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Testing for asymmetric information using "unused observables" in insurance markets: evidence from the U.K. annuity market.


This article tests for asymmetric information in the U.K. annuity market of the 1990s by trying to identify "unused observables," attributes of individual insurance buyers that are correlated both with subsequent claims experience and with insurance demand but that insurance companies did not use to set insurance prices. Unlike the widely used positive correlation test for asymmetric information, which searches for a positive correlation between insurance demand and risk experience, the unused observables test is not confounded by heterogeneity in individual preference parameters that may affect insurance demand. We identify residential location as an unused observable in the U.K. annuity market of this period. Even though residential location was observed by all market participants, the decision not to condition prices on it created the same types of market inefficiencies that arise when annuity buyers have private information about mortality risk. Our findings raise questions about how insurance companies select the set of buyer attributes that they use in setting policy prices. In the decade following the period that we study, U.K. insurance companies changed their pricing practices and began to condition annuity prices on a buyer's postcode.


Asymmetric information is widely recognized as hindering the efficient operation of insurance markets, but whether it is present in specific markets remains a subject of active research. In recent years, numerous studies have tested for asymmetric information in a variety of different insurance markets. This work has been largely based on the "positive correlation" test described by Chiappori and Salanie (2000). This test rejects the null hypothesis of symmetric information when there is a positive correlation between insurance purchases and risk occurrence, conditional on the buyer characteristics that are used to set insurance prices.

A limitation of the positive correlation test, noted by Finkelstein and McGarry (2006) and Chiappori et al. (2006), is that it breaks down when individuals have private information about characteristics other than risk type, such as risk preferences, and when these other characteristics affect insurance demand. A number of studies, reviewed by Cutler, Finkelstein, and McGarry (2008) and by Einav, Finkelstein, and Levin (2010), suggest that this type of preference heterogeneity plays an empirically important role in many insurance markets.

This article illustrates an alternative, and quite straightforward, test for asymmetric information that is robust to the existence of preference heterogeneity in insurance demand. When some attributes of insurance buyers that are correlated with insurance demand and subsequent risk experience are not used to price insurance policies, then insurance buyers effectively have private information about their risk type. This may occur even when insurance companies observe, or could observe, the relevant individual characteristics, but choose not to use them in pricing. We refer to this situation as one of "asymmetrically used" information to distinguish it from the more classic "asymmetric information" that results when features of the contracting environment make it impossible for the insurer to observe risk-relevant characteristics of consumers. Asymmetrically used information has similar implications for market equilibrium and market efficiency as the more classic "asymmetric information."

We test for asymmetrically used information by asking if we can identify individual characteristics that are risk relevant and correlated with insurance demand, but that are not used by insurance companies in designing the contract menus facing individuals. We refer to this as the "unused observables" test.

Regulation can be one source of "asymmetric use" of information in insurance markets. When insurance companies are prevented from using some individual characteristics in pricing insurance policies, buyers who know these characteristics and their relationship to risk type can exploit this information. In many insurance markets, however, asymmetrically used information occurs because insurance companies voluntarily choose not to price on the basis of risk-related buyer information that they collect, or could collect. We explore this ostensible puzzle in more detail below. We suggest that concerns about regulatory response and consumer backlash may contribute to this behavior, but we stop short of providing any evidence to support this conjecture.

We illustrate the use of the unused observables test in the retirement annuity market in the United Kingdom in the 1990s. In the United Kingdom, those who saved for retirement through tax-preferred savings vehicles--the equivalent of IRAs or 401(k)s in the United States--were, until 2011, required to purchase annuities. Even when annuitization was compulsory, annuity buyers nevertheless had substantial flexibility with regard to their contract choice, and we test for whether asymmetric information appears to affect these choices.

Understanding the nature of the information structure in retirement annuity markets is of substantial interest in its own right. Annuity markets have attracted attention in light of Social Security reform proposals in various countries to partly or fully replace government-provided defined benefit, pay-as-you-go retirement systems with defined contribution systems in which individuals would accumulate assets in individual accounts. Whether the government should require individuals to annuitize some or all of their balance and whether it should allow choice over the type of annuity product purchased are two important policy design issues. The relative attractiveness of these various options can depend critically on the information structure in the private annuity market.

We implement the unused observables test with a data set containing information on the annuity policies sold by a large U.K. insurance company in the late 1980s and the 1990s. During the time period we study, the company collected information on the annuitant's place of residence but did not use this information to set prices. In this regard, the firm we study was following standard practice in the industry at the time. We find that conditional on the insurance company's risk classification, which is based on the annuitant's age and gender, an annuitant's place of residence helps to predict future mortality experience. In particular, summary measures describing the socioeconomic status in the annuitant's postcode have such predictive power. Moreover, annuitants in higher socioeconomic status residential locations purchase larger annuities. These two findings lead us to conclude that place of residence is an unused observable variable that, when not used in annuity pricing, gives rise to a market that operates as though there was asymmetric information.

In Finkelstein and Poterba (2004), we applied the positive correlation test in the U.K. annuity market, using data from a different insurance company and for the time period 1981-1998. We rejected the null of symmetric information. Implementing the unused observables test in the same market serves several purposes. First, as we discuss in more detail below, the unused observables test is a more robust test of asymmetric information than the positive correlation test. Second, the unused observables test may offer some insight into the sources of private information about mortality risk. In our context, it suggests that socioeconomic status is one key source of mortality information that is not priced by insurance companies. Finally, our current analysis raises interesting questions concerning why insurance companies voluntarily forgo pricing on risk-relevant observable characteristics.

This article is divided into six sections. The first describes previous work on asymmetric information, in particular the widely used positive correlation test. The second section explains the unused observables test. We discuss its strengths and limitations relative to both the positive correlation test of Chiappori and Salanie (2000) and the cost curve test of Einav, Finkelstein, and Cullen (2010). Section 3 summarizes the data set on annuity policies that we analyze. Section 4 presents our key findings and discusses their interpretation. The fifth section discusses why insurance companies might voluntarily choose not to price on risk-relevant observable characteristics, and briefly describes more recent developments in the U.K annuity market that have resulted in widespread use of postcode-based prices. We suspect that political economy concerns are likely to play an important role in company decisions. The sixth section is a brief conclusion that considers the implications of our findings for equilibrium in other insurance markets.


Most of the classic models of equilibrium with either adverse selection or moral hazard predict that those who buy more insurance should be more likely to experience the insured risk (Cawley and Philipson, 1999; Chiappori and Salanie, 2000). With moral hazard, insurance coverage lowers the cost of the insured outcome and thus increases the expected loss. With adverse selection, the insured knows more about risk type ex ante than the insurance company does, and at a given price, those who are a higher risk type have more demand for insurance.

This insight underlies the most common test for asymmetric information in insurance markets: the positive correlation test. This test estimates the correlation between the amount of insurance an individual buys and his ex post risk experience, conditional on the observable characteristics that are used in pricing insurance policies. It is essential to condition on all the information that is used to set insurance prices. Finding, for example, that smokers demand more life insurance than nonsmokers, and that they also have higher mortality risk, does not provide evidence of asymmetric information if insurance contracts are priced differently for smokers and nonsmokers. Results from the positive correlation test as well as the unused observables test are always conditional on the risk classification that the insurance company assigns to the individual.

The canonical positive correlation test involves estimating two reduced-form econometric models: one for insurance coverage (C) and the other for risk of loss (L). For simplicity we present linear versions of both models. The explanatory variables (X) in both equations are the set of variables that the insurance company uses to place the buyer into a risk class. The estimating equations are:

[C.sub.i] = [X.sub.i] * [beta] + [[epsilon].sub.i] (1a)


[L.sub.i] = [X.sub.i] * [gamma] + [[mu].sub.i]. (1b)

Under the null hypothesis of symmetric information, [[epsilon].sub.i] and [[mu].sub.i] should be uncorrelated. A statistically significant positive correlation between the two rejects the null hypothesis and points to asymmetric information.

Positive correlation tests have yielded a variety of findings in different insurance markets. Cohen and Siegelman (2010) review this literature. In health insurance markets, the preponderance of evidence, reviewed, for example, by Cutler and Zeckhauser (2000), suggests a positive correlation between insurance coverage and risk occurrence, although there are important exceptions such as Cardon and Hendel (2001). In other health-related markets, however, the findings are less supportive. Finkelstein and McGarry (2006) find a negative correlation between insurance coverage and risk occurrence in long-term care insurance, and Fang, Keane, and Silverman (2008) present a similar finding for Medigap insurance. In the automobile insurance market, Chiappori and Salanie (2000), Dionne, Gourieroux, and Vanasse (2001), and Chiappori et al. (2006) find that insurance coverage and risk occurrence are uncorrelated, while Cohen (2005) finds a positive correlation.

A striking--and potentially revealing--difference emerges when the positive correlation test is applied in life insurance and annuity markets, two markets that insure opposite mortality risks.

In the life insurance market, Cawley and Philipson (1999) and McCarthy and Mitchell (2010) find no evidence of a positive correlation between insurance purchase and the risk of dying soon. However, in the annuity market, Finkelstein and Poterba (2002, 2004) and McCarthy and Mitchell (2010) find a positive correlation between annuity demand and the risk of long life. One possible explanation for these different findings is that insurance demand is determined not only by private information about risk type but also by heterogeneity in risk tolerance. All else equal, more risk-averse individuals are likely to demand more annuity coverage and more life insurance. Wealthier individuals might also demand more insurance of both types. However, risk aversion and wealth are likely to be negatively correlated with the risk of dying early, and positively correlated with the risk of living a long time, since more risk-averse and wealthier individuals may invest more in life-extending activities. Cutler, Finkelstein, and McGarry (2008) provide evidence consistent with this explanation. (1)

As the foregoing discussion illustrates, when individuals have different tastes for insurance, the correlation between [[epsilon].sub.i], and [[mu].sub.i], in Equations (1a) and (1b) can no longer be attributed only to unobserved differences in risk of loss. When individuals have private information about their risk type ([Z.sub.1]) and they also exhibit different degrees of risk aversion ([Z.sub.2]), the residuals from (1a) and (1b) can be written

[[epsilon].sub.i] = [Z.sub.1,i] * [[pi].sub.1] + [Z.sub.2,i]*[[pi].sub.2] + [[eta]'.sub.i] (2a)


[[u].sub.i] = [Z.sub.1,i] * [[rho].sub.1] + [Z.sub.2,i] * [[rho].sub.2] + [v.sub.i]. (2b)

The logic of the positive correlation test assumes that private information risk type ([Z.sub.1]) is positively correlated with both insurance coverage and the risk of loss ([[pi].sub.1] > 0 and [[rho].sub.i] > 0). If risk aversion ([Z.sub.2]) is also positively correlated with coverage, but it is negatively correlated with risk of loss ([[pi].sub.2] > 0 and [[pi].sub.2] < 0), then the correlation between [[epsilon].sub.i], and [[mu].sub.i] may be negative or zero. In this case, the positive correlation test would fail to reject the null hypothesis of symmetric information even in the presence of private information about risk type.

This example illustrates how unobserved heterogeneity in individual preferences can lead to Type II errors in applications of the positive correlation test. De Meza and Webb (2001), Jullien, Salanie, and Salanie (2007), Chiappori et al. (2006), and others develop equilibrium models that illustrate how preference-based selection may offset risk-based selection, making insurance coverage and risk occurrence uncorrelated or even negatively correlated (so-called "advantageous" or "propitious" selection). Einav and Finkelstein (2011) illustrate graphically the nature of equilibrium with adverse and advantageous selection, illustrating how advantageous selection creates overinsurance relative to the efficient allocation, in contrast to the classic underinsurance created by adverse selection.

Several empirical studies suggest the practical importance of preference heterogeneity in insurance markets. Davidoff and Welke's (2004) analysis of the reverse annuity mortgage market, Fang, Keane, and Silverman's (2008) study of the Medigap market, and Finkelstein and McGarry's (2006) study of the long-term care insurance market provide evidence that unobserved preferences for insurance are negatively correlated with unobserved risk type. In contrast, Cohen and Einav's (2007) study of auto insurance and Einav, Finkelstein, and Schrimpf's (2010) analysis of the U.K. annuity market suggest that unobserved preferences for contracts are positively correlated with risk-selection-related demand, thus reinforcing the positive correlation between insurance coverage and risk occurrence created by private information about risk type.


In a symmetric information environment, when it is costless for an insurance company to observe buyer attributes and condition the price of insurance policies on these attributes, insurance contracts should be conditioned on any buyer characteristics that are correlated with both demand for insurance coverage and risk of loss. Finding a buyer characteristic that is either unknown to or unused by the insurer, and that is correlated both with demand for insurance coverage and with ex post risk of loss, implies that the insurance market operates as if there were asymmetric information. The "as if" statement is important because even if there are no technical barriers to the insurer observing some buyer attributes, if insurers do not condition policy prices on this information, the efficiency attributes of the market equilibrium will resemble those of a market in which sellers are prevented from observing buyer type.

The unused observables test that we implement involves a straightforward search for observable buyer attributes that are both demand related and correlated with risk of loss. This test can be formalized using the foregoing notation in which X denotes the attributes that are used to assign a potential insurance buyer to a risk class, C denotes insurance coverage, and L denotes risk of loss. W, a candidate unused observable variable, could be an element of either [Z.sub.1] (risk type) or [Z.sub.2] (risk preference). The estimating equations for the unused observable test are:

[C.sub.i] = [X.sub.i] * [beta] + [W.sub.i] * [alpha] + [[epsilon]'.sub.i] (3a)


[L.sub.i] = [X.sub.i] * [gamma] + [W.sub.i] * [delta] + [[mu]'.sub.i]. (3b)

Rejecting {[alpha] = 0, [delta] = 0} is tantamount to rejecting the null hypothesis of symmetric information, regardless of the signs of [alpha] and [delta]. By investigating several candidate W variables, we can also learn something about the nature of private information in the insurance market.

Implementation of the unused observables test requires individual data on (1) insurance coverage, (2) ex post risk experience, (3) the characteristics used by insurance companies in pricing insurance, and (4) at least one individual characteristic that is not used in setting prices. The positive correlation test requires the first three types of data, and the settings in which it has been applied often provide opportunities for collecting the fourth. Household surveys, for example, have been used to implement the positive correlation test in various insurance markets. Such surveys often include information on individual attributes such as wealth, parental health history, seat belt use, and occupation, most of which are not used to condition insurance prices. These attributes vary in the extent to which they could be collected by the insurance company, and in the cost that would be involved in verifying the reports. Proprietary data that insurance companies have provided to researchers studying insurance makers, which have often been used in positive correlation tests, sometimes include information that companies have not used in pricing. For example, a policyholder's address is almost always collected and used for billing purposes, but it is not always used in setting prices. In addition, in some cases insurance company data may be supplemented with survey information that contains unused observables. For example, Hemenway (1990) conducted an in-person survey of seat belt use and insurance purchases among rental car drivers, and Ivaldi (1996) supplemented a French data set on automobile insurance with a survey of the insured's smoking behavior. Neither variable is used in pricing the respective insurance products.

The unused observables test thus overcomes a limitation of the positive correlation test when there is unobserved preference heterogeneity. An important drawback of the unused observables test, however, is that it is one-sided. Failure to find individual characteristics that are not used in pricing, but that are correlated with risk of loss and insurance demand, may simply reflect a lack of sufficiently rich data, rather than the absence of asymmetric information. Another limitation is that, like the positive correlation test, the unused observables test does not distinguish between adverse selection and moral hazard. We discuss below how it is sometimes possible to use supplementary information to do so.

The "cost curve" test for selection developed by Einav, Finkelstein, and Cullen (2010) is robust to the presence of preference heterogeneity and it is unaffected by the presence, or absence, of moral hazard. However, it imposes a substantially higher data hurdle than either the positive correlation or the unused observables test. In particular, while all three tests require that the econometrician observe insurance coverage and ex post claims (or other measures of expected costs) among individuals who are offered the same set of insurance contracts, the cost curve test also requires variation in the price of insurance coverage that is uncorrelated with insurance demand. Einav and Finkelstein (2011) provide a graphical illustration of the relationship between these tests.


We apply the unused observables test to the United Kingdom's compulsory annuity market in the 1990s. Annuities pay a prespecified payment stream to their beneficiaries, the annuitants, for as long as they are alive, thereby providing a way of spreading an accumulated stock of resources over a lifetime of uncertain length and thus insuring against the risk of outliving one's resources. From the perspective of an insurance company, a higher risk annuitant is one who has a higher chance of a long life.

Insurance Company Data and Descriptive Statistics

During our sample period, 1988 through 1998, retirees who had accumulated savings in tax-preferred retirement saving accounts in the United Kingdom were required to annuitize a large portion of their accumulated balance. They could, however, choose among a number of annuity options that offered different amounts of insurance. There were no restrictions on the characteristics that U.K. insurance companies could use in pricing annuities in this market. Ainslie (2000) reports that in the United Kingdom in the 1990s, the vast majority of annuities, including all of the ones sold by the company that provided data for this study, were priced solely on the basis of the annuitant's gender and age at the time of purchase. This is no longer the case, and the annuity market changed substantially during the most recent decade, as we explain below. To apply the unused observables test for our sample period, we need data on the characteristics used in pricing--gender and age--as well as another characteristic that is related to both survival prospects and annuity demand.

We obtained data from one of the largest U.K. annuity sellers. These data were also used by Einav, Finkelstein, and Schrimpf (2010) to analyze the welfare cost of asymmetric information in the U.K. annuity market. The data set includes information on all of the company's compulsory annuities that were in force in 1998 and that were sold between January 1, 1988 and December 31, 1998. We observe the annuitant's date of death if he died over the 6-year period between January 1, 1998 and February 29, 2004. We also observe detailed information on the type of annuity purchased, and the three characteristics of the annuitant that are used in pricing the annuity: the date of purchase, the annuitant's date of birth, and the annuitant's gender. Finally, we observe a characteristic not used in pricing: the individual's postcode, which indicates his place of residence.

For analytical tractability, we restrict our sample in several ways. We focus on the approximately 60 percent of the sample firm's annuities that insure a single life. The mortality experience of the single life annuitant provides a convenient ex post measure of risk type; measuring the risk type of a joint life policy that insures multiple lives is less straightforward. We also restrict the sample to the approximately 80 percent of annuitants who hold only one annuity policy, thereby avoiding the complexity of modeling the total annuity stream for individuals who hold multiple policies. We restrict attention to the approximately 90 percent of policies sold in England or Wales because we cannot map postcodes in Scotland into the same type of geographic unit that we can for England and Wales. Finally, we exclude annuitants who purchased annuities before age 50, and limit our sample to those who purchased annuities with guarantee periods of 5 or 10 years. These exclusions affect less than 1 percent of our sample. Our final sample consists of 52,824 annuitants.

Table 1 presents summary information on our data sample. The average age at annuity purchase is 62, and 59 percent of the purchasers are male. Our sample characteristics appear to match the characteristics of the broader market, described by Murthi, Orszag, and Orszag (1999), and of other individual firms in the market, such as the one studied in Finkelstein and Poterba (2004). The table also presents summary information on annuity product characteristics that we will discuss below.

Residential Location as an Unused Observable

Each postcode--which encompasses about 40 people--lies wholly within a ward. A ward consists of about 9,000 residents. Our sample includes annuitants from 49,123 unique postcodes and 8,941 unique wards, out of a possible 1.24 million postcodes and 9,527 wards in England and Wales. We link the annuitant's ward to ward-level data on socioeconomic characteristics from the 1991 U.K. Census. The public use version of the U.K. Census does not contain postcode-level data.

Two measures of ward-level socioeconomic status are available in the U.K census: educational attainment and occupation. Educational attainment is reported as the percent of the ward population aged 18 and over that is "qualified," which requires an educational credential above the level of the A-level standard, the equivalent of a good high school degree in the United States. Table 2 provides summary statistics on educational attainment. We report two sets of summary statistics, one weighting each ward by its population and the other weighting each ward by the number of policies from that ward in our sample. The average person in England and Wales comes from a ward in which about 13 percent of individuals are qualified. The average annuitant in our sample, however, comes from a ward in which about 16 percent of individuals are qualified.

The ward-level census data also report the percent of employed people in each ward in different "social classes," which are roughly occupational categories. We compare three groups: professional and managerial (social classes I and II), skilled manual or nonmanual (social class III), and partly skilled or unskilled (social classes IV and V). Table 2 shows that the average person in England and Wales lives in a ward in which about 32 percent of the employed individuals are in professional and managerial occupations, 44 percent in skilled manual or nonmanual occupations, and 22 percent in partly skilled or unskilled occupations. A small "omitted" group is in the armed forces or in another setting that is difficult to classify. The average annuitant in our sample is drawn from a higher social class ward than the average individual in the population. This is consistent with Banks and Emmerson's (1999) findings on annuitants in the U.K. Family Resources Survey.

Census data provide a number of other measures of the attributes of each ward's population. One is a variable on the percent of persons in the ward having a "long-term illness, health problem, or handicap which limits his/her daily activities or the work he/she can do." The average person in England and Wales comes from a ward in which about 12 percent of the population reports having a long-term illness; our average annuitant lives in one in which about 11 percent of the population reports such illness. We investigate whether this ward characteristic helps to predict annuitant survival, since it represents a variable that is not directly related to socioeconomic status but that, if it is known by annuitants but not the insurance company, may provide annuitants with private information about their mortality prospects.

Characteristics of the ward population convey some predictive information about the characteristics of a randomly drawn individual within the ward, but substantially less information than knowing the individual's own characteristics. We calibrate the difference in information by computing the ratio of the variance of an average characteristic across wards to the variance of the characteristic in the population. This ratio is 0.11 for long-term illness, 0.23 for education qualification, 0.26 for an indicator variable for membership in social class I or II, 0.14 for an indicator for social class III, and 0.21 for an indicator for social class IV or V. These ratios suggest that using ward-level means to proxy for an individual's private information is likely to understate the actual degree of asymmetric information in insurance markets. Our estimates of the informational value of the characteristics of an annuitant's ward are also likely to understate the information potentially available to insurers, who observe postcodes rather than wards and could correspondingly have more detailed information on their insurance buyers, particularly if they invested in private information collection efforts that provided more finely graded data than are available in the public-use census.


We test whether the socioeconomic characteristics of the annuitant's ward help to predict the annuitant's survival probability, conditional on the other characteristics that are used in annuity pricing, and then explore the analogous conditional relationship between socioeconomic characteristics and annuity demand.

Geographic Location and Annuitant Survival Rates

We begin by estimating a modified version of Equation (3b), which assumes a linear relationship between risk of loss and the unused observable. In the annuity context, the "risk of loss" is the risk of survival; this is more appropriately estimated by a proportional hazard model of the length of time the annuitant lives after purchasing an annuity:

[lambda](t, [x.sub.i], [beta],[[lambda].sub.0]) = exp([x'.sub.i] [beta]) [[lambda].sub.0](t). (4)

[lambda](t, [x.sub.i], [beta], [[lambda].sub.0]) denotes a hazard function for the probability that an annuitant with characteristics [x.sub.i], dies t periods after 1998, conditional on living until t. Following Cox (1972, 1975), we estimate a continuous-time, semiparametric, partial likelihood proportional hazard model. This allows us to estimate the [beta] coefficients without making parametric assumptions about the form of the baseline hazard [[lambda].sub.0](t). The Cox model readily handles the left truncation and right censoring in our data. In our earlier study of another company's annuitant data, Finkelstein and Poterba (2004), we obtained very similar results using the Cox model and alternative models that allow for a discrete rather than continuous nonparametric baseline hazard as in Han and Hausman (1990). The main covariates of interest are socioeconomic status measures of the annuitant's ward and the annuitant characteristics that are used in pricing.

Table 3 presents our findings. The first column includes as covariates only the annuitant characteristics used in pricing. The only coefficient shown is for the indicator variable identifying male annuitants; mortality hazards are higher for males. The other covariates, single year- and age-specific indicator variables, are not reported to conserve space, but their coefficients display sensible patterns, such as a rising mortality hazard with age. The second and third columns add ward-level soecioeconomic status measures to the basic specification. Conditional on the characteristics that are used in pricing, the socioeconomic status of the annuitant's ward is statistically significantly and positively correlated with annuitant survival. Column (2) indicates that annuitants from wards in which more individuals are educationally qualified have a statistically significantly lower mortality hazard. Column (3) indicates that those from wards with a greater proportion in managerial and professional occupations (social classes I and II) have a statistically significantly lower mortality hazard than both those in wards with a greater proportion in skilled occupations (social class III) and those in our reference category, partly skilled, or unskilled occupations (social classes IV and V). Finally, column (4) indicates that annuitants from wards in which a greater proportion of the population suffers from long-term illness have a statistically significantly higher mortality hazard.

To illustrate the substantive importance of the findings in Table 3, we use the estimate of the baseline hazard and the hazard model coefficients to compute the implied impact of a change in ward characteristics on the 5-year annuitant mortality rate. Table 4 shows the results. We estimate, for example, that a 65-year-old male annuitant who purchases a policy in 1994 in a ward with the average proportion of qualified individuals and survives until 1998 has a 10.7 percent chance of dying within the next 5 years. The same individual from a ward in which the proportion educationally qualified is one standard deviation above the national average has only a 9.7 percent chance of dying. Similarly, a 65-year-old male has only a 9.3 percent chance of dying if he is from a ward in which the fraction of the population from managerial and professional occupations is one standard deviation above average.

Survival differences of this magnitude can affect the expected present discounted value of an annuity payout stream. We illustrate this by computing how much annual annuity payments would change if insurance companies adjusted prices in an actuarially fair way to account for the relationship we find between ward-level socioeconomic status and annuitant mortality. Our calculation ignores any demand response to such price changes. The actuarially fair annual payment from an annuity depends on the characteristics of the annuity, the annuitant mortality table used, and the interest rate. We focus on a nominal annuity with no guaranteed payments. Since we can only estimate mortality over a 6-year span using our data, for this illustrative calculation we use the annuitant mortality tables for the compulsory annuity market described in Finkelstein and Poterba (2002) for our baseline mortality hazard. We consider a 65-year-old who purchases an annuity on January 1, 1998, and discount future annuity payments using the zero-coupon yield curve of nominal U.K. Treasury securities.

The mortality differences associated with the coefficient estimates in Table 3 imply that if annuity payments were adjusted in an actuarially fair manner based on the proportion of the ward that is educationally qualified, 11 percent of male 65-year-old annuitants and 4 percent of 65-year-old female annuitants would experience a payout change of at least 5 percent. If payments were adjusted based on the proportion of the ward in the managerial and professional class, about 17 percent of men and 8 percent of women would experience a change in annuity payments of 5 percent of more.

Place of Residence as Predictor of Product Selection

The second component of the unused observables test requires examining whether annuitant ward characteristics are correlated with the choice of annuity contract, conditional on the annuitant characteristics used in pricing. In the spirit of Equation (3a), we relate insurance purchases and ward characteristics as follows:

[C.sub.iw] = [alpha] * [X.sub.i] + [beta] * [WARD.sub.w], + [[epsilon].sub.iw]. (5)

In this equation, [C.sub.iw] denotes the type of insurance purchased by annuitant i in ward w, and [X.sub.i] denotes the annuitant characteristics that are used in pricing. As before, X.sub.i], consists of indicator variables for annuitant's gender, age at time of purchase, and year of annuity purchase. Our coefficient of interest is [beta], which is related to the conditional correlation between a ward-level characteristic and insurance demand.

The payouts from the annuity contracts in our data set can be characterized by three features: the initial annual annuity payment, the tilt of the annuity payment stream over time, and the length of the annuity guarantee period. We display summary statistics in Table 1 for these product characteristics for the annuities in our sample. These summary statistics show that 90 percent of the annuities in our sample pay a constant nominal payment stream; the rest provide a payment stream that increases in nominal terms over time. About 82 percent of the annuitants choose guaranteed annuities. During the guarantee period, the insurance company will continue to make payments to the annuitant's estate, even if the annuitant dies. Annuitants are allowed to select guarantee periods of up to 10 years; almost 90 percent of guaranteed annuities in our data set have 5-year guarantees.

To estimate Equation (5), we stratify our sample of annuity contracts into subsamples that vary on only one contract dimension, such as the amount of initial payout. We then look at the relationship between ward-level SES and that contract feature. Specifically, we restrict our analysis to the 90 percent of our sample policies that provide constant nominal payments, and stratify these constant nominal annuities into three samples: those with no guarantee, those with 5-year guarantees, and those with 10-year guarantees. Within each of these three subsamples, we examine the relationship between ward-level SES and the log of the initial annual annuity payment. We use a log transformation because of the skewness in the distribution of initial payments.

Table 5 reports the results. The three different panels report results using different ward-level characteristics as right-hand-side variables. The table thus presents results from 12 separate regressions. Across all dependent variables (columns) and all ward-level measures (panels), the results suggest that individuals in wards of higher socioeconomic status or better health are likely to purchase annuities with larger initial payments.

One concern with these results is that our sample of policies is left truncated, since the annuitant must survive from the date of policy purchase until 1998. While such left truncation is easily handled in the hazard model analysis in Table 3, it may bias the linear regression analysis in Table 5. We verified that our results are robust to limiting the sample to the subsample of policies, about 13 percent, sold in 1998. The left truncation problem does not apply to those policies, and the basic findings for this subsample are similar to those for the full sample.

While statistically significant, the magnitude of the relationship between ward-level characteristics and annuity characteristic is modest. A one standard deviation, or 8.1 percentage point, increase in the proportion of the annuitant's ward that is educationally qualified is associated with only a 0.13-0.22 percent increase in initial annuity payment. Results using the other ward-level measures are similarly small in magnitude. Even if the substantive magnitude of the coefficients is modest, the qualitative finding that ward-level socioeconomic status attributes are correlated with insurance demand, taken in conjunction with our earlier finding of a link between these characteristics and survival rates, constitutes a rejection of the null hypothesis of symmetric information.


Our findings provide some information about the form of the private information in annuity markets. The correlation between ward-level socioeconomic status and annuity demand suggests that some of the asymmetric information is related to socioeconomic status. This may reflect "active" adverse selection as prospective annuity buyers recognize that their socioeconomic status may affect their survival prospects. It could also reflect "passive" or "preference-based" selection if socioeconomic status affects demand for insurance for reasons other than its effect on longevity risk, for example, because it is correlated with risk aversion. It is also possible that the findings reflect differences in the degree to which annuitization promotes investments in life-lengthening activities across different groups. Regardless of which effect is operating, there are still adverse efficiency consequences from the asymmetric information.

Our finding that the share of the annuitant's ward reporting long-term illness is also related to the annuitant's insurance purchase seems to offer some support for traditional "active" selection, since long-term illness is less likely to be a marker for preferences for insurance than for risk type. However, ward-level health and socioeconomic characteristics are highly correlated, which makes it difficult to determine the relative importance of these various selection factors.

A related question is whether the positive correlation between insurance demand and annuitant survival found in earlier studies can be explained by the unused observables we have identified, or whether other unobservable factors underlie selection. We investigate this by replicating the previous positive correlation finding in the current data set. Following Finkelstein and Poterba (2004), we estimate a proportional hazard model of length of time lived after purchasing an annuity, as in Equation (4). The covariates of interest are the three annuity product characteristics that affect the quantity of insurance in the annuity contract: initial annual annuity payment, length of guarantee period, and degree of backloading. We control for annuitant characteristics used in annuity pricing and for payment frequency.

The first column of Table 6 presents the results of this replication exercise. We find evidence of positive correlation: annuitants who purchase guaranteed policies, which offer lower payouts than nonguaranteed annuities in the state of the world in which the annuitant survives, display higher mortality rates, that is, are lower risk from the insurance company's perspective, than annuitants who do not purchase guarantees. Those who choose larger initial annuity policies have a lower mortality risk, that is, are higher risk. There is a statistically insignificant finding that annuitants who purchase constant nominal annuities exhibit higher mortality rates than individuals who purchase more backloaded ones.

The remaining columns of Table 6 add controls for characteristics of the annuitant's ward to the analysis in the first column. The results in columns (2) through (4) indicate that the addition of ward-level characteristics does not fully attenuate the positive correlation between dimensions of the insurance contract that provide additional coverage and ex post risk type. This suggests that there are additional unobserved annuitant characteristics that we have not measured that affect selection in this market.

Moral Hazard Versus Selection

The unused observables test, like the positive correlation test, is a test for asymmetric information. Without additional information, rejecting the null hypothesis of symmetric information does not offer evidence on the question of whether asymmetric information results from moral hazard or from selection. In some cases, such additional information may be available. For example, when a researcher has evidence suggesting that an unused observable variable is correlated with risk of loss even among individuals who have identical insurance coverage, then finding that individuals with certain values of the unused observable select more insurance coverage supports the presence of selection based on ex ante private information rather than of moral hazard based on ex post private information. In contrast, the positive correlation test cannot distinguish between selection and moral hazard.

Since our empirical findings suggest that socioeconomic status is related to mortality risk and annuity demand, the central question concerns whether socioeconomic status is correlated with mortality risk even in the absence of any induced differences in individual behavior that may be associated with interpersonal differences in insurance coverage. If it is, then socioeconomic status represents a source of ex ante private information for would-be annuity buyers. A substantial body of evidence, surveyed, for example, by Cutler, Deaton, and Lleras-Muney (2006) and Meara, Richards, and Cutler (2008), documents the positive relationship between socioeconomic status and survival. Examples of studies that support this pattern are Attanasio and Emmerson (2001) and Attanasio and Hoynes (2000).

Analysts differ on why socioeconomic status is correlated with survival rates, but our reading of the available evidence suggests that differential annuity coverage is unlikely to be a primary factor. In the United States, where the private annuity market is small and annuitized income comes predominantly from employer-provided defined benefit pension plans and the public Social Security system, Brown and Finkelstein (2008) show that a larger proportion of wealth is annuitized for lower than for higher socioeconomic status individuals. Annuity-induced moral hazard effects would therefore operate to offset the observed positive correlation between survival rates and socioeconomic status, rather than to reinforce it. In the United Kingdom, there is evidence that the positive relationship between socioeconomic status and longevity also exists among preretirement individuals who are not receiving any annuitized payments. Data from the Office of National Statistics (1997) show that cumulative survival probabilities in the United Kingdom for men below age 55 are higher for men in higher social classes, even though men at these ages are not likely to be enrolled in any annuity-type schemes.

In light of this external evidence, we interpret our finding of a link between a ward's socioeconomic characteristics and annuitant product choice as supporting the presence of selection. We do not rule out the potential presence of moral hazard as well. Further work on the distinction between selection and moral hazard is a high priority, since the two have very different implications for public policy.


Our empirical results suggest that U.K. insurance companies in the 1990s were not using all of the publicly available information that was related to mortality risk and annuity demand in pricing annuities. This raises the interesting question of why these firms were not taking advantage of the opportunity to price on an observable risk factor. Similar questions arise in many other insurance markets. For example, for automobile insurance, Carter (2005) reports that in the United States, most insurers use simple pricing formulae based on a driver's age and place of residence. In the French automobile insurance market, Ivaldi (1996) finds a difference between automobile accident rates for smokers and nonsmokers that is as large as the difference between men and women, yet insurance is not priced on the basis of smoking status. Brown and Finkelstein (2007) find that at the time of their study, premiums in the U.S. long-term care insurance market were constant across place and gender, even though these attributes predict substantial differences in expected nursing home utilization and cost. In early 2013, Stern (2013) reports, Genworth, the largest seller of long-term care insurance in the United States, introduced differential pricing for men and women, Many other long-term care insurers were expected to follow suit.

Profit-Maximizing Conditioning on Buyer Attributes

In general, one would expect insurers to use a risk-related characteristic of the insured in pricing whenever the costs of collecting the information and differentiating policy prices on the basis of it is less than the incremental profitability of using the variable in differentiating prices. Regulation may alter this calculus. In many U.S. states, for example, regulators restrict the characteristics that may be used in pricing automobile insurance. In such cases, it is relatively uninteresting to test the null hypothesis of symmetric information. The key question is the extent of asymmetric information created by such regulations and the magnitude of the associated efficiency effects.

The more interesting cases, like those from the U.K. annuity market, the U.S. long-term care insurance market, and the French automobile insurance market, involve information on individual characteristics that insurance companies could collect and use in setting prices, but that they choose not to use. The puzzle of unexploited information is particularly acute for variables such as gender and geography that are collected by default. Although there may be some cost to processing this information and determining how to set characteristic-based prices, it seems unlikely that costs of information acquisition can explain the limited use of such data.

We can offer four potential explanations--there are surely others-for why insurance companies choose not to use information that they collect, or could collect at low cost, in pricing insurance. We view one of these explanations, which focuses on political economy concerns, as the most likely to feature in the explanation.

First, insurance companies may choose not to use easily available, relevant information in pricing if such information is not quantitatively important in improving the prediction of loss outcomes. While this may explain why some buyer characteristics are not used in pricing, our estimates suggest that this explanation does not apply for annuities. The association between ward-level socioeconomic status and annuitant mortality is large enough to translate into nontrivial changes in payouts for a substantial fraction of annuity buyers. Presumably the relationship between annuitant socioeconomic status, a variable that is not currently measured but that could be collected, and annuitant mortality is even larger. There are large disparities based on nonpriced attributes in other markets, too. For example, Brown and Finkelstein (2007) document that the unisex pricing of long-term care insurance generates gender-based effective load differentials valued at nearly half of the policy cost. In this market, insurance companies appear to choose not to condition prices on individual attributes that could materially affect prices.

Second, the predictive content of characteristics such as place of residence may be limited because such characteristics might be subject to change in response to characteristic-based pricing. For a sufficiently large difference in the cost of an insurance policy across different locations, a potential buyer might seek to represent himself as resident in one location, when in fact he resided elsewhere. While this might explain why place of residence was not used in pricing annuities, since a buyer could establish a sham residence, it seems unlikely to be a general answer to the lack of characteristic-based pricing. There are some difficult to change attributes, such as educational attainment and gender, that appear to be correlated with the risk of loss in many insurance markets, but are not used in pricing. These attributes are also likely to be verifiable by the insurance company at modest cost.

Third, using a previously unexploited buyer characteristic for pricing may involve considerable up-front investment to determine the appropriate pricing structure, and competitors may copy the pricing rule without incurring the initial costs. These issues were faced by U.K. insurers as they developed the "impaired life" annuity market shortly after the end of our sample period. Cannon and Tonks (2011) describe the growth of this market. Firms in this market offer substantial discounts to smokers and other individuals who are likely to be in poor health. The initial pricing of these impaired life products involved both considerable investment in actuarial analysis and product development. One of the developers of impaired life products analyzed a database of medical records from life insurance sales around the world to try to predict the relationship between various medical conditions and annuitant mortality. Another impaired life annuity seller contracted with one of the U.K. health authorities for their data on the mortality of individuals in nursing homes and hospitals and then devoted considerable resources to analyzing these data to derive relationships between mortality and health conditions.

The firms that introduced impaired life annuities seem to have been concerned about pricing errors, but not about other firms free-riding on their pricing decisions without paying the costs of determining the appropriate pricing structure. Insurance executives told us that one of the incentives to enter this market early was to build up statistical experience that can be used to refine subsequent pricing. Early entrants gain an informational advantage relative to later-entering competitors, because new rivals can observe the new policy's pricing structure but not the innovator's sales practices and underwriting rules. Potential imitators will not know the criteria that the initial entrant uses to deny coverage to some applicants, and this can be a key determinant of profitability. Firms that emulate the innovator by introducing policies with similar pricing would likely attract some potential buyers who were denied policies by the innovator, and would therefore have a less attractive risk pool than that of the innovator.

While the risk of emulation may not be a primary factor discouraging the use of additional information in annuity pricing, changing practices at other insurers is likely to reduce the profitability of any policy pricing innovation. If the innovator's rivals ultimately adopt pricing rules that condition on the newly exploited individual characteristics, the result may simply be an equilibrium in which all firms incur more up-front costs in pricing insurance policies. The gain in profitability in such a setting may be much smaller than the gain to a monopoly insurer using new information in pricing.

Finally, we consider the political economy issues surrounding the use of new individual characteristics for insurance pricing. Introducing more refined pricing distinctions can have large public relations costs for individual firms and for the insurance industry and trigger regulatory changes to ban the use of such information in pricing. Insurance firms contemplating more refined pricing may be concerned about the direct costs of negative publicity, as well as by the prospect of triggering new regulatory initiatives in the largely unregulated annuity market. Postal (2007) describes the adverse public reaction to proposals to use information on credit scores in pricing automobile insurance in U.S. states.

The behavior of large and small firms provides some support for these political economy concerns. Adverse publicity and fear of future regulation should have less impact on small firms or new entrants who do not internalize the costs of increased regulation or lost goodwill to the same extent that large existing firms do. Consistent with this, Ainslie (2000) reports that impaired life annuities were introduced to the U.K. market by new, start-up companies formed expressly for the purpose of offering the impaired annuity products to individuals in observably poor health. Incumbent firms did not follow suit, until, about 5 years after the introduction of these products, the impaired life market had grown to the point where the cream skimming of good risks by the impaired life companies created pressure on the existing companies to expand their pricing system. By that point, the political economy costs of offering impaired life annuities had presumably declined as the public had become accustomed to such products.

The Rise of Postcode Pricing

While postcode pricing was not used for annuities during the sample period we consider, in the 15 years since the end of our sample, it has become standard practice in the U.K. annuity market. When firms initially proposed such pricing rules, in 2003, they faced negative public reaction, illustrated by newspaper stories on "Postcode Prejudice" (Sunday Times, July 13, 2003) and "Postcode Peril" (Manchester Evening News, July 7, 2003). Yet at least one firm chose to proceed in the face of such public concern: in 2007, Legal and General adopted postcode-based payouts. By offering higher payouts to those in relatively poor and unhealthy locations, the firm saw an opportunity to expand market share while still earning an acceptable return on these policies because of the higher average mortality risk of the insured population. Within a few years of this development, postcode pricing had become the norm, as other insurance firms saw that the consumer reaction to these products was in fact modest, and as competitive forces dictated matching the favorable payouts offered in some locations by firms that used postcode information.

U.K. insurance companies in many cases created several pricing categories to which postcodes were assigned. Lander (2008), for example, reports that when Norwich Union, a large annuity provider, began to condition its annuity prices on a buyer's postcode, marital status, and smoking habits, it classified postcodes into nine distinct pricing bands. De (2011) collected data on annuities that were offered to residents in the Bristol metropolitan area, and found that most insurers offered a relatively small number (often less than 10) of different postcode-based prices. There was variation across insurers in the relative prices in different postcodes. Actuaries describing the shift to using postcodes noted that this evolution of the annuity market was natural, since other markets, such as those for auto and homeowner's insurance, already use location-based prices. Burrows (2010) illustrates the differences in the annual annuity payment to a 65-year-old man purchasing a 100,000 [pounds sterling] policy at the start of 2010. A resident of London would receive payouts 4.28 percent smaller than those of someone residing in Glasgow or Birmingham, cities with a higher population share in lower socioeconomic status, and less healthy, categories. Cities such as Bristol (2.14 percent) and Cardiff (3.04 percent) were also lower than Glasgow, but not by as much as London.

One factor some commentators identified as facilitating the introduction of postcode-based prices, noted, for example, in Lander (2008), was the increasing availability of detailed data on health and mortality. Insurance companies used such publicly available data, along with their own policy experience, to determine prices for location-specific policies. This suggests that the challenges of pricing based on observed attributes may be a potential barrier to the introduction of these products.

As the U.K. annuity market has become more segmented since the time period of our analysis, with both enhanced annuities for those with medical conditions that might result in shorter-than-average life expectancy as well as postcode pricing, the choice set confronting potential annuity buyers has expanded. Cumbo (2012) reports on a study by MGM Advantage, a financial adviser, which compares annuity purchases by retirees who worked with a financial adviser and those who did not. The former group was much more likely to purchase an enhanced annuity, which offers a higher payout. For those without a financial adviser, MGM estimates that only 2 percent of retirees purchased an enhanced product, even though 70 percent of those over 55 had a medical condition that would qualify them for such a product. The differences between enhanced and standard annuities are substantially larger than those for annuities sold to different postcodes. For Cardiff in 2012, for example, Cumbo (2012) reports that a healthy annuitant would receive 6,223 [pounds sterling] per year when buying a 100,000 [pounds sterling] policy, while a smoker would receive 7,162,15 [pounds sterling] percent more. An annuity buyer with stage one cancer--someone with localized cancer who had received treatment such as chemotherapy in the last 6 months--would receive a payout of 7,677,23 [pounds sterling] percent higher than the healthy buyer. These substantial payout disparities underscore the role that buyer-specific information can play in annuity pricing.

The U.K.'s adoption of postcode pricing does not provide definitive evidence on the factors that lead insurance companies to alter the information set that they use for pricing, but it does offer some guidance. When the costs of processing and underwriting based on a given type of information decline, that information is more likely to be used. It is more difficult to determine how firms assess the consumer and regulatory consequences of new pricing rules, since anything that creates greater heterogeneity in prices is likely to be criticized on distributional grounds. This is an important topic for future analysis.


This article tests for asymmetric information in the U.K. annuity market by implementing an unused observables test involving the annuitant's place of residence. This variable was clearly observed by the company and by outside data analysts, but it was not used by insurance companies in pricing annuities in the 1990s. It is used today, confirming our conclusion that it contained relevant information about future mortality risks.

The unused observable test rejects the null of symmetric information if a characteristic of the individual that is not priced by the insurance company is correlated with both insurance coverage and risk occurrence. This offers a more robust approach to testing for asymmetric information than the widely used positive correlation test. However, the test is one-sided: failure to detect asymmetric information using the unused observable test may simply reflect a lack of sufficiently rich data on potential unused observables, rather than the absence of asymmetric information.

We show that in the U.K. annuity market of the 1990s, the socioeconomic characteristics of an annuitant's geographic location were correlated with both his survival probability and his annuity contract choice. This provides evidence of asymmetric information in the market. As postcodes have become a standard pricing variable more recently, the extent of such private information has declined. Our findings provide some insight into the nature of individuals' private information in the period we study, suggesting that at least part of their private information consisted of information about their socioeconomic status.

Our findings have implications beyond the operation of annuity markets. There is no a priori reason to expect socioeconomic selection to operate in the same direction in all insurance markets, and empirical evidence suggests that it does not. In the annuity market, our findings suggest that socioeconomic selection draws longer-lived, and therefore higher risk, individuals into the market. It therefore reinforces any selection based directly on private information about risk type. In the life insurance market, Banks and Tanner (1999) find that selection based on socioeconomic status also appears to draw longer-lived individuals into the market. Such individuals, however, are low-risk life insurance buyers. Socioeconomic selection may help more generally in explaining differences across insurance markets in the correlations between risk of loss and the quantity of insurance purchased.

A complete understanding of the limited use in pricing of available or collectible risk-related information on insurance buyers remains an open issue. Our reading of the available evidence suggests that the political economy of insurance regulation may play an important role in determining the pricing function. Studying the history of characteristic-based pricing of insurance policies, and the evolution of such pricing in various markets, may offer further insights into how insurance companies decide which variables to use in setting prices. Comparing insuring prices in states with elected and appointed insurance commissioners, for example, might offer insights on the role of endogenous regulation in affecting pricing behavior. These issues are left for future study.

DOI: 10.1111/j.1539-6975.2013.12030.x


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(1) Survival bias is another potential explanation for the absence of finding a positive correlation in life insurance. He (2009) revisits the Cawley and Philipson (1999) life insurance study but restricts attention to potential new life insurance buyers. She finds a positive correlation between life insurance and mortality, and argues that the difference between her results and those in earlier studies is that her analysis avoids survival bias. She notes that those who have private information that they are high mortality buy life insurance and have an elevated risk of early death, which means that they are underrepresented in cross-sectional samples. This is an interesting insight that bears further exploration in other contexts.

Amy Finkelstein and James Poterba are at the Department of Economics, MIT, 77 Massachusetts Avenue, E17-214, Cambridge, MA 02139. They can be contacted via e-mail: and The authors are also affiliated with the National Bureau of Economic Research. They thank Edmund Cannon, Pierre-Andre Chiappori, Richard Disney, Liran Einav, Carl Emmerson, Michael Orszag, Casey Rothschild, Ian Tonks, Michael Wadsworth, Jonathan Zinman, and especially Jeff Brown and Keith Crocker for helpful comments and encouragement; Hui Shan for outstanding research assistance; the National Institute of Aging and the National Science Foundation (Poterba) for financial support; and the generous employees at the firm that provided the data for this study. Poterba is a trustee of the College Retirement Equity Fund (CREF) and of the TIAA-CREF mutual funds, entities that sell retirement saving products including annuities.

Summary Statistics on Annuitant Population at Sample Firm

Number of policies                                      52,824
Number (%) of annuitants who die within sample      5,592 (10.6%)
Number (%) of annuitants who are male               31,329 (59.3%)
Average age at purchase                                  62.2
Number (%) of policies that are constant nominal    47,370 (89.7%)
Number (%) of policies that have guarantees         43,259 (81.9%)
Mean initial payment ([pounds sterling])                1,819
Median initial payment ([pounds sterling])               901
Standard deviation of initial payment                   3,682
  ([pounds sterling])
Average premium ([pounds sterling])                     19,550

Note: The sample consists of single life compulsory
annuities sold between 1988 and 1998 that were still in
force in 1998. The text describes further sample
restrictions. Mortality experience covers the period January
1, 1998 through February 29, 2004. Policies that do not have
constant nominal payouts have payouts that increase over
time in nominal terms. Policies with guarantees continue to
make payments to annuitant estate if the annuitant dies
during the guarantee period. Premium and initial payment are
converted to 1998[pounds sterling] using annual values of
the Retail Prices Index (RPI).

Summary Statistics on Ward-Level Socioeconomic Status and Health Status

                              Annuitant Weighted    Population Weighted

Social Economic Status              Standard              Standard
Measure                   Average   Deviation   Average   Deviation

Qualified                   13.4%      8.00       15.9%      8.15
Social class:               31.6       12.13      36.1       12.13
  Professional and
  managerial (I and II)
Social class: Skilled       43.6       6.95       41.7       7.48
Social class: Partly        21.6       8.03       19.4       2.47
  skilled or unskilled
  (IV and V)
Presence of long-term       12.1       3.44       11.4       3.12

Note: Based on ward-level statistics from 1991 U.K. census.
Population-weighted estimates are constructed weighting each
ward by its population; annuitant-weighted estimates are
constructed weighting each ward by the number of policies
the sample firm has in that ward. The omitted social class,
which consists of those in the armed forces, receiving
annuity payments through government schemes, and "unknown,"
accounts for 3 percent (2.8 percent) of the population-
weighted (annuitant-weighted) sample.

Hazard Models Relating Annuitant Mortality Experience to
Annuitant Gender and Ward-Level Socioeconomic Status

                            (1)      Education (2)

Male                     0.638 ***     0.629 ***
                         (0.0349)      (0.0347)
Percentage of ward                    -0.0150 ***
  that is                              (0.0017)
Percentage of ward
  in professional or
  occupations (social
  classes I and II)
Percentage of ward
  in skilled
  occupations (social
  class III)
Percentage of ward
  with long-term

                         Occupation (3)   Illness (4)

Male                       0.628 ***       0.636 ***
                            (0.0348)       (0.0347)
Percentage of ward
  that is
Percentage of ward        -0.0118 ***
  in professional or        (0.0017)
  occupations (social
  classes I and II)
Percentage of ward          -0.0029
  in skilled                (0.0027)
  occupations (social
  class III)
Percentage of ward                        0.0248 ***
  with long-term                           (0.0043)

Note: Coefficients are from Cox proportional hazard model of
time lived since 1998 (see Equation (4)). N=52,824. In
addition to the covariates shown in the table, all
regressions contain indicator variables for age at purchase
and year of purchase. Heteroskedasticity-robust standard
errors clustered at the ward level are in parentheses. In
column 3, the omitted category is percentage of ward in
partly skilled or unskilled occupations (social class IV or
V). *** denotes statistical significance at the 1 percent

The Effect of Varying Ward Characteristics on Implied
5-Year Mortality Rates for Annuitants

                 Fraction of Ward          Fraction of Ward in
                 Qualified                 Social Class I or II

                    One Standard              One Standard
                      Deviation                 Deviation

          Average   Above Average   Average   Above Average

Male       10.7          9.7         10.7          9.3
Female      4.3          3.7          4.3          3.7

                 Fraction of Ward
                 With Long-Term

                    One Standard

          Average   Below Average

Male       10.9         10.2
Female      4.2          3.8

Notes: Table reports the post-1998 5-year cumulative
mortality probability of an individual who purchased an
annuity at age 65 in 1994, conditional on having survived
until 1998. Cumulative mortality probabilities are derived
from the coefficient estimates in Table 3 and the
corresponding estimate of the baseline hazard (not
reported). For the change in the proportion of the ward in
social class I or II, the individuals are moved to social
class IV or V.

Ward Socioeconomic Status Characteristics and
Quantity of Insurance Purchased

                                       Dependent Variable: Log Initial

                                        Policies With    Policies With
                       Policies With        5-Year          10-Year
                        No Guarantee      Guarantee        Guarantee
                        [N = 7,964]      [N = 35,042]     [N = 4,366]

Percentage of ward     0.0223           0.0271           0.016
  that is                (0.0017) ***     (0.0011) ***     (0.0022) ***
Percentage of ward     0.0154           0.0201           0.0103
  in professional or     (0.0018) ***     (0.0013) ***     (0.0022) ***
  occupation (social
  classes I and II)
Percentage of ward     -0.0012          -0.0010          -0.0054
  in skilled             (0.0029)         (0.0020)         (0.0035)
  (social class III)
Percentage of ward     -0.0373          -0.0438          -0.0284
  with long-term         (0.0046) ***     (0.0029) ***     (0.0052) ***
Mean dependent         6.63             6.30             7.23
  variable ([pounds
  sterling] 1998)

Note: The table reports OLS estimates of Equation (5) on the
sample of policies with constant nominal payouts. Different
columns report results using different dependent variables;
they are all measured in constant, 1998 s[pounds sterling].
Different panels report results using different ward
characteristics on the right-hand side. Each cell (defined
by a column and a panel) reports a coefficient from a
different regression. In addition to the covariates shown in
the table, all regressions include indicator variables for
age and year of purchase and for gender of annuitant. In
Panel B, the omitted category is partly or unskilled social
class (social class IV or V). Standard errors,
heteroskedasticity-robust and clustered at the ward level to
allow for within-ward correlation in the error term, are
shown in parentheses. *** denotes statistical significance
at the 1 percent level.

Hazard Model Relating Mortality to Annuity Policy
Characteristics and Ward Characteristics

                                  (1)           (2)

Male                          0.630 ***     0.621 ***
                              (0.0355)      (0.0354)
Constant nominal              0.047         0.048
  indicator                   (0.049)       (0.049)
Guarantee indicator           0.083 **      0.076 *
                              (0.0391)      (0.0400)
Initial payment               -0.013 ***    -0.009
  (1,000 [pounds sterling])   (0.0040)      (0.0058)
Percentage of ward that                     -0.014 ***
  is educationally                          (0.0018)
Percentage of ward
  with long-term
Percentage of ward in
  professional or
  occupation (social
  classes I and II)
Percentage of ward in
  skilled occupations
  (social class III)

                                  (3)           (4)

Male                          0.628 ***     0.620 ***
                              (0.0354)      (0.0355)
Constant nominal              0.045         0.050
  indicator                   (0.049)       (0.049)
Guarantee indicator           0.079 **      0.076 *
                              (0.0400)      (0.0400)
Initial payment               0.012 **      -0.009
  (1,000 [pounds sterling])   (0.0059)      (0.0058)
Percentage of ward that
  is educationally
Percentage of ward            0.024 ***
  with long-term              (0.0043)
Percentage of ward in                       -0.011 ***
  professional or                           (0.0017)
  occupation (social
  classes I and II)
Percentage of ward in                       -0.003
  skilled occupations                       (0.0027)
  (social class III)

Note: Coefficients are from Cox proportional hazard model of
time lived since 1998 (see Equation (4)). N = 52,824. In
addition to the covariates shown in the table, all
regressions contain individual dummies for age at purchase
and year of purchase (1988-1998) and frequency of annuity
payments. Standard errors are in parentheses. They are
heteroskedasticity-robust standard errors and are clustered
at the ward level to allow for within-ward correlation in
the error term. ***, **, * denote statistical significance
at the 1 percent, 5 percent, and 10 percent levels,
respectively. Reference category for "constant nominal
indicator" is a more backloaded annuity. In column 4, the
omitted category is social classes IV and V (partially
skilled or unskilled occupation).
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Article Details
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Author:Finkelstein, Amy; Poterba, James
Publication:Journal of Risk and Insurance
Article Type:Abstract
Geographic Code:4EUUK
Date:Dec 1, 2014
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