and Cihák (2014) and Cummins, Rubio-Misas and Vencapp (2017). As suggested by Kasman and Kasman (2015), the log-log function is used to deal with the issue of heteroscedasticity.
As shown in Equation 3.6, the dependent variable can be selected as either the insurer’s profit 𝜋𝑖𝑡 or its market share 𝑀𝑆𝑖𝑡 at time t. Canton et al. (2005) argue that any one of these is reasonable to choose because both would react stronger on marginal cost as the competition strengthened. Although the relative profit is originally used to develop the theory by Boone, observations with negative profit need to be dropped due to the
1 According to van Leuvensteijn et al. (2011) and Tabak, Fazio and Cajueiro (2012), there is a possibility that the β can be positive, which means increasing firm’s marginal cost will earn more market share. van Leuvensteijn et al. (2011) offered two reasons, (1) the level of collusion is exceptionally high in the market;
(2) preventing new entrants by increasing the marginal cost in the market as a whole.
logarithms function form of the model. However, working with market share provides two advantages as mentioned by van Leuvensteijn et al. (2011); first, there is a clear visible relation between an individual’s efficiency and market share. Secondly, market share only provides positive value. And another difference between these is that the profit represents the profitability of past businesses while the latter reflects the current business (Canton et al., 2005).
Therefore, by following Bikker and Popescu (2014) and Bikker (2016), and the discussed advantages with using market share, the Equation 3.6 is modified as:
ln 𝑀𝑆𝑖𝑡 = 𝛼 + ∑ 𝛽𝑡𝐷𝑡ln 𝑀𝐶𝑖𝑡 individual’s premium written to the market premium at a time point. By involving both time dummy variables (𝐷𝑡, for year 1 to T) and their interactions in the Equation 3.7, it is able to capture the time effect. And, 𝜀𝑖𝑡 is the error term.
The primary challenge of adopting Boone's (2008)’s approach is that the marginal cost needs to be constructed as it is not directly gatherable. The conventional method adopts to obtain marginal cost1, which is derived from the translog cost function as showed on Page 150 and estimated it by using stochastic frontier analysis (Koetter, Kolari and Spierdijk, 2012). Then, the marginal cost can be expressed as the following form:
𝑀𝐶𝑖𝑡 = ∑ 𝑀𝐶𝑖𝑔𝑡 3.3.3 Data: Independent variables and other control variables
Independent variables
1 Two methods are widely used to determine marginal cost in financial studies. First, an average cost, defines as the ratio of total cost (or management cost) to total premium (income), that is an easy calculated proxy of marginal cost (e.g., Schaeck and Cihák, 2010, 2014; Mirza, Bergland and Khatoon, 2016;
Cummins, Rubio-Misas and Vencappa, 2017). Second, a marginal cost can be derived from a translog cost function, while it is a complex process (e.g., van Leuvensteijn et al., 2011; Tabak, Fazio and Cajueiro, 2012;
Kasman and Kasman, 2016). By using both methods, Bikker and van Leuvensteijn (2008) point out that outcomes from both a similar. However, average cost is less accurate due to the fact that no distinguish between variable and fixed costs (Canton et al., 2005).
Following Pandey (2004), Guney, Li and Fairchild (2011) and Soedarmono, Machrouh and Tarazi (2013), the square term of competition is included to capture the non-linearity effect of competition on the insurer’s capital structure. In addition, to test the other hypotheses on pecking order theory (H1b), firm’s volatility (H3), the usage of reinsurance (H4) and their interactions with competition (H5), the key variables are defined below.
According to the pecking order theory, firms prefer to use internal sources to raise capital rather than external sources. Park and Pincus (2001) explain that using internal funding should be more efficient, and the cost of it should be lower than external sources.
Therefore, the Retained Earnings, the primary source of internal funding, is collected from insurers’ financial statements to verify Hypothesis 1b 1. A negative relationship between Retained Earning is expected if the pecking order hypothesis is satisfied.
Firms with a higher level of volatility (lower stability) generally lower the leverage ratio to maintain financial soundness. According to Cummins, Rubio-Misas and Zi (2004) and Eling and Jia (2018), business volatility is one of the fundamental indicators to determine an insurer's failure, as a higher the business volatility would lead to a higher likelihood of insolvency. Therefore, it can be expected that there is a negative relationship between the insurer’s volatility and its leverage level. Following both Eling and Marek (2014) and Eling and Jia (2018), Income Volatility is measured by the standard deviation of return on shareholder’s fund (ROSF) with a three year rolling window. This indicator measures an insurer’s return volatility at the firm’s aggregated risk level. A higher figure represents that the insurer has less certainty of its future returns, and it may face a higher likelihood of failure. Thus, the insurer may need to pay more attention to monitor its risk-tolerance and capital position.
Eling and Marek (2014) also suggest that an insurer’s volatilities come from various sources, not only its asset holdings but also its issued products, etc. Then, from this perspective, the insurer’s volatility may also be raised from claim uncertainty associated with business written. To be more specific, the insurer has more uncertainties about the future value of losses (from claim/benefit payments), and thus contributes to the insurer’s
1 Alternatively, it is also reasonable to assume that the insurers with better abilities to generate profits should have sufficient internal funds that can be converted into capital as in the form of retained earnings.
Thus, the insurer’s profit efficiency, which is found by Stochastic Frontier Analysis, that is also adopted to make the robustness check.
aggregate level of risks, damaging its stability, when the loss ratio is highly volatile. Both Hoerger, Sloan and Hassan (1990) and Mankaï and Belgacem (2016) support that the increased loss (claim) volatility of claims would have an impact on the insurer’s aggregated risk-level. Therefore, Bussiness Volatility is also involved to represent the insurer’s volatility from another prespective, and it is approximated by the standard deviation of the loss ratio1 with a three-year rolling window. So the expected impact of claim volatility is negative on the leverage ratio.
Regarding Hypothesis 4 - the impact of reinsurance uasge on the insurer’s capital structure - the traditional ratio of Reinsurance Ceded to Gross Premium Written is used to denote the usage of Reinsurance. This measurement is widely used by Fecher et al.
(1993), Lin, Lai and Powers (2014), Alhassan and Biekpe (2015), Liu, Shiu and Liu (2016), Cummins, Rubio-Misas and Vencappa (2017) and Sheikh, Syed and Ali Shah (2018), and among others. Then, Hypothesis 4 can be verified by concerning the coefficient of this variable, and a positive sign would be expected.
Control Variables
The cost of either raising or holding capital is a vital factor of the capital level (Modigliani and Miller, 1958; Kielholz, 2000). It is difficult to measure the cost of capital directly in practice. For example, Cummins and Lamm-Tennant (1994) suggested that the cost of equity capital should be estimated by using the CAPM. However, due to the lack of market data, the CAPM is not suitable to use. Following Mankaï and Belgacem (2016), the cost of equity capital is approximated by the most recent three-year average of positive return on shareholder’s fund (ROSF).
Following both Shiu (2011) and Mankaï and Belgacem (2016), the insurer’s size is included as one of the control variables. For instance, Shiu (2011) assumed a positive relationship between the firm size and leverage under trade-off theory, while a negative one appeared under the pecking order theory. The rationale for this relationship is that larger firms have easier access to capital markets and is easier to borrow at a favourable intereste rate (Ferri and Jones, 1979). The natural logarithm of total assets is used to measure the insurer’s size.
1 The loss ratio measures the total incurred losses in relation to the total gross premium written.
The insurer’s liquidity is a widely used indicator to represent the ability to fulfill its the short-term obligations. Panno (2003) suggest two possible effects on capital structure.
First, the postive relationship existes when the liquid assets are used to support a relative higher debt ratio. Second, if the liquid assets are used to finance finance the firm’s investment,then a negative relationship can be expected. Current ratio, defined as the ratio of liquid asset to total liability, is used to represent the insurer’s liquidity level.
In line with preceding literture from Pandey (2004), Chen et al. (2009), Najjar and Petrov (2011), Fier, McCullough and Carson (2013) and Chang et al. (2015), profitability is also chosen as a control variable. In this study, Investment Return, is measured as return on investment assets, denotes the insurer’s profitability. In addition, according to Modigliani and Miller's (1963) tax shield effect, the insurer would like to use more debt when the tax rate is higher. Thus, the amount of tax payment is used and a positive relationship should be expected.
Following Sheikh, Syed and Ali Shah (2018), the interest rate and inflation are closely related to the insurer’s capital structure. For example, an increase in the interest rate would result in bond price falling, and insurers then face questions of whether to issue new equity capital. However, issuing equity is costly due to various costs.1 And inflation also has direct impact on premium pricing and bond pricing. For instance, higher inflation rates reduce the insurer’s profit margins. Therefore, these two variables are included to control the cost of borrowing at the market level. Finally, growth in GDP is also included to control the overall economic condition.
3.3.4 Empirical Models and Estimation Techniques
Following Shrieves and Dahl (1992), Cummins and Sommer (1996), Baranoff and Sager (2002), Flannery and Rangan (2006), Cheng and Weiss (2012a), Lin, Lai and Powers (2014) and Mankaï and Belgacem (2016), a partial adjustment model is used to determine whether insurers have a target capital structure and the speed of adjustments, and then to test the discussed hypotheses related to different explanatory factors. In a frictionless world, the insurers would always maintain their target capital structure.
However, the optimal capital structure is unobservable in the real world, and it is easy to
1 For example, the transaction costs arising from underwriting and the adverse selection costs due to information asymmetry
vary across individual insurers and over time. The general target capital structure equation is estimated:
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡∗ = α𝑋𝑖,𝑡
Equation (3.9) where 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡∗ represents the measure of target capital structure, the leverage ratio is adopted in this study, for insurer i at time t. 𝑋𝑖,𝑡 is a vector of the insurer’s specific factors that influence the insurer’s capital structure. α is the coefficients corresponding to the vactor of insurer’s specific factors, and indicates a long-run impact of firm-specific factors on capital strcuture. And Equation (3.9) is an unbiased relationship (an equilibrium relation) in which the error term is not required. Then, the standard partical adjustment model is expressed as:
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡− 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡−1
= 𝛿[𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡∗ − 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑎𝑡𝑖𝑜𝑖,𝑡−1] + 𝜀𝑖,𝑡
Equation (3.10) in Equation (3.10), the difference in the capital ratio on the left-hand side indicates the
Equation (3.10) in Equation (3.10), the difference in the capital ratio on the left-hand side indicates the