# Interactions between risk taking, capital, and reinsurance for property-liability insurance firms.

INTRODUCTIONTo reduce the likelihood of their failure, insurance firms have always been subject to various constraints related to risk taking and capital holding. In this respect, capital adjustments are generally made through earnings retention or new shares issuance. Hoerger, Sloan, and Hassan (1990) and Garven and Lamm-Tennant (2003) demonstrate that reinsurance, which involves ceding part of the assumed underwriting risk, may affect these decisions by reducing loss volatility and acting as contingent capital. More recently, the role of reinsurance has become even more important in view of regulatory developments that are more amenable to defining capital requirements in terms of some of its qualitative aspects (Eling and Holzmuller, 2008; Scordis and Steinorth, 2012). Understanding the relationship between capital, risk, and reinsurance is of great significance for regulators, who must craft prudential rules to regulate insurers' solvency. (1) Shareholders are also concerned with the possible transmission of shocks to capital resulting from unanticipated losses. Negative shocks often entail forced sales of assets, which adversely affect the firm value.

Among the relationships between the three decision variables considered in this article, those between capital and risk are by far the most discussed in the literature. Several hypotheses related to moral hazard, agency costs, and regulatory pressures have been posited to explain their mutual interactions. The first hypothesis, based on agency costs and buffer capital theory, predicts a positive relationship between capital and risk. An alternative hypothesis, based on information asymmetry, predicts a negative relationship. The conflicting predictions of these two hypotheses paved the way for an active empirical research. Shrieves and Dahl (1992) were the first to examine this relationship for U.S. banks. In a subsequent article, Cummins and Sommer (1996) investigate the issue for nonlife insurance firms and provide empirical support for a positive relationship between capital and risk. Baranoff and Sager (2002) empirically explore these interactions in the case of life insurance, finding a positive (negative) relationship between capital and asset (liability) risk. Shim (2010) also confirms the positive relationship between these variables.

While the association between capital and risk has been extensively studied in the literature, few articles to date have explored the relationship between risk and reinsurance usage (e.g., Cole et al., 2011), and even fewer, the joint interactions between the three decision variables. Reinsurance mitigates underwriting and solvency risks and enables insurers to increase their capacity to underwrite new business. There are several reasons to believe that reinsurance is endogenously influenced by the choice of capital and risk, and vice versa. In this respect, MacMinn (1987) and Plantin (2006) find that the reinsurance ratio is determined together with the capital structure. Dionne and Triki (2004) document a strong positive relationship between leverage as a subscription risk indicator and reinsurance demand. In the same vein, Shiu (2011) focuses on the endogenous nature of reinsurance and finds that it is positively related to leverage, and vice versa. All these results support the hypothesis of interdependence between reinsurance, capital, and risk.

This study analyzes capitalization policy and its relationship with risk taking and reinsurance usage. More specifically, we aim to determine the nature of adjustments between these decisions and how they move to their target levels. The contribution of this article to the existing literature is twofold. First, we attempt to fill the gap in the literature by examining interactions among these three decision variables instead of studying them in pairs. We believe that much is to be gained through a joint analysis acknowledging the simultaneity associated with decisions made in this regard. The second contribution is an extensive empirical analysis of the interactions following several factors, such as the level of regulatory pressure, group affiliation, firm size, and organizational form. We show that capital, risk, and reinsurance interact in both directions and vary according to the transversal factors. We also provide empirical evidence that the capital ratio moves slowly toward a target level.

This article is organized as follows. The second section sketches the theoretical underpinnings of the interactions between risk taking, capitalization, and reinsurance and develops a set of hypotheses. The third section identifies and discusses the main determinants of each decision. The fourth section presents the econometric model and estimation technique. The fifth section describes the data set and provides summary statistics. The sixth section reports and discusses empirical results and provides some robustness checks. The seventh section provides concluding remarks.

THEORETICAL BACKGROUND AND RESEARCH HYPOTHESIS

In this section, we briefly outline the theoretical literature that highlights the interactions between capital, reinsurance usage, and risk taking and we posit our hypotheses.

Interactions Between Capital and Risk

Interactions between capital and risk have been the focus of active research, particularly in the banking sector. Since its introduction in 1994, the riskbased capital (RBC) system appears to have steadily reinforced the interdependence between these two decisions for insurance firms. Several theoretical arguments related to agency costs, moral hazard, and regulatory pressures have been proposed to explain such interactions.

The literature makes contradictory predictions regarding the nature of such interactions. The first hypothesis refers to insurers' incentives to exploit guaranty funds, which provide last-resort protection when insurers are unable to fulfill their contractual commitments. Failure costs are borne by all guaranty fund members. When members' contribution to the fund are not correlated with actual risk, that is, when premiums are flat fee rather than risk based, adverse incentives can result for insurers to increase risk and reduce capital (Cummins, 1988). However, the importance of this hypothesis is tempered by the fact that the coverage of the guaranty fund is less complete than in the banking sector and by the growing effectiveness of supervisory mechanisms and market discipline (Cheng and Weiss, 2012). Therefore, the incentive to take excessive risk for nonlife insurers is restricted. Another explanation for a negative relationship between capital and risk for U.S. insurers may be due to flaws in the RBC formula. Cheng and Weiss (2012) argue that some risks are overweighed, while others are underweighted. This discrepancy encourages insurers to rearrange their portfolios by choosing assets or lines of business with low weights. Thus, insurer aggregate risk may increase while capital requirements decrease, resulting in a negative relationship.

The second hypothesis suggests a positive relationship between these two variables. According to the capital buffer theory, insurers hold excess capital above the regulatory minimum as a guaranty against unanticipated extreme losses and to avoid regulatory costs (Shim, 2010). Most empirical evidence supports the positive relationship between capital and risk for both nonlife and life insurance firms (Cummins and Sommer, 1996; Baranoff and Sager, 2002; Shim, 2010). The relationship between capital and risk is more important for insurers with relatively low capital levels. These firms are expected to respond more extensively in terms of capital adjustment to risk taking because of regulatory pressure and market discipline. Fonseca and Gonzalez (2010) argue that self-regulation encouraged by market discipline can further affect the recapitalization decision. Insurers exposed to high market discipline are pushed into adjusting their capital more extensively. Based on the recent empirical results, our first hypotheses are as follows:

[H1.sub.A]: Capital and risk adjustments are positively related.

[H1.sub.B]: Capital and risk adjustments are more highly positively related for low-capitalized insurers than for high-capitalized insurers.

Interactions Between Capital and Reinsurance

The analysis of the relationship between capital and reinsurance is poorly documented in the financial literature. Stulz (1996) and Adiel (1996) demonstrate that reinsurance affects the solvency and can function as off-balance-sheet capital. In addition, reinsurance increases the insurer's surplus and strengthens its underwriting capacity (Graham and Rogers, 2002; Aunon-Nerin and Ehling, 2008; Zou and Adams, 2008; Cole et al., 2011). Under the renting capital hypothesis, reinsurance is typically viewed as a substitute for capital (Armstrong and Dror, 2007). It is also considered a risk transfer tool that reduces the required capital on the insurer's balance sheet by enabling the use of capital "rented" from the reinsurer. Using traditional sources of capital, such as corporate debt, contingent capital, or new equity, in response to a shock is typically an expensive and difficult operation. Thus, insurers will choose reinsurance rather than holding more capital as it allows them to maintain an acceptable level of solvency. Cummins et al. (2008) show that the optimal use of reinsurance can improve shareholder value by substituting for equity, which thereby reduces the cost of capital and increases returns from underwriting activities. When the benefit of the risk mitigation exceeds the expected return sacrifice, reinsurance increases the value of the company, leading to the following hypothesis

[H.sub.2]: There is a negative relationship between capital and reinsurance in both directions. Interactions Between Reinsurance and Risk

One way to reduce volatility and insolvency risk is to use reinsurance, particularly when the capital level moves closer to solvency constraints (Adams, 1996). Transferring risk relaxes capital restrictions and allows insurers to expand their capacity to issue new policies. Highly leveraged insurers are more exposed than others to the risk of insolvency and are expected to use more reinsurance, suggesting positive interactions (Shiu, 2011). In this regard, Froot, Scharstein, and Stein (1993) argue that risk management techniques such as reinsurance enhance the market value of insurance firms by enabling managers to realize positive net present value (NPV) projects when risk capacity is binding. However, the impact of reinsurance usage on risk taking is not clear. De Haan and Kakes (2010) assume that this relationship depends on the capital level. Based on this discussion, we propose the following hypothesis:

[H.sub.3]: There is a positive relationship between risk and reinsurance in one direction. Impact of Transversal Factors

The neoclassical theory of the firm identifies several factors that may affect the main financial decisions of insurers.

Size. Firm size plays an important role in influencing the insurer's risk appetite through its effect on investment opportunities, reinsurance usage, and the firm's access to capital. Large firms are generally subject to lower information asymmetry between managers and potential investors, which reduces the cost of capital (Smith, 1977). Moreover, large firms are likely to have a better qualitative and geographical allocation of risks and hold proportionally less capital than small firms. Due to economies of scale in risk management and their greater ability to raise capital in the short run, large firms are expected to require less capital to operate and to undertake greater risk (Titman and Wessels, 1988). Numerous studies document that firm size negatively affects the demand for reinsurance (Hoerger, Sloan, and Hassan, 1990; Powell and Sommer, 2007). Small insurers depend more on reinsurance usage because they do not have economies of scale and scope, and they have higher financing costs when raising external funds for at least two main reasons. First, the direct costs of financial failure are not proportional to the size of a company (Warner, 1977). Second, raising capital in financial markets is an expensive undertaking. Cole and McCullough (2006) view firm size as an inverse measure of bankruptcy costs and find a negative relationship between this variable and the demand for reinsurance. Thus, large insurers will rely less on reinsurance to expand their underwriting capacity. Thus, we formulate the following hypothesis:

H4: Large insurers hold less capital, use less reinsurance, and take more risk than small insurers.

Organizational Form. There are two main forms of organization in the insurance industry: mutual firms and stock firms. In mutual organizations, customers provide capital, bear risk, and own the residual value of the firm. In stock organizations, the shareholders bring capital and receive the residual value, whereas the risk is shared between shareholders and policyholders. The implications of the pecking order theory vary, depending on organizational form. Stock firms have greater access to the financial markets. Mutual firms have more difficulties in raising capital than stock insurers. Agency costs also vary with organizational form. The shareholderspolicyholders and shareholders-managers conflicts may impact the choice of capital level. Managers have an incentive to maximize their perquisite consumption and to protect their own human capital (Mayers and Smith, 1990). However, shareholders have more control over managers in stock firms than in mutual firms. Harrington and Niehaus (2002) find that mutual insurers tend to hold more capital than stock insurers and are more likely to manage risk through reinsurance. Indeed, Cole and McCullough (2006) note that mutual firms, which have less access to capital markets in cases of catastrophic loss, use more reinsurance. Thus, we formulate the following hypothesis:

[H.sub.5]: Mutual insurers hold more capital, use more reinsurance, and take less risk than stock insurers.

Group Affiliation. Group membership is a potential factor that may affect interactions among the decisions of interest. Cheng and Weiss (2012) argue that capital and risk for insurers within a group might be determined strategically at the group parent level. Insurers belonging to a group generally hold less capital and have incentives to take more risk, as they have access to internal resources provided by other group members. Cummins and Sommer (1996) find that group-affiliated insurers are associated with greater risk relative to single unaffiliated insurers. It is also easier for affiliated insurers to obtain capital injections from parent firms when their capital levels become insufficient. Powell, Sommer, and Eckles (2008) find evidence that internal capital markets play a significant role in investment behavior. Powell and Sommer (2007) note the importance of reinsurance transactions with affiliated insurers, hypothesizing that reinsurance from internal sources should be more cost effective than from external markets. Mayers and Smith (1990) and Cole and McCullough (2006) find evidence supporting a positive and significant correlation between the use of reinsurance and group membership. This result is confirmed by Powell and Sommer (2007), who argue that transactions within a group have lower asymmetric information costs than those with nongroup firms and, thus, lower monitoring costs. Reinsurers have incentives to monitor the underwriting risk of the insurers with whom they do business (Cole et al., 2011). The relationship between risk and reinsurance is more significant for affiliated than for nonaffiliated reinsurers since the monitoring costs will be higher for the latter. Accordingly, decisions of interest are made differently following group membership:

[H.sub.6] Insurers belonging to a group hold less capital, take more risk, and use more reinsurance than nongroup firms.

CONTROL VARIABLES

In addition to the transversal variables assumed to affect capital, risk, and reinsurance simultaneously, the empirical literature identifies several specific factors that may individually have an impact on these variables. Here, we present the most important factors to be considered in the empirical model developed below.

Determinants of Capital

Performance. Firms with high profitability generally have sufficient internal funds that may be transformed into capital. According to the pecking order theory, firms prefer internal sources of funding (such as retained earnings) to external financing (i.e., debt or new equity) because internal sources of financing are less expensive and more efficient (Park and Pincus, 2001). Alternatively, in the presence of asymmetric information, the use of external funding may convey negative information to the market about the firm's value. Thus, we expect performance to positively affect capital levels. Following Titman and Wessels (1988) and Fama and French (2002), we use return on assets as an indicator of this variable.

Cost of Capital. The cost of holding capital is an important determinant of capital levels (Estrella, 2004). Various costs, such as agency and information asymmetry costs, are related to the use of equity capital. The level of capital is expected to be inversely related to such costs. The cost of holding capital is difficult to measure in practice. Similar to Ayuso, Perez, and Saurina (2004) and Jokipii and Milne (2008), we approximate it as the average of positive returns on equity (ROE) over the most recent 5 years.

Information Symmetry. Signal theory suggests that information asymmetry along with the opacity of the insurance industry are important determinants of the capitalization level (Pottier and Sommer, 2006; Morgan, 2002). Insurers with volatile incomes are likely to use retained earnings rather than external capital to cover future losses or cope with external shocks. Insurers can overcome information asymmetry by building capital stock during periods of high profitability. We use the volatility of ROE as a measure of this variable (Cummins and Nini, 2002; Grubisic and Leadbetter, 2007).

Growth Opportunities. Insurers with better growth opportunities are expected to hold more capital. The literature uses the book-to-market ratio or changes in R&D expenses to measure this variable. Hovakimian, Opler, and Titman (2001) and Fama and French (2002) use the book-to-market ratio as a proxy for a firm's growth opportunities (GROWTH). This proxy is defined as the ratio of the book value of total assets minus the book value of equity and debt plus the ratio of market value of equity and debt to the book value of total assets (Barclay and Smith, 1995; Rajan and Zingales, 1995). However, due to a lack of data, we use an alternative measure, following Carayannopoulos and Kelly (2004), namely, the past growth (over 5 years) in premiums.

Exposure to Extreme Risk. Exposure to extreme risks is likely to influence the level of capital. Zanjani (2002) demonstrates that companies insuring heavily against natural disasters have higher capital levels than those less exposed to such events. The level of exposure to extreme risk is measured in our model as the proportion of direct premiums written on property insurance in Eastern coastal states and on earthquake insurance (Powell and Sommer, 2007).

Liquidity Risk. Insurers with a large share of liquid assets are more likely to be exempt from regulatory constraints than others (Meyer et al., 2013). The low risk associated with these assets allows for easy adjustments of capital levels. Therefore, insurers with more liquid assets are expected to have less capital and take more risks. De

Ceuster and Masschelein (2003) find that the major source of illiquidity is the asset-liability mismatch, which may encourage insurance firms to hold more capital. In this study, liquidity risk is measured by the ratio of liabilities to liquid assets.

Deficit. This variable is used to test for the existence of a preference order among funding sources for insurers. It may reflect the need for external financing when internal cash flows are exhausted. According to the pecking order theory, firms with high deficits have higher leverage and lower capital as they prefer to finance investments internally (De Bie and De Haan, 2007). Thus, the financial deficit has a negative impact on the capital ratio. In the same way, this variable may have a mechanical negative effect on capital since it would deplete it. The deficit variable is measured as the total amount of cash dividends, investments, and change in working capital minus internal cash flow.

Determinants of Risk Taking

Previous theoretical and empirical work suggests that risk taking is affected by various factors, including the following.

Business Mix. The business mix is the degree of centering on a firm's core business. A high concentration of premiums in certain lines of business exposes insurers to significant risk. However, high concentration may also reflect specialization and better risk pricing. Thus, we expect a positive relationship between the degree of centering and risk taking. This variable is approximated by the Herfindahl index of the four major branches of nonlife insurance business, namely, short- and longterm personal insurance and short- and long-term commercial insurance.

Loss Volatility. When the loss ratio is highly volatile, the insurer has less certainty about the future value of losses and may thus need to reduce risk taking to guard future possible insurance payouts. However, Hoerger, Sloan, and Hassan (1990) argue that the increased volatility of claims generates increased risk. This factor is approximated by the standard deviation of the loss ratio gross of reinsurance over the last 3 years.

Geographic Concentration. An insurer may reduce its overall risk by holding a portfolio whose components are not perfectly correlated across regions and/or activities. Empirical studies find that in the banking sector, diversification is associated with moderate risk taking (Hughes, Lang, and Mester, 1996; Deng, Elyasiani, and Mao, 2007), which is a hypothesis based on the benefits of cost reduction and income synergy (Saunders and Cornett, 2007). Alternatively, diversification may be associated with higher risk taking because of the agency problem and competition. The degree of diversification is measured by the Herfindahl index percentages of direct premiums written by geographical area.

Determinants of Reinsurance

Researchers have documented that reinsurance can be affected by several firmspecific factors.

Business Mix. Mayers and Smith (1990) examine the effects of the composition of a firm's portfolio of activities on the demand for reinsurance. They observe that an increased concentration of activities increases the volatility of cash flows and the risk of bankruptcy. Reinsurance might be a solution to the risk of insolvency arising from this source.

Moreover, Shortridge and Avila (2004) and Cole and McCullough (2006) demonstrate that this factor reflects the degree of centering on the core business. By contrast, the economic benefits of specialization can reduce demand for reinsurance.

Leverage. Highly leveraged insurers are exposed to a higher likelihood of insolvency and thus higher expected bankruptcy costs (Shiu, 2011). Moreover, it is more difficult for them to raise capital in financial markets at low cost. Thus, reinsurance may act as a substitute for capital and reduce the probability of insolvency (Garven and Lamm-Tennant, 2003). Higher leveraged insurers have more incentives to increase their reinsurance demand. Thus, we expect a positive relationship between leverage and reinsurance.

Geographic Concentration. Geographical concentration reflects the degree of diversification of an insurer across states. Cole and McCullough (2006) find a negative relationship between geographic concentration and reinsurance and between lines-of-business concentration and reinsurance. Garven and LammTenant (2003) and Mayers and Smith (1990) also find a negative relationship using a different measure of diversification. This variable is measured by the Herfindahl index of the percentage of direct premiums written by geographic area.

METHODOLOGY

Model

In this section, we investigate the relationships between capital, reinsurance, and risk adjustments using a simultaneous equations model. Note that the observed variations of these variables are both discretionary and caused by factors exogenous to the insurer (Shrieves and Dahl, 1992; Jacques and Nigro 1997; Shim, 2010). To account for this behavior, we introduce lagged variables as partial adjustment components (cf. the Appendix). The model has the following specifications:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [e.sub.i,t], [v.sub.i,t], and [u.sub.i,t] are error terms. Cap, Reins, and Risk denote the capital ratio, reinsurance ratio, and risk taking, respectively. The definitions of the control variables are listed in Table 1. Time effects are included in the model to capture systematic events and high losses associated with manmade and natural disasters. In capturing interactions between capital, risk, and reinsurance, simultaneous equations models have shown better performance than estimating the equations individually. The system of equations considers two specifications, which alternatively exclude and include the regulatory pressure mechanisms. Following Shim (2010), we introduce further interaction between the degree of insurer capital and the key variable adjustments.

Variable Construction

Capital (Cap). Because most of the insurers in our sample are not listed, it is not possible to determine their market values. Similar to Cummins and Sommer (1996) and Shim (2010), we proxy the capital ratio by the book value of the surplus divided by the total value of assets.

Reinsurance (Reins). This variable is given, for each insurer, by the ratio of reinsurance premiums ceded to total premiums written, which include direct premiums written and reinsurance premiums assumed (Garven and Lamm-Tennant, 2003; Cole and McCullough, 2006; Powell and Sommer, 2007).

Risk Taking (Risk). Unlike capital and reinsurance measures, which have straightforward definitions, risk assessment remains an open issue. Several measures have been proposed in the literature, especially in the banking sector: the standard deviation of the loss ratio (Meyers, 1989), insurer's exposure to external factors as captured by market betas (Eling and Schuhmacher, 2007), and equity volatility, which reflects both external and firm-specific factors (systematic and nonsystematic risk). Shim (2010) argues that those measures do not fully capture the complex risk profile of the insurance business. An alternative measure proposed in the literature (Cummins and Sommer, 1996; Rime, 2001; Shim, 2010) is the proportion of risky assets and liability. Based on portfolio theory, we measure total risk by the volatility of the asset-to-liability ratio. According to Cummins and Sommer (1996) and Shim (2010), an insurer's asset-liability volatility can be expressed as follows:

[sigma] = [square root of ([[sigma].sup.2.sub.A] + [[sigma].sup.2.sub.L] 2[[sigma].sub.A,L])], (4)

where [[sigma].sub.A] and [[sigma].sub.L] are the volatility measures of the insurer's assets and liabilities, respectively, and [[sigma].sub.A,L] is the covariance of the logarithms of the assets and liability values. Let us denote the proportion of assets of asset type i in the investment portfolio by [x.sub.i] and the proportion of liabilities from business line j by [y.sub.j]. The respective volatilities of the asset and liability portfolios and the covariance of the logarithms of the liability and asset returns are given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote the volatilities of the log of asset type i and the log of liabilities in business line j, respectively. The parameter reflects the correlation between the log of the ith asset and the log of the liabilities in the jth business line, whereas N is the number of asset categories and M is the number of lines of business.

To measure asset-liability volatility, one must first define different lines of activities and asset categories. Following Shim (2010), we aggregate each insurer's lines of business into 12 categories: homeowners/farmowners, auto physical damage, auto liability, commercial multiple peril, special property, fidelity/surety, accident, health, financial guaranty, medical malpractice, workers' compensation, other liability, special liability, and miscellaneous liability. The types of assets are classified into 7 categories: stocks, government bonds, corporate bonds, real estate, mortgages, cash and other invested assets, and noninvested assets. A second risk measure is used to assess the robustness of our results and it is defined as the mean of two conventional risk measures. The first is asset risk approximated by the value of investments in equities and real estate divided by total invested assets. The second component is underwriting risk, which is defined as the proportion of premiums written in risky lines (commercial auto liability, allied lines, earthquake, surety, theft, inland marine, fire, international, boiler and machinery, reinsurance, and medical malpractice occurrence).

Estimation Methodology

Estimating the equations individually ignores the problem of the potential endogeneity that violates the condition of no correlation between exogenous variables and the error terms (Baltagi, 2005). To address this problem and to avoid biased ordinary least squares (OLS) estimates, we use the three-stage least squares (3SLS) technique (Shim, 2010; Rime, 2001; Jacques and Nigro, 1997). This methodology also treats ''suspicious'' endogeneity of some control variables using instrumental variables. First, we estimate the model using the OLS and 3SLS methods and compare the results using the Hausman test. As we find significant differences in the estimates, the endogeneity problem is confirmed.

To examine the interactions between capital, risk, and reinsurance, it is crucial to determine whether such variables are endogenous or exogenous. It is also important to check the exogeneity of the control variables. For that purpose, the Durbin-Wu-Hausman (DWH) test is performed for all variables that are individually regressed against all the exogenous variables and instrumental variables. The residuals obtained from the first stage are then added as an additional independent variable in their respective equation. The results of the DWH test are summarized in Table 1. According to the test, all left-hand-side variables in the model are endogenously determined. Some of the control variables (exposure to extreme risks, performance, liquidity risk, and leverage) are endogenous. Therefore, we take this result into account by treating them as endogenous when we estimate the model.

Regarding the choice of instruments, we identify them according to the extant literature and the Sargan-Hansen test. In the model, we use the largest number possible for which the Sargan statistic for overidentification restrictions is still satisfied. Specifically, we choose a large list of variables used in the literature (Shim, 2011; Jokipii and Milne, 2011; Shiu, 2012). We first examine the OLS results to identify variables that affect one of the three variables of interest but not the remaining two. We find that the two-period-lagged risk and reinsurance variables, the economic growth rate variable, and the variable for the ratio of unrealized gains (with no lag and one period lagged) are valid instruments. Second, in order to improve our estimations, we add additional exogenous variables used in the model as supplementary valid instruments. Prior to estimation, we verify whether the time series are stationary based on the Levin-Lin-Chu test.

DATA

Sample

The data used in this study are collected from the National Association of Insurance Commissioners (NAIC) annual statement database for U.S. property-liability insurers from 1999 to 2008. The sample is limited to solvent insurers reporting positive values of admitted assets, gross and net premiums written, equity capital, and ceded reinsurance premiums. We retain only active insurers with no regulatory actions in process. After applying these sample screens, our final sample consists of 12,511 year-firm observations. Our sample thus accounts for 82 percent (85 percent) of the entire U.S. property-liability market in terms of total assets in the year 1999 (2008). We use an unbalanced data panel to allow for a comprehensive evaluation of the property-liability market. The sample includes firms that entered or left the market during the study period. In addition to the NAIC database, we also collected data from DataStream to estimate asset returns. (2)

Descriptive Statistics and Correlation Analysis

Table 2 presents descriptive statistics of all variables used in this study. The mean and median of the capital ratio are approximately 42 and 38 percent, respectively. These statistics are (39 and 34 percent) and (2.7 and 0.4 percent) for the reinsurance ratio and risk level, respectively. The distributions of the two risk measures are positively skewed. With regard to the diversification profiles measured by the two Herfindahl indices (Higeo and Mix), we note small variations across insurers. Approximately 74 percent of insurers are stock firms and 73 percent are group affiliated.

Before conducting the regression analysis, we first considered the possibility of multicollinearity among independent variables, which may lead to biased estimates. Table 3 presents the Pearson correlation between the variables included in the regression model, which indicates that the correlation between capital and risk is positive and confirms the hypothesis that insurers adjust their capital levels upward following increases in risk. Note that correlations between all exogenous variables classified in Table 1 are modest and do not exceed 0.3. Nonetheless, we report some significant correlation between endogenous variables, which confirms our choice to treat them as endogenous in the estimation procedure. Another notable result outlined in Table 3 is the high correlation between the two risk measures. Consistent with standard econometric practice, we assess the degree of multicollinearity among the independent variables using the variance inflation factor (VIF). All VIF values reported in Table 4 range between 1.01 and 2.2. Thus, no multicollinearity is detected among the explanatory variables.

RESULTS

This section reports and discusses empirical results. We estimate the model first for the full sample and then for various subsamples by following the level of capital, affiliation with a group, firm size, and organizational form. In the second phase, we perform some robustness tests.

Full Sample

The main hypotheses tested in this paper are related to the existence of mutual interactions between risk taking, capital, and reinsurance. Table 5 displays the full sample estimation of equations system ((1)-(3)) using asset-liability volatility (Risk1) as a risk measure. A closer look at the individual equations' coefficients indicates that most of the results are consistent with expectations. First, let us consider the baseline results without regulatory pressure mechanisms in the regressions. Overall, the coefficients related to the capital equation are significant, except those related to exposure to extreme risks and the transversal factors. The risk variable is positive and statistically significant, which is consistent with the capital buffer hypothesis and suggests that an increase in risk taking leads to positive adjustments of capital as a guaranty against unanticipated extreme losses (Jokipii and Milne, 2011). Second, the negative sign of the reinsurance variable supports the original hypothesis regarding the substitutability effect between these two variables. This result is consistent with the findings of Stulz (1996) and Armstrong and Dror (2006), who put forward the fact that reinsurance can serve as off-balance-sheet capital that reduces the capital requirement and allows new policies to be issued. The speed of adjustment toward the desired capital ratio, captured by the lagged depended variable, is low (0.0389) and can be explained by the presence of various adjustment costs.

Regarding control variables, performance appears to have a significant and positive effect on capital, confirming pecking order theory. Because of its lower cost, profitable firms seem to rely more on retained earnings to raise capital. The cost of capital variable is negative and significant, which highlights the importance of this variable on the use of capital. An increase in information asymmetry, as measured by the volatility of ROE, drives insurers to hold more capital. To some extent, this variable may reflect an alternative measure of risk and thereby confirms the positive relationship between this variable and capital. The coefficients of the liquidity risk and the deficit variables are negative and significant. We also note the presence of significant temporal effects, which may be explained by the impact of various macroeconomic shocks or extreme loss periods. The introduction of regulatory pressure mechanisms in the second specification slightly alters the estimation results, and only the coefficient on [Reg.sub.t-1] x [Reins.sub.t-1] is positive and statistically significant. These results indicate that highly leveraged companies in the previous period tend to increase their levels of reinsurance to adjust their capital levels to avoid regulatory costs.

Table 5 also presents the estimation results for the equation of the ratio of reinsurance. The [chi square] statistic is significant at the 1 percent level, which illustrates the validity of the estimation. Positive adjustments of risk taking or capital generate an increase in the ratio of reinsurance. Unlike the capital equation, we find that capital is not a substitute for reinsurance. This result can be explained by the imperfect substitutability between the two variables in the sense that reinsurance can play the same role as capital, whereas the reverse is not the case. For example, capital does not reduce the volatility of losses. Estimation results show also that the partial adjustment factor is not significant and illustrate that the reinsurance policy is not adjusted to its target level. Consistent with the argument that the economic benefits of specialization can reduce the demand for reinsurance, the coefficient of the business mix variable is negative. Stock firms appear to use less reinsurance than mutual firms. This result supports the idea that stock firms have easier access to external funding and are less dependent on reinsurance than mutual firms. Regulatory pressure does not change the pattern of results.

The last part of Table 5 presents the estimation results for the risk equation. The [chi square] statistic is significant at the 0.001 level. An asymmetric relationship between capital and risk adjustments is notable. A positive capital adjustment leads to lower risk. Although surprising, this result can be explained by the fact that capital adjustment as a result of a stricter capital-based regulation may reduce risk taking (Mailath and Mester, 1994). Note that a positive adjustment of reinsurance increases this risk. This finding is consistent with the view of Shiu (2011) and Aunon-Nerin and Eling (2008), who document that the heavy use of reinsurance leads to high risk taking. The partial adjustment factor is not significant, which indicates that risk taking is not adjusted to its target level. The Mix variable, which reflects the degree of concentration of the main underwriting branches and lines of business, is positive and significant. As the activities of the company become more concentrated, the company's risk taking increases in the short term. As expected, stock firms are positively related to risk taking. The Sargan-Hansen test shows the validity of the selected instrumental variables used to address the endogeneity issue for models I and II.

Subsample Analysis

To reduce the effect of sample heterogeneity and the aggregation bias that it may imply, we divide the overall sample into subsamples following the transversal factors discussed previously. The first distinction is based on the RBC ratio, that is, the ratio of observed capital to regulatory capital. We estimate model I by selecting two subsamples: the bottom third of firms (low-capitalized firms) and the top third (high-capitalized firms). The estimation results (displayed in Table 6) demonstrate that lowcapitalized insurers adjust capital, risk, and reinsurance more extensively than highcapitalized insurers. Most coefficients of the key variables are significant and higher for low-capitalized than for high-capitalized firms. In the former, the relationship between capital adjustment and risk remains positive. The coefficient is significant with a relatively high value, indicating a high sensitivity of the capital to risk. Adjustments of reinsurance appear to have a greater impact on capital. Reinsurance seems to be a more outstanding substitute for capital for these companies. All the dependent variables are adjusted to their target levels, with speeds greater than those observed in the overall sample, which is also the case for high-capitalized firms.

The second distinction made in our entire sample is based on group affiliation. Table 7 provides the results of the two estimations and shows that the methodology used in this article and the hypotheses tested are more consistent with affiliated insurers than with nonaffiliated insurers. First, the estimation results of the former are similar to those from the entire sample. Second, most of the variables used in the model-and some of those of interest--are nonsignificant for nonaffiliated insurers. This result can be explained by the fact that internal market plays a significant role. As affiliated insurers can better control decisions regarding the capital level, the risk level, and the reinsurance level (Cheng and Weiss, 2012; Powell, Sommer, and Eckles, 2008), the interactions among the three decision variables are more pronounced for affiliated than for nonaffiliated insurers. Furthermore, the results show that reinsurance usage for affiliated insurers seems to serve as a substitute for capital, which is not the case for nonaffiliated insurers that have more difficulties in using reinsurance since the monitoring costs are more important for them (Cole et al., 2011).

Table 8 provides estimation results following the size of the firm. We consider two subsamples related to the lower-third and upper-third groups in term of size. The empirical results from our first set of equations generally provide evidence that large insurers tend to purchase less reinsurance due to their stronger financial ability than small firms. This result can be explained by the fact that size may influence the insurer's risk appetite through its effect on investment opportunities and firm's access to capital. Moreover, large firms are likely to have a better allocation of risk and hold less capital than small firms.

Table 9 distinguishes between stock and mutual insurers and sheds light on some more interesting results. First, we confirm the links between the three variables of interest (i.e., capital, risk, and reinsurance) in at least one way for both stock and mutual insurers. The signs of interactions remain the same as in the first estimation (Table 5). Second, both the capital adjustment and the reinsurance relationship with risk are more pronounced for mutual firms than for stock insurers. This result is not in line with the pecking order theory (c.f. the second section), but confirms the findings of Cummins, Phillips, and Smith (2001) that mutual firms are more risk averse and respond more rapidly to capital and regulatory requirements and tend to manage risk through reinsurance. We also find empirical support for the organizational form theory; in other words, mutual companies have more limited access to external capital, so they have a greater demand for reinsurance than their stock counterparts. As shown by a Hausman test, all differences between the two subsamples in Tables 6-9 are systematic.

Robustness Checks

In this section, we conduct additional robustness tests covering other aspects of the empirical analysis, such as the risk measurement, the sample structure, and the choice of instrumental variables. It is possible that the previous results outlined regarding the interactions between the key variables are sensitive to the construction of the risk measure. We provide new estimates of the model using the alternative risk measure (Risk2) defined above and reported in Table 10. We confirm the interactions initially obtained, which remain significant in all cases and have the same sign.

The second robustness test is related to the sample structure. Indeed, we use an unbalanced panel such that the final sample contains missing years that may affect the quality of the results. This consideration is particularly important when there are several consecutive years missing in the sample. To resolve this issue, we introduce a data screen requiring that an insurer appears in the sample for at least k consecutive periods. This condition was not applied in the original sample. We find that when k is up to 5, all interactions between capital, risk, and reinsurance remain significant. Similarly, when k is greater than 5 (i.e., 5 consecutive years), some of the relationships become insignificant because of information loss. A third robustness test concerns the choice of instrumental variables, a central step in the estimation process using the 3SLS method. Therefore, we reestimate the model with other instruments, including those proposed by Shim (2010), such as the deviation of earnings over the medium term, the size over the last 5 years, and the average loss. Overall, we find that the results remain stable and significant.

CONCLUSION

This article analyzes interactions between capital, reinsurance, and risk taking for property-liability insurance firms. Our main purpose is to determine the nature of adjustments between these decision variables. Such issues are of particular importance to regulators interested in how insurers have responded to prudential rules. To this end, we estimate a simultaneous equations model to identify the potential links between these variables while controlling for endogeneity.

Empirical results based on a sample of U.S. property-liability insurance firms are consistent with our theoretical hypotheses that predict the existence of significant relationships between the variables of interest, supporting the view that they are jointly determined. In their efforts to maximize firm value, insurers simultaneously adjust various decision variables. The adjustments between risk and capital are positive. This result, found only in one direction, provides interesting insights into the effects of regulation on insurer behavior. By contrast, reinsurance is negatively associated with capital, for which it acts as a substitute. The capital ratio is slowly adjusted to its target level. Furthermore, the results show that for lowcapitalized insurers, capital, risk, and reinsurance adjustments are more extensive than for their high-capitalized counterparts. Interactions between the variables of interest are also sensitive to group affiliation, size, and organizational form.

Regulatory pressures play an active role in moderating risk taking and capital to acceptable levels. Adjustments depend on the level of capital held in excess of the minimum requirement. Low-capitalized insurers reconstruct a buffer capital by raising equity or by reducing risk. In contrast, adequately capitalized insurers maintain their capital reserves and increase both their risk and reinsurance levels. In both cases, higher capital ratios may prevent moral hazard and mitigate informational frictions between policyholders and shareholders. However, these results cannot tell us whether insurers operate efficiently.

APPENDIX

The observed changes in the insurer's capital, reinsurance, and risk-taking levels are the sum of two components, a discretionary adjustment and a change caused by factors exogenous to the insurer. Formally, the three equations are as follows:

[DELTA][Cap.sub.i,t] = [phi]Cap[DELTA][Cap.sup.d.sub.i,t-1] + [v.sub.i,t] (A1)

[DELTA][Reins.sub.i,t] = [[phi].sub.Reins][DELTA][Reins.sup.d.sub.i,t-1] + [u.sub.i,t] (A2)

[DELTA][Risk.sub.i,t] = [[phi].sub.Risk][DELTA][Risk.sup.d.sub.i,t-1] + [e.sub.i,t], (A3)

where [DELTA][Cap.sub.i,t], [DELTA][Reins.sub.i,t], and [[DELTA].sub.Riski,t] are the observed changes in capital, reinsurance, and risk levels, respectively, for insurer i at time t. The variables [DELTA][Cap.sup.d.sub.i,t-1], [DELTA][Reins.sup.d.sub.i,t-1], and [DELTA][Risk.sup.d.sub.i,t-1] represent discretionary adjustments, whereas [v.sub.i,t], [u.sub.i,t], and [e.sub.i,t] are exogenous adjustments of capital, reinsurance, and risk, respectively. The partial adjustment model supposes that insurers may not be able to adjust their desired capital, risk, and reinsurance levels instantaneously. Thus, discretionary changes are proportional to the differences between target levels and the levels observed in the last period:

[DELTA][Cap.sup.d.sub.i,t] = [[phi].sub.Cap] ([Cap.sup.*.sub.i,t] [Cap.sub.i,t-1])

[DELTA][Reins.sup.d.sub.i,t] = [[phi].sub.Rein] ([Reins.sup.*.sub.i,t] [Reins.sub.i,t]) (A5)

[DELTA][Risk.sup.d.sub.i,t] = [[phi].sub.Risk] ([Risk.sup.*.sub.i,t] [Risk.sub.i,t-1]) (A6)

The coefficients [[phi].sub.Cap], [[phi].sub.Reins], and [[phi].sub.Risk] measure the speed of adjustments. Cap*t, [Reins.sup.*.sub.i,t], and [Risk.sup.*.sub.i,t] are target capital, risk, and reinsurance levels, respectively. Substituting Equations (A4), (A5), and (A6) into (A1), (A2), and (A3) yields the following:

[DELTA][Cap.sup.d.sub.i,t] = [[phi].sub.cap] ([Cap.sup.*.sub.i,t] [Cap.sub.i,t-1]) (A7)

[DELTA][Reins.sub.i,t] = [[phi].sub.Reins] ([Reins.sup.*.sub.i,t] [Reins.sub.i,t-1]) + [u.sub.i,t] (A8)

[DELTA][Risk.sub.i,t] = [[phi].sub.Risk] ([Risk.sup.*.sub.i,t] - [Risk.sub.i,t1]) + [e.sub.i,t]. (A9)

The target levels of capital, risk, and reinsurance are not observable. As documented in Flannery and Rangan (2006), Rime (2001), and Shim (2010), these target levels may differ across insurers or over time and depend on the insurer's specific characteristics. Thus, the target levels of capital, risk, and reinsurance can be written as follows:

[Cap.sup.*.sub.i,t] = [rho] x [X.sub.i,t] (A10)

[Reins.sup.*.sub.i,t] = [omega] x [Y.sub.i,t] (A11)

[Risk.sup.*.sub.i,t] = [theta] x [Z.sub.i,t]. (A12)

Substituting Equations (A13), (A14), and (A15) into (A10), (A11), and (A12), we obtain this final form of the structural model:

[DELTA][Cap.sub.i,t] = -[[phi].sub.Cap][Cap.sub.i,t-1] + [[phi].sub.Cap][rho] x [X.sub.i,t] + [v.sub.i,t] (A13)

[DELTA][Reins.sub.i,t] = -[[phi].sub.Reins][Reins.sub.i,t-1] + [[phi].sub.Reins][omega] x [Y.sub.i,t] + [u.sub.i,t] (A14)

[DELTA][Risk.sub.i,t] = -[[phi].sub.Risk][Risk.sub.i,t-1] + [[phi].sub.Risk][theta] x [Z.sub.i,t] + [e.sub.i,t]. (A15)

DOI: 10.1111/jori.12080

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Selim Mankai is at the IPAG Business School. Aymen Belgacem is at the University of Orleans, Technology Institute of Bourges, Laboratoire d'Economie d'Orleans. Selim Mankai can be contacted via e-mail: selim.mankai@udamail.fr.

(1) The theoretical literature often develops conflicting arguments about the effects of regulatory pressure (Scannella, 2012). Strict regulation may create distortions in the operations of solvent firms. By contrast, permissive regulations may lead to high risk exposure, threatening the creditworthiness of insurers. This situation frequently implies a slowdown in innovation, inefficient investment strategies, or passive capital accumulation, and to encourage good risk management practices.

(2) We use the S&P 500 Global Index, Barclays Capital, U.S. 20-year Treasury bond, Dow Jones Corporate Bond Index, Merrill Lynch Mortgage, U.S. Real Estate & Rental & Leasing, and the 3-month U.S. Treasury bill as proxies for asset returns.

Table 1 Variable Definitions and Endogeneity Variable Description Dependent variables Capital Cap Ratio of surplus to total admitted assets Reinsurance Reins Ratio of premiums ceded to direct premiums written plus reinsurance premiums assumed Volatility of asset Risk1 Volatility of the asset and liability to liability ratio Ratio of risky Risk2 Ratio of risky assets assets and and liabilities liabilities Control variables Regulatory Reg 1 if firm's net pressure premium to surplus ratio [greater than or equal to] 300 percent, 0 otherwise Performance Perf Return on assets ratio (ROA) Cost of capital Cost_cap Average of positive ROE over the last 5 years Exposure to Extreme Proportion of direct extreme risk premiums written for property insurance in Eastern coastal states and for earthquake insurance Information Assy The standard asymmetry deviation of the firm's ROE over the last 5 years Business mix Mix Herfindahl index of short and long tails of personal and commercial lines Liquidity risk Lqt_risk Ratio of liabilities to liquid assets Loss volatility Loss_vol Standard deviation of the loss ratio, gross of reinsurance over the last 3 years Leverage Lev Ratio of direct business written to surplus Geographic Higeo Herfindahl index of diversification direct premium written across geographic areas Growth Growth Percentage growth of opportunities written premiums Deficit Deficit Financial deficit ratio calculated as cash dividends plus investments plus change in working capital minus internal cash flow Stock vs. mutual Stock 1 if the insurer is a stock firm, 0 if it is a mutual firm Group affiliation Group 1 if the insurer is a member of a group in year t, 0 otherwise Size Size The logarithm of total assets Time effects Year Annual temporal effect Variable Expected Signs [DELTA] [DELTA] [DELTA] Cap Reins Risk Dependent variables Capital Cap (+/-) (+/-) Reinsurance Reins (-) (+) Volatility of asset Risk1 (+) (+) and liability Ratio of risky Risk2 (+) (+) assets and liabilities Control variables Regulatory Reg pressure Performance Perf (+) Cost of capital Cost_cap (-) Exposure to Extreme (+) extreme risk Information Assy (+) asymmetry Business mix Mix (+/-) (+) Liquidity risk Lqt_risk (+) (+) Loss volatility Loss_vol (+) Leverage Lev (+) Geographic Higeo (+) (+/-) diversification Growth Growth (+/-) opportunities Deficit Deficit (+) Stock vs. mutual Stock (-) Group affiliation Group (-) Size Size (-) Time effects Year Variable DWH Test of Endogeneity Dependent variables Capital Cap Endogenous Reinsurance Reins Endogenous Volatility of asset Risk1 Endogenous and liability Ratio of risky Risk2 Endogenous assets and liabilities Control variables Regulatory Reg Exogenous pressure Performance Perf Endogenous Cost of capital Cost_cap Exogenous Exposure to Extreme Endogenous extreme risk Information Assy Exogenous asymmetry Business mix Mix Exogenous Liquidity risk Lqt_risk Endogenous Loss volatility Loss_vol Exogenous Leverage Lev Endogenous Geographic Higeo Exogenous diversification Growth Growth Exogenous opportunities Deficit Deficit Exogenous Stock vs. mutual Stock Exogenous Group affiliation Group Exogenous Size Size Exogenous Time effects Year Note: This table describes the variables used in the empirical model. Endogeneity tests for dependent and control variables not reported are available from the authors upon request. Table 2 Descriptive Statistics Mean Median Standard 5 Percent Deviation Quantile Cap 0.420 0.381 0.169 0.211 Reins 0.394 0.345 0.283 0.024 Risk1 0.027 0.004 0.192 0.0009 Risk2 0.017 0.001 0.174 0.0004 Perf 0.024 0.026 0.049 -0.054 Cost_cap 0.056 0.062 0.110 0.001 Extreme 0.084 0.047 0.196 0 Assy 0.079 0.049 0.104 0.009 Lqt_risk 0.746 0.733 0.514 0.255 Mix 0.331 0.278 0.321 0.000 Loss vol 1.461 0.754 5.076 0.241 Up 1.742 1.285 1.639 0.109 Higeo 0.388 0.377 0.095 0.264 Growth 0.122 0.049 0.646 -0.395 Deficit 0.057 0.056 0.157 -0.159 Stock 0.740 1 0.439 0 Group 0.731 1 0.443 0 Size 18.510 18.418 1.815 15.721 Reg 0.018 0.000 0.133 0 95 Percent Skew Kurt Quantile Cap 0.764 0.977 0.667 Reins 0.899 0.617 0.778 Risk1 0.071 12.608 17.747 Risk2 0.014 17.163 31.493 Perf 0.091 -0.057 14.694 Cost_cap 0.203 -0.950 13.740 Extreme 0.549 2.958 8.520 Assy 0.241 5.512 52.209 Lqt_risk 1.190 18.164 55.039 Mix 0.931 0.590 -0.931 Loss vol 3.606 21.185 50.094 Up 5.207 1.960 4.554 Higeo 0.500 0.018 -1.634 Growth 0.763 1.571 61.047 Deficit 0.295 -1.064 10.801 Stock 1 -1.096 -0.799 Group 1 -1.042 -0.914 Size 21.668 0.298 -0.069 Reg 1 7.238 50.397 Note: This table reports the mean, median, standard deviation, 5th percentile, 95th percentile, skewness, and kurtosis of all variables. The data are collected from the NAIC and Datastream databases covering U.S. property-liability insurance firms from 1999 to 2008. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; Cost_Cap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business the insurer. mix; Lqt_risk, liquidity risk; Loss_vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of TABLE 3 Correlation Coefficient Matrix 1 2 3 4 5 1. Cap 1 1 2. Reins 0.012 1 3. Risk1 0.046* -0.029* 1 4. Risk2 -0.033* -0.013 0.243* 1 5. Perf 0.206* -0.059* -0.0023 -0.032* 1 6. Cost_cap 0.090* -0.084* 0.0113 -0.0141 0.6368* 7. Extreme 0.127* 0.072* -0.034* -0.0162 0.0008 8. Assy -0.238* 0.017 -0.022 -0.0048 -0.1704* 9. Lqt_risk -0.504* 0.149* -0.0261 0.0109 -0.1363* 10. Mix 0.072* 0.050* -0.068* -0.0232 -0.0336* 11. Loss_vol 0.084* 0.084* 0.021 -0.007 -0.0785* 12. Lev -0.384* 0.460* -0.0503* -0.0212 -0.1121* 13. Higeo 0.155* -0.183* -0.0541* -0.0286 -0.0015 14. Growth -0.031* -0.047* -0.0154* -0.000* -0.0819* 15. Deficit -0.145* 0.044* 0.0058 0.009 0.0255 16. Stock -0.106 0.215* 0.0414* 0.0012 0.0434* 17. Group -0.117* 0.230* 0.0067 0.0436* -0.0081 18. Size -0.375* -0.042* -0.0031 0.0823* 0.0602* 19. Reg -0.157* -0.056* -0.0129 -0.0094 -0.0878* 6 7 8 9 10 1. Cap 1 2. Reins 3. Risk1 4. Risk2 5. Perf 6. Cost_cap 1 7. Extreme -0.052* 1 8. Assy -0.400* 0.736* 1 9. Lqt_risk -0.079* -0.0492* 0.1339* 1 10. Mix -0.053* 0.4085* -0.013 -0.0955* 1 11. Loss_vol -0.103* 0.015 0.0906* -0.022 -0.0066 12. Lev -0.111* 0.0288 0.1759* 0.3954* -0.095* 13. Higeo 0.054* 0.180* 0.055* -0.0728* 0.0499* 14. Growth 0.025 -0.003 -0.0249 0.0531* 0.0028 15. Deficit 0.058* -0.0212 -0.0621* 0.1306* -0.001 16. Stock 0.048* -0.1614* 0.0395* 0.0973* -0.2312* 17. Group 0.020 -0.0477* -0.0284 0.0798* -0.1193* 18. Size 0.157* -0.1195* -0.0418* 0.1586* -0.067* 19. Reg -0.101* -0.0225 0.1558* 0.1021* -0.0151 11 12 13 14 15 1. Cap 1 2. Reins 3. Risk1 4. Risk2 5. Perf 6. Cost_cap 7. Extreme 8. Assy 9. Lqt_risk 10. Mix 11. Loss_vol 1 12. Lev -0.028 1 13. Higeo 0.0121 -0.0017 1 14. Growth 0.0950* 0.067* -0.0107 1 15. Deficit 0.0157 0.1260* 0.0022 0.392* 1 16. Stock 0.0316* 0.0965* -0.237* 0.0389* 0.0363* 17. Group 0.0201 0.0261 -0.317* -0.0001 -0.023 18. Size -0.0457* -0.1094* -0.479* -0.24 0.027 19. Reg -0.0151 0.2115* 0.0503* 0.0474* 0.048* 16 17 18 19 1. Cap 1 2. Reins 3. Risk1 4. Risk2 5. Perf 6. Cost_cap 7. Extreme 8. Assy 9. Lqt_risk 10. Mix 11. Loss_vol 12. Lev 13. Higeo 14. Growth 15. Deficit 16. Stock 1 17. Group 0.302* 18. Size 0.0833* 1 1 19. Reg 0.022 -0.038* -0.038* 1 Note: Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; Cost_Cap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt_risk, liquidity risk; Loss_vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer. * represents statistical significance at the 1 percent level. Table 4 Variance Inflation Factors Eq [DELTA]Cap Eq [DELTA] Eq [DELTA] Reins Risk1 [DELTA]Reins 1.1 [DELTA]Cap 1.02 [DELTA]Reins 1.01 [DELTA]Risk1 1 [DELTA]Risk1 1 [DELTA]Cap 1.02 [Cap.sub.t-1] 1.65 [Reins.sub. 1.47 [Risk1.sub. 1.01 t-1] t-1] Perf 1.86 Mix 1.1 Loss_vol 1.01 Cost_cap 2.06 Lev 1.34 Mix 1.07 Extreme 1.06 Higeo 1.43 Higeo 1.39 Assy 1.27 Stock 1.22 Stock 1.2 Lql_risk 1.38 Group 1.38 Group 1.32 Growth 1.34 Size 1.51 Size 1.46 Deficit 1.24 Stock 1.16 Group 1.32 Size 1.44 Mean VIF 1.38 Mean VIF 1.28 Mean VIF 1.16 Note: Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; Cost_Cap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt_risk, liquidity risk; Loss_vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer. Table 5 Estimation Results of the Simultaneous Eequations Using Asset-Liability Volatility (Risk1) as a Risk Measure Model I [DELTA][Cap.sub.t] [DELTA][Reins.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -- -- 0.556 *** 5.91 [DELTA][Reins.sub.t] -0.180 *** -3.72 -- -- [DELTA][Risk1.sub.t] 0.354 *** 2.94 1 979 *** 19.96 [Cap.sub.t-1] -0.0389 * -1.9 -- - [Reins.sub.t-1] -- -- -0.0044 -0.49 [Risk1.sub.t-1] -- -- -- -- [Reg.sub.t-1] X -- -- -- -- [Cap.sub.t-1] [Reg.sub.t-1] X -- -- -- -- [Reins.sub.t] [Reg.sub.t-1] X Risk1 -- -- -- -- Perf 0.553 *** 22.34 -- -- Costcap -0.0568 *** -4.98 -- -- Extreme 0.0159 0.53 -- -- Assy 0.0576 *** 4.37 -- -- Lqt_risk -0.013 *** -4.08 -- -- Mix -- -- -0.354 *** -4.8 Lossvol -- -- -- -- Lev -- -- 00006 0.44 Higeo -- -- -0.0681 -1.33 Growth -0.029 *** -9.16 -- -- Deficit -0.107 *** -12.62 -- -- Stock 0.0021 0.69 -0.0665 *** -4.18 Group 0.0025 1.05 -0.0017 -0.15 Size -0.0001 -0.12 -0.005 * -1.71 2001 .year -0.018 *** -2.77 -0.106 *** -5.89 2002.year 0.0222 *** 3.35 0.0868 *** 4.96 2003 .year 0.0272 *** 7.85 -0.023 -1.38 2004.year 0.0168 *** 4.98 -0.015 -0.93 2005.year 0.0185 *** 5.09 -0.011 -0.64 2006.year 0.0234 *** 6.44 -0.0166 -0.9 2007.year 0.0170 *** 4.84 -0.0074 -0.41 Intercept 0.0034 0.13 0.310 *** 3.52 [chi square] 1730.25 453.4 p-value 0.0000 0.0000 Sargan-Hansen 42.740 statistic p-value 0.2748 Model I Model II [DELTA][Risk1. [DELTA][Cap.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -0.276 *** -3.7 -- -- [DELTA][Reins.sub.t] 0.505 *** 26.4 -0.181 *** -3.82 [DELTA][Risk1.sub.t] -- -- 0.319 ** 2.68 [Cap.sub.t-1] -- -- -0.0242 -1.14 [Reins.sub.t-1] -- -- -- -- [Risk1.sub.t-1] 0.0029 0.44 -- -- [Reg.sub.t-1] X -- -- -- -- [Cap.sub.t-1] [Reg.sub.t-1] X -- -- 0.0567 *** 3.33 [Reins.sub.t] [Reg.sub.t-1] X Risk1 -- -- 0.174 0.69 Perf -- -- 0.540 *** 21.97 Costcap -- -- -0.0511 *** -4.45 Extreme -- -- 0.0063 0.22 Assy -- -- 0.0584 *** 4.46 Lqtrisk -- -- -0.012 *** -3.52 Mix 0.187 *** 5.27 -- -- Lossvol 0.00008 0.36 -- -- Lev -- -- -- -- Higeo 0.0353 1.34 -- -- Growth -- -- -0.029 *** -9.65 Deficit -- -- -0.107 *** -12.87 Stock 0.0349 *** 4.42 0.0017 0.58 Group 0.0013 0.23 0.0025 1.1 Size 0.0028 * 1.72 0.0001 0.18 2001 .year 0.0540 *** 6.02 -0.016 * -2.51 2002.year -0.043 *** -5.03 0.0208 *** 3.22 2003 .year 0.0116 1.33 0.0280 *** 8.31 2004.year 0.00764 0.9 0.0178 *** 5.4 2005.year 0.00583 0.61 0.0195 *** 5.53 2006.year 0.00823 0.85 0.0240 *** 6.84 2007.year 0.00374 0.39 0.0175 *** 5.15 Intercept -0.163 *** -3.63 -0.0084 -0.3 [chi square] 963.62 887.21 p-value 0.0000 0.0000 Sargan-Hansen statistic p-value Model II [DELTA][Reins.sub.t] [DELTA][Risk1.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] 0.553 *** 4.03 -0.279 *** -3.74 [DELTA][Reins.sub.t] -- -- 0.516 *** 24.24 [DELTA][Risk1.sub.t] 1.934 *** 18.12 -- -- [Cap.sub.t-1] -- -- -- -- [Reins.sub.t-1] -0.0062 -0.68 -- -- [Risk1.sub.t-1] -- -- 0.0039 0.53 [Reg.sub.t-1] X -0.347 ** -2.6 0.197 *** 2.78 [Cap.sub.t-1] [Reg.sub.t-1] X -- -- -0.007 -0.52 [Reins.sub.t] [Reg.sub.t-1] X Risk1 0.017 0.06 -- -- Perf -- -- -- -- Costcap -- -- -- -- Extreme -- -- -- -- Assy -- -- -- -- Lqt_risk -- -- -- -- Mix -0.369 *** -4.96 0.204 *** 5.48 Lossvol -- -- 0.0001 0.43 Lev 0.0009 -- -- -- Higeo -0.0701 -1.41 0.0375 1.41 Growth -- -- -- -- Deficit -- -- -- -- Stock -0.0676 *** -4.33 0.037 *** 4.61 Group -0.0031 -0.28 0.0024 0.4 Size -0.00577 * -1.89 0.003 * 1.92 2001 .year -0.104 *** -5.94 0.0545 *** 6.08 2002.year 0.0849 *** 4.99 -0.043 *** -5.03 2003 .year -0.0223 -1.39 0.0114 1.32 2004.year -0.0163 -1.03 0.0083 0.97 2005.year -0.0119 -0.67 0.0060 0.63 2006.year -0.0165 -0.93 0.0083 0.87 2007.year -0.0081 -0.47 0.0042 0.44 Intercept 0.327 *** 3.78 -0.179 *** -3.91 [chi square] 399.26 901.86 p-value 0.0000 0.0000 Sargan-Hansen 52.666 statistic p-value 0.1047 Note: This table reports the results of the 3SLS estimation for the full sample, without (Model I) and with (Model II) interaction terms. The Sargan- Hansen test evaluates the validity of the instruments. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; CostCap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt risk, liquidity risk; Loss vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer; Year, time effects. *, **, and *** represent statistical significance at the 10, 5, and 1 percent levels, respectively. Table 6 Estimation Results Following the Capital Level Low Cap [DELTA][Cap.sub.t] [DELTA][Reins. sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -- -- 0.821* 2.28 [DELTA][Reins.sub.t] -0.385 *** -3.16 -- -- [DELTA][Risk1.sub.t] 1.334 ** 1.98 3.25*** 4.54 [Cap.sub.t-1] -0.260 ** -2.2 -- -- [Reins.sub.t-1] -- -- -0.238** -3.4 [Risk1.sub.t-1] -- -- -- -- Perf 0.549 3.86 -- -- Costcap -0.099 *** -2.25 -- -- Extreme 0.082 0.61 -- -- Assy -0.006 -0.16 -- -- Lqt_risk -0.128 *** -3 -- -- Mix -- -- 0.353 1.48 Lossvol -- -- -- -- Lev -- -- 0.026*** 2.61 Higeo 0.1 0.67 Growth -0.008 -0.47 -- -- Deficit -0.083 -1.63 -- -- Stock 0.029 ** 2.38 0.072* 1.72 Group -0.005 -0.45 -0.02 -0.71 Size -0.0035 -1.35 0.007 0.93 2001 .year -0.056 -1.56 -0.126** -2.08 2002.year 0.071 * 1.65 0.186*** 2.81 2003.y ear 0.0023 0.13 -0.045 -0.93 2004.year 0.006 0.36 -0.015 -0.31 2005.year -0.001 -0.05 -0.025 -0.5 2006.year 0.0017 0.09 -0.0103 -0.21 2007.year 0.0172 0.76 -0.005 -0.1 Intercept 0.250 ** 2.94 -0.294 -1.12 [chi square] 108.67 43.63 p-value 0.0000 0.0000 Sargan-Hansen 33.834 statistic p-value 0.1392 Hausman test [chi square] p-value Low Cap High Cap [DELTA][Risk1. [DELTA][Cap.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -0.073 -0.77 -- -- [DELTA][Reins.sub.t] 0.150 *** 3.8 -0.161 ** -2.03 [DELTA][Risk1.sub.t] -- -- 0.543 *** 2.6 [Cap.sub.t-1] -- -- -0.172 *** -5.51 [Reins.sub.t-1] - -- -- -- [Risk1.sub.t-1] -0.46 * -1.65 -- -- Perf -- -- 0.503 *** 7.92 Costcap -- -- --0.081 ** -2.16 Extreme -- -- 0.0247 0.48 Assy -- -- -0.178 *** -3.85 Lqtrisk -- -- -0.04 *** -3.17 Mix 0.0608 1.47 -- -- Loss_vol 0.0017 ** 2.23 -- -- Lev -- -- -- -- Higeo -0.0304 -0.73 Growth -- -- -0.0162 *** -2.81 Deficit -- -- -0.125 *** -4.85 Stock 0.0038 0.37 -0.003 -0.4 Group -0.001 -0.16 -0.0014 -0.24 Size 0.0013 0.62 -0.0049 *** -3.08 2001 .year 0.057 *** 4.01 -0.0327 *** -2.98 2002.year -0.0213 -0.96 0.017 1.26 2003.y ear 0.0142 1.07 0.016 * 1.71 2004.year 0.005 0.45 0.009 1.04 2005.year 0.008 0.59 0.014 1.42 2006.year 0.0122 0.86 0.0189 2.17 2007.year 0.008 0.5 0.0136 1.52 Intercept -0.038 -0.67 0.196 *** 4.75 [chi square] 122.95 364.45 p-value 0.0000 0.0000 Sargan-Hansen statistic p-value Hausman test 29.21 [chi square] p-value 0.014 High Cap [DELTA][Reins.sub.t] [DELTA][Risk1.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] 0.119 0.93 -0.041 -0.33 [DELTA][Reins.sub.t] -- -- 0.701 * 6.42 [DELTA][Risk1.sub.t] 0.888 *** 5.43 -- -- [Cap.sub.t-1] -- -- -- -- [Reins.sub.t-1] -0.0719 *** -3.73 -- -- [Risk1.sub.t-1] -- -- -0.514 *** -3.02 Perf -- -- -- -- Costcap -- -- -- -- Extreme -- -- -- -- Assy -- -- -- -- Lqt_risk -- -- -- -- Mix -0.169 ** -1.98 0.197 *** 2.84 Lossvol -- -- 0.0018 1.42 Lev 0.005 * 1.71 -- -- Higeo -0.012 -0.2 -0.127 * -1.93 Growth -- -- -- -- Deficit -- -- -- -- Stock -0.0273 -1.32 0.046 *** 2.58 Group -0.0117 -0.9 0.015 1.34 Size -0.008 ** -2.35 0.008 ** 2.35 2001 .year -0.054 *** -2.72 0.063 *** 3.47 2002.year 0.031 1.63 -0.011 -0.58 2003.y ear -0.011 -0.63 0.0127 0.68 2004.year 0.004 0.22 0.0087 0.47 2005.year 0.013 0.67 0.0044 0.22 2006.year 0.009 0.56 -0.018 -1.12 2007.year 0.0012 0.07 -0.009 -0.55 Intercept 0.266 *** 2.86 -0.210 * -2.33 [chi square] 77.13 81.34 p-value 0.0000 0.0000 Sargan-Hansen 27.070 statistic p-value 0.2530 Hausman test [chi square] p-value Note: This table reports the results of the 3SLS estimation following the buffer level. Following our sample split, an insurer is considered to be high capitalized if RBC ratio [less than or equal to] 6.5 and low capitalized if RBC ratio [less than or equal to] 2.5 The Sargan-Hansen test evaluates the validity of the instruments. The null hypothesis of this test is that overidentifying restrictions are valid. The null hypothesis of the Hausman test is that the difference in coefficients between the two subsamples is not systematic. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; CostCap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt risk, liquidity risk; Lossvol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer; Year, time effects.*, **, and *** represent statistical significance at the 10, 5, and 1 percent levels, respectively. Table 7 Estimation Results Following Group Affiliation Affiliated Insurers [DELTA][Cap.sub.t] [DELTA][Reins. sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -- -- 0.406 *** 2.67 [DELTA][Reins.sub.t] -0.195 *** -2.88 -- -- [DELTA][Risk1.sub.t] 0.913 *** 5.81 1.952 *** 12.9 [Cap.sub.t-1] -0.189 *** -11.71 -- -- [Reins.sub.t-1] -- -- -0.0035 -0.35 [Risk1.sub.t-1] -- -- -- -- Perf 0.697 *** 18.5 -- -- Costcap -0.0696 *** -4.82 -- -- Extreme 0.0954 * 1.68 -- -- Assy -0.03 -1.61 -- -- Lqt_risk -0.03 *** -8.88 -- -- Mix -- -- -0.379 *** -3.26 Lossvol -- -- -- -- Lev -- -- 0.00045 0.16 Higeo -- -- -0.0296 -0.47 Growth -0.013 *** -2.88 -- -- Deficit -0.122 *** -10.6 -- -- Stock 0.0015 0.27 -0.0401 ** -2.19 Group -- -- -- -- Size -0.003 *** -2.85 -0.00074 -0.21 2001.year -0.065 *** -5.07 -0.159 *** -6.51 2002.year 0.0580 *** 5.29 0.0899 ** 4.03 2003.y ear 0.0171 *** 2.8 -0.0455 ** -2.23 2004.year 0.0099 * 1.66 -0.0299 -1.5 2005.year 0.0127 * 1.93 -0.019 -0.85 2006.year 0.0091 1.37 -0.0364 -1.61 2007.year 0.0106 1.63 -0.0243 -1.1 Intercept 0.137 *** 5.75 0.208 * 1.9 [chi square] 183.60 732.88 p-value 0.0000 0.0000 Sargan-Hansen 31.984 statistic p-value 0.1005 Hausman test [chi square] p-value Affiliated Insurers Nonaffiliated Insurers [DELTA][Risk1.sub.t] [DELTA][Cap.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -0.204 *** -2.56 -- -- [DELTA][Reins.sub.t] 0.507 *** 22.27 -0.312 -0.68 [DELTA][Risk1.sub.t] -- -- -0.417 *** -3.15 [Cap.sub.t-1] -- -- -0.111 ** -2.22 [Reins.sub.t-1] -- -- -- -- [Risk1.sub.t-1] 0.0048 0.05 -- -- Perf -- -- 0.382 *** 8.06 Costcap -- -- -0.0393 -1.28 Extreme -- -- -0.0256 -0.23 Assy -- -- -0.0024 -0.08 Lqtrisk -- -- -0.0273 ** -2.06 Mix 0.199 *** 3.09 -- -- Loss_vol 0.00007 0.21 -- -- Lev -- -- -- -- Higeo 0.0145 0.4 -- -- Growth -- -- -0.101 -1.37 Deficit -- -- -0.0562 -1.81 Stock 0.0210 ** 2.14 0.00752 1.42 Group -- -- -- -- Size 0.00034 0.18 -0.0033 -1.44 2001.year 0.0818 *** 7.29 0.0023 0.15 2002.year -0.0463 *** -3.84 -0.0042 -0.23 2003.y ear 0.0232 ** 2.18 0.0181 1.26 2004.year 0.0152 1.46 0.00705 1 2005.year 0.00961 0.83 0.00674 0.76 2006.year 0.0184 1.56 0.00195 0.23 2007.year 0.0124 1.07 0.00594 0.51 Intercept -0.107 * -1.8 0.125 *** 3.96 [chi square] 672.46 449.84 p-value 0.0000 0.0000 Sargan-Hansen statistic p-value Hausman test 37.294 [chi square] p-value 0.0011 Nonaffiliated Insurers [DELTA][Reins. [DELTA][Risk1.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] 0.435 * 1.9 -0.250 ** -2.04 [DELTA][Reins.sub.t] -- -- 0.503 *** 8.25 [DELTA][Risk1.sub.t] 1.702 *** 5.68 -- -- [Cap.sub.t-1] -- -- -- -- [Reins.sub.t-1] 0.02 0.38 -- -- [Risk1.sub.t-1] -- -- -0.158 -1.08 Perf -- -- -- -- Costcap -- -- -- -- Extreme -- -- -- -- Assy -- -- -- -- Lqt_risk -- -- -- -- Mix -0.174 -1.35 0.0558 1.14 Lossvol -- -- -0.0012 -0.39 Lev -0.00854 -1 -- -- Higeo -0.0303 -0.31 0.00053 0.01 Growth -- -- -- -- Deficit -- -- -- -- Stock -0.0556 -1.58 0.0259 * 1.85 Group -- -- -- -- Size -0.00918 -1.29 0.00262 0.73 2001.year 0.0374 1.28 -0.0204 -1.35 2002.year 0.0636 ** 2.13 -0.0335 ** -2.22 2003.y ear 0.0423 1.42 -0.0195 -1.33 2004.year 0.022 0.76 -0.0101 -0.7 2005.year 0.0142 0.46 -0.00853 -0.54 2006.year 0.0426 1.36 -0.0246 -1.57 2007.year 0.0412 1.35 -0.0245 -1.58 Intercept 0.247 1.38 -0.0586 -0.65 [chi square] 45.14 120.50 p-value 0.0000 0.0000 Sargan-Hansen 42.666 statistic p-value 0.1419 Hausman test [chi square] p-value Note: This table reports the results of the 3SLS estimation according to group affiliation. The Sargan-Hansen test evaluates the validity of the instruments. The null hypothesis of the Hausman test states that the difference in coefficients between the subsamples is not systematic. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; CostCap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt risk, liquidity risk; Loss vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer; Year, time effects. *, **, and *** represent statistical significance at the 10,5, and 1 percent levels, respectively. Table 8 Estimation Results for Small and Large Sized Firms Small [DELTA][Cap.sub.t] [DELTA][Reins.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -- -- 0.509 *** 4.87 [DELTA][Reins.sub.t] -0.408 *** -5.26 -- -- [DELTA][Risk1.sub.t] 1.568 *** 6.65 1.496 *** 11.38 [Cap.sub.t-1] -0.0463 -1.08 -- -- [Reins.sub.t-1] -- -- -0.0791 *** -5.69 [Risk1.sub.t-1] -- -- -- -- Perf 0.532 *** 10.73 -- -- Costcap -0.0597 * -3.03 -- -- Extreme -0.00146 -0.15 -- -- Assy 0.0557 ** 2.14 -- -- Lqt_risk -0.0239 *** -2.78 -- -- Mix -- -- 0.0254 0.84 Lossvol -- -- -- -- Lev -- -- 0.0112 *** 4.94 Higeo -- -- -0.0842 * -1.74 Growth -0.00948 -1.2 -- -- Deficit -0.230 *** -8.71 -- -- Stock -0.00162 -0.22 -0.0062 -0.44 Group -0.0103 -1.38 0.00926 0.92 Size 0.0057 1.11 -0.00509 -0.8 2001.year 0.000726 0.06 -0.01 18 -0.7 2002.year -0.00285 -0.24 -0.00721 -0.43 2003 .year 0.0517 *** 3.78 -0.0047 -0.28 2004.year 0.0304 ** 2.32 -0.0141 -0.82 2005.year 0.0391 *** 2.75 0.00974 0.51 2006.year 0.0311 ** 2.18 -0.0152 -0.79 2007.year 0.0287 * 2.04 -0.00574 -0.3 Intercept -0.0818 -0.79 0.125 1.15 [chi square] 301.81 180.84 p-value 0.0000 0.0000 Sargan-Hansen 49.147 statistic p-value 0.1063 Hausman test [chi square] p-value Small Large [DELTA][Risk1. [DELTA][Cap.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -0.175 * -1.72 -- -- [DELTA][Reins.sub.t 0.462 *** 6.39 -0.495 *** -5.45 [DELTA][Risk1.sub.t] -- -- 1.303 ** 2.85 [Cap.sub.t-1] -- -- 0.0136 0.35 [Reins.sub.t-1] -- -- -- -- [Risk1.sub.t-1] -0.0109 -0.72 -- -- Perf -- -- 0.506 *** 8.98 Costcap -- -- -0.0578 *** -3.67 Extreme -- -- -0.00812 -0.61 Assy -- -- 0.0679 *** 4.2 Lqtrisk -- -- -0.00508 -1.56 Mix 0.0131 0.54 -- -- Loss_vol 0.00160 ** 2.51 -- -- Lev -- -- -- -- Higeo 0.0121 0.45 -- -- Growth -- -- -0.0457 *** -7.1 Deficit -- -- -0.0300 ** -2.91 Stock 0.0112 0.95 0.0000195 0 Group 0.0044 0.52 0.0103 1.54 Size -0.00068 -0.13 0.000663 0.39 2001.year 0.00602 0.41 -0.146 ** -2.98 2002.year 0.00307 0.21 0.152 * 2.88 2003 .year -0.0060 -0.4 0.0332 ** 4.94 2004.year 0.0017 0.12 0.0144 * 2.27 2005.year -0.0106 -0.63 0.0181 * 2.42 2006.year 0.00239 0.14 0.0341 *** 4.59 2007.year -0.0015 -0.09 0.0226 *** 3.68 Intercept -0.0073 -0.08 -0.048 -1.25 [chi square] 58.65 500.27 p-value 0.0000 0.0000 Sargan-Hansen statistic p-value Hausman test 182.84 [chi square] p-value 0.0000 Large [DELTA][Reins. [DELTA][Risk1.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] 0.668 * 1.7 -0.174 -1.4 [DELTA][Reins.sub.t] -- -- 0.289 *** 13 [DELTA][Risk1.sub.t] 3.529 *** 4.73 -- -- [Cap.sub.t-1] -- -- -- -- [Reins.sub.t-1] -0.0095 -0.68 -- -- [Risk1.sub.t-1] -- -- -0.0628 -0.43 Perf -- -- -- -- Costcap -- -- -- -- Extreme -- -- -- -- Assy -- -- -- -- Lqt_risk -- -- -- -- Mix -0.0296 -0.41 0.00852 0.37 Lossvol -- -- -0.000034 -0.1 Lev 0.000763 0.48 -- -- Higeo -0.0468 -0.73 0.0109 0.56 Growth -- -- -- -- Deficit -- -- -- -- Stock -0.0083 -0.43 0.00262 0.44 Group 0.0266 0.95 -0.00743 -0.86 Size 0.00479 0.65 -0.00088 -0.35 2001.year -0.365 *** -4.22 0.104 *** 10.73 2002.year 0.405 *** 4.5 -0.108 *** -5.87 2003 .year 0.00556 0.19 -0.00191 -0.21 2004.year -0.00117 -0.04 0.000142 0.02 2005.year -0.00006 0 0.000071 0.01 2006.year 0.00957 0.28 -0.00295 -0.28 2007.year 0.00814 0.29 -0.00232 -0.27 Intercept -0.0979 -0.61 0.0201 0.39 [chi square] 156.26 178.34 p-value 0.0000 0.0000 Sargan-Hansen 20.960 statistic p-value 0.3995 Hausman test [chi square] p-value Note: This table reports the results of the 3SLS estimation according to firm size. The Sargan-Hansen test evaluates the validity of the instruments. The null hypothesis of the Hausman test states that the difference in coefficients between the subsamples is not systematic. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; CostCap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt risk, liquidity risk; Loss vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer; Year, time effects. *, **, and *** represent statistical significance at the 10, 5, and 1 percent levels, respectively. Table 9 Estimation Results for Stock and Mutual Firms Stock [DELTA][Cap.sub.t] [DELTA][Reins.sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -- -- 0.595 *** 4.59 [DELTA][Reins.sub.t] -0.246 *** -5.52 -- -- [DELTA][Risk1.sub.t] 0.468 *** 3.91 1.625 *** 13.29 [Cap.sub.t-1] -0.0562 ** -2.42 -- -- [Reins.sub.t-1] -- -- -0.0213 * -1.69 [Risk1.sub.t-1] -- -- -- -- Perf 0.534 *** 16.22 -- -- Costcap -0.0594 *** -4.01 -- -- Extreme 0.00626 0.17 -- -- Assy 0.0555 *** 3.47 -- -- Lqt_risk -0.0146 *** -4.47 -- -- Mix -- -- -0.270 *** -3.91 Lossvol -- -- -- -- Lev -- -- 0.00296 1.56 Higeo -- -- -0.0104 -0.22 Growth -0.0277 *** -8.41 -- -- Deficit -0.115 *** -12.06 -- -- Stock -- -- -- -- Group 0.00384 1.2 0.0147 1.33 Size -0.000859 -0.79 0.0026 0.9 2001.year -0.0236 *** -3.3 -0.0738 *** -4.3 2002.year 0.0257 *** 3.85 0.0561 *** 3.38 2003 .year 0.0254 *** 5.4 -0.0259 * -1.67 2004.year 0.0142 *** 3.1 -0.0115 -0.75 2005.year 0.0167 *** 3.46 -0.00749 -0.45 2006.year 0.0212 *** 4.41 -0.0119 -0.7 2007.year 0.0160 *** 3.42 -0.00728 -0.44 Intercept 0.0292 0.96 0.037 0.59 [chi square] 968.80 236.53 p-value 0.0000 0.0000 Sargan-Hansen 46.820 statistic p-value 0.1544 Hausman test [chi square] p-value Stock Mutual [DELTA][Risk1. [DELTA][Cap.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] -0.334 *** -3.67 -- -- [DELTA][Reins.sub.t] 0.604 *** 15.07 -0.371 *** -6.88 [DELTA][Risk1.sub.t] -- -- 0.334 ** 2.21 [Cap.sub.t-1] -- -- -0.164 *** -13.94 [Reins.sub.t-1] -- -- -- -- [Risk1.sub.t-1] 0.00992 0.89 -- -- Perf -- -- 0.569 *** 19.24 Costcap -- -- 0.002 -0.15 Extreme -- -- -0.012 -1.24 Assy -- -- 0.0542 *** 3.76 Lqtrisk -- -- -0.089 *** 13.99 Mix 0.204 *** 4.95 -- -- Loss_vol 0.000262 0.63 -- -- Lev -- -- -- -- Higeo 0.000342 0.01 -- -- Growth -- -- -0.082 *** -8.38 Deficit -- -- -0.101 *** -10.48 Stock -- -- -- -- Group -0.00743 -0.98 0.0074 ** -3.21 Size -0.00208 -1.06 -0.0020 ** -3.13 2001.year 0.0471 *** 4.22 -0.0086 -0.68 2002.year -0.0348 ** -3.23 0.0363 ** 2.66 2003 .year 0.0152 1.41 0.0338 *** 7.7 2004.year 0.00633 0.6 0.0217 *** 5.54 2005.year 0.0037 0.32 0.0192 *** 4.29 2006.year 0.00588 0.5 0.0221 *** 5.1 2007.year 0.0038 0.33 0.0185 *** 4.25 Intercept -0.0221 -0.52 0.143 *** 8.88 [chi square] 368.14 1604.26 p-value 0.0000 0.0000 Sargan-Hansen statistic p-value Hausman test 95.01 [chi square] p-value 0.0000 Mutual [DELTA][Reins. [DELTA][Risk1.sub.t] sub.t] Coef t-stat Coef t-stat [DELTA][Cap.sub.t] 0.194 -0.7 -0.0746 -0.70 [DELTA][Reins.sub.t] -- -- 0.377 *** 21.5 [DELTA][Risk1.sub.t] 2.669 *** 6.81 -- -- [Cap.sub.t-1] -- -- -- -- [Reins.sub.t-1] -0.0061 -0.58 -- -- [Risk1.sub.t-1] -- -- -0.002 -0.03 Perf -- -- -- -- Costcap -- -- -- -- Extreme -- -- -- -- Assy -- -- -- -- Lqt_risk -- -- -- -- Mix 0.0302 -1.07 -0.011 -0.98 Lossvol -- -- -0.0001 -0.18 Lev 0.00035 -0.2 -- -- Higeo -0.00392 -0.04 0.0007 -0.02 Growth -- -- -- -- Deficit -- -- -- -- Stock -- -- -- -- Group 0.001 -0.05 -0.0009 -0.01 Size 0.0009 -0.16 -0.0004 -0.17 2001.year -0.156 *** -3.76 0.0582 *** 4.55 2002.year 0.192 *** 4.64 -0.0719 *** -5.12 2003 .year 0.00479 -0.14 -0.0017 -0.13 2004.year -0.013 -0.39 0.00501 -0.38 2005.year -0.00224 -0.06 0.00103 -0.07 2006.year -0.0143 -0.36 0.00559 -0.36 2007.year 0.00734 -0.18 -0.00261 -0.17 Intercept -0.0295 -0.21 0.0122 -0.22 [chi square] 59.41 612.88 p-value 0.0000 0.0000 Sargan-Hansen 32.714 statistic p-value 0.7121 Hausman test [chi square] p-value Note: This table reports the results of the 3SLS estimation according to the organizational form. The Sargan-Hansen test evaluates the validity of the instruments. The null hypothesis of the Hausman test states that the difference in coefficients between the subsamples is not systematic. Cap, capital; Reins, reinsurance; Risk1, volatility of assets and liabilities; Risk2, risky assets and liabilities; Reg, regulatory pressure; Perf, performance; Cost Cap, cost of capital; Extreme, exposure to extreme risk; Assy, information asymmetry; Mix, business mix; Lqt risk, liquidity risk; Loss vol, loss volatility; Lev, leverage; Higeo, geographic diversification; Growth, growth opportunities; Deficit, deficit; Stock, stock versus mutual; Group, group affiliation; Size, size of the insurer; Year, time effects. *, **, and *** represent statistical significance at the 10,5, and 1 percent levels, respectively.

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Author: | Mankai, Selim; Belgacem, Aymen |
---|---|

Publication: | Journal of Risk and Insurance |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Dec 1, 2016 |

Words: | 15484 |

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