Asymmetric Information Problems in Taiwan's Automobile Insurance Market: The Effect of Policy Design on Loss Characteristics

This article investigates asymmetric information problems for the automobile insurance market in Taiwan. Using panel data for the comprehensive automobile insurance coverage from 1995 to 1999, this article analyzes how types of coverage, deductible amounts, and experience ratings have affected the adverse selection and moral hazard problems in Taiwan's automobile insurance market. The empirical results provide partial evidence to demonstrate that the loss frequency and loss ratio were reduced by the addition of self-selection mechanisms in policies with different levels of coverage. In addition, the deductible amounts, experience ratings, and better control of underwriting and claims processing were shown possibly to have decreased potential losses from adverse selection and moral hazard problems.     

On Compulsory Per-Claim Deductibles in Automobile Insurance

The purposes of this paper are to analyze the theoretical characteristics of the compulsory deductible system and to verify the rationality of an increasing per-claim deductible in automobile insurance. We derive the optimal variable per-claim deductible by assuming the insurers are financially balanced and the expected utility of the insured is maximized in the absence of moral hazard. Our result suggests that a variable per-claim deductible increasing with the number of claims per year is not optimal. Instead, deductibles should be charged in a decreasing rate forming a second-best solution.     

Multiple Losses, EX ANTE Moral Hazard, and the Implications for Umbrella Policies

Under certain cost conditions the optimal insurance policy offers full coverage above a deductible, as Arrow and others have shown. However, many insurance policies currently provide coverage against several losses although the possibilities for the insured to affect the loss probabilities by several prevention activities (multiple moral hazard) are substantially different. This article shows that optimal contracts under multiple moral hazard generally call for complex reimbursement schedules. It also examines the conditions under which different types of risks can optimally be covered by a single insurance policy and argues that the case for umbrella policies under multiple moral hazard is limited in practice.     

The Incentive Effects of Increasing Per-Claim Deductible Contracts in Automobile Insurance

A new rating system of automobile insurance for vehicle damage in Taiwan was launched in 1996, introducing a deductible that increases with the number of claims. In this article, we provide a theoretical rationale for the existence of an increasing per‐claim deductible system and show that the new system is most likely an optimal choice for those insured who tend to have lower claims probability when incentives are present. Using a unique dynamic data set, we are able to conduct a natural experiment to examine the incentive effects (both positive and negative) by looking at the change in claim tendency before and after switching between two deductible plans: an increasing per‐claim deductible and a zero deductible. Our results provide direct evidence of the effects of deductible structures on claim behavior.     

Moral hazard,adverse selection,and health expenditures: A semiparametric analysis

Theoretical models predict asymmetric information in health insurance markets may generate inefficient outcomes due to adverse selection and moral hazard. However, previous empirical research has found it difficult to disentangle adverse selection from moral hazard in health care consumption. We propose a two‐step semiparametric estimation strategy to identify and estimate a canonical model of asymmetric information in health care markets. With this method, we can estimate a structural model of demand for health care. We illustrate this method using a claims‐level data set with confidential information from a large self‐insured employer. We find significant evidence of moral hazard and adverse selection.     

A Note on Deductible Insurance and Production

This paper examines the optimal production decision of a firm facing revenue risk. We show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm is not only risk averse but also prudent. If the firm's perferences satisfy constant absolute risk aversion, buying actuarially unfair deductible insurance unambiguously enhances production should the positive loading factor be sufficiently small. When there are moral hazard problems in that the firm's output cannot be contracted upon, we show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm's utility function is quadratic.     

An Examination of Adverse Selection in the Public Provision of Insurance

Using a unique data set from Florida's residual property insurer, we test for adverse selection in the public provision of homeowners’ insurance in Florida. We find a significant relationship between the losses and deductible choices of insureds in Florida's residual homeowners’ insurance market. This relationship provides strong evidence of the existence of an adverse selection problem in Florida's residual property insurance market. While this relationship is important to Florida regulators (and taxpayers) specifically, a finding of an adverse selection problem in residual markets in general has implications more broadly for government providers of insurance as an adverse selection problem in these settings will impact the public policy debates and decisions involving these markets.     

A Voluntary Deductible in Social Health Insurance with Risk Equalization: “Community‐Rated or Risk‐Rated Premium Rebate?”

On January 1, 2006 a new mandatory basic health insurance will be introduced in the Netherlands. One aspect of the new scheme is that the insured can choose to have a deductible. This option should increase the individual responsibility and reduce moral hazard. In the new scheme, a risk equalization system is aimed at avoiding preferred risk selection and insolvency of insurance companies with a relatively high‐risk pool. A crucial issue with respect to a voluntary deductible in this type of social health insurance is whether the premium rebate should be community rated or risk rated. The Dutch government has chosen the former, which means that the premium rebate will be independent of health status and risk. Our analysis shows that, in a situation with “accurate” risk equalization, a community‐rated premium rebate could lead to an adverse selection spiral. Over time, this spiral results in none of the insured taking a deductible and thus no reduction in moral hazard.     

On the design of optimal health insurance contracts under ex post moral hazard

We analyze the design of optimal medical insurance under ex post moral hazard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-off between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when insurers’ rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.     

General Insurance Deductible Ratemaking

Insurance claims have deductibles, which must be considered when pricing for insurance premium. The deductible may cause censoring and truncation to the insurance claims. However, modeling the unobserved response variable using maximum likelihood in this setting may be a challenge in practice. For this reason, a practitioner may perform a regression using the observed response, in order to calculate the deductible rates using the regression coefficients. A natural question is how well this approach performs, and how it compares to the theoretically correct approach to rating the deductibles. Also, a practitioner would be interested in a systematic review of the approaches to modeling the deductible rates. In this article, an overview of deductible ratemaking is provided, and the pros and cons of two deductible ratemaking approaches are compared: the regression approach and the maximum likelihood approach. The regression approach turns out to have an advantage in predicting aggregate claims, whereas the maximum likelihood approach has an advantage when calculating theoretically correct relativities for deductible levels beyond those observed by empirical data. For demonstration, loss models are fit to the Wisconsin Local Government Property Insurance Fund data, and examples are provided for the ratemaking of per-loss deductibles offered by the fund. The article discovers that the regression approach is actually a single-parameter approximation to the true relativity curve. A comparison of selected models from the generalized beta family discovers that the usage of long-tail severity distributions may improve the deductible rating, while advanced frequency models such as 01-inflated models may have limited advantages due to estimation issues under censoring and truncation. In addition, in this article, models for specific peril types are combined to improve the ratemaking.     

逆向选择、系统性风险与政策性农业保险可持续发展

本文介绍了政策性农业保险在发达国家的成功经验和我国的发展状况,对政府补贴情境下的农业保险市场均衡模型进行了研究,并得到了市场均衡条件下的免赔率方程。利用上述市场均衡模型,针对农业保险市场普遍存在的系统性风险、逆向选择和道德风险问题,从统一的政策性农业保险公司、多层次再保险体系建设等方面阐述了政策性农业保险体系的可持续发展策略。     

Optimal Insurance Under Random Auditing

We provide a characterization of an optimal insurance contract (coverage schedule and audit policy) when the monitoring procedure is random. When the policyholder exhibits constant absolute risk aversion, the optimal contract involves a positive indemnity payment with a deductible when the magnitude of damages exceeds a threshold. In such a case, marginal damages are fully covered if the claim is verified. Otherwise, there is an additional deductible that disappears when the damages become infinitely large. Under decreasing absolute risk aversion, providing a positive indemnity payment for small claims with a nonmonotonic coverage schedule may be optimal.     

农业保险可以减轻自然灾害对农业经济的负面影响吗?

建立融合自然灾害、农业保险以及道德风险的动态模型.模型显示:自然灾害会降低农业产出,而农业保险可以降低自然灾害对农业生产的负面影响,但前提是道德风险的影响较小.实证表明,每增加1元农业保险保费对应的保障水平,可以降低由自然灾害导致的第一产业产出约8.19元的损失.同时,未发现农业保险市场在省级加总层面存在显著的道德风险.     

Effects of Competition on Insurance Contract Formation

For an insurance transaction between a single risk-averse buyer and single risk-neutral seller with positive transaction costs, it is well known that the buyer will prefer a policy contract with an ordinary deductible. More detailed results demonstrate the Pareto optimality of an insurance contract characterized by a deductible (followed by coinsurance) for a single risk-averse buyer and single risk-averse seller. In the present work, we employ a market-game model to solve for the equilibrium insurance contract. This formulation, which approximates the behavior of excess property insurance and property catastrophe reinsurance markets, reveals that the equilibrium policy is described by full insurance up to a given policy limit, with no deductible or coinsurance. Our analysis shows further that this solution persists regardless of the numbers of buyers and sellers in the market, and in particular that the market-game equilibrium does not converge to a Pareto-optimal result because of boundary constraints on the number of sellers. Finally, we test our price-formation mechanism against an important generalization, and find that the policy-limit contract persists.     

Ex Post Moral Hazard and Bayesian Learning in Insurance

We study a dynamic insurance market with asymmetric information and ex post moral hazard. In our model, the insurance buyer's risk type is unknown to the insurer; moreover, the buyer has the option of not reporting losses. The insurer sets premia according to the buyer's experience rating, computed via Bayesian estimation based on buyer's history of reported claims. Accordingly, the buyer has strategic incentive to withhold information about losses. We construct an insurance market information equilibrium model and show that a variety of reporting strategies are possible. The results are illustrated with explicit computations in a two‐period risk‐neutral case study.     

A Continuous-Time Optimal Insurance Design with Costly Monitoring

We provide a theoretical and numerical framework to study optimal insurance design under asymmetric information. We consider a continuous-time model where neither the efforts nor the outcome of an insured firm are observable to an insurer. The insured may then cause two interconnected information problems: moral hazard and fraudulent claims. We show that, when costly monitoring is available, an optimal insurance contract distinguishes the one problem from the other. Furthermore, if the insured’s downward-risk aversion is weak and if the participation constraint is not too tight, then a higher level of the monitoring technology can mitigate both problems.     

The Demand for Insurance With an Upper Limit on Coverage

The demand for insurance is examined when the indemnity schedule is subject to an upper limit. The optimal contract is shown to display full insurance above a deductible up to the cap. Some results derived in the standard model with no upper limit on coverage turn out to be invalid; the optimal deductible of an actuarially fair policy is positive and insurance may be a normal good under decreasing absolute risk aversion. An increase in the upper limit would induce the policyholder with constant absolute risk aversion to reduce his or her optimal deductible and therefore this would increase the demand for insurance against small losses.     

Moral hazard,asymmetric information and IPO lockups

Moral hazard and asymmetric information have both been proposed as the motive behind the use of IPO lockup provisions, with each receiving empirical support in the literature. Rather than consider them to be mutually exclusive motivations, we hypothesize that each is dominant for a different set of firms. We provide novel empirical support for the underwriter certification hypothesis then use this hypothesis to categorize the firms in our sample. Firms that are certified by a reputable underwriter see a reduction in the severity of asymmetric information relative to other firms and therefore will be more likely to see moral hazard as the friction that motivates the use of the lockup provision. For those firms that are unable to obtain high reputation underwriter certification it is relatively more likely that asymmetric information is the motivation for the use of the lockup provision. Based on this separation of firms we introduce and provide empirical support for a novel set of hypotheses concerning the lockup period.     

Adverse selection and moral hazard: Quantitative implications for unemployment insurance

A model of optimal unemployment insurance with adverse selection and moral hazard is constructed. The model generates both qualitative and quantitative implications for the optimal provision of unemployment insurance. Qualitatively, for some agents, incentives in the optimal contract imply consumption increases over the duration of non-employment. Calibrating the model to a stylized version of the U.S. economy quantitatively illustrates these theoretical predictions. The optimal contract achieves a welfare gain of 1.94% relative to the current U.S. system, an additional 0.87% of gains relative to a planner who ignores adverse selection and focuses only on moral hazard.     

Disease‐Specific Moral Hazard and Optimal Health Insurance Design for Physician Services

This article analyzes disease‐specific moral hazard effects in the demand for physician office visits and explores whether optimal insurance for physician services should be designed to have disease‐specific cost sharing. Generalized method of moments is implemented to address the endogeneity of private health insurance, and the nonnegativity and the discreteness of physician services use. The results indicate that the moral hazard effect varies considerably across disease‐specific specialist care. The strongest moral hazard (for no‐condition related specialist visits) is almost twice the moral hazard effect of the weakest (for chronic condition related specialist visits). Although the findings indicate some variation in the moral hazard effect across disease‐specific general practitioner visits, the variation is less considerable. The main policy implication is that optimal insurance for physician services should be designed to have differential cost sharing based on disease status rather than to have uniform cost sharing.