Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

• Date: 01 December 2014
• Published date: 01 December 2014
• Author: Ruud H. Koning,Laura Spierdijk
• DOI: http://doi.org/10.1111/j.1539-6975.2013.01518.x

©

DOI: 10.1111/j.1539-6975.2013.01518.x

803

ESTIMATING OUTSTANDING CLAIM LIABILITIES:

THE ROLE OF UNOBSERVED RISK FACTORS

Laura Spierdijk

Ruud H. Koning

ABSTRACT

This article proposes a new method for estimating claim liabilities. Our

approach is based on the observation from contract theory that there is

information asymmetry between the insurer and the policyholder about the

risks incurred by the latter. We show that unobserved heterogeneity allows

for a form of experience learning that can reduce this asymmetry, which

makes it easier for the insurer to distinguish between high-risk and low-risk

claimants. We evaluate our approach in the context of disability insurance

for self-employed and show that it results in more accurate best estimates of

outstanding claim liabilities.

INTRODUCTION

Risk-based estimates of liabilities are the basis for determining evidence-based un-

derwriting criteria and calculating insurance premiums. Moreover, the Solvency II

Directive requires insurance companies to base loss reserves on risk-based estimates

of liabilities (Sandstr¨

om, 2011).

The actuarial literature describes two ways of estimating liabilities in the general

insurance business. The first approach uses aggregate claim data, which makes it

hard to relate person-specific risk factors to individual claim sizes (Zhao and Zhou,

2010). The second approach is based on a statistical model that captures the relation

between individual claim sizes on the one hand and person-specific characteristics or

other relevant risk factors on the other hand (e.g., Czado and Rudolph, 2002; Larsen,

2007; Zhao, Zhou, and Wang 2009; Antonio and Plat, 2010; Zhao and Zhou, 2010;

Levantesi and Menzietti, 2012). The statistical model is used to estimate the claim

size distribution of a single policyholder with certain risk factors, which provides

Laura Spierdijk and Ruud H. Koning are at the Department of Economics, University of

Groningen. The authors can be contacted via e-mail: l.spierdijk@rug.nl and r.h.koning@rug.nl,

respectively.The authors are grateful to seminar participants at Vrije Universiteit Amsterdam,

Utrecht School of Economics, University of Mannheim, and Achmea. In particular, we thank

Bas van der Klaauw, Maarten Lindeboom, Gerard van den Berg, Wolter Hassink, Gijsbert

van Lomwel, Theo Beekman, and two anonymous referees for their useful comments. We are

grateful to Bob Dr¨

oge for advice on the use of the Millipede cluster. The usual disclaimer

applies.

The Journal of Risk and Insurance, 2013, Vol. 81, No. 4, 803–830

804 THE JOURNAL OF RISK AND INSURANCE

input for the estimate of an individual liability.Subsequent aggregation of individual

liabilities yields a risk-based liability at the aggregate portfolio level.

The economic literature has emphasized the importance of individual-specific unob-

served heterogeneity (alternatively known as frailty) in modeling individual-specific

risks such as unemployment and disability (Van den Berg,2001). Unobserved hetero-

geneity is generally modeled as an individual-specific random effect that is uncor-

related with the model’s observed risk factors. Ignoring unobserved heterogeneity

may result in biased model coefficients; in survival models it may also lead to overes-

timation of the degree of negative duration dependence (Lancaster, 1990). Actuarial

studies usually ignore unobserved heterogeneity (see also “Literature Review”).

The goal of this research is to make a connection between the actuarial and economic

literature by accounting for individual-specific unobserved heterogeneity in the esti-

mation of insurance liabilities from individual claim data. Our approach is based on

the observation from contract theory that there is information asymmetry between

the insurer and the policyholder about the risks incurred by the latter (Chiappori and

Salanie, 2003). We show that unobserved heterogeneity allows for a form of experi-

ence learning that can reduce this asymmetry, which makes it easier for the insurance

company to distinguish between high-risk and low-risk claimants. The experience

learning entails that we update the distribution of a claimant’s unobserved risk fac-

tors on the basis of his or her claim history. This approach is expected to result in

more accurate best estimates of outstanding claim liabilities.

The principle of experience learning is well known in the actuarial literature (see e.g.,

Herzog, 2010). In practice, it is widely applied in automobile insurance, where the

information asymmetry between insurer and policyholder about the latter’s riskiness

is mitigated by means of a bonus-malus system (Ludovski and Young, 2010). The

difference with our approach concerns the role of the unobserved risk factors, but we

share the goal of reducing the information asymmetry between insurer and claimant

by using the information contained in the claim history.

Our approach is general and can be applied to several types of insurance, including

disability,long-term care, and unemployment insurance. In this study we use disabil-

ity insurance (also known as income insurance) for self-employed workers to illustrate

our approach. Unobserved heterogeneity has been shown to explain a substantial part

of the differences in the return-to-work process between self-employed (see Spierdijk

et al., 2009). Examples of unobserved risk factors are risk aversion, motivation to

recover, willingness to take prescribedmedication, and individual workplace hetero-

geneity. We evaluate the performance of our method using a data set of approved

disability claims filed by Dutch self-employed workers during the period August

2004–July 2010.

In our method of calculating liabilities for income insurance the unobserved risk

factors account for the phenomenon of inertia: claimants who have been sick for

several months have a higher risk of being trapped in long-term disability than similar

individuals who have just started a disability spell. The former group of claimants

is more likely to have unfavorable unobserved risk factors that account for long

and severe disability durations. The longer his or her outstanding claim duration,

ceteris paribus, the higher an existing claimant’s risk of suffering from unfavorable