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Models of mortality often require constraints in order that parameters may be estimated uniquely. It is not difficult to find references in the literature to the “identifiability problem”, and papers often give arguments to justify the choice of particular constraint systems designed to deal with this problem. Many of these models are generalised linear models, and it is known that the fitted values (of mortality) in such models are identifiable, i.e., invariant with respect to the choice of constraint systems. We show that for a wide class of forecasting models, namely ARIMA $(p,\delta, q)$ models with a fitted mean and $\delta = 1$ or 2, identifiability extends to the forecast values of mortality; this extended identifiability continues to hold when some model terms are smoothed. The results are illustrated with data on UK males from the Office for National Statistics for the age-period model, the age-period-cohort model, the age-period-cohort-improvements model of the Continuous Mortality Investigation and the Lee–Carter model.

The Age-Period-Cohort-Improvement (APCI) model is a new addition to the canon of mortality forecasting models. It was introduced by Continuous Mortality Investigation as a means of parameterising a deterministic targeting model for forecasting, but this paper shows how it can be implemented as a fully stochastic model. We demonstrate a number of interesting features about the APCI model, including which parameters to smooth and how much better the model fits to the data compared to some other, related models. However, this better fit also sometimes results in higher value-at-risk (VaR)-style capital requirements for insurers, and we explore why this is by looking at the density of the VaR simulations.

Longevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.

Mortality data are often classified by age at death and year of death. This classification results in a heterogeneous risk set and this can cause problems for the estimation and forecasting of mortality. In the modelling of such data, we replace the classical assumption that the numbers of claims follow the Poisson distribution with the weaker assumption that the numbers of claims have a variance proportional to the mean. The constant of proportionality is known as the dispersion parameter and it enables us to allow for heterogeneity; in the case of insurance data the dispersion parameter also allows for the presence of duplicates in a portfolio. We use both the quasi-likelihood and the extended quasi-likelihood to estimate models for the smoothing and forecasting of mortality tables jointly with smooth estimates of the dispersion parameters. We present three main applications of our method: first, we show how taking account of dispersion reduces the volatility of a forecast of a mortality table; second, we smooth mortality data by amounts, ie, when deaths are amounts claimed and exposed-to-risk are sums assured; third, we present a joint model for mortality by lives and by amounts with the property that forecasts by lives and by amounts are consistent. Our methods are illustrated with data from the Continuous Mortality Investigation.

Several important classes of liability are sensitive to the direction of future mortality trends, and this paper presents some recent developments in fitting smooth models to historical mortality-experience data. We demonstrate the impact these models have on mortality projections, and the resulting impact which these projections have on financial products. We base our work round the Lee-Carter family of models. We find that each model fit, while using the same data and staying within the Lee-Carter family, can change the direction of the mortality projections. The main focus of the paper is to demonstrate the impact of these projections on various financial calculations, and we provide a number of ways of quantifying, both graphically and numerically, the model risk in such calculations. We conclude that the impact of our modelling assumptions is financially material. In short, there is a need for awareness of model risk when assessing longevity-related liabilities, especially for annuities and pensions.

Late-life mortality patterns are of crucial interest to actuaries assessing longevity risk. One important explanatory variable is year of birth. We present the results of various analyses demonstrating this, including a statistical model which lends weight to the importance of year-of-birth effects in both population and insured data. We further find that a model based on age and year of birth fits United Kingdom mortality data better than a model based on age and period, suggesting that cohort effects are more significant than period effects. The financial implications of these cohort effects are considerable for portfolios with long-term longevity exposure, such as annuities written by insurance companies and defined benefit pension schemes.

The endemic Seychelles Scops-owl Otus insularis is a Critically Endangered restricted range species currently only recorded in the upland forest of Mahé, the largest (152 km2) and highest (903 m) island in the granitic Seychelles. We studied the response of colour-ringed individuals to playback of conspecific calls, to determine factors affecting playback reaction, to monitor behaviour and to assess the reliability of current monitoring techniques. Playback of the territorial waugh call was conducted at fixed points (c. 200 m apart) every month along a total transect length of 8.4 km between April 1999 and May 2001. On the basis of responses and movements of marked individuals we identified 12 territories and noted their boundaries. Mean territory length was 2.92 points (approximately 400 m), equivalent to a conservative estimated territory size of c. 12–16 ha. Males were more frequently detected than females/pairs. The probability of detection (males vs. females/pairs) was 0.87 vs. 0.50 on territory; 0.65 vs. 0.26 at fixed points within territories; and 0.58 vs. 0.22 at fixed points along the transect. There was some significant seasonal variation in detection rates at fixed points within territories for both males and pairs, and in general there was a low probability of detecting individuals around June-August and a high probability of detection around April and, to a lesser degree, October. Response times and owl-recorder distances were not influenced by moon phase or time of playback. This study provides the first baseline data on individual responses to the systematic repeated use of playback in Seychelles Scops-owl. We discuss the implications for current monitoring and its application to other similar Otus species.

A joint model for plot yield in response to fertility trends and interplot competition is described. The model combines the mixed model representation of a cubic smoothing spline to model fertility and a regression model with auto-regressive terms to model competition. Estimation is based on a generalization of residual maximum likelihood. The methods were applied to a series of 70 sugar beet trials conducted by the Plant Breeding Institute, Cambridge, UK, and the results summarized.

Although the adverse consequences of changes in social behavior following traumatic brain injury (TBI) are well documented, relatively little is known about possible underlying neuropsychological deficits. Following a model originally developed for social behavior deficits in schizophrenia, we investigated whether impairments in emotion recognition, understanding of other people’s intentions (“theory of mind”), and cognitive flexibility soon after first TBI or 1 year later were associated with self and proxy ratings of behavior following TBI. Each of the three functions was assessed with two separate tests, and ratings of behavior were collected on three questionnaires. Patients with TBI (n 5 33) were impaired in emotion recognition, “theory of mind,” and cognitive flexibility compared with matched orthopedic controls (n 5 34). Proxy ratings showed increases in behavioral problems 1 year following injury in the TBI group but not in the control group. However, test performance was not associated with questionnaire data. Severity of the impairments in emotion recognition, understanding intention, and flexibility were unrelated to the severity of behavioral problems following TBI. These findings failed to confirm the used model for social behavior deficits and may cast doubt on the alleged link between deficits in emotion recognition or theory of mind and social functioning. (JINS, 2008, 14, 318–326.)

In designing an expansionary fiscal package, a key consideration is the exchange rate. This is because undue and possibly destabilising movements in the exchange rate in response to domestic expansion could trigger expectations that the policy will be reversed, and such expectations might indeed be fulfilled. An understanding of the consequences of domestic expansion for the exchange rate is therefore crucial.

The central focus of this paper is on the conduct of fiscal policy. But the influence of fiscal policy cannot sensibly be examined separately from other aspects of macroeconomic policy, such as monetary, exchange rate and incomes policies. Because of this, we the opportunity to range quite widely. Two broad themes emerge. The first concerns the consequences of consistent forward-looking expectations for the design of policy. The second concerns the global consequences of adopting generally in many countries policy rules designed in the single open economy context. Since policy appraisal is usually conducted in the single economy context, and policy design with consistent expectations is still relatively underdeveloped, it is useful to take stock of these two issues.