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What policy features determine life insurance lapse? An analysis of the German market.

ABSTRACT

With the largest data set ever used for this purpose (covering more than 1 million contracts), we analyze the impact of product and policyholder characteristics on lapse in the life insurance market. The data are provided by a German life insurer and cover two periods of market turmoil that we incorporate into our proportional hazards and generalized linear models. The results show that product characteristics such as product type or contract age and policyholder characteristics such as age or gender are important drivers for lapse rates. Our findings improve the understanding of lapse drivers and might be used by insurance managers and regulators for value-and risk-based management.

INTRODUCTION

In this work, we analyze the impact of product and policyholder characteristics on lapse and surrender in the German life insurance industry using proportional hazards and generalized linear models (GLMs). (1) A proper understanding of lapse drivers and their dynamics is important for insurance managers and regulators. Lapse influences an insurer's liquidity and profitability (see Kuo et al., 2003; Prestele, 2006). First, the insurer might suffer high losses from lapsed policies due to up-front investments for acquiring new business (Pinquet et al., 2011). Second, the insurer faces the loss of future profits from lapsed contracts. Third, the insurer might face adverse selection with respect to mortality and morbidity. (2) Fourth, the insurer might be exposed to a liquidity risk when forced to pay a surrender value for many lapsed policies at the same time. On the one hand, lapses influence the flow of futures premiums for contracts with periodic premiums, which in turn determine the embedded value of the company. On the other hand, asset-liability mismatches stem from possible discrepancies between contract values and market values, which should be a major issue for endowment policies, but not for unit-linked contracts.

The importance of lapse has been discussed in the field of valuation and management of embedded options in life insurance contracts. Historically, the right to lapse a life insurance contract was not explicitly taken into account in the pricing process (Gatzert and Schmeiser, 2008). The possibility to lapse a contract, however, constitutes an implicit option present in life insurance contracts and its value can be quite substantial (see, e.g., Albizzati and Geman, 1994; Grosen and Jorgensen, 2000; Bacinello, 2003; Gatzert and Schmeiser, 2008). The decline of Equitable Life in the United Kingdom, which was related to pension policies including guaranteed annuity options, intensified this discussion (see O'Brien, 2006). In the 1990s, market annuity rates in the United Kingdom dropped significantly below the guaranteed level, making that option particularly valuable for the customer, an aspect especially relevant for endowment policies. Therefore, insurers need to pay attention to all embedded options, including the policyholder's option to lapse a life insurance policy. In addition, regulators have identified lapse as one of the major risk components of life insurance companies and hence lapse behavior should be monitored and managed carefully. For example, under the new European Union regulatory framework Solvency II, lapse risk constitutes the largest submodule in terms of solvency capital requirement within the life underwriting risk module, accounting for almost 40 percent of the capital requirement in this module (see EIOPA, 2011, pp. 77-78). (3) The life underwriting risk itself accounts for almost 20 percent of the total capital requirements, constituting the second most material component in terms of capital requirements (behind market risk).

The empirical literature on lapse can be distinguished based on the explanatory variables considered. The first set of literature uses environmental characteristics, including macroeconomic indicators and company data. Initially, only the impact of interest rates and unemployment on lapse has been studied; these are the interest rate and emergency fund hypotheses (see, e.g., Dar and Dodds, 1989; Outreville, 1990; Kuo et al., 2003). This work has been extended by Kim (2005a, 2005b), Cox and Lin (2006), and Kiesenbauer (2012) considering additional economic indicators, such as gross domestic product, and capital markets development as well as company characteristics, including company size and legal form. The second set of literature uses single contract data to assess the impact of product and policyholder characteristics on lapse. So far, only few such analyses are available. Renshaw and Haberman (1986), Kagraoka (2005), Cerchiara et al. (2009), and Milhaud et al. (2010) cover the Scottish, Japanese, Italian, and Spanish life insurance markets. Using generalized linear models, these papers indicate that factors such as calendar year, policyholder age, or method of payment significantly influence lapse. Recently, Pinquet et al. (2011) analyze a product bundle of health, life, and long-term care insurance contracts using proportional hazards models.

Our study contributes to the literature in four ways. First, we consider the largest data set ever used for such purposes (covering more than 1 million contracts). The data are obtained from one large German life insurer and include six product categories including traditional and unit-linked products. We are thus able to investigate whether different products exhibit different lapse behavior, in particular, comparing traditional and unit-linked products. To date, such differences have not been studied empirically. Second, to our knowledge this is the first empirical study for the German life insurance market; we analyze the impact of product and policyholder characteristics on lapse using individual contract data. (4) So far, only the relationship between surplus participation rates and lapse rates has been discussed by Cottin et al. (2007), Eling and Kiesenbauer (Forthcoming), and Kiesenbauer (2012) using market data. Third, the analyzed time period from 2000 to 2010 is of particular interest since it incorporates two phases of crisis (the stock market plunge from 2001 to 2003 and the 2008 financial crisis) that can be integrated in the analysis. Finally, the available data address some of the shortcomings mentioned in previous studies. Having detailed information on the date of policy inception, exact policy durations can be calculated, not only in terms of calendar years (see Renshaw and Haberman, 1986). Furthermore, the data are already split into disjoint and homogeneous product categories so problematic ex post grouping is not necessary (see Cerchiara et al., 2009). Moreover, we extend the literature by considering distribution channel and supplementary cover, which will be shown to be significant lapse drivers. (5)

We find that all considered product and policyholder characteristics have a statistically significant impact on the lapse rate development, but the magnitude of the effects varies. The largest variations are observed for calendar year, contract age, and premium payment (single vs. regular). The direction of impact is consistent with the literature (Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010), except for product type, which has only a limited effect on lapse rates. We extend the existing knowledge in that we show that distribution channel and supplementary cover are significant lapse drivers. Finally, we consider interactions between one fixed variable and all other characteristics in order to assess whether there are differences for the different levels of product categories, distribution channels, supplementary cover, or premium payment. The impact on lapse rates for all policy(holder) characteristics is very consistent across product categories. All these results are helpful for insurance managers and regulators, especially in the context of risk- and value-based management.

The remainder of this article is structured as follows. The "Empirical Literature on Life Insurance Lapse" section summarizes the empirical literature on life insurance lapse. The "Data, Hypotheses, and Methodology" section describes the methodology, our hypotheses, and the data. The "Results" section presents and discusses the results. We conclude in the "Conclusion" section.

EMPIRICAL LITERATURE ON LIFE INSURANCE LAPSE

The research on environmental root causes of life insurance lapse has traditionally focused on the so-called interest rate and emergency fund hypotheses. The interest rate hypothesis assumes that lapse rates are negatively related to internal rates of return (e.g., surplus participation) and positively related to external rates of return (e.g., market interest rates or stock returns); for details see Dar and Dodds (1989) or Kuo et al. (2003). The emergency fund hypothesis conjectures that personal financial distress or liquidity constraints forces policyholders to lapse their contracts in order to access the surrender value (see, e.g., Outreville, 1990). These two hypotheses have been studied empirically by Dar and Dodds (1989), Outreville (1990), and Kuo et al. (2003) with attention to different life insurance markets and product types. It is hence not surprising that the results are not completely consistent, especially as the variable specifications vary widely (see Kiesenbauer, 2012, for a more detailed discussion). These studies focus on information on interest rates or unemployment (as an indicator for adverse economic conditions), but do not take into account other economic factors (e.g., stock returns, gross domestic product), company characteristics, or product and policyholder information.

Kim (2005a) provides the first empirical study considering a broader set of economic explanatory variables including economic growth rates and seasonal effects. Moreover, the contract age since policy inception is considered as product characteristic. Kim (2005a) models the aggregate lapse rates of a South Korean life insurer for four product categories (endowment, annuity, protection plan, and education) using the logit and complementary log-log model. The results indicate that policyholder lapse behavior indeed depends on additional exogenous factors beyond interest rates and unemployment rates. Using a similar set of explanatory variables to analyze single premium deferred annuities in the United States, Kim (2005b) and Cox and Lin (2006) arrive at similar conclusions by deploying a logit and Tobit model. In addition, Cox and Lin (2006) indicate that the Poisson and the negative binomial regression model are more appropriate to model lapse behavior, but these models require individual (i.e., single contract) rather than aggregate lapse rate data. All these models (i.e., logit, complementary log-log, Tobit, Poisson, and negative binomial) belong to the same broad class of models, the so-called generalized linear models. Kiesenbauer (2012) analyzes lapse rates in the German life insurance market using the same modeling approach as Kim (2005a). The author employs market data to study lapse behavior with respect to economic indicators and additional company characteristics such as company age, company size, or legal form. The analysis is based on publicly available market data and does not take into account any product or policyholder characteristics, except for the product split distinguishing endowment, annuity, term life, group, and unit-linked business. The results support the conclusion that factors beyond interest rates and unemployment influence lapse behavior, including company characteristics. (6)

The empirical literature analyzing life insurance lapse with respect to product and policyholder characteristics is rather limited, possibly because lapse data are treated as highly confidential by most life insurers. Therefore, only aggregated lapse rate information is usually publicly available in most life insurance markets. An analysis of product and policyholder characteristics requires a more detailed data split that can only be provided by life insurers. The first empirical study, by Renshaw and Haberman (1986), dates to the mid-1980s, but only recently has the topic attracted more attention. This is driven by accounting and regulatory changes that require an appropriate assessment of lapse. Table 1 provides a detailed overview of the empirical literature in terms of the time period covered, sample size, products and policyholder characteristics considered, and modeling approaches.

Renshaw and Haberman's (1986) study is the only analysis of multiple companies based on a data set provided by the former Scottish Faculty of Actuaries. It is also the only work to consider different product categories. All other studies focus on data of a single life insurer and only one product category. All empirical studies of the impact of product and policyholder characteristics on lapse behavior use generalized linear models to assess the relevant contract features and policyholder characteristics. (7) Because of the data samples and especially the different explanatory variables, the results of the empirical studies analyzing product and policyholder characteristics are not directly comparable. The results are, however, consistent to the extent that all studies identify several significant explanatory variables and indicate their importance for lapse behavior. Renshaw and Haberman (1986) find an additional significant interaction between policy type and duration of policy, meaning that the lapse rate depends not only on single factors but also on the combination of factors. All characteristics considered in Kagraoka (2005) are identified as significant, including the change in unemployment rate as an economic indicator. The latter result supports the emergency fund hypothesis. Such effects are captured only indirectly in the other studies using calendar-year information. Cerchiara et al. (2009) show the importance of policy duration, calendar year, and product class. Milhaud et al. (2010) find the biggest surrender risks for policies including a fiscality constraint (i.e., surrender charges only apply for a certain part of the policy duration). (8) As soon as the contract has reached the point when the policyholder can surrender it without penalty, the lapse risk increases significantly. Other relevant risk factors include policyholder age or method of payment (i.e., regular vs. single premiums where regular premiums are divided into monthly, bimonthly, quarterly, half-yearly, and annual installments). (9)

DATA, HYPOTHESES, AND METHODOLOGY

Data

The data analyzed in this article have been provided by a German life insurer, cover the time period 2000 to 2010, and include only contracts that have been newly issued during this time. (10) The data set comprises six product types: (traditional) annuity, unit-linked annuity, endowment, term life insurance, Riester pensions, and Rurup pensions. While the first four products are common for many insurance markets, the latter two are specific to the German market. Riester and Rurup products constitute state-aided private pension schemes. (11) Furthermore, as the unit-linked business accounts for a significant portion of all policies, we are able to assess whether or not there are significant differences between this business and traditional policies (endowment, annuity). (12) Beyond (1) the product type, we consider (2) the calendar year, (13) (3) the contract age, (14) (4) the age of the policyholder, and (5) the distribution channel (tied agents, brokers, banks, and other). Moreover, we include (6) whether there are additional covers (supplementary covers include term life insurance, disability insurance, accident insurance, and surviving dependents insurance; we only model whether a policy includes any supplementary cover or not), (7) the policyholders' sex, and (8) the premium payment mode (single vs. regular premium). Changes in the underlying policy(holder) characteristics for a single contract as well as premium exemptions or reductions are identified comparing year-end values for the entire portfolio from one year to the next. For simplicity reasons, we assume that contract modifications always take place on the anniversary of the contract. It might be interesting to investigate seasonal effects (see, Kagraoka, 2005). This requires, however, monthly or quarterly data, which tremendously increases the cost of data provision.

Some characteristics change during the life time of an insurance contract (e.g., policyholder age or contract age). Therefore, the data need to be prepared for the analysis as follows. Each contract is split into all possible combinations of considered product and policy(holder) characteristics. We denote such a combination of characteristics as model point. A sample model point would consist of endowment (product type), 2005 (calendar year), 5 (contract age), 25 (policyholder age), broker (distribution channel), no (supplementary cover), male (policyholder sex), and regular (premium payment). For each model point, the exposure of all contracts in the portfolio needs to be determined, that is, the time (measured in years on a daily basis) all contracts belong to the corresponding model point. Finally, we determine the number of early and late lapse events for each model point. Each lapsed contract is counted as a lapse in the model point, which represents the product and policy(holder) characteristics at the lapse date.

The considered data set covers more than 1 million contracts representing the broadest study in terms of sample size compared to all existing analyses. As only new business written from 2000 onward is considered, the number of both policies and contract years is strongly increasing during the first years and stabilizing in later years. In this work, we measure lapse rates using sum insured according to the definitions of the German regulator BaFin (differentiating among early, (15) late, and total lapse), but also consider regular premiums and the number of contracts. This allows investigating whether or not significant differences exist.

Hypotheses Development

Based on the existing literature, a number of hypotheses are validated in the statistical analysis. We consider eight product characteristics, six of which have already been considered for other countries. Reconsidering both the literature and the specifics of the German life insurance market, the following hypotheses can be derived:

1. Product type: The existing literature has documented variations in lapse rates when different product types are considered (see Renshaw and Haberman, 1986; Cerchiara et al., 2009; Milhaud et al., 2010). The results of Renshaw and Haberman (1986) indicate that term life insurance has higher lapse rates than endowment policies; unit-linked products suffer the most lapses. Country-specific differences between the products should, however, be kept into mind when interpreting the results. Overall, we expect significant differences in lapse rates depending on the product type.

2. Calendar year: Calendar year effects should reflect the economic environment, that is, the interest rate hypothesis and the emergency fund hypothesis. Cerchiara et al. (2009) are the only researchers to consider calendar-year effects. In their case, lapse rates fell until the end of the 1990s. In the following years, the lapse rate increased and reached its maximum in 2007. We might thus expect increasing lapse rates from the beginning of our investigation period (2000) onward. Moreover, both global and local developments should be reflected in the calendar-year results, for example, the financial crisis at the global level and the German trend toward single-premium business (since 2008) at the local level.

3. Contract age: Contract age is considered an explanatory variable in all empirical studies (see Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010). These results are very consistent in that the lapse rate is highest for the first contract years and then gradually decreases. We thus expect decreasing lapse rates with increasing contact age. 4 5

4. Policyholder age: Existing empirical studies document decreasing lapse rates with increasing policyholder age (see Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010). However, the modeling approach differs. Cerchiara et al. (2009) are the only researchers to consider the current policyholder age as we do; all other studies focus on the underwriting age of the policyholder, that is, the age of the policyholder at policy inception. We use the current policyholder age because it reflects current policyholder status, which might be more relevant for the lapse decision. All other studies use age classes combining up to 40 years instead of considering the effects for each age. Moreover, the considered range of age values differs across studies. Therefore, our results are not directly comparable to the existing findings. Nevertheless, we expect to find significant variations for the lapse rates with respect to the policyholder age. For example, for young policyholders the contracts might be purchased by the parents so that the lapse rate might be relatively low. Prior to retirement, lapse rates might be relatively high because of financial needs.

5. Distribution channel: We are the first to analyze the distribution channel in this context. The general insurance literature discusses two main hypotheses to explain the coexistence of different distribution channels in the insurance industry: the product quality hypothesis and the market imperfection hypothesis (Trigo-Gamarra, 2008). The former conjectures that the service quality, among others, differs among distribution channels. Trigo-Gamarra (2008) and Eckardt and Rathke-Doppner (2010) find evidence of an increased service level among independent agents (i.e., brokers) for the German market. These differences might also manifest in different lapse rates.

6. Supplementary cover: Supplementary insurance covers has not yet been considered as an explanatory factor in the literature. It is not clear what effect supplementary cover might have on lapse rates since different effects are imaginable. For example, contracts with additional covers might experience fewer lapses, as it gets more expensive to obtain identical insurance coverage at a higher entry age. It might, however, also be that especially such bundle products are sold to people with insufficient knowledge of insurance products. Moreover, the higher contract volume might increase the likelihood for lapse in case of financial distress.

7. Policyholder sex: Kagraoka (2005) documents a lower lapse rate for females and argues that housewives purchase life insurance only if the household income is sufficiently high. We thus expect to find lower lapse rates for females compared to male policyholders.

8. Premium payment: Milhaud et al. (2010) compare four product groups of endowment policies based on profit participation (with vs. without) and premium payment (single vs. regular). When comparing with-profit policies, single premium business is lapsed less often than regular premium business. We also expect that single premium is less likely to be lapsed for various reasons. Policyholders investing a large amount into a single premium policy might have a more profound knowledge of the product. Moreover, as there is no obligation for future premium payments, such a contract is less likely to be lapsed due to financial distress. Finally, single premiums most often occur with policies having a rather short policy duration.

Methodology

We use the proportional hazards model and generalized linear models (GFMs, i.e., the Poisson and binomial models) to analyze lapse rates depending on the considered product and policy(holder) characteristics. This approach is in line with the existing empirical literature (see Table 1). Proportional hazards models belong to the class of survival models in statistics, while GLMs have been introduced by Nelder and Wedderburn (1972) as an extension to linear regression models weakening the restrictive assumptions of those models (i.e., normally distributed errors, constant variance, and additivity of explanatory variables). Both types of model represent standard statistical tools such that we do not provide a detailed description of these models. Instead, we refer to statistics textbooks such as McCullagh and Nelder (1989) for a detailed discussion.

Based upon the discussion in the previous section, we present the levels for each product and policy(holder) characteristic in Table 2. In order to have a common reference level for all analyses, we use the value that has the largest exposure (the reference level for the distribution channel is chosen arbitrarily in order to maintain confidentiality). In order to reduce the number of regression coefficients to be estimated, the reference levels of all characteristics are combined with the intercept of the linear predictor. Each model point as introduced in the "Data" section defines a specific combination of the product and policy(holder) characteristics considered. Furthermore, each contract has a unique path through a certain subset of all possible model points. The time each contract belongs to a certain model point is called exposure (time). The identical consideration can be applied for lapsed regular premiums and lapsed sum insured assuming that each single euro can either be lapsed or not. Thus, the same modeling approach is used, except that the exposure is measured in euros instead of years. The exposure of regular premiums and sum insured for the model point of a single contract is determined as product of timely exposure (in years) multiplied by yearly premium and total sum insured, respectively.

We not only consider single effects of the explanatory variables (e.g., product category or calendar year) in our analyses. Instead, the combination of different variables is also taken into account, such as, the effects of calendar year 2008 for Riester pensions. These so-called interactions allow not only changes within one explanatory characteristic, but also combinations of two or more characteristics to be taken into account (see, e.g., Renshaw and Haberman, 1986; Cerchiara et al., 2009). We focus on interactions between only two factors because interactions complicate the model and tremendously increase the run time of the corresponding analyses. (16) The same reference levels are considered for the models including interactions as for the models without interactions.

RESULTS

We present the results of two model specifications. The results of the model without interactions are discussed in the section "Models Without Interactions." The results including interactions between product category, supplementary cover, premium payment, and distribution channel, respectively, with all other characteristics (as described in the "Methodology" section) can be found in the "Models Including Interactions" section.

Models Without Interactions

Table 3 displays the parameter estimates for total lapse considering the proportional hazards, binomial, and Poisson models, respectively, neglecting interactions. The resulting lapse rates are slightly different for each model. The effects of the considered product and policy(holder) characteristics relative to the reference level are, however, very consistent. Most of the variables are consistently significant at the 1 percent level and the hazard ratios are close to each other. The parameter estimates for the proportional hazards model represent the natural logarithm of the multiplicative effect relative to the reference level. For instance, a value of 0.15 for endowment (using number of contracts to measure exposure) means that, ceteris paribus, the lapse rate for endowment policies is exp(0.15) = 1.16 times the lapse rate of annuities representing the reference level; in other words, the lapse rate for endowments is 16 percent higher than the lapse rate of traditional annuities. (17)

We now discuss the results of each characteristic in detail, focusing on the proportional hazards model. In Figure 1 and the following figures the results are visualized using a similar format as that used by Cerchiara, Gambini, and Edwards (2009). The solid, dashed, and dotted lines represent the estimated regression coefficients for total (as displayed in Table 3), late, and early lapse, respectively (left axis). (18) The estimate for the reference level is set to zero as it is included in the intercept term (see the "Methodology" section). The columns represent the share of exposure corresponding to the different levels of the considered characteristic (right axis). The exposure for the analysis of early lapse (light gray boxes) is hence usually less than the exposure for late and total lapse (additional dark gray boxes). We use the same scale for both axes in all figures to facilitate the comparability of the magnitude of the effects across different characteristics. Whenever possible, our results are compared to the results of previous studies.

Product Type. The total lapse rate does not vary much across product categories (see Figure la). Compared to the lapse rate of traditional annuities, which constitutes the reference level, the lapse rates of the other products are between exp(-0.33) = 0.72 for Rurup pensions and exp(0.15) = 1.16 for endowments, that is, from 28 percent less to 16 percent higher. Endowments experience the highest lapse rate, followed by Riester pensions. While this result might be expected for Riester pensions (due to the complicated product introduction and the recent discussion on the high acquisition and administration cost of those products), it is rather surprising for endowments. The latter effect might be explained by the restriction of our data to new business written since 2000 (neglecting the large portfolio of policies in force for a long time and hence less prone to lapse). This indicates, however, that customer lapse behavior for endowments might change in the future. There are only minor differences between traditional and unit-linked annuities as latter have a 3 percent lower total lapse rate. Compared to annuities, Rurup pensions experience so far reduced lapse rates. Rurup pensions are designed for self-employed people and are state-aided. As those customers might be better financially educated and the federal subsidies might be lost in case of lapse, this might explain the lower lapse rates. The potential loss of federal subsidies, however, has no observable impact on Riester policies. The significantly lower early lapse rate for Riester policies can be attributed to the different treatment of acquisition costs in these policies. They have to be distributed equally over the first 5 years of the contract term. Therefore, a surrender value is built up much earlier such that a lapse in the first contract years is counted as late lapse instead of early lapse; it is a reclassification of lapse that has only a minor impact on the overall lapse rate. This effect is reversed for term life insurance. These products provide almost pure risk cover and have only a very limited savings component. Therefore, most of these policies have no surrender value when they are lapsed. Most lapses are for this reason classified as early lapse.

Regarding the existing literature, product types have also been considered by Renshaw and Haberman (1986), Cerchiara et al. (2009), and Milhaud et al. (2010). As mentioned, the results of Renshaw and Haberman (1986) indicate that term life insurance has higher lapse rates than endowment policies and unit-linked products suffer the highest lapse rate. These results are different from our results, which might be credited to the differences in the underlying products, so life insurance in the United Kingdom and Germany might not be directly comparable. In particular, the guarantee levels of unit-linked products might have changed. While these policies initially possessed almost no guarantee (Renshaw and Haberman, 1986, use data from 1976), today these products usually include a variety of guarantees, for example, investment guarantees at contract maturity (see, e.g., Gatzert et al., 2011). Cerchiara et al. (2009) categorize the analyzed portfolio consisting exclusively of savings policies into reasonably homogeneous product groups, but without offering further details on the exact methodology. They find that the product group has a strong effect varying from -56 percent to +421 percent relative to the reference product group. Four product groups of endowment policies are distinguished by Milhaud et al. (2010) based on profit participation (with vs. without) and premium payment (single vs. regular). As there are no and only two lapse events for nonprofit policies with regular and single premiums, respectively, the regression result seems not to be representative and reliable for these groups. When comparing with-profit policies, single premium business is lapsed less often than regular premium business.

Calendar Year. The development of lapse rates with respect to calendar year is displayed in Figure 1(b). The total lapse rate was 73 percent lower in 2000 compared to 2008. Lapse rates have steadily increased from 2000 to 2004 in the years of and following the stock market plunge. They remained stable from 2004 to 2007, but rose steeply in 2008 and 2009 (+25 percent and +22 percent over the previous year), the year of and following the 2008 financial crisis. This lapse rate increase is consistent with the empirical results presented by Cerchiara et al. (2009). Lapse rates begin to deteriorate again in 2010 reaching almost the 2008 level. Therefore, increasing lapse rates might be a consequence of economic crises. This assumption is consistent with the emergency fund hypothesis and with the assertions of German life insurers (see, e.g., Lier, 2010). While the development of the late lapse rate is almost identical to that of total lapse, the development of the early lapse rate is different. Developing similarly until 2007, the early lapse rate fell steadily from 2007 to 2010. This might also be related to the different treatment of acquisition cost. The courts have ruled that this cost has to be distributed over the first contract years instead of being deducted completely from the first premium(s). This yields (higher) surrender values from the contract beginning such that lapsed policies are classified more often as late lapse, which is also in line with the fact that the late lapse rate increases more strongly than the total lapse rate. Additionally, new business volume of regular premium business has decreased following the 2008 financial crisis and thus early lapse volume might have been further reduced.

Contract Age. The differentiation of early and late lapses might seem odd when contract age is considered. The difference between both lapse rates is the (non)existence of a surrender value. This is not necessarily related to the contract age and depends on product design and regulation. Therefore, it still makes sense to consider these lapse types separately for contract age. Total and late lapse rates are highest for young policies and are afterward steadily decreasing with contract age; see Figure 1(c). These results are consistent with the empirical findings by Renshaw and TIaberman (1986), Kagraoka (2005), Cerchiara et al. (2009), and Milhaud et al. (2010). Most policyholders realize quickly whether they really need a purchased policy and have been advised appropriately by the salesperson. If the customer, for instance, cannot afford the regular premium payments, the customer might lapse the contract within the first years after policy inception. If a product really fits the policyholder's need, it is less likely that the policy will be lapsed. Life insurance savings might then only be used in case of personal financial distress according to the emergency fund hypothesis (see, e.g., Dar and Dodds, 1989; Kuo, Tsai, and Chen, 2003). The development of the early lapse rate is slightly different, as it first decreases and increases again. This is driven by term life insurance policies. (19) As those products are almost pure risk insurance, no surrender value is built up. Any lapse--independent of contract age--is hence classified as early lapse. Moreover, term life insurance is often used to backup mortgages. As soon as the mortgage is repaid, the insurance coverage might no longer be required, explaining the lapse rate increase with increasing contract age.

Policyholder Age. When considering the relationship between age of the policyholder and lapse rates in Figure 1(d), the magnitude of the age effect is limited as the corresponding curves are relatively flat. Three age groups can be distinguished: policyholders until age 25, policyholders between 26 and 40, and policyholders older than 40. Policyholders in the middle group have an almost constant lapse rate at the level of the reference age of 39. (20) The lapse rate for the youngest policyholders is significantly below, but steadily increasing. Such policies might initially be purchased by the policyholder's parents. When the family circumstances change (e.g., marriage or birth of children), the needs might change and the insurance premiums are no longer affordable. Lapse rates for the oldest age group increase steadily until age 60, before decreasing again. For products with a savings component, a possible explanation for this effect is that people older than 50 might find it especially difficult to find a new job. According to the emergency fund hypothesis (see Outreville, 1990), they might use their life insurance savings as emergency funds. Other customers in their late 50s might retire early and live on their life insurance savings until they can draw a pension. The subsequent decline might be driven by two effects. First, the likelihood of immediate access to life insurance savings (due to unemployment or early retirement) decreases with age. Second, single-premium business might increase in this age group (i.e., paying a lump sum into a deferred annuity to receive a life-long annuity later). As this business experiences less lapse (see later), it might yield lower lapse rates. As mentioned, our results are not directly comparable with the existing literature, since we use a different modeling approach.

Distribution Channel. Most German life insurance companies use different distribution channels including tied agents, brokers, and banks, but have one main distribution channel. The insurer providing the data follows a similar strategy. Early, late, and total lapse rates are close to each other for the different distribution channels considered. Compared to the tied agent channel, the lapse rate in the bank channel is 25 percent higher, while it is 5 percent lower for brokers. (21) Distribution channels have not yet been considered as an explanatory factor in the literature on life insurance lapse. But our results support the existing literature studying the product quality hypothesis in Germany (Trigo-Gamarra, 2008; Eckardt and Rathke-Doppner, 2010). Although the product quality hypothesis has only been studied for dependent and independent agents, it might also apply to the bank channel. Bank agents might focus on meeting short-term sales targets, while tied agents should focus to maintain a long-term customer relationship. This increases the risk of miscounseling and hence lowers service quality in the bank channel providing a possible explanation for the higher lapse rate.

Supplementary Cover. Contracts including supplementary cover(s), such as disability insurance, exhibit higher lapse rates than contracts without those additional covers. The effect amounts to +20 percent for total lapse, +21 percent for late lapse, and +13 percent for early lapse. On the one hand, this result might be surprising since one might expect that policies with additional covers experience fewer lapses, as it gets more expensive (if possible at all) to obtain identical insurance coverage for the additional covers, for instance, by purchasing stand-alone disability insurance at a higher entry age. On the other hand, the premium for policies including additional cover is higher than for stand-alone policies. In case of financial distress, it is more likely that a policyholder is forced to lapse such a product bundle. Additionally, Pinquet et al. (2011) conclude that customers' insufficient knowledge of insurance products can cause lapse. Product bundles including insurance covers that are not necessary might be sold more often to customers who are not sufficiently familiar with insurance matters. Due to the usually higher premium of such contracts, those are more likely to be lapsed when the customer discovers that the product bundle does not fit his or her needs. Finally, the product bundle might include unnecessary or duplicate insurance coverage. As supplementary covers often cannot be lapsed separately, the customer might decide to lapse the entire contract.

Policyholder Sex. The total lapse rate for females is 9 percent lower than it is for males. The early lapse rate is 18 percent lower, while the late lapse rate is only 7 percent lower. This might be explained by higher risk aversion among females in financial matters (see, e.g., Halek and Eisenhauer, 2001). Females might be less willing to purchase insurance products they do not completely understand or if they are not sure whether they can afford long-term premium payments. This result is in line with Kagraoka (2005) who also finds that the lapse rate of female policyholders is less than for male customers.

Premium Payment. As expected, the total lapse rate is 90 percent less for single-premium business compared to regular-premium business. Single-premium business represents so far only a minor part of the analyzed portfolio in terms of exposure years, since this business has usually only a short policy duration. Moreover, savings policies are designed to accumulate funds through regular payments over a longer period of time. Single-premium business has been of limited relevance for the German life insurance industry to date, but its relevance has increased in the wake of the 2008 financial crisis. Many policyholders "park" their money in single-premium life insurance, so this type of business has increased significantly. It is still not clear whether the corresponding funds will stay long term or will be lapsed again when the financial markets recover. Early lapses are not relevant for single-premium business as there is a surrender value for such products starting from policy inception. The finding that single-premium business has lower lapse rates is in line with Milhaud et al. (2010).

Table 4 summarizes the results of the analysis for the eight product characteristics. In terms of calendar year, contract age, policyholder age and sex, and premium payment, our results are in line with the literature. However, we do find notable differences when product type is considered. We neither observe large variations in lapse rates for different product types (see Cerchiara et al., 2009) nor find evidence that unit-linked products experience higher lapse rates as Renshaw and Haberman (1986) do. Moreover, we add new findings to the literature for distribution channel and supplementary cover: (1) lapse rates for banks (brokers) are higher (lower) compared to tied agents and (2) with supplementary cover the lapse rate is higher.

Models Including Interactions

Both Renshaw and Haberman (1986) and Cerchiara et al. (2009) use interactions in their lapse analyses. Cerchiara et al. investigate interactions between product class and (1) contract age and (2) calendar year. The authors find that the effects of age and year are in general very similar across product categories. They conjecture that these results are related to the arbitrary definition of the product groups. Renshaw and Haberman consider four explanatory variables: product type, policyholder age (at entry), contract age, and company. The authors investigate all six possible interactions of two factors and find the most important interaction between product type and contract age. For all product types, lapses reduce substantially with increasing policy age. Additionally, nonprofit products have higher lapse rates than with profit policies at each contract age. Analyzing more detailed lapse information for one specific insurance company, Renshaw and Haberman find a significant interaction between product type and policyholder age, which might, however, be attributed to inconsistencies in the data (see Renshaw and Haberman, 1986, p. 485). Both Renshaw and Haberman (1986) and Cerchiara et al. (2009) focus on the interaction between two factors, since more complex interactions are much more difficult to analyze (exponentially increasing model complexity and thus run time).

We follow the approach of the literature when considering interactions between two factors. We, however, do not only analyze interactions including product type, but also consider distribution channel, (non)existence of supplementary cover, and premium payment. Since the model complexity increases tremendously when interactions are added, we use a simplified modeling approach for policyholder age for the sake of simplicity. Instead of considering each level separately, we group the levels into five classes. (22) When presenting the results of the analyses, we again restrict ourselves to total lapse in terms of number of contracts and the proportional hazards model. We do not present the results for all interactions, but focus on the most significant findings. Moreover, we only present the regression estimators and omit the p-values and hazard ratios. All this information is available upon request.

Interactions Between Product Type and Other Characteristics. Since empirical evidence suggests that the most significant interactions exist for product type, we consider interactions of product type with all other explanatory variables. (23) The interaction effects between product type and calendar year, contract age, and distribution channel, respectively, for total lapse in terms of number of contracts are displayed in Table 5. Note that missing values in this and the following tables indicate variable combinations for which there is no lapse event in the data and hence a lapse rate cannot be estimated. For example, the first Riester pensions were lapsed in 2003 although they were introduced in 2002. For comparison, the effects for the simplified model neglecting interactions--modeling policyholder age with classes--are included in the first row and last column, respectively. The results of this simplified model deviate only slightly from the results presented in the section "Models Without Interactions."

Considering calendar-year effects by product type (see Panel A in Table 5), these effects are consistent with the results for the model not taking interactions into account. The lapse rate for unit-linked annuities is higher than for traditional annuities during and after the 2008 financial crisis. This might indicate that many customers become nervous when stock markets fall, as unit-linked products are directly linked to stock market returns. Helfenstein and Barnshaw find a significant positive relationship of single-premium unit-linked life insurance sales and stock market performance in the United Kingdom using data from 1972 to 2001. Based on this observation, Helfenstein and Barnshaw conjecture that lapse rates vary with substantial changes in market conditions as policyholders may want to benefit from gains in booming markets and limit their losses in declining ones. Lapse rates increased for all products (except term life) during and following the 2008 financial crisis (Lier, 2010). This provides further evidence for the emergency fund hypothesis as a short-term economic downturn accompanied the financial crises. Term life insurance as a different product category (no surrender value) is, however, not affected by the calender year. No major deviations between product categories can be identified when distribution channels are considered except that the overall lapse rates differ by product type (see Panel B in Table 5). For most product types, the bank channel exhibits a higher lapse rate than tied agents, while brokers experience the smallest lapse rate. This result is identical with the model neglecting interactions. For all other policy(holder) characteristics, the effects are very similar across product type and consistent compared to the model without interactions. Only the overall lapse rate differs by product type. Detailed results are available upon request.

The results regarding interactions including product type are consistent with Renshaw and Haberman (1986) and Cerchiara et al. (2009) insofar as we find (at least) some significant interactions for each combination of product type and any of the other policy(holder) characteristics. The difference in magnitude of the effects, however, can probably be attributed to the different products considered.

Interactions Between Distribution Channel and Other Characteristics. Since this is the first study with data on distribution channels, we consider interactions of distribution channels with the other product and policy(holder) characteristics. The

results are very consistent for most characteristics compared to the results of the model without interactions, except for the difference in the overall lapse rate for the different distribution channels (i.e., lapse rates for banks are higher than for tied agents, while brokers have the lowest lapse rate). Only for policyholder age and supplementary cover, major deviations can be observed (see Table 6). Tied agent interaction

While lapse rates are rather flat for the bank and other channels across the different age groups, they are not for tied agents and brokers (see Panel A of Table 6). For tied agents, the lapse rates for the oldest age groups are substantially less than for the other age groups. This can be interpreted as indicative of different relationship levels. Agents seem to have a closer relationship with people who are about to retire. As shown in Panel B of Table 6, lapse rates for banks and other channels are higher for policies including supplementary coverage. For tied agents and brokers, however, lapse rates are almost identical, independent of the (non)existence of a supplementary cover. This supports the hypothesis regarding service quality, which should be highest for brokers, followed by tied agents and banks.

Interactions Between Supplementary Cover and Other Characteristics. In order to understand the drivers behind the higher lapse rate for policies including a supplementary cover, we analyze the interactions between supplementary cover and all other product and policy(holder) characteristics. The result of higher lapse rates for business with supplementary cover is consistent across the other characteristics, except for product type. Moreover, the development of lapse rates with and without supplementary cover is similar but at different levels, except for policyholder age. We thus focus on the results for interactions with product type and policyholder age in Table 7.

Lapse rates for traditional annuities and endowments are higher when they include a supplementary cover, while the lapse rates are smaller for all other product categories (see Panel A of Table 7). (24) Therefore, the overall effect is driven by annuities and endowments, which account for less than 50 percent of the portfolio but represent more than 50 percent of all contracts with supplementary coverage (measured in terms of exposure). The relationship of premium payment and policyholder age is shown in Panel B of Table 7. While for the youngest customers the lapse rate with supplementary cover is almost unchanged, it is larger for all other age groups and the gap to business without supplementary cover widens with age. In particular, lapse rates for business with supplementary cover are significantly higher for policyholders older than 45. This might support the conclusion regarding unnecessary coverage. When the mortgage is repaid or the children leave the family home, term life or disability cover might no longer be required. As these supplementary covers cannot be lapsed separately, the entire contract will be lapsed.

Interactions Between Premium Payment and Other Characteristics. Single-premium business significantly increased during and after the 2008 financial crisis. Customers and investors exited the stock markets and used this vehicle as "safe haven" for their money. Some insurers very actively promoted the single-premium business. (25) As the German regulator assumed the liquidity risk to be substantial for such business in case of lapse, a cap for the capitalization business has been introduced, but for single-premium business only qualitative requirements have been defined (i.e., the actuarial reserve of capitalization products needs to be less than 3 percent of the total actuarial reserve, while the policy design of single-premium business should rule out speculations against the portfolio in force, for example, through appropriate surrender charges or reduced profit participation; see BaFin, 2010a, 2010b). For both the German regulator and insurance managers, it is thus very relevant to analyze the lapse characteristics of the single-premium business, especially if it has suffered an increased lapse in recent years. We analyze interactions between premium payment and all other characteristics to assess the differences between regular- and single-premium business. Significant interactions are found only for product type, calendar year, and contract age. These results are presented inTable 8 for total lapse (in terms of number of contracts).

Consistent with the results without interactions, the lapse rate for single-premium business is much smaller than it is for regular-premium business. The lapse rate development of regular- and single-premium business, however, varies according to certain characteristics. The lapse rates of single-premium business are consistently much smaller than for regular-premium business for all product types, as depicted in Panel A of Table 8. This might be attributed to better insurance knowledge, the fact that no further premium payments are required, and the fact that the policy inception for many contracts might be shortly before retirement. While the lapse rate for regular-premium business increased beginning in 2007, the lapse rate of single-premium business decreased even further (see Panel B of Table 8). As mentioned above, the volume of single-premium business increased during and after the 2008 financial crisis. As lapse volumes seem to remain stable, decreasing lapse rates are the consequence. This effect, however, might be reversed in the future if lapse volume increases and/or if new business volume decreases. It is thus important to monitor whether single-premium business will suffer increased lapse in the future. As shown in Panel C of Table 8, the lapse rate of regular-premium business decreases more or less linearly from the second contract year. Overall, single-premium business shows a similar but not identical pattern. Note also that single-premium business represents only a minor part of the portfolio (1.3 percent of the total exposure). Lapse rates are thus more volatile with regard to changes in lapse volume.

CONCLUSION

In this article we assess the impact of eight product and policy(holder) characteristics on life insurance lapse, including product type, policyholder age, and policyholder sex. Following analyses for United Kingdom (Renshaw and Haberman, 1986), Japan (Kagraoka, 2005), Italy (Cerchiara et al., 2009), and Spain (Milhaud et al., 2010), proportional hazards models and GLMs are used to assess the relationship between lapse rates and those characteristics. We consider the largest database ever used for this purpose and extend the empirical literature by studying a time period of particular interest (two market turmoils) and factors that had not yet been analyzed (distribution channel and supplementary cover).

The article has three main findings. First, all considered product and policy(holder) characteristics have a statistically significant impact on lapse rates. The spread of lapse rates is largest for calendar year (increasing lapse rates, especially in phases of crisis), contract age (decreasing lapse rate with increasing contract age), and premium payment (lapse rate for single-premium business 90 percent lower compared to regular-premiums). Second, there are no major differences between unit-linked and traditional business; this is a major departure from the findings of earlier studies of other insurance markets. Lapse rates for unit-linked annuities are slightly below those of traditional annuities. Starting with the 2008 financial crisis, we find that lapse rates for unit-linked products are higher than those of traditional products. This effect is, however, limited and the time horizon is too short to draw final conclusions on the sustainability of this effect. Third, interactions of premium payment, supplementary cover, and distribution channel with all other characteristics are analyzed: (a) starting from 2007, lapse rates for regular-premium business have increased while lapse rates for single-premium business have decreased, perhaps because of a shift toward more volatile single-premium business; (b) the observed higher lapse rates for policies with supplementary cover is exclusively driven by endowments and traditional annuities as the opposite effect is observed for all other product types; and (c) the lapse rate development for the distribution channels considered varies by policyholder age (rather stable for banks, increasing for brokers, and decreasing for tied agents).

This work offers an initial empirical assessment of lapse determinants for the German life insurance market. Instead of modeling the explanatory factors categorically, alternative modeling approaches might be investigated, including fitting of polynomials or other appropriate functions to the different levels of the considered factors; this will prove to be particularly helpful for a more detailed analysis of interaction effects. Future research can build upon these results in order to develop a prediction model for future lapse rates. This can help life insurers to implement measures in terms of risk- and value-based management and to set up programs focusing on selected customers who are likely to lapse (Prestele, 2006). This requires additional model validation procedures, such as splitting the data set into fitting and testing samples (see, e.g., Cerchiara et al., 2009; Kiesenbauer, 2012), which go beyond the scope of this article. In addition, calendar-year effects might be linked to economic indicators such as unemployment rate, interest rate, or growth of gross domestic product. Moreover, within the new European regulatory framework for insurance companies (Solvency II), lapse has been identified as one of the main risk drivers for life insurers. The Solvency II model itself, however, differentiates lapse rates only for retail and nonretail business. Obviously, Solvency II neglects numerous important drivers of lapse that might be integrated into a company-specific (partial) internal model. Finally, it is surprising to see that lapse drivers have not been studied using U.S. data. There is thus much room for future research to further validate the findings presented here.

DOI: 10.1111/j.1539-6975.2012.01504.x

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Martin Eling is with the University of St. Gallen. Dieter Kiesenbauer is with the University of Ulm. The authors can be contacted via e-mail: martin.eling@unisg.ch and dieter.kiesenbauer@ alumni.uni-ulm.de.

(1) Lapse and surrender both refer to the termination of an insurance contract before maturity, but there is a slight difference between these two terms (see, e.g., Kuo et al., 2003; Gatzert et al., 2009). While lapse refers to the termination of policies without payout to policyholders, surrender usually indicates that a surrender value is paid out to the policyholder. In accordance with Renshaw and Haberman (1986) and Kuo et al. (2003), lapse is used throughout this article to refer to both surrender and lapse. This is consistent with standard measures of lapse as they typically include both lapsed policies and surrendered ones.

(2) For example, customers in poor health might be less likely to lapse a contract including death cover as they will hardly find comparable insurance coverage at the same premium level. Analyzing long-term care insurance, Pinquet et al. (2011) find that policyholders lapsing contracts have better health histories than do their peers continuing the contracts.

(3) Under Solvency II, the capital requirement for the lapse risk submodule is calculated as maximum of three stress scenarios defined as follows (see CEIOPS, 2010, pp. 155-159, for details): (1) a long-term decrease of lapse rates by 50 percent, (2) a long-term increase of lapse rates by 50 percent, and (3) a mass lapse event of 30 percent of all policyholders. For more details on Solvency II, see also European Parliament and Council (2009).

(4) Lapse is usually measured in terms of the sum insured in the German market. Additionally, we consider lapse rates in terms of the number of contracts and regular premiums as robustness measures. The modeling approach is the same as for other studies in this field, that is, generalized linear models, which allows comparing our results with the existing ones.

(5) Other studies indicate further possibly relevant characteristics identifying different client segments based on socioeconomic information (e.g., policyholder income, area of residence, or tenant vs. homeowner). Due to strict regulation of data protection, insurers are only allowed to ask for information relevant for the risk assessment and pricing. Therefore, just like in all other studies, such information is not available in the German market. For confidentiality reasons, actual lapse rates and volume numbers (number of policies, number of contract years, lapse events) are not presented in this article. Instead, like Cerchiara et al. (2009), we restrict ourselves to relative effects when presenting the results.

(6) Additionally, Kiesenbauer (2012) examines the extent to which the interest rate and emergency fund hypotheses hold for the German life insurance market. Neither of the hypotheses hold for traditional (i.e., not unit-linked) life insurance products, while they are supported when unit-linked business is considered.

(7) Milhaud et al. (2010) also consider the CART model, which does not belong to the class of generalized linear models. Recently, Pinquet et al. (2011) use proportional hazards models to analyze long-term insurance contracts.

(8) This specific contract feature does not exist in all insurance markets. In particular, surrender fees always apply in case of lapsing before maturity in the German life insurance market.

(9) For a discussion of reasons why consumers let their policies lapse, we also refer to the yearly published FSA work on the U.K. market; see, for example, Financial Services Authority (FSA) (2011). Among others, their work shows how lapse risk can be affected by factors as distribution channels or bad publicity.

(10) Lapse rate information is treated highly confidential by life insurance companies. Therefore, confidentiality needs to be maintained throughout the article. We are thus not able to show absolute lapse rates and summary statistics. Instead we present effects relative to a reference level, that is, how much smaller or higher is the lapse rate for a certain level (e.g., endowment) compared to a reference level (e.g., traditional annuity). This still allows to draw conclusions on the importance of the considered product and policy(holder) characteristics and the magnitude of the corresponding effects. Additionally, we can indicate neither the portfolio composition nor the distribution mix of the company as it potentially allows identifying the company.

(11) Riester and Rurup pensions are tax-subsidized pension products introduced in 2002 and 2005, respectively. See Borsch-Supan et al. (2008) and Corneo et al. (2010) for more details on these products.

(12) Note that asset-liability mismatches stem from possible discrepancies between contract values and market values. In Germany the discrepancies between contract values and market values are an issue for endowment policies and traditional annuities (both are in the balance sheet at book values), but not for unit-linked policies (which are in the balance sheet at market values). The two pension products (Riester and Rurup) can be sold both in a traditional and in a unit-linked style so that no clear statement can be made with respect to asset-liability mismatch.

(13) Strictly speaking, the calendar year constitutes an exogenous variable not being directly related to an insurance contract. The lapse behavior of customers, however, usually also depends on exogenous factors (see the above discussion on the emergency fund and interest rate hypotheses). The consideration of calendar-year effects allows, for instance, to assess systematic deviations in lapse rates for certain years, such as the stock market plunge from 2001 to 2003, the enforced tax treatment in 2005, or during and following the 2008 financial crisis.

(14) A contract age of t means that a policy is in its tth contract year. This variable allows drawing conclusions on the counseling and service quality of the insurer, but also might reflect changes in customer needs.

(15) Contrary to the BaFin definition, we model the early lapse rate in terms of total business in force instead of using only new business. This changes the absolute lapse rate, but should have only a limited impact on the relative effects. Using generalized linear models for the analyses and focusing on new business completely neglects all early lapse events that do not occur within in the first year after policy inception which might bias the results heavily.

(16) For each interaction of two factors, the number of additional variables is calculated as the product of the number of levels for each considered characteristic less one. For instance, the consideration of interactions between product category and distribution channel introduces 15 = (6 - 1) x (4 - 1) additional regression coefficients to be estimated.

(17) In Table 3, we present the results focusing on the number of contracts as lapse rate measure. We have also calculated the corresponding results for regular premiums and sum insured, which are consistent and lead to similar conclusions. Moreover, in Table 3 we focus on total lapse. While the results for late lapse are consistent with those for total lapse, the results for early lapse are different. The latter differences are displayed in Figure 1 and will be discussed in the following. All additional results are available form the authors upon request.

(18) These columns are not presented in Figure 1(a), because for confidentiality reasons, we cannot reveal the concrete portfolio composition, in particular, the weight of the different product categories.

(19) When the same analysis is performed excluding term life insurance, the early lapse rate quickly decreases to zero within the first 4 contract years. Results are available upon request.

(20) As the estimates of the corresponding regression coefficients are close to zero, the corresponding variables are not statistically significantly different from zero.

(21) Overall, the variations between different distribution channels is rather limited. Correlation analyses have been performed to rule out that this effect might be driven by highly correlated explanatory factors. The correlation between distribution channel and other variables is very close to zero in all cases, indicating that such relationships do not exist. Detailed results are available upon request.

(22) The policyholder age is grouped into 18-25, 26-35, 36-45,46-55, and > 56 years.

(23) In order to assess the presence of heterogeneity between different product categories, we additionally analyze each product category separately. The results are consistent with the results when interactions between product type and all other explanatory factors are considered. Detailed results are available upon request.

(24) Note that the Riester pension is designed to increase private pension savings and is federally subsidized. Therefore, supplementary covers are usually not included in these policies.

(25) Single-premium payments are available for all product categories considered, except for Rurup pensions. It is, however, not limited to those products. In particular, capitalization products are explicitly designed for this purpose. No information on this product category is available for our analysis.

TABLE 1
Overview of the Empirical Literature Regarding Analysis of Product
and Policyholder Characteristics

                    Renshaw and             Kagraoka
                    Haberman (1986)         (2005)

Country             Scotland                Japan
Companies           7                       1
Time period         1976                    1993-2001
Contracts           >750,000                about 76,000
Policy years
Lapse events
Products            With-profit endowment   Annuity-type
                                              personal
                    Nonprofit endowment       accident

                    (Open-ended
                      endowment) (c)
                    (Unit-linked
                      endowment) (c)
                    With-profit
                      whole-life
                    Nonprofit whole-life
                      Temporary insurance
Available           Policyholder age--at    Policyholder
  characteristics     entry                   age--at entry
                    (Policyholder           Policyholder sex
                      sex) (c)
                    Contract age            Contract age
                    Product type
                    (Premium payment) (c)
                    (Distribution
                      channel) (c)
                    (Sum insured) (c)

                    Company                 Seasonality

                    (Original               Unemployment
                      premium-paying          rate
                      term) (c)
                                            Heterogeneity (e)
Modeling            Logistic regression     Poisson model
  approaches          model
                    Binomial model          Negative
                                            binomial
                                            model

                    Cerchiara et al.        Milhaud et al.
                    (2009)                  (2010)

Country             Italy                   Spain
Companies           1                       1
Time period         1991-2007               1999-2007
Contracts                                   28,506
Policy years        6,129,000
Lapse events        279,000                 15,571
Products            Saving (a)              Endowment

                                            --PP (b) with PB (b)

                                            --PP (b) without
                                              PB (b)
                                            --SP (b) with PB (b)
                                            --SP (b) without
                                              PB (b)

                                            (Pure saving) (c)

Available           Policyholder            Policyholder age--
  characteristics     age--current            at entry
                    (Policyholder             (Policyholder
                      sex) (c)                sex) (c)
                    Contract age            Contract age
                    Product type (a)        Product type
                                            Premium payment

                    Calendar year
                                            Sum insured
                                            Risk premium
                                            Saving premium
                    (Policy inception       (Termination
                      year) (c)               reason) (c)

Modeling            Poisson model           Logistic regression
  approaches                                  model
                                            CART (f) model

                    Pinquet et al.
                    (2011)                  Current Article

Country             Spain                   Germany
Companies           1                       1
Time period         1993-2006               2000-2010
Contracts           150,000                 >1,000,000
Policy years        1,163,645               >>1,000,000
Lapse events                                >>100,000
Products            one product with        Endowment
                      three
                    policies (product       Traditional annuity
                      bundle):
                    death benefit           Unit-linked annuity
                      insurance,
                    health coverage, and    Riester pension
                    long-term care          Riirup pension
                      component

                                            Term life

Available           Policyholder age--      Policyholder
  characteristics     at entry                age--current
                      (Policyholder         Policyholder sex
                      sex) (c)
                    Contract age            Contract age
                                            Product type
                                            Premium payment
                                            Distribution channel
                    Calendar year           Calendar year
                                            (Sum insured) (d)
                                            (Premium) (d)

                    (Termination
                      reason) (c)
                    Health bonus-malus      Supplementary
                      coefficient             cover

                                            (Heterogeneity)0
Modeling            Proportional hazards    Poisson model
  approaches          model
                                            Binomial model

                                            Negative binomial
                                              model
                                            Proportional hazards
                                              model

(a) Focus on single/premium or recurrent single/premium products;
large number of products (without further details) is grouped into a
smaller number of product classes with similar observed lapse/
surrender levels. (b) PP = periodic premium; PB = profit benefit; SP
= single/premium. (c) Parentheses indicate that the variable/
characteristic is available in the data set but has not been used
for the analysis. (d) These variables are used as response variables
measuring lapse volume. (e) The negative binomial model has one
additional parameter that allows incorporating unobserved
heterogeneity among the policyholders, for example, residential
type, occupation, annual income, loan amount. Classification and
regression tree.

TABLE 2
Levels of All Considered Product and Policy(Holder) Characteristics

                       No. of
Variable               Levels                  Levels

Product type             6       Annuity     Unit-linked   Endowment
                                               annuity
Calendar year            11        2008         2000         2001
Contract age             11         1             2            3
Policyholder age         63         39           18           19
Distribution channel     4      Tied agent     Broker        Bank
Supplementary cover      2          No         Yes (b)
Policyholder sex         2         Male        Female
Premium payment          2       Regular       Single

Variable                  Levels

Product type                 Term life
                       ...
Calendar year          ...     2010
Contract age           ...      11
Policyholder age       ...    80 (a)
Distribution channel           Other
Supplementary cover
Policyholder sex
Premium payment

(a) The maximum policyholder age varies by product.

(b) Contracts with at least--but not limited to--one
additional cover.

TABLE 3
Model Results for Total Lapse Without Interactions

                        Pro. Hazards Model

                                             Hazard
                        Est.     p-value     Ratio

Product type (reference level: annuity)
  Unit-linked annuity   -0.03    0.000 ***   0.97
  Endowment              0.15    0.000 ***   1.16
  Riester                0.13    0.000 ***   1.14
  Rurup                 -0.33    0.000 ***   0.72
  Term life             -0.06    0.000 ***   0.94
Calendar year (reference level: 2008)
  2000                  -1.32    0.000 ***   0.27
  2001                  -0.78    0.000 ***   0.46
  2002                  -0.70    0.000 ***   0.49
  2003                  -0.41    0.000 ***   0.67
  2004                  -0.23    0.000 ***   0.79
  2005                  -0.28    0.000 ***   0.76
  2006                  -0.27    0.000 ***   0.76
  2007                  -0.22    0.000 ***   0.80
  2009                   0.20    0.000 ***   1.22
  2010                   0.07    0.000 ***   1.08
Contract age (reference level: 1)
  2                      0.17    0.000 ***   1.19
  3                      0.09    0.000 ***   1.09
  4                     -0.06    0.000 ***   0.94
  5                     -0.20    0.000 ***   0.82
  6                     -0.31    0.000 ***   0.73
  7                     -0.51    0.000 ***   0.60
  8                     -0.67    0.000 ***   0.51
  9                     -1.04    0.000 ***   0.35
  10                    -1.12    0.000 ***   0.33
  11                    -1.37    0.000 ***   0.26
Policyholder age (reference level: 39)
  18                    -0.91    0.000 ***   0.40
  19                     0.06    0.000 ***   1.06
  20                     0.19    0.000 ***   1.21
  21                     0.28    0.000 ***   1.32
  22                     0.31    0.000 ***   1.36
  23                     0.32    0.000 ***   1.38
  24                     0.34    0.000 ***   1.40
  .                       .       .           .
  .                       .       .           .
  .                       .       .           .
  76                    -0.48    0.000 ***   0.62
  77                    -0.47    0.000 ***   0.63
  78                    -0.31    0.000 ***   0.73
  79                    -0.36    0.000 ***   0.70
  80                    -0.41    0.000 ***   0.66
Distribution channel (reference level: tied agent)
  Bank                   0.22    0.000 ***   1.25
  Broker                -0.06    0.000 *' *  0.95
  Other                  0.19    0.000 ***   1.21
Supplementary cover (reference level: no)
  Yes                    0.18    0.000 ***   1.20
Policyholder sex (reference level: Male)
  Female                -0.09    0.000 ***   0.91
Premium payment (reference level: regular premiums)
  single premiums       -2.33    0.000 ***   0.10

                        Binomial Model

                                             Hazard
                        Est.     p-value     Ratio

Product type (reference level: annuity)
  Unit-linked annuity   -0.03    0.000 ***   0.97
  Endowment              0.14    0.000 ***   1.15
  Riester                0.15    0.000 ***   1.15
  Rurup                 -0.33    0.000 ***   0.73
  Term life             -0.07    0.000 ***   0.93
Calendar year (reference level: 2008)
  2000                  -1.27    0.000 ***   0.29
  2001                  -0.77    0.000 ***   0.47
  2002                  -0.69    0.000 ***   0.51
  2003                  -0.40    0.000 ***   0.68
  2004                  -0.24    0.000 ***   0.80
  2005                  -0.27    0.000 ***   0.77
  2006                  -0.26    0.000 ***   0.78
  2007                  -0.22    0.000 ***   0.81
  2009                   0.20    0.000 ***   1.21
  2010                   0.07    0.000 ***   1.07
Contract age (reference level: 1)
  2                      0.18    0.000 ***   1.18
  3                      0.09    0.000 ***   1.09
  4                     -0.06    0.000 ***   0.94
  5                     -0.19    0.000 ***   0.83
  6                     -0.30    0.000 ***   0.75
  7                     -0.51    0.000 ***   0.61
  8                     -0.66    0.000 ***   0.53
  9                     -1.01    0.000 ***   0.37
  10                    -1.09    0.000 ***   0.35
  11                    -1.29    0.000 ***   0.28
Policyholder age (reference level: 39)
  18                    -0.91    0.000 ***   0.42
  19                     0.05    0.003 ***   1.04
  20                     0.18    0.000 ***   1.19
  21                     0.27    0.000 ***   1.30
  22                     0.31    0.000 ***   1.34
  23                     0.32    0.000 ***   1.35
  24                     0.34    0.000 ***   1.38
  .                       .       .           .
  .                       .       .           .
  .                       .       .           .
  76                    -0.50    0.000 ***   0.62
  77                    -0.49    0.000 ***   0.63
  78                    -0.34    0.000 ***   0.72
  79                    -0.39    0.000 ***   0.69
  80                    -0.44    0.000 ***   0.66
Distribution channel (reference level: tied agent)
  Bank                   0.22    0.000 ***   1.23
  Broker                -0.05    0.000 ***   0.95
  Other                  0.19    0.000 ***   1.20
Supplementary cover (reference level: no)
  Yes                    0.18    0.000 ***   1.19
Policyholder sex (reference level: Male)
  Female                -0.09    0.000 ***   0.92
Premium payment (reference level: regular premiums)
  single premiums       -1.79    0.000 ***   0.17

                        Poisson Model

                                             Hazard
                        Est.     p-value     Ratio

Product type (reference level: annuity)
  Unit-linked annuity   -0.03    0.000 ***   0.97
  Endowment              0.14    0.000 ***   1.15
  Riester                0.14    0.000 ***   1.15
  Rurup                 -0.33    0.000 ***   0.72
  Term life             -0.07    0.000 ***   0.93
Calendar year (reference level: 2008)
  2000                  -1.32    0.000 ***   0.27
  2001                  -0.77    0.000 ***   0.46
  2002                  -0.69    0.000 ***   0.50
  2003                  -0.40    0.000 ***   0.67
  2004                  -0.23    0.000 ***   0.79
  2005                  -0.27    0.000 ***   0.76
  2006                  -0.26    0.000 ***   0.77
  2007                  -0.21    0.000 ***   0.81
  2009                   0.20    0.000 ***   1.22
  2010                   0.07    0.000 ***   1.08
Contract age (reference level: 1)
  2                      0.18    0.000 ***   1.19
  3                      0.09    0.000 ***   1.10
  4                     -0.06    0.000 ***   0.95
  5                     -0.19    0.000 ***   0.83
  6                     -0.30    0.000 ***   0.74
  7                     -0.50    0.000 ***   0.60
  8                     -0.66    0.000 ***   0.52
  9                     -1.02    0.000 ***   0.36
  10                    -1.11    0.000 ***   0.33
  11                    -1.36    0.000 ***   0.26
Policyholder age (reference level: 39)
  18                    -0.93    0.000 ***   0.39
  19                     0.05    0.000 ***   1.05
  20                     0.18    0.000 ***   1.20
  21                     0.27    0.000 ***   1.31
  22                     0.30    0.000 ***   1.35
  23                     0.32    0.000 ***   1.37
  24                     0.34    0.000 ***   1.40
  .                       .       .           .
  .                       .       .           .
  .                       .       .           .
  76                    -0.50    0.000 ***   0.60
  77                    -0.49    0.000 ***   0.61
  78                    -0.34    0.000 ***   0.71
  79                    -0.39    0.000 ***   0.68
  80                    -0.44    0.000 ***   0.64
Distribution channel (reference level: tied agent)
  Bank                   0.22    0.000 ***   1.24
  Broker                -0.05    0.000 ***   0.95
  Other                  0.19    0.000 ***   1.21
Supplementary cover (reference level: no)
  Yes                    0.18    0.000 ***   1.20
Policyholder sex (reference level: Male)
  Female                -0.09    0.000 ***   0.91
Premium payment (reference level: regular premiums)
  single premiums       -2.31    0.000 ***   0.10

*** indicates significance at the 1% level (Wald [chi square]-test).

TABLE 4
Summary of Results for the Models Without Interactions Compared
to Existing Literature

Characteristic         Results                 Existing Literature

Product type           Minor variations in     Result is different
                         total lapse rate,       compared to
                         early lapse rate        Renshaw and
                         lower for Riester       Haberman (1986) and
                         pensions                Cerchiara et
                                                 al. (2009)
Calendar year          Increasing lapse        Consistent with
                         rates from 2000         Cerchiara et
                         to 2009                 al. (2009)
Contract age           Decreasing lapse        Consistent with all
                         rates with              empirical studies
                         increasing contract     (Renshaw and
                         age                     Haberman, 1986;
                                                 Kagraoka, 2005;
                                                 Cerchiara et al.,
                                                 2009; Milhaud et
                                                 al., 2010)
Policyholder age       Three age groups:       Consistent with all
                         policyholders up to     empirical studies
                         25 (increasing          (Renshaw and
                         lapse, but below        Haberman, 1986;
                         the other groups),      Kagraoka, 2005;
                         policyholders           Cerchiara et al.,
                         between 26 and 40       2009; Milhaud et
                         (constant lapse         al., 2010)
                         rate), and
                         policyholders older
                         than 40 (first
                         increasing lapse,
                         then decreasing)
Distribution channel   Lapse higher for        Not considered in
                         banks, lower for        existing literature
                         brokers
Supplementary cover    Higher lapse with       Not considered in
                         supplementary cover     existing literature
Policyholder sex       9% lower lapse rate     Consistent with
                         for female              Kagraoka (2005)
                         policyholders
Premium payment        90% lower lapse rate    Consistent with
                         for single premium      Milhaud et
                         business compared       al. (2010)
                         to regular premiums

TABLE 5
Interaction Effects Between Product Type and Selected
Policy(holder) Characteristics on Total Lapse Rates

                        Annuity

                                                      Riester   Rurup
              Traditional   Unit-Linked   Endowment   Pension   Pension

Effect w/o     0.000        -0.032         0.141       0.137    -0.323
interaction

Panel A: Calendar Year

2000          -1.022                      -4.810
2001          -0.540                      -0.780
2002          -0.304                      -0.485
2003          -0.044                      -0.342      -0.543
2004          -0.018        -0.443        -0.182       0.458
2005          -0.178        -0.361        -0.189       0.812
2006          -0.103        -0.098        -0.041      -0.078    -1.599
2007          -0.043         0.080        -0.002      -0.184    -0.745
2008           0.000         0.184         0.091       0.358     0.005
2009           0.225         0.414         0.292       0.575     0.338
2010           0.319         0.385         0.242       0.389     0.302

Panel B: Distribution Channel

Tied agent     0.000         0.184         0.091       0.358     0.005
Bank           0.100         0.241         0.323       0.764    -0.128
Broker        -0.255         0.206        -0.100       0.207    -0.170
Other          0.179         0.404         0.282       0.389     0.135

              Term      Effect w/o
              Life      Interaction

Effect w/o    -0.065
interaction

Panel A: Calendar Year

2000          -1.198    -1.321
2001          -0.791    -0.781
2002          -0.714    -0.705
2003          -0.478    -0.408
2004          -0.338    -0.234
2005          -0.359    -0.279
2006          -0.380    -0.270
2007           0.392     0.218
2008          -0.384     0.000
2009          -0.309     0.198
2010          -0.530     0.074

Panel B: Distribution Channel

Tied agent    -0.384     0.000
Bank          -0.440     0.226
Broker        -0.222    -0.049
Other         -0.119     0.197

TABLE 6
Interaction Effects Between Distribution Channel and Selected
Policy(holder) Characteristics on Total Lapse Rates

                                                     Effect w/o
               Tied Agent   Bank    Broker   Other   Interaction

Effect w/o       0.000      0.226   -0.049   0.197
Interaction

Panel A: Policyholder Age

18-25            0.110      0.920   -0.010   0.802      0.282
26-35            0.179      0.784   -0.096   0.683      0.187
36-45            0.000      0.608   -0.232   0.442      0.000
46-55            -0.065     0.534   -0.280   0.322     -0.079
>=56             -0.504     0.409   -0.271   0.222     -0.271

Panel B: Supplementary Cover

No               0.000      0.608   -0.232   0.442      0.000
Yes              0.018      0.861   -0.198   0.597      0.191

TABLE 7
Interaction Effects Between Supplementary Cover and Selected
Policy(holder) Characteristics on Total Lapse Rates

                       Supplementary
                           Cover

                        No      Yes

Effect w/o            0.000    0.191
interaction

Panel A: Product Type

Annuity               0.000     0.052    0.000   Riester
Unit-linked annuity   0.013    -0.089   -0.032   Rurup
Endowment             0.127     0.170    0.141   Term life

Panel B: Policyholder Age

18-25                 0.294    0.306    0.282    46-55
26-35                 0.189    0.230    0.187    >=56
36-45                 0.000    0.052    0.000

                       Supplementary
                           Cover

                        No        Yes     Effect w/o
                                          Interaction

Effect w/o             0.000     0.165
interaction

Panel A: Product Type

Annuity                0.149               0.137
Unit-linked annuity   -0.303    -0.310    -0.323
Endowment             -0.042    -0.083    -0.065

Panel B: Policyholder Age

18-25                 -0.080     0.020    -0.079
26-35                 -0.272     0.006    -0.271
36-45

TABLE 8
Interaction Effects Between Premium Payment and Selected
Policy(holder) Characteristics on Total Lapse Rates

              Regular     Single    Effect w/o
              Premiums   Premiums   Interaction

Effect w/o     0.000      -2.346
interaction

Panel A: Product Type

Annuity         0.000     -2.593       0.000
UL annuity     -0.031     -2.881      -0.032
Endowment       0.145     -4.943       0.141

Panel B: Calendar Year

2000           -1.320     -3.966      -1.321
2001           -0.782     -3.727      -0.781
2002           -0.707     -3.395      -0.705
2003           -0.411     -2.857      -0.408
2004           -0.236     -2.605      -0.234
2005           -0.281     -2.599      -0.279

Panel C: Contract Age

1               0.000     -2.593       0.000
2               0.180     -1.184       0.182
3               0.097     -1.257       0.099
4              -0.056     -1.617      -0.054
5              -0.193     -1.451      -0.191
6              -0.304     -1.714      -0.301

                          Regular     Single    Effect w/o
                          Premiums   Premiums   Interaction

Effect w/o                 0.000      -2.346
interaction

Panel A: Product Type

Annuity       Riester      0.137                   0.137
UL annuity    Rurup       -0.320                  -0.323
Endowment     Term life   -0.064      -2.607      -0.065

Panel B: Calendar Year

2000            2006      -0.271      -2.534      -0.270
2001            2007      -0.218      -2.705      -0.218
2002            2008       0.000      -2.593       0.000
2003            2009       0.199      -2.603       0.198
2004            2010       0.075      -2.821       0.074
2005

Panel C: Contract Age

1                 7        -0.502     -1.811      -0.499
2                 8        -0.665     -2.191      -0.663
3                 9        -1.040     -1.800      -1.036
4                10        -1.116                 -1.114
5                11        -1.369     -2.160      -1.365
6
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Author:Eling, Martin; Kiesenbauer, Dieter
Publication:Journal of Risk and Insurance
Geographic Code:4EUGE
Date:Jun 1, 2014
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