Detecting Information Asymmetries

Empirical evidence for the existence of IAs is mixed. Cohen and Siegelman (2010) provide a metastudy on testing for adverse selection in a wide range of insurance markets. They focus on the positive correlation approach and find a correlation

2_{http://www.nhshistory.net/a guide to the nhs.htm} 3_{http://www.londonhealth.co.uk/nhs/index.html}

between risk and insurance in some studies but not others. For example, evidence in health insurance markets appears strongly heterogeneous. Looking at studies which focus on the US market, they find evidence for both the existence of IAs and market efficiency. They also assert that it is necessary to distinguish between different kinds of IA. They conclude that it might be useful to evaluate the circumstances under which adverse selection does or does not arise. This perspective is particularly relevant from a policy perspective, given that we would like to be able to predict efficiency changes based on initial market conditions in the face of any institutional changes. In their work, Cohen and Siegelman (2010) mainly focus on an approach

to detecting IA, developed by Chiappori and Salani´e (1997), which is usually called

the ‘positive correlation test’. This test is still widely used today, despite ongoing developments in the field. The main thrust of the test is to jointly estimate two separate equations. The first captures the probability of buying an insurance contract given the information about an individual which an insurance company will use to calculate the risk premium. The second measures the correlation between these variables and the probability of the insurer making a loss on the contract. The error term in both equations covers all the information about both events which is not used for pricing purposes. If risk and insurance coverage are correlated, this is usually interpreted as indicating that a self-selection process is occurring based on unused variables. Hence, it is useful to estimate the correlation between both equations’ error terms. This approach is often called the ‘positive correlation test’. Formally, this approach can be described by the following equations, where I is an indicator of insurance status and R is an indicator of being at risk, while X is a matrix containing the variables used by the insurance company to calculate the risk premium:

I = Xφ +  (4.1)

and

R = Xψ + η (4.2)

Subsequent literature assesses the problem of multiple dimensions of private in- formation in the context of detecting IA, which is also a focus of this chapter. As Finkelstein and McGarry (2006) (FMG) argue, the correlation between error terms in the ‘Chiappori approach’ is neither a necessary nor a sufficient condition for the

existence of IAs. The authors suggest that misleading results may arise if several characteristics have an impact on both dependent variables (some negatively, some positively) and effects cancel out on average. For example, in addition to an in- dividual’s class of risk, heterogeneity in consumer risk preferences might offset the correlation between the two equations’ error terms. The authors assert that if an econometrician can identify such relevant information, and this information is not used by the insurer for pricing, then including this variable as an additional ex- planatory variable into equations (4.1) and (4.2) will make it possible to detect and separate out this kind of self-selection, despite the second relevant variable having an offsetting effect. This approach, which we call the ‘unused characteristics’ approach, is based on the following equations:

I = Xφ + Zδ +  (4.3)

and

R = Xψ + Zβ + η. (4.4)

where Z represents a matrix containing additional information about the insured but which is not used for pricing. The condition for recognising IAs is that any new variable included in the model affects the probability of both getting insurance and ‘being at risk’. In their study, Finkelstein and McGarry use information that is assumed to be unknown to the insurer in the market for long term care (LTC) in the US.

The unused characteristics approach described above can also be useful if we are interested in selection in terms of pricing, without using ‘unobserved’ information. In contrast to the case mentioned above, Finkelstein and Poterba (2014) focus on a scenario where insurance companies observe, or could observe, relevant customer characteristics, but do not use this information when calculating their risk premium. Analysing the UK annuity market, they show that annuity purchases and the an- nuitant’s mortality are regionally correlated. Assuming that regional information is not used to calculate the risk premium, this is interpreted as an indicator of ad- verse selection. Finkelstein and Poterba’s results raise the question of why insurance companies do not tend to use this kind of information.

Cutler et al. (2008) look for selection within several insurance markets in the US, based on data from the Health and Retirement Study. They also use a dual-

equation model with insurance status and risk occurrence as dependent variables. While conditioning on variables used for insurance pricing, they also include some behavioural variables which are used to measure heterogeneity in risk preference (e.g., seatbelt usage, preventative activities) and individual risk behaviour (e.g., alcohol consumption), which are probably not available to an insurance company. Their findings suggest advantageous selection in the market for life and LTC insurance, but adverse selection for annuities.

Fang et al. (2008) (FKS) develop a similar approach that tries to reveal unused characteristics that drive selection in insurance markets. Assuming unused infor- mation is already partialled out, their approach is based on the regression model:

I = α1+ α2R + νi (4.5)

followed by a regression which includes an unobserved variable, z:

I = γ1+ γ2R + γ3z + µi. (4.6)

It can be shown that the regression based on (4.5) will result after applying the expectation operator into E(ˆα2) = γ2 + γ3θ32, where θ is based on the auxiliary

regression R = θ + θ32z + λi. The detection of IAs is based on the difference between

the estimates for α2 and γ2. Hence, the detected IAs induced by z are defined as

E( ˆα2) − E(ˆγ2) = E(γ2) + E(γ3θ32) − E(γ2) = E(γ3θ32). For advantageous selection,

this difference will be negative, i.e., (γ2 > α2) if γ3 < 0 and z is partially positively

correlated with R. Unlike the approach suggested by FMG, the evidence is not directly based on comparing two different outcomes for z, but on a single coefficient and the partial correlation between z and R.

Both approaches are applied in the literature. For example, Cutler et al. (2008) apply the FMG approach and look for IAs within several insurance markets in the US, based on data from the Health and Retirement Study. Bolhaar et al. (2012) also implement the FMG framework to assess multidimensional asymmetric information in Ireland, whereas the approach developed by FKS is applied by Buchmueller et al. (2013), who analyse advantageous selection using Australian data.

There is little evidence on selection in the market for PHI in England. Prop- per et al. (2001) analyse the dynamics in the demand for PHI between 1978 and 1996 in the UK, using the Family Expenditure Survey. Controlling for consumer

characteristics and health service quality measures, they find that the availability of private healthcare facilities and cohort effects, which might indicate changes in tastes/attitude to PHI, are important factors in deciding whether to purchase PHI. Wallis (2004) also looks for the determinants of demand for PHI in the UK, based on data from the British Household Panel Survey (BHPS). The author evaluates individuals’ switching behaviours and focuses on characteristics which influence the probability of purchasing insurance and those which influence the individual cost of PHI (i.e., the risk premium). The study differentiates between consumer demand- side characteristics and supply-side factors that can influence insurance status, e.g., quality of service.

Another study using BHPS data was carried out by Olivella and Vera-Hern´andez

(2013), who focused on adverse selection in the market for PHI, using hospitalisa- tion as a measure for being at risk. Assuming that an individual’s health status is independent of receiving PHI as a fringe employment benefit, their results suggest the existence of adverse selection in the PHI market in England.

Until now, there has been no empirical investigation into whether specific sources of selection exist in the English PHI market.