Nico Keilman

Citations at Google Scholar

Papers in peer reviewed journals

• Maiolo, Valeria; Keilman, Nico & Gjertsen, Finn (2023). Sex-differences in life expectancy at birth: A descriptive analysis of the contributions of age and causes of death to the gap in Norway, 1881–2011. Social Sciences & Humanities Open. 8(1), p. 1–9. doi: 10.1016/j.ssaho.2023.100450. Show summary
• Keilman, Nico (2020) Evaluating probabilistic population forecasts. Economie et Statistique. ISSN 0336-1454. 520-521, s 49- 64. https://doi.org/10.24187/ecostat.2020.520d.2033 
• Keilman, Nico (2020) Modelling education and climate change. Nature Sustainability April 2020. ISSN 2398-9629.  https://doi.org/10.1038/s41893-020-0515-8 
• Keilman, Nico (2019) Mortality shifts and mortality compression in period and cohort life tables. Demographic Research 41(40), 1147-1196
• Borgan, Ørnulf & Keilman, Nico (2018). Do Japanese and Italian women live longer than women in Scandinavia?. European Journal of Population.  ISSN 0168-6577. . doi: 10.1007/s10680-018-9468-2
• Linder, Dennis; Frigessi, Arnoldo; Piaserico, Stefano & Keilman, Nico (2017). Simulating the life course of psoriasis patients: the interplay between therapy intervention and marital status. Journal of the European Academy of Dermatology and Venereology.
• Keilman, Nico (2016). A combined Brass-Random Walk approach to probabilistic household forecasting: Denmark, Finland, and the Netherlands 2011-2041. Journal of Population Research () 1-27. 
• Keilman, Nico (2016). Household forecasting: Preservation of age patterns. International Journal of Forecasting 32(3) 726-735.
• Measures for human reproduction should be linked to both men and women (first author, with Krzysztof Tymicki and Vegard Skirbekk). International Journal of Population Research 2014.                      http://dx.doi.org/10.1155/2014/908385. [pdf]
• Utilising expert opinion to improve the measurement of international migration in Europe (fifth author, with Arkadiusz Wisniowski, Jakub Bijak, Solveig Christiansen, Jonathan Forster, James Raymer, Peter Smith). Journal of Official Statistics 29(4)2013, 583-607, http://dx.doi.org/10.2478/jos-2013-0041 [pdf]
• Hvor robust er det nye pensjonssystemet med hensyn til levealdersutviklingen? ("How robust is the new public pension system for life expectancy development?") (first author, with Lisa Keller). Samfunnsøkonomen 09/2013 [doc]
• Probabilistic household forecasts based on register data: The case of Denmark and Finland (second author, with Solveig Christiansen). Demographic Research 06/2013; 28:1263. [pdf]
• Cohen, Joel; Kravdal, Øystein & Keilman, Nico (2011). Childbearing impeded education more than education impeded childbearing among Norwegian women. Proceedings of the National Academy of Science of the United States of America.  ISSN 0027-8424.  108(29), s 11830- 11835 . doi: 10.1073/pnas.1107993108
• Juha Alho and Nico Keilman, On future household structure. Journal of the Royal Statistical Society Series A 173(1)2010, 117-143
• Nico Keilman and Solveig Christiansen, Norwegian elderly less likely to live alone in the future. European Journal of Population, DOI 10.1007/s10680-009-9195-9
• Nico Keilman, Concern in the European Union about Low Birth Rates, European View 2008
• Nico Keilman, European demographic forecasts have not become more accurate during the past 25 years, Population and Development Review, 2008, 34(1)
• Maarten Alders, Nico Keilman and Harri Cruijsen, Assumptions for long-term stochastic population forecasts in 18 European countries, European Journal of Population, 2007, 23:33-69
• Juha Alho, Maarten Alders, Harri Cruijsen, Nico Keilman, Timo Nikander and Dinh Quang Pham, New forecast: Population decline postponed in Europe, Statistical Journal of the United Nations ECE12, 2006, 23:1-10
• Nico Keilman, The Impact of Demographic Uncertainty on Liabilities for Public Old Age Pensions in Norway, New Zealand Population Review 31(1), 2005, 35-50
• Juha Alho, Maarten Alders, Harri Cruijsen, Nico Keilman, Timo Nikander and Dinh Quang Pham, Population decline postponed in Europe, Statistical Magazine, 2005
• Nico Keilman and Dinh Quang Pham, Time series based errors and empirical errors in fertility forecasts in the Nordic countries, International Statistical Review 72(1), 2004, 5-18, summary
• Nico Keilman, Biodiversity: The threat of small households, Nature 421, 30 January 2003, 489-490
• Nico Keilman, Dinh Quang Pham and Arve Hetland, Why population forecasts should be probabilistic - illustrated by the case of Norway, Demographic Research 6-15 May 2002, 409-454
• Nico Keilman, TFR predictions and Brownian motion theory, Yearbook of Population Research in Finland 38, 2002, 209-221
• Nico Keilman, Data quality and accuracy of United Nations population projections, 1950-95, Population Studies 55(2), 2001, 149-164
• Nico Keilman, Uncertain population forecasts, Nature 412, 6846, 2001, 490-491
• Nico Keilman and Dinh Quang Pham, Predictive intervals for age-specific fertility, European Journal of Population 16(1), 2000, 41-66
• Nico Keilman, How accurate are the United Nations' world population projections?,Population and Development Review supplement to Volume 24, 1998, 15-41

• Alho, Juha & Keilman, Nico (2026). Assessing the accuracy of probabilistic population forecasts. International Journal of Forecasting. ISSN 0169-2070. doi: 10.1016/j.ijforecast.2025.12.005. Full text in Research Archive Show summary

  Stochastic demographic forecasts indicate to their users the ex ante level of uncertainty to be expected. There are approximately 25 years’ worth of data for population stocks and flows on the performance of such forecasts. The demographic context has numerous special features. The data come in the form of counts. The vital processes of births and deaths, and migration, combine to produce the future counts, so it is not obvious how their separate effects might be assessed. Finally, the ex post assessment is hampered by quality problems in the official population data. These issues are tackled in the context of a stochastic forecast of Norway for the years 2003–2023. A novel approach infers predictions of births, deaths, and net migration from changes in predicted population stocks in carefully chosen age segments. We use the deviance as a scoring rule to measure the lack of fit between the predictive distribution and the realized value. For a 20-year forecast horizon, predictive distributions for deaths in ages 80 years and over are less accurate than the birth distributions. The situation is the reverse for ages below 75 years. The accuracy of the predictive distribution for births appears to deteriorate much more rapidly than that of age-specific deaths for forecast horizons beyond 20 years. Forecasts for net migration are systematically less accurate than those for births or deaths.

• Smith, Peter; Keilman, Nico; Aristotelous, Georgios & Bijak, Jakub (2024). Estimating European migration flows, From Uncertainty to Policy: A Guide to Migration Scenarios. Edward Elgar Publishing. ISSN 9781035319794. p. 53–64. doi: 10.4337/9781035319800.00014. Full text in Research Archive
• Maiolo, Valeria; Keilman, Nico & Gjertsen, Finn (2023). Sex-differences in life expectancy at birth: A descriptive analysis of the contributions of age and causes of death to the gap in Norway, 1881–2011. Social Sciences & Humanities Open (SSHO). 8(1). doi: 10.1016/j.ssaho.2023.100450. Full text in Research Archive Show summary

  Official mortality statistics provide ample evidence that women live longer than men. In many European countries, the sex difference in life expectancy began to increase near the end of the nineteenth century, peaking between the 1960s and the 1980s, before declining again. In Norway, there was another earlier peak before the sex gap started to converge to that in other European countries. This study investigated changes in sex differences in life expectancy at birth in Norway from 1881 to 2011 as well as the contribution of broad age groups and causes of death to those differences. The total sex gap was broken down by age and cause using decomposition methods. Available mortality statistics were used for every tenth year between 1881 and 2011, excluding the war year of 1941. We regrouped the causes of death into 14 categories to reduce comparability problems across different classification systems. At the end of the 19th century, the gap in life expectancy at birth was largely due to the excessive mortality in males aged 15–29, particularly external causes of death, and in infant mortality in boys (under 1 year) due to perinatal and congenital causes. Since the 1970s, excess mortality in males aged 60 years and over has explained more than half of the sex gap, and the most relevant contributors have been circulatory diseases, neoplasms, and external causes. The recent narrowing of this gap has been related to the increase in pathologies affecting women in old age, such as senility and dementia. Differences in smoking behavior have likely played a role as well: women started smoking a few decades later than men, and they also reduced their smoking later.

• Keilman, Nico (2023). Can We Rely on Projections of the Immigrant Population? The Case of Norway. European Journal of Population. ISSN 0168-6577. 39(1). doi: 10.1007/s10680-023-09675-2. Full text in Research Archive Show summary

  Demographic forecasters must be realistic about how well they can predict future populations, and it is important that they include estimates of uncertainty in their forecasts. Here we focus on the future development of the immigrant population of Norway and their Norwegian-born children (“second generation”), grouped by three categories of country background: 1. West European countries plus the United States, Canada, Australia, and New Zealand; 2. Central and East European countries that are members of the European Union; 3. other countries. We show how to use a probabilistic forecast to assess the reliability of projections of the immigrant population and their children. We employ the method of random shares using data for immigrants and their children for 2000–2021. We model their age- and sex-specific shares relative to the whole population. Relational models are used for the age patterns in these shares, and time series models to extrapolate the parameters of the age patterns. We compute a probabilistic forecast for six population sub-groups with immigration background, and one for non-immigrants. The probabilistic forecast is calibrated against Statistics Norway’s official population projection. We find that a few population trends are quite certain: strong increases to 2060 in the size of the immigrant population (more specifically those who belong to country group 3) and of Norwegian-born children of immigrants. However, prediction intervals around the forecasts of immigrants and their children by one-year age groups are so wide that these forecasts are not reliable.

• Divino, Fabio; Belay, Denekew Bitew; Keilman, Nico & Frigessi, Arnoldo (2021). Spatial modelling of Lexis mortality data. Spatial Statistics. 44. doi: 10.1016/j.spasta.2021.100532. Full text in Research Archive Show summary

  We present a spatial approach to investigate mortality data referenced over a Lexis structure. We decompose the force of mortality into two interpretable components: a Markov random field, homogeneous with respect to age, period and cohort which explains the main pattern of mortality; and a secondary component of independent shocks, accounting for additional non structured patterns. Inference is based on a hierarchical Bayesian model with Markov chain Monte Carlo computations. We present an application to data from the Human Mortality Database, with respect to Italy and Sweden, two countries with very different histories in terms of demographic and epidemiological transitions. For each country the primary surface of spatially structured mortality and the secondary surface of additional mortality are estimated. The importance of each component is valuated by the estimated value of the respective precision parameter. In both Italy and Sweden, we discovered an interesting band of extra mortality in the secondary surface across the time domain, in the age interval between 60 and 90 years, with a slightly positive slope. The band represents a significant amount of extra mortality for the elderly population, which is otherwise incompatible with a structured dynamics in age, period and cohort.

• Kastrati, Avni & Keilman, Nico (2021). Culture, tradition, and the registration of deaths: The case of Kosovo. Statistical Journal of the IAOS. ISSN 1874-7655. 37(4), p. 1125–1137. doi: 10.3233/SJI-210840. Full text in Research Archive Show summary

  Population statistics for Kosovo show an unusually high share of male deaths (SMD) among all deaths. Women have a very low status in traditional parts of Kosovo – a direct consequence of the so-called Kanun of Lekë Dukagjini. This set of behavioural rules, practiced in Northern Albania and Kosovo, is strongly associated with a patriarchal culture. According to the code, a woman cannot own immovable property. Thus, to register the death of a family member at the office for civil registration is less urgent for women than for men. We assume that female deaths are under-registered. (i) A high SMD is more prevalent among the population with primary education, compared to secondary or tertiary education. (ii) More women aged 65+ receive the basic pension than there are resident women in that age group. (iii) Islamic societies report SMDs in 2017–2019 that are markedly lower than SMDs from vital registration. Registration of a death at the Islamic society is required before the funeral can take place. Other factors could also explain the high SMD: under-registration of deaths among Serbs in Kosovo, violent deaths and smoking among men, and bad physical and mental health among veterans of the war of 1999.

• Keilman, Nico (2020). Uncertainty in population forecasts for the twenty-first century. Annual Review of Resource Economics. ISSN 1941-1340. 12, p. 449–470. doi: 10.1146/annurev-resource-110319-114841. Full text in Research Archive
• Keilman, Nico (2020). Evaluating probabilistic population forecasts. Economie et Statistique. ISSN 0336-1454. 520-521, p. 49–64. doi: 10.24187/ecostat.2020.520d.2033. Full text in Research Archive Show summary

  We demonstrate how a probabilistic population forecast can be evaluated, when observations for the predicted variables become available. Statisticians have developed various scoring rules for that purpose, but there are hardly any applications in population forecasting literature. A scoring rule measures the distance between the probability distribution of the predicted variable, and the actual outcome. We use scoring rules that reward accuracy (the outcome is close to the expected value of the prediction)and sharpness (the predictive distribution has low variance, which makes it difficult to hit the target). We evaluate probabilistic population forecasts for France, the Netherlands, and Norway. For all three countries, we use results from the UPE-project ("Uncertain Population of Europe"). We inspect prediction intervals for population size in the period 2004-2019 and 3000 sample paths for population pyramids for the year 2010. For the Netherlands and for Norway, we compare the UPE-results with findings from the official probabilistic population forecast by Statistics Netherlands (2001-2019) and from a probabilistic forecast for Norway (1997-2019). All forecasts were computed using the cohort-component method and stochastically varying parameters for fertility, mortality and migration. We show that the UPE-forecasts for the Netherlands and for Norway performed better than the other forecasts for these two countries. The error in the jump-off population caused a bad score for the French forecast. We evaluate the 3000 UPE-simulations of the age and sex composition predicted for the year 2010. When normalized for population numbers in each age-sex category, the predictions for the Netherlands received the best scores, except for the oldest old. The age pattern for the Norwegian score reflects the under-prediction of immigration after the enlargement of the European Union in 2005.

• Keilman, Nico & Kristoffersen, Sigve (2020). European Mortality Forecasts: Are the Targets Still Moving? In Mazzuco, Stefano & Keilman, Nico (Ed.), Developments in Demographic Forecasting. Springer Nature. ISSN 9783030424718. p. 179–192. doi: 10.1007/978-3-030-42472-5_9. Full text in Research Archive Show summary

  Many statistical agencies routinely produce population forecasts, and revise these forecasts when new data become available, or when current demographic trends indicate that an update is necessary. When the forecaster strongly revises, from one forecast round to the next one, a forecast for a certain target year (for instance the life expectancy in 2050), this indicates large uncertainty connected to mortality predictions. The aim of this chapter is to shed more light on the uncertainty in mortality forecasts, by analysing the extent to which life expectancy predictions for 2030 and 2050 were revised in subsequent rounds of population forecasts published by statistical agencies in selected countries. It updates and extends earlier work that focused on United Nations and Eurostat forecasts published between 1994 and 2004. There the conclusion was that life expectancy forecasts for 18 European countries for the year 2050 had been revised upwards systematically, by around 2 years on average during the 10-year publication period. A recent analysis based on official population forecasts for Norway published in the period 1999–2018 led to the same conclusion. Here we will show that the period of upward revisions seems to have ended for some European countries.

• Keilman, Nico (2020). Évaluer les prévisions probabilistes de population. Economie et Statistique. ISSN 0336-1454. 520-521, p. 51–68. Full text in Research Archive Show summary

  Résumé – Les statisticiens ont développé des règles de notation pour évaluer les prévisions probabilistes par rapport aux observations. Toutefois, on en trouve peu d’applications dans la littérature sur les prévisions de population. Une règle de notation mesure la distance entre la distribution prédictive et le résultat. Nous passons en revue les règles de notation qui privilégient l’exactitude (le résultat est proche de l’espérance de la distribution) et la précision (la distribution présente une faible variance, de sorte qu’il est difficile d’atteindre l’objectif). Nous évaluons les prévisions de population probabilistes établies pour la France, les Pays‑Bas et la Norvège. Les prévisions de la taille de la population totale des Pays‑Bas et de la Norvège ont obtenu de bons scores. L’erreur sur la population de base a engendré un mauvais score pour la prévision française. Nous évaluons aussi la prévision de la composition par âge et par sexe pour 2010. Les prédictions relatives aux Pays‑Bas ont reçu les meilleurs scores, excepté celles concernant les personnes très âgées. Pour la Norvège, le score de la structure par âge reflète la sous‑prédiction de l’immigration après l’élargissement de l’Union européenne en 2005.

• Keilman, Nico (2020). Modelling education and climate change. Nature Sustainability. p. 497–498. doi: 10.1038/s41893-020-0515-8. Full text in Research Archive Show summary

  The Intergovernmental Panel on Climate Change (IPCC) is preparing its Sixth Assessment Report, to be published in 2022. The IPCC provides policy makers with the latest scientific insights on global climate change, its consequences and risks, and suggests possibilities for adaptation and mitigation. Because the future is unknown, the IPCC uses various models and scenarios for exploring how greenhouse gas emissions and other factors of climate change might develop, determined by natural science variables and socioeconomic variables. Here I argue that not only do the scenarios fail to cover a large enough range of possible futures, we do not know how probable they are, and that confuses policy makers.

• Keilman, Nico (2019). Erroneous population forecasts. In Bengtsson, Tommy & Keilman, Nico (Ed.), Old and New Perspectives on Mortality Forecasting. Springer Nature. ISSN 9783030050740. p. 95–111. doi: 10.1007/978-3-030-05075-7. Full text in Research Archive Show summary

  Given a history of sizable forecasting errors, this chapter addresses the question of why demographic forecasts are uncertain. It summarizes main patterns in ex-post observed errors in historical population forecasts, and discusses probabilistic forecasts. Illustrations come from a probabilistic forecast for the population of Norway.

• Borgan, Ørnulf & Keilman, Nico (2019). Do Japanese and Italian Women Live Longer than Women in Scandinavia? European Journal of Population. ISSN 0168-6577. 35(1), p. 87–99. doi: 10.1007/s10680-018-9468-2. Full text in Research Archive Show summary

  Life expectancies at birth are routinely computed from period life tables. When mortality is falling, such period life expectancies will typically underestimate real life expectancies, that is, life expectancies for birth cohorts. Hence, it becomes problematic to compare period life expectancies between countries when they have different historical mortality developments. For instance, life expectancies for countries in which the longevity improved early (like Norway and Sweden) are difficult to compare with those in countries where it improved later (like Italy and Japan). To get a fair comparison between the countries, one should consider cohort data. Since cohort life expectancies can only be computed for cohorts that were born more than a hundred years ago, in this paper we suggest that for younger cohorts one may consider the expected number of years lost up to a given age. Contrary to the results based on period data, our cohort results then indicate that Italian women may expect to lose more years than women in Norway and Sweden, while there are no indications that Japanese women will lose fewer years than women in Scandinavia. The large differences seen for period data may just be an artefact due to the distortion that period life tables imply in times of changing mortality.

• Keilman, Nico (2019). Family projection methods: A review. In Schoen, Robert (Eds.), Analytical Family Demography. Springer Nature. ISSN 9783319932279. p. 277–301. doi: 10.1007/978-3-319-93227-9_12. Full text in Research Archive Show summary

  I review methods for projecting the family structure of a population into the future. The focus is on Western countries. I define the concept of “family”, and stress the close link between family and household. There is an important distinction between family position (the attribute of individuals) and family type (the attribute of families). I propose a typology of family projection models, and review a large number of approaches. Consistency problems (being a generalization of the two-sex problem of demography) arise when interrelated events experienced by members of the same family are modelled. Little is known about the accuracy of various types of family projection models. The chapter concludes with an evaluation and assessment of various types of family projection models, using criteria such as data requirements, output detail, ease of programming, and extrapolation of parameters. Agent Based Models and probabilistic projection models are promising avenues for future work. © Springer International Publishing AG, part of Springer Nature 2019

• Keilman, Nico (2019). Mortality shifts and mortality compression in period and cohort life tables. Demographic Research. ISSN 1435-9871. 41(40), p. 1147–1196. doi: 10.4054/DEMRES.2019.41.40. Full text in Research Archive Show summary

  Background: When age-specific mortality falls, period life tables give a distorted view of the life expectancy (LE) and the degree of mortality compression in birth cohorts. Objective: To derive mathematical expressions for the link between LEs and compression in period life tables on the one hand and corresponding variables in birth cohorts on the other hand. Methods: We analyse the age at death distribution (AADD) computed from the life table’s d(x)-column. We derive general expressions for the moments of this distribution in a series of annual period life tables, written as functions of the moments in the AADD of cohorts. Results: We use data for Norwegian men and women to illustrate simple versions of the new expressions. The LE increases twice as fast across cohorts compared to what period life tables suggest under this model. Compression in Norwegian mortality, expressed in terms of decreasing variance of the AADDs, is approximately 40% slower in period than in cohort mortality. Conclusions: We show how one can analyse the amount of distortion in period LEs compared to cohort LEs. In addition, we show how period compression is determined by cohort compression, together with both period and cohort LEs. Contribution: We derive new expressions that link the period AADD to the cohort AADD. Under a simple linear model, we show why compression in the period AADD often goes together with increases in the period LE.

• Keilman, Nico (2018). Psoriasispasientenes livsløp - påvirker behandling deres parforhold? BestPractice Dermatologi. 9(28), p. 18–19. Full text in Research Archive Show summary

  Vår analyse viser at matematisk modellering av samspillet mellom sosiale og helsevariabler i prinsippet er mulig. Vår modell er en makromodell som simulerer livsløpet til en gruppe pasienter, som befinner seg i ulike tilstander i løpet av livet. Imidlertid trenger vi mer komplekse modeller som omfatter flere variabler (for eksempel sysselsettingsstatus, depresjon, fedme etc.) for mer realistiske simuleringer av interaksjoner som studeres. Flere variabler medfører mer komplekse simuleringsmodeller. I slike tilfeller kan det være nødvendig å bytte fra en makromodell til en mikromodell. I en slik modell simuleres livsløpet til hver enkelt person.

• Keilman, Nico (2018). Eldrebølgen avlyst? Bedre termometer, men pasienten er fortsatt syk. Forskning.no. ISSN 1891-635X. Full text in Research Archive
• Keilman, Nico (2018). Økende optimisme om forventet levealder. Forskning.no. ISSN 1891-635X. Full text in Research Archive
• Linder, Dennis; Frigessi, Arnoldo; Piaserico, Stefano & Keilman, Nico (2017). Simulating the life course of psoriasis patients: the interplay between therapy intervention and marital status. Journal of the European Academy of Dermatology and Venereology. ISSN 0926-9959. 32(1), p. 62–67. doi: 10.1111/jdv.14567. Full text in Research Archive Show summary

  Background Psoriasis, a chronic relapsing inflammatory disease affecting primarily the skin, shows multiple comorbidities including depression, cardiovascular diseases and other relevant conditions. Psoriasis patients experience social isolation, job loss, financial difficulties and partnership problems. Inversely, psychosocial impairments may negatively influence the disease course. Objective To explore the feasibility of a model describing the interaction of psychosocial and clinical factors over the life course of patients. Methods We considered only seven states for members of a hypothetical population: single and healthy, single and having a psoriasis flare, single and ‘cured’, coupled and healthy, coupled and having a psoriasis flare, coupled and ‘cured’, and dead. Transition probabilities between states were taken from the Norwegian Population Register for the healthy population and from epidemiological research articles. Clinical experience allowed adjustments on the assumed parameters. Results Our macromodel, which simulates the effect of therapy intervention on patients’ partnership status, yields a description of the transitions between the seven states. Treatment efficacy shows only a negligible effect on the chances of living with a partner. Conclusions Mathematical modelling of interactions between social and health variables is in principle feasible. However, complex models, comprising more variables (for instance: employment status, depression level, obesity etc.), are needed for more realistic simulations for the interactions studied. As increasing the number of variables leads to an exponential increase of the model’s state space, switching to micromodelling (representing each individual separately) may be necessary.

• Keilman, Nico (2016). A combined Brass-random walk approach to probabilistic household forecasting: Denmark, Finland, and the Netherlands, 2011–2041. Journal of Population Research. ISSN 1443-2447. 34(1), p. 17–43. doi: 10.1007/s12546-016-9175-y. Full text in Research Archive Show summary

  Probabilistic household forecasts to 2041 are presented for Denmark, Finland, and the Netherlands. Future trends in fertility, mortality and international migration are taken from official population forecasts. Time series of shares of the population in six different household positions are modelled as random walks with drift. Brass’ relational model preserves the age patterns of the household shares. Probabilistic forecasts for households are computed by combining predictive distributions for the household shares with predictive distributions of the populations, specific for age and sex. If current trends in the three countries continue, we will witness a development towards more and smaller households, often driven by increasing numbers of persons who live alone. We can be quite certain that by 2041, there will be between two and four times as many persons aged 80 and over who live alone when compared with the situation in 2011.

• Keilman, Nico (2016). Household forecasting: Preservation of age patterns. International Journal of Forecasting. ISSN 0169-2070. 32(3), p. 726–735. doi: 10.1016/j.ijforecast.2015.10.007. Full text in Research Archive Show summary

  We formulate a time series model for household dynamics for different age groups. We model the share of the population who are in a certain household position (living alone, living with partner etc.). These household positions have very pronounced age patterns. The age profiles change slowly over time, caused by changes in home leaving behaviour of young adults, differences in survival of men and women, etc. When forecasting household positions to 2040, we want to preserve the characteristics of the age profiles. We test the Lee-Carter model and the Brass Relational method using household data for the Netherlands for the period 1996-2010. Annual shares of the population by household position, age, and sex are modeled as Random Walks with a Drift (RWD). While the Brass model has its limitations, in our application it performs better than the Lee-Carter model. The predicted age patterns based on the Brass model look more reasonable, because the Brass model is a two-parameter model, while the Lee-Carter model contains only one parameter. Also, the model parameters and standard errors of the Brass model are easier to estimate than those of the Lee-Carter model.

• Keilman, Nico; Tymicki, Krzysztof & Skirbekk, Vegard (2014). Measures for human reproduction should be linked to both men and women. International Journal of Population Research. ISSN 2090-4029. doi: 10.1155/2014/908385. Full text in Research Archive Show summary

  We introduce the two-sex net reproduction rate (2SNRR) and the two-sex total fertility rate (2STFR)—two demographic indicators that reflect the number of children born, given age specific fertility and mortality of the adults. The main quality of these indicators is that they measure the childbearing behaviour of both women and men. The indicators have intuitive value, since they tell us to what extent adults are replaced by children. While the traditional net reproduction rate (NRR) describes general replacement trends among women only, the 2SNRR is an indicator of a population’s growth potential, irrespective of sex. We demonstrate the use of the indicators with data from Bejsce parish in Poland for the period 1800–1967 and with data from UN projections for China for future years. We discuss the consequences for our understanding of fertility trends when sex ratios deviate from normal levels.

• Christiansen, Solveig Tobie Glestad & Keilman, Nico (2013). Probabilistic household forecasts based on register data - the case of Denmark and Finland. Demographic Research. ISSN 1435-9871. 28, p. 1263–1302. doi: 10.4054/DemRes.2013.28.43. Full text in Research Archive Show summary

  BACKGROUND Household forecasts are important for public planning and for predicting consumer demand. OBJECTIVE The purpose of this paper is to compute probabilistic household forecasts for Finland and Denmark, taking advantage of unique housing register data covering the whole populations dating back to the 1980s. A major advantage is that we do not have to rely on small population samples, and we can get quite reliable estimates even for infrequent transitions. A further merit is having time series containing the population in different household positions (dependent child, living with a spouse, living in a consensual union, living alone, lone parent, living in other private household and institutional households) by age and sex. METHODS These series enable us to estimate the uncertainty in the future distribution of the population across household positions. Combining these uncertainty parameters with expected shares computed in a deterministic household forecast, we simulate 3000 sample paths for the household shares for each age and sex. These paths are then combined with 3000 simulations from a stochastic population forecast covering the same period to obtain the predicted number of households and persons in each household position by age and sex. RESULTS According to our forecasts, we expect a strong growth in the number of private households during a 30-year period, of 27% in Finland and 13% in Denmark. The number of households consisting of a married couple or a person who lives alone are the most certain, and single parents and other private households are the most uncertain.

• Keilman, Nico & Keller, Lisa Dahl (2013). Hvor robust er det nye pensjonssystemet med hensyn til levealdersutviklingen? Samfunnsøkonomen. ISSN 1890-5250. p. 28–38. Full text in Research Archive
• Wisniowski, Arkadiusz; Bijak, Jakub; Christiansen, Solveig Tobie Glestad; Forster, Jonathan; Keilman, Nico & Raymer, James [Show all 7 contributors for this article] (2013). Utilising Expert Opinion to Improve the Measurement of International Migration in Europe. Journal of Official Statistics. ISSN 0282-423X. 29(4), p. 583–607. doi: 10.2478/jos-2013-0041. Full text in Research Archive
• Cohen, Joel; Kravdal, Øystein & Keilman, Nico (2011). Childbearing impeded education more than education impeded childbearing among Norwegian women. Proceedings of the National Academy of Sciences of the United States of America (PNAS). ISSN 0027-8424. 108(29), p. 11830–11835. doi: 10.1073/pnas.1107993108. Full text in Research Archive
• Keilman, Nico & Christiansen, Solveig Tobie Glestad (2010). Norwegian Elderly Less Likely to Live Alone in the Future. European Journal of Population. ISSN 0168-6577. 26(1), p. 47–72. doi: 10.1007/s10680-009-9195-9. Full text in Research Archive Show summary

  We analyse the future household status of elderly men and women in Norway. An important finding is that persons aged 80+ are less likely to live alone in the future, and more often with a partner. The level of mortality, the mortality sex gap, union dissolution at young and intermediate ages, and entry into and exit from institutions for the elderly are possible determinants for this new trend. We use the macro simulation program LIPRO to simulate the household dynamics in Norway to 2032, and investigate the demographic reasons for the increased likelihood of living with a partner among Norwegian elderly. Mortality plays an important role, but part of the trend is already embodied in the household structure of the current population. Keywords: Elderly, Living arrangements, Household projection, Norway, LIPRO

• Alho, Juha & Keilman, Nico (2010). On future household structure. Journal of the Royal Statistical Society, Series A (Statistics in Society). ISSN 0964-1998. 173, p. 117–143. Full text in Research Archive Show summary

  We develop a method for computing probabilistic household forecasts which quantifies uncertainty in the future number of households of various types in a country. A probabilistic household forecast helps policy makers, planners and other forecast users in the fields of housing, energy, social security etc. in taking appropriate decisions, because some household variables are more uncertain than others. Deterministic forecasts traditionally do not quantify uncertainty.We apply the method to data from Norway.We find that predictions of future numbers of married couples, cohabiting couples and one-person households are more certain than those of lone parents and other private households. Our method builds on an existing method for computing probabilistic population forecasts, combining such a forecast with a random breakdown of the population according to household position (single, cohabiting, living with a spouse, living alone etc.). In this application, uncertainty in the total numbers of households of different types derives primarily from random shares, rather than uncertain future population size. A similar method could be applied to obtain probabilistic forecasts for other divisions of the population, such as household size, health or disability status, region of residence and labour market status. Keywords: Household forecast; Norway; Population forecast; Probabilistic forecast; Random shares

• Keilman, Nico (2010). On age structures and mortality. In Tuljapurkar, Shripad; Ogawa, Naohiro & Gauthier, Anne (Ed.), Ageing in Advanced Industrial States. Springer. ISSN 9789048135523. p. 23–46. Full text in Research Archive
• Keilman, Nico; Cruijsen, Harri & Alho, Juha (2008). Changing views of future demographic trends. In Alho, Juha; Jensen, Svend Hougaard & Lassila, Jukka (Ed.), Uncertain demographics and fiscal sustainability. Cambridge University Press. ISSN 9780521877404. p. 11–33. Full text in Research Archive
• Alho, Juha; Cruijsen, Harri & Keilman, Nico (2008). Empirically based specification of forecast uncertainty. In Alho, Juha; Jensen, Svend Hougaard & Lassila, Jukka (Ed.), Uncertain demographics and fiscal sustainability. Cambridge University Press. ISSN 9780521877404. p. 34–54. Full text in Research Archive
• Keilman, Nico (2008). Erroneous population forecasts. In Festy, Patrick & Sardon, Jean-Paul (Ed.), Hommage à Gérard Calot - Profession: démographe. Institut national d'études démographiques. ISSN 9782733240236. p. 237–254. Full text in Research Archive
• Keilman, Nico (2008). European demographic forecasts have not become more accurate over the past 25 years. Population and Development Review. ISSN 0098-7921. 34(1), p. 137–153. Full text in Research Archive Show summary

  Nowadays, demographers, population statisticians, and population forecasters have richer data, more refined theories of demographic behavior, and more sophisticated methods of analysis than they had two or three decades ago. This scientific progress should have made it easier to predict demographic behavior. But my analysis of the errors in old forecasts shows that demographic forecasts published by statistical agencies in 14 European countries have not become more accurate over the past 25 years. The findings demonstrate that scientific progress in population studies during the previous two to three decades has not kept up with less predictable demographic behavior of populations in European countries. There is no reason to be more optimistic about US Census Bureau forecasts. Population forecasts are intrinsically uncertain, and hence should be couched in probabilistic terms.

• Keilman, Nico (2007). UK national population projections in perspective: How successful compared to those in other European countries? Population Trends. ISSN 0307-4463. p. 20–30. Full text in Research Archive Show summary

  Compared to population forecasts of other European countries, those made in the United Kingdom during the past 30 years had somewhat larger forecast errors for fertility and smaller errors for mortality. Migration forecasts in the UK were about as accurate as the European average. After controlling for various effects such as relative data volatility both at the time a projection is made and during the period of the projection, there is no indication that recent forecasts in European countries have been more accurate than older ones. Hence population forecasts are intrinsically uncertain, and a forecast for the UK in the form of probability distributions is presented.

• Alders, Maarten; Keilman, Nico & Cruijsen, Harri (2007). Assumptions for long-term stochastic population forecasts in 18 European countries. European Journal of Population. ISSN 0168-6577. 23, p. 33–69. doi: 10.1007/s10680-006-9104-4. Full text in Research Archive Show summary

  The aim of the ‘Uncertain Population of Europe’ (UPE) project was to compute long-term stochastic (probabilistic) population forecasts for 18 European countries. We developed a general methodology for constructing predictive distributions for fertility, mortality and migration. The assumptions underlying stochastic population forecasts can be assessed by analysing errors in past forecasts or model-based estimates of forecast errors, or by expert judgement. All three approaches have been used in the project. This article summarizes and discusses the results of the three approaches. It demonstrates how the––sometimes conflicting––results can be synthesized into a consistent set of assumptions about the expected levels and the uncertainty of total fertility rate, life expectancy at birth of men and women, and net migration for 18 European countries.

• Alho, Juha; Alders, Maarten; Cruijsen, Harri; Keilman, Nico; Nikander, Timo & Pham, Dinh Quang (2006). New forecast: Population decline postponed in Europe. Statistical Journal of the United Nations Economic Commision for Europe ECE12. ISSN 0167-8000. 23(1), p. 1–10. Full text in Research Archive Show summary

  We present results of a probabilistic forecast for the population in 18 European countries, to 2050. Other forecasts have recently predicted a falling population size for those countries. However, there are reasons to expect higher immigration and lower mortality than the earlier forecasts did. Hence, we find that population decline is postponed in our forecast. The forecast also alerts us to the fact that many demographic developments cannot be forecasted accurately. Although ageing is certain, the extent to which this will occur is difficult to predict accurately. The number of elderly persons is very uncertain in the long run. This has major implications for all European countries in which reforms for pension systems and the provision of health care for the elderly are considered. The reforms must be robust against unexpected demographic developments.

• Keilman, Nico (2006). Demographic Translation: From Period to Cohort Perspective and Back. In Wunsch, Guillaume; Caselli, Graziella & Vallin, Jacques (Ed.), Demography: Analysis and Synthesis, A Treatise in Population Studies Volume 1. Elsevier. ISSN 9780127656601. p. 213–223. Full text in Research Archive
• Keilman, Nico (2006). Households and families. In Wunsch, Guillaume; Caselli, Graziella & Vallin, Jacques (Ed.), Demography: Analysis and Synthesis. Academic Press. ISSN 9780127656649. p. 457–476. Full text in Research Archive Show summary

  The aim of the current chapter is to give not only a broad overview of trends in family and household developments in Europe (Section 5), but also to discuss concepts and definitions concerning the household, the family, and their members (Section 2): what constitutes a household, a family, what is a consensual union, a child, a one-parent family, a reconstituted family? Next I review various issues connected to measuring household and family developments (Section 3): de facto or de jure place of residence, measuring household and family structure at one point in time, measuring household and family dynamics over a certain period, the individual or the group as unit of measurement, the problem of longitudinal households, relationships between the events that several members of the same household may experience (e.g. a lone mother becomes a one-person household when her last child leaves the parental home), and the representativeness of the data. The strengths and weaknesses of various data sources often used to map household and family developments are discussed in Section 4. Finally, the main trends in family and household developments in Europe after World War II are summarized in Section 5.

• Keilman, Nico (2005). The Impact of Demographic Uncertainty on Liabilities for Public Old Age Pensions in Norway. New Zealand Population Review. ISSN 0111-199X. 31(1), p. 35–50. Full text in Research Archive Show summary

  The paper analyses the importance of demographic uncertainty for the net present value (NPV) of public old age pension obligations in Norway. A probabilistic population forecast is combined with a deterministic macro model for future pension expenditures. The model is applied to Norwegian data for the period 2003-2100. Under the current pension system, the liabilities are likely to grow by a factor of ten towards the end of the century. The demographic driving force is an assumed increase in the life expectancies of men and women by some 13-16 years over the next 95 years. The results show also that long-run relative uncertainty is larger for total population than for the NPV, due to the enormous uncertainty in the number of births in the long run. In 2100, the 80 per cent prediction interval of population size is 1.5 times as wide as the median value. For the NPV, this relative uncertainty ratio is 80 per cent. Also for earlier years, the relative uncertainty in the NPV is approximately half that in population size. There is no single broad age group, in which relative uncertainty is similar to that in the NPV during the entire period.

• Keilman, Nico & Pham, Quang Dinh (2005). Hvor lenge kommer vi til å leve? Levealder og aldersmønster for dødeligheten i Norge, 1900–2060. Økonomiske analyser. ISSN 0800-4110. p. 43–49. Full text in Research Archive Show summary

  Vi presenterer en analyse av levealderen og aldersmønsteret i dødeligheten for norske menn og kvinner siden 1900. Vi har brukt den såkalte Lee-Cartermodellen for å kunne gi anslag på dødelighetsutviklingen i framtiden. Vi forventer en fortsatt økning i levealderen, helt opp til 86 år for menn og 90 år for kvinner i 2060.

• Keilman, Nico (2005). Erroneous population forecasts. In Keilman, Nico (Eds.), Perspectives on Mortality Forecasting No. 2: Probabilistic Models. Swedish Social Insurance Agency. ISSN 9789175003269. p. 7–26. Full text in Research Archive Show summary

  The purpose of this chapter is to give a broad review of the notions of population forecast errors and forecast accuracy. Why are population forecasts inaccurate? How large are the errors involved, when we analyse historical forecasts of fertility, mortality, and the age structure? Moreover, how can we compute expected errors in recent forecasts? We shall see that probabilistic population forecasts are necessary to assess the expected accuracy of a forecast, and that such probabilistic forecasts quantify expected accuracy and expected forecast errors much better than traditional deterministic forecasts do. The chapter concludes with some challenges in the field of probabilistic population forecasting.

• Alho, Juha; Alders, Maarten; Cruijsen, Harri; Keilman, Nico; Nikander, Timo & Pham, Quang Dinh (2005). Befolkningsnedgang i EØS-området utsatt. SSB-Magasinet. Full text in Research Archive Show summary

  FN og Eurostat har nylig spådd en befolkningsnedgang for 18 europeiske land. Nå viser resultatene fra en ny befolkningsprognose at vi har grunn til å vente større innvandring og høyere levealder enn det som FN og Eurostat har spådd. Nedgangen kommer derfor senere enn antatt, kanskje ikke i det hele tatt før 2050. For Norge forventes det et folketall på 5,75 millioner i 2050, litt høyere enn midtalternativet i SSBs befolkningsframskrivninger fra 2002.

• Keilman, Nico Willem & Pham, Dinh Quang (2004). Time series based errors and empirical errors in fertility forecasts in the Nordic countries. International Statistical Review. ISSN 0306-7734. 72, p. 5–18. Full text in Research Archive Show summary

  We use time series models to derive model based prediction intervals for the Total Fertility Rate (TFR) in Norway, Sweden, Finland, and Denmark up to 2050. For the short term (5-10 yrs), expected TFR-errors are compared with empirical forecast errors observed in historical population forecasts prepared by the statistical agencies in these countries since 1969. Medium-term and long-term (up to 50 years) errors are compared with error patterns based on so-called naïve forecasts, i.e. forecasts that assume that recently observed TFR-levels also apply for the future.

• Keilman, Nico Willem (2004). Démographie des ménages et de la famille: Application aux pays développés. In Caselli, Graziella; Vallin, Jacques & Wunsch, Guillaume (Ed.), Démographie: Analyse et synthèse. Volume VI: Population et société. Institut National d'Etudes Démographiques. ISSN 9782733220160. p. 345–388. Full text in Research Archive
• Keilman, Nico Willem (2003). Pensjonskommisjonen bør ta usikkerhet i befolkningsutviklingen alvorlig. Økonomiske analyser. ISSN 0800-4110. p. 16–24. Full text in Research Archive Show summary

  Pensjonskommisjonens utredning av et nytt pensjonssystem har naturlig nok et langsiktig perspektiv, faktisk helt frem til år 2050 og enda lenger. En viktig variabel i denne sammenheng er antall eldre. Men den foreløpige rapporten som Pensjonskommisjonen la frem september 2002, inneholdt ingen analyse av den fremtidige utvikling av antall eldre. Anslagene over hvor mange eldre Norge kan ha i 2050 varierer med flere hundre tusen, og vi vet ikke hvilket av anslagene som kommer til å bli riktig � bare at noen av dem er mer sannsynlige enn andre. Det er særlig levealderen som avgjør hvor mange eldre vi vil få, og fremtidig levealder er vanskelig å beregne. Når vi vet at økningen i forventet levealder i mange tilfeller er blitt betydelig underestimert de siste førti årene, er det all grunn til å ta hensyn til demografisk usikkerhet i en ny pensjonsordning, og skape pensjonssystemer som hele tiden er fleksible for demografiske forandringer.

• Keilman, Nico Willem (2003). Types of Models for Projecting Mortality. In Bengtsson, Tommy & Keilman, Nico Willem (Ed.), Perspectives on Mortality Forecasting. Social Insurance Board. ISSN 9789189303249. p. 19–27. Full text in Research Archive Show summary

  This chapter presents a systematic overview of various types of models for projecting mortality. The framework is that of population forecasts of the cohort-component type for the elderly at the national level. I distinguish between demographic and non-demographic models (Sections 1 and 2). Demographic models are rather mechanistic, although they involve varying degrees of judgment. In this category, I distinguish between extrapolation models and interpolation models (Sections 1.1 and 1.2). Non-demographic models are much more causal in nature than demographic ones. I differentiate between macro models (Section 2.1) and micro models (Section 2.2). Finer distinctions and further qualifications are also given.

• Keilman, Nico Willem (2003). Discussion: Should fertility intentions inform fertility forecasts? In Spencer, Gregory (Eds.), The direction of fertility in the United States. COPAFS. ISSN 9780972059602. p. 179–181. Full text in Research Archive
• Keilman, Nico Willem (2003). Biodiversity: The threat of small households. Nature. ISSN 0028-0836. 421, p. 489–490. Full text in Research Archive Show summary

  Many studies have suggested that the increasing global human population is having a negative effect on biodiversity. According to new work, another threat comes from the rising number of households.

• Keilman, Nico Willem (2002). TFR predictions based on Brownian motion theory. Yearbook of Population Research in Finland. ISSN 0506-3590. XXXVIII, p. 207–219. Full text in Research Archive Show summary

  In stochastic population forecasts, the predictive distribution of the TFR is of central concern. Time series models can be used to predict the TFR and its moments on the short run (up to 10 or 20 years), but on the long run (40-50 years) they often result in excessively wide prediction intervals. To restrict the interval width, I model the time series of log TFR-values as a Brownian motion with absorbing upper barrier. I analyse (i) expressions for the predictive distribution of the log of the TFR; (ii) expressions for the first and second moments of the predictive distribution of the log of the TFR. Using this model I find that the second moment of the predictive distribution for the long-run TFR in Norway is insensitive for ceiling levels beyond a threshold of approximately 3.4 children per woman. This conclusion holds for a fairly broad range of innovation variances. If the log of the TFR follows a random walk, sample paths that exceed approximately 3.4 children per woman may be rejected when simulating future fertility in Western countries. This will not have any major effect on the width of the long-term predictive distribution.

• Keilman, Nico Willem; Pham, Quang Dinh & Hetland, Arve (2002). Why population forecasts should be probabilistic - illustrated by the case of Norway. Demographic Research. ISSN 1435-9871. 6, p. 407–454. doi: 10.4054/DemRes.2002.6.15. Full text in Research Archive Show summary

  Deterministic population forecasts do not give an appropriate indication of forecast uncertainty. Forecasts should be probabilistic, so that their expected accuracy can be assessed. We review three main methods to compute probabilistic forecasts, namely time series extrapolation, analysis of historical forecast errors, and expert judgement. We illustrate, by the case of Norway up to 2050, how elements of these three methods can be combined when computing prediction intervals for a population¿s future size and age-sex composition. We show the relative importance for prediction intervals of various sources of variance, and compare our results with those of the official population forecast computed by Statistics Norway.

• Keilman, Nico Willem (2001). Data quality and accuracy of United Nations population projections, 1950-95. Population Studies. ISSN 0032-4728. 55(2), p. 149–164. Full text in Research Archive Show summary

  Between 1951 and 1998, the United Nations (UN) published 16 sets of population projections for the world, its major regions, and countries. This paper reports the accuracy of the projection results. I analyse the quality of the historical data used for the base population of the projections, and for extrapolating fertility and mortality. I study also the impact this quality has had upon the accuracy of the projection results. Results and assumptions for the sets of projections are compared with corresponding estimates from the UN 1998 Revision for total fertility and life expectancy at birth, total population, and the projected age structures. The report covers seven major regions (Africa, Asia, the former USSR, Europe, Northern America, Latin America, and Oceania) and the largest ten countries of the world as of 1998 (China, India, the USA, Indonesia, Brazil, Pakistan, Russia, Japan, Bangladesh, and Nigeria).

• Keilman, Nico Willem (2001). Uncertain population forecasts. Nature. ISSN 0028-0836. 412, p. 490–491. Full text in Research Archive Show summary

  Traditional population forecasts made by statistical agencies do not quantify uncertainty. But demographers and statisticians have developed methods to calculate probabilistic forecasts.

• Keilman, Nico Willem (2001). La translation démographique: des indicateurs du moment aux indicateurs de génération et réciproquement. In Caselli, Graziella; Vallin, Jacques & Wunsch, Guillaume (Ed.), Démographie: analyse et synthèse. Volume I: La dynamique des populations. Editions de l'Institut National d'Etudes Démographiques. ISSN 9782733220115. p. 359–378. Full text in Research Archive Show summary

  Ce chapitre donne un aperçu général sur la théorie de la translation démographique. Le point de départ est une matrice de taux par âge et année de calendrier. Je donne les relations mathématiques entre l'intensité et le calendrier du moment, et ces deux indicateurs de la génération. L'objectif de cette formulation mathématique est de faire la lumière sur l'ampleur de la "distortion translationelle", autrement dit, de prédire le niveau et le calendrier de la descendance finale au vu des tendences de la fécondité du moment, et réciproquement.

• Keilman, Nico Willem (2001). La traslazione demografica: dalla prospettiva di periodo a quella per generazione e viceversa. In Caselli, Graziella; Vallin, Jacques & Wunsch, Guillaume (Ed.), Demografia: La dinamica della popolozioni. Carocci, Roma. ISSN 9788843018833. p. 439–461. Full text in Research Archive Show summary

  Ce chapitre donne un aperçu général sur la théorie de la translation démographique. Le point de départ est une matrice de taux par âge et année de calendrier. Je donne les relations mathématiques entre intensité et le calendrier du moment, et ces deux indicateurs de la génération. L'objectif de cette formulation mathématique est de faire la lumière sur l'ampleur de la "distortion translationelle", autrement dit, de prédire le niveau et le calendrier de la descendance finale au vu des tendences de la fécondité du moment, et réciproquement.

• Keilman, Nico Willem & Pham, Quang Dinh (2000). Predictive intervals for age-specific fertility. European Journal of Population. ISSN 0168-6577. 16(1), p. 41–66. doi: 10.1023/1006385413134. Full text in Research Archive Show summary

  A multivariate ARIMA model is combined with a Gamma curve to predict confidence intervals for age-specific birth rates by one-year age groups. The method is applied to observed age-specific births in Norway between 1900 and 1995, and predictive intervals are computed for each year up to 2050. The predicted two-thirds confidence intervals for Total Fertility (TF) around 2010 agree well with TF-errors in old population forecasts made by Statistics Norway. The method gives useful predictions for age-specific fertility up to the years 2020-2030. For later years, the intervals become too wide. Methods which do not take account of estimation errors in the ARIMA-model coefficients underestimate the uncertainty for future TF-values. The findings suggest that the margin between high and low fertility variants in official population forecasts for many Western countries are too narrow.

• Keilman, Nico Willem (2000). Précision et incertitudes des prévisions nationales de population. In Wattelar, Christine & Duchêne, Josianne (Ed.), Le Défi de l'Incertitude: Nouvelles Approches en Perspectives et Prospective Démographique. Academia-Bruylant/L'Harmattan, Louvain-la-Neuve, Belgique. ISSN 9782872095254. p. 33–67. Full text in Research Archive Show summary

  The existing literature on ex-post errors observed for historical population forecasts made by statistical agencies in 15 industrialized countries is reviewed. The amount and type of data in these studies (total population size, age structure, population growth rate, components of change), the level of detail (numbers of births and deaths, crude rates, total fertility rates, life expectancies), and the period covered vary considerably among the countries. Attention is given to forecast accuracy for total population size, population growth rates, fertility, mortality, the age structure, and the dependency ratio. Among the issues to be taken up are relative errors for fertility and mortality, and common patterns across the countries. On the basis of a data set from Norway (covering the period 1969-1989, forecasts made between 1969 and 1987) and one from the Netherlands (for the period 1950-1986, forecasts made between 1950 and 1980) we investigate a possible reduction in forecast errors over time. The paper concludes with suggestions for including results from ex-post evaluations in official population forecasts, in order to communicate forecast uncertainty to the user.

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• Bijak, Jakub & Keilman, Nico (2024). From Uncertainty to Policy: A Guide to Migration Scenarios. Edward Elgar Publishing. ISBN 9781035319794. 184 p. Full text in Research Archive
• Mazzuco, Stefano & Keilman, Nico (2020). Developments in Demographic Forecasting. Springer Nature. ISBN 9783030424718. 261 p. Full text in Research Archive Show summary

  This open access book presents new developments in the field of demographic forecasting, covering both mortality, fertility and migration. For each component emerging methods to forecast them are presented. Moreover, instruments for forecasting evaluation are provided. Bayesian models, nonparametric models, cohort approaches, elicitation of expert opinion, evaluation of probabilistic forecasts are some of the topics covered in the book. In addition, the book is accompanied by complementary material on the web allowing readers to practice with some of the ideas exposed in the book. Readers are encouraged to use this material to apply the new methods to their own data. The book is an important read for demographers, applied statisticians, as well as other social scientists interested or active in the field of population forecasting. Professional population forecasters in statistical agencies will find useful new ideas in various chapters.

• Bengtsson, Tommy & Keilman, Nico (2019). Old and New Perspectives on Mortality Forecasting. Springer Nature. ISBN 9783030050740. 350 p. Full text in Research Archive Show summary

  More than 10 years have gone since the Swedish Social Insurance Agency published a series of booklets entitled Perspectives on Mortality Forecasting. Five volumes appeared in print, on different topics that all are relevant for anyone faced with the task of computing a forecast of mortality in future years. Each volume contained the papers presented in a series of workshops organized by the Stockholm Committee on Mortality Forecasting during the years 2002–2007. The current volume contains reprints of the contributions to the five booklets. Each part of this book corresponds to one original booklet. The field of mortality forecasting is in continuous change. The purpose of the current volume is to track this development by showing the reader what the main issues were some 10–15 years ago, together with an update. Therefore, the book starts with an introductory chapter, which summarizes recent new insights on the following topics: – The need for accurate mortality forecasting today for systems for pension, health care, and elderly care – Determinants and dynamics of life expectancy – Causes of death and lifestyle factors, such as smoking and obesity – Cohort and period perspectives – Compression of mortality – Joint forecasting of mortality in similar populations – From scenarios to stochastic modelling – The way conditions in early life affect mortality in later life – The increasing gap in life expectancy with respect to position in the income distribution Some of the material in the introductory chapter relates to only one of the five sections, while other items in the list above cut across themes. The last item brings up a new topic of mortality forecasting, which was not dealt with in any of the workshops.

• Keilman, Nico (2005). Perspectives on Mortality Forecasting No. 2: Probabilistic Models. Swedish Social Insurance Agency. ISBN 9789175003269. 79 p. Full text in Research Archive Show summary

  This is the second volume in a series presenting papers from workshops on mortality organized by the Stockholm Committee on Mortality Forecasting. The chapters focus on probabilistic (also labeled as stochastic) forecasts, in other words forecasts in which uncertainty has been quantified. Given a history of sizable forecasting errors, the first paper, by Nico Keilman, addresses the question of why demographic forecasts are uncertain. In the second paper Juha Alho outlines the statistical background of uncertain events and forecasts of these. In the third paper Maarten Alders and Joop de Beer sketch the approach taken by Statistics Netherlands in their stochastic forecast of mortality, while in the fourth paper Shripad Tuljapurkar presents a model for mortality analysis and forecasting that has proven to be feasible for probabilistic forecasts. He gives illustrations of US and Swedish mortality, and discusses also possible implications of uncertain mortality for future pension expenditures.

• Bengtsson, Tommy & Keilman, Nico Willem (2003). Perspectives on Mortality Forecasting. Social Insurance Board. ISBN 9789189303249. 97 p. Full text in Research Archive Show summary

  Mortality projections are an essential input for projections of the financial development of pension schemes. Governments and insurance companies all over the world rely on good mortality projections for efficient administration of their pension commitments. But the historical record shows that, during recent decades, demographers have continually underestimated improvements in life expectancy for persons 60 and older. The demographic models used in projecting mortality are usually based on statistical modeling of historical data. The question is, is it possible to improve forecast accuracy of mortality models, and if so, what do demographers need to do to achieve this result? This is the question that provided the impetus for forming the Stockholm Committee on Mortality Forecasting. It brings together a broad range of disciplines, and the work will be reported in the series �Social Insurance Studies�. The committee�s first volume addresses general issues. Why are we interested in improving mortality projections? Which forecast models are in use? How can we forecast life expectancy? How would an epidemiologist improve existing models? How can we use historical experience in getting forecasting right? Which projection models are currently in use in Finland, Norway, and Sweden? Key words: mortality forecasting, pensions, social insurance, statistics, epidemiology, history, Nordic countries

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• Leknes, Stefan; Løkken, Sturla A K; Thomas, Michael; Jia, Zhiyang; Bergsvik, Janna & Rattsø, Jørn Gisle [Show all 9 contributors for this article] (2025). FUTUREPOP project kickoff meeting. Full text in Research Archive
• Keilman, Nico (2023). Projections of migrant and ethnic minority populations. Full text in Research Archive Show summary

  I discuss some of the issues connected to projections and forecasts of migrant and ethnic minority populations. Focusing on examples from the United Kingdom and Norway, I will address problems around definitions of ethnic minority and migrant groups, of data availability, of the handling of components of change, and of forecast uncertainty. I illustrate the latter topic more in detail by a probabilistic forecast to 2060 for the immigrant population of Norway and their Norwegian-born children ("second generation"), grouped by three categories of country background: 1. West-European countries plus the United States, Canada, Australia, and New Zealand; 2. Central and East-European countries that are members of the European Union; 3. other countries. I show how to use a probabilistic forecast to assess the reliability of projections of the immigrant population and their children. The results suggest that a few population trends are quite certain: strong increases to 2060 in the size of the immigrant population (more specifically those who belong to group 3) and of Norwegian-born children of immigrants. However, prediction intervals around the forecasts of immigrants and their children by one-year age groups are so wide that these forecasts are not reliable.

• Keilman, Nico (2022). Recent demographic trends in Nordic countries, with a focus on fertility in Finland and Norway. Full text in Research Archive
• Keilman, Nico (2021). Trends in population health and demography. The Lancet. ISSN 0140-6736. 398(10300), p. 581–581. doi: 10.1016/S0140-6736(21)01113-2. Full text in Research Archive
• Keilman, Nico (2021). New population forecasts predict too few births in sub-Saharan countries. The Lancet. ISSN 0140-6736. 398. Full text in Research Archive
• Keilman, Nico (2020). A probabilistic forecast for the population of Norway, Norway’s 2020 population projections: National level results, methods and assumptions. Statistics Norway. ISSN 9788258711497. p. 177–182. Full text in Research Archive
• Keilman, Nico & Mazzuco, Stefano (2020). Introduction. In Mazzuco, Stefano & Keilman, Nico (Ed.), Developments in Demographic Forecasting. Springer Nature. ISSN 9783030424718. p. 1–20. doi: 10.1007/978-3-030-42472-5_1. Full text in Research Archive Show summary

  Future trends in population size, age structure, regional distribution, and other demographic variables are important for a wide range of planning situations. Hence, many statistical agencies and independent researchers compute demographic forecasts at various levels of detail. The primary aim of this book is to sketch new developments in the field of demographic forecasting. This chapter addresses various issues taken up by the authors of this volume. We discuss deterministic and probabilistic approaches to forecast uncertainty, Bayesian and frequentist perspectives, the role of experts compared to purely data driven methods, and ways to communicate forecast results to the users.

• Keilman, Nico (2019). Probabilistic household and living arrangement forecasts. Full text in Research Archive Show summary

  First, we discuss the shortcomings of deterministic forecasting models, and argue why probabilistic household and living arrangement forecasts are necessary for informed decision-making. Probabilistic forecasts inform the user of the uncertainty around expected household trends. As opposed to a deterministic forecast, which predicts only a few numbers (when projection variants are used) for a certain year, a probabilistic forecast tells us how likely it is that the number of households for a given year in the future will be within a certain range. Information of this kind allows policy makers, planners, and other forecast users in the fields of housing, energy, social security etc. to take appropriate decisions, because some household variables are more difficult to predict, and hence more uncertain, than others. It also guides them once actual developments start to deviate from the most likely path. New actions or updated plans are unnecessary as long as developments are likely to remain close to the expected future. Next, we review probabilistic household forecasts published since the turn of the century. An important issue is how to evaluate, ex-post facto, the accuracy of these probabilistic forecasts. We introduce the notion of a scoring function, the general idea of which is that a forecast that predicts the actual outcome with high probability should receive a better score than one that predicts the same outcome with lower probability. Scoring functions are useful for evaluating both interval forecasts (given in the form of prediction intervals with pre-specified coverage probability), and forecasts available in the form of a full probability distribution, either analytically or as a sample. Finally, we give empirical results for scoring functions applied to the first known probabilistic household forecasts.

• Bengtsson, Tommy; Keilman, Nico; Alho, Juha; Christensen, Kaare; Palmer, Edward & Vaupel, James W. (2019). Introduction. In Bengtsson, Tommy & Keilman, Nico (Ed.), Old and New Perspectives on Mortality Forecasting. Springer Nature. ISSN 9783030050740. p. 1–19. Full text in Research Archive Show summary

  More than 10 years have gone since the Swedish Social Insurance Agency published a series of booklets entitled Perspectives on Mortality Forecasting. Five volumes appeared in print, on different topics that all are relevant for anyone faced with the task of computing a forecast of mortality in future years. Each volume contained the papers presented in a series of workshops organized by the Stockholm Committee on Mortality Forecasting during the years 2002–2007. The current volume contains reprints of the contributions to the five booklets. Each part of this book corresponds to one original booklet. The field of mortality forecasting is in continuous change. The purpose of the current volume is to track this development by showing the reader what the main issues were some 10–15 years ago, together with an update. Therefore, the book starts with an introductory chapter, which summarizes recent new insights on the following topics: – The need for accurate mortality forecasting today for systems for pension, health care, and elderly care – Determinants and dynamics of life expectancy – Causes of death and lifestyle factors, such as smoking and obesity – Cohort and period perspectives – Compression of mortality – Joint forecasting of mortality in similar populations – From scenarios to stochastic modelling – The way conditions in early life affect mortality in later life – The increasing gap in life expectancy with respect to position in the income distribution Some of the material in the introductory chapter relates to only one of the five sections, while other items in the list above cut across themes. The last item brings up a new topic of mortality forecasting, which was not dealt with in any of the workshops.

• Keilman, Nico (2019). Probabilistic household and living arrangement forecasts. Full text in Research Archive Show summary

  First, we discuss the shortcomings of deterministic forecasting models, and argue why probabilistic household and living arrangement forecasts are necessary for informed decision-making. Information from probabilistic forecasts allows policy makers, planners, and other forecast users in the fields of housing, energy, social security etc. to take appropriate decisions, because some household variables are more difficult to predict, and hence more uncertain, than others. It also guides them once actual developments start to deviate from the most likely path. New actions or updated plans are unnecessary as long as developments are likely to remain close to the expected future. Next, we review probabilistic household forecasts published since the turn of the century. An important issue is how to evaluate, ex-post facto, the accuracy of these probabilistic forecasts. We introduce the notion of a scoring function, the general idea of which is that a forecast that predicts the actual outcome with high probability should receive a better score than one that predicts the same outcome with lower probability. Scoring functions are useful for evaluating both interval forecasts (given in the form of prediction intervals with pre-specified coverage probability), and forecasts available in the form of a full probability distribution, either analytically or as a sample. Finally, we give empirical results for scoring functions applied to the first known probabilistic household forecasts.

• Feeney, Griffith; Keilman, Nico; Schmertmann, Carl & Bijak, Jakub (2019). Editorial: The past, present, and future of demographic research. Demographic Research. ISSN 1435-9871. 41, p. 1197–1204. doi: 10.4054/DEMRES.2019.41.41. Full text in Research Archive
• Bengtsson, Tommy & Keilman, Nico (2019). Preface. Demographic Research Monographs. ISSN 1613-5520. p. vii–viii. Full text in Research Archive
• Syse, Astri; Pham, Quang Dinh & Keilman, Nico (2018). Dødelighet og levealder. In Leknes, Stefan; Løkken, Sturla Andreas Kise; Syse, Astri & Tønnessen, Marianne (Ed.), Befolkningsframskrivingene 2018: Modeller, forutsetninger og resultater. Statistics Norway. ISSN 9788253797670. p. 57–86. Full text in Research Archive Show summary

  Denne rapporten gjennomgår hvordan den norske befolkningen ble framskrevet i 2018. Den gir en beskrivelse av resultatene for den nasjonale befolkningen fram til 2100 og den regionale befolkningen fram mot 2040. Rapporten dokumenterer framskrivingsmodellene BEFINN og BEFREG, og beskriver hvilke forutsetninger som ligger til grunn for dette årets framskrivinger.

• Keilman, Nico (2018). Mortality shifts and mortality compression in period and cohort life tables. Full text in Research Archive
• Keilman, Nico (2018). Increasing (but insufficient?) optimism about future life expectancy. N-IUSSP. Full text in Research Archive Show summary

  In June 2018, Statistics Norway (2018) published its latest population forecast. The agency expects that the lifespan of men will increase to 87 years in 2050. This is six years more than the current value of 81 years. In a forecast published in 1993, the life expectancy prediction for 2050 was eight years lower than in today's population forecast. For women, the life expectancy prediction for 2050 increased by "only" four and a half years - from 84.5 years in the 1993 forecast to 89 years now. Demographers and other social scientists, in Norway as well as in other developed countries, have systematically underestimated the rate of increase of the life expectancy. Governments should be concerned about stronger ageing than official forecasts suggest.

• Keilman, Nico (2018). Morgendagens eldre: større sjanse for å bo med partner og mindre sjanse for å bo alene. Full text in Research Archive
• Keilman, Nico (2018). Training Course on Demographic Analysis and Population Projections, Pristina, Kosovo, 4-7 December 2018. Full text in Research Archive
• Keilman, Nico (2018). Forventet levealder og komprimering av dødelighet: perioder og kohorter. Full text in Research Archive Show summary

  Forventet levealder beregnet for et bestemt kalenderår kan gi et misvisende bilde av den virkelige levealderen. Jeg viser hvordan periode-levealderen endrer seg når aldersmønsteret for dødelighet i kohorter endrer seg. Jeg analyserer også komprimering av dødelighet rundt forventet levealder i kohorter og perioder. Jeg viser hvorfor det er stadig sterkere komprimering i periode-dødeligheten. Funnene er basert på periode- og kohortdødelighet fra Human Mortality Database for 10 land, inkludert Norge.

• Keilman, Nico (2017). Population Projection in Kosovo, 2017-2061: Methodology and key findings. Full text in Research Archive
• Keilman, Nico (2017). Period and cohort life expectancy, mortality compression, and age at death distribution. Full text in Research Archive Show summary

  We analyse the age at death distribution (AADD) of the life table, conventionally known as its d(x)-column. We derive general analytical expressions for the moments of this distribution in a period life table, written as functions of the moments in a cohort life table. The first moment is the life expectancy, while the second moment reflects compression of the age at death. The expressions are partly based on an empirical regularity that we found for Norway in observed mortality data for the years 1900-2015, and projected mortality trends until 2100. Using the formula for the first period moment of the AADD, we derive the conditions under which cohort life expectancy increases faster than period life expectancy. We also find expressions for the period life expectancy in the year a birth cohort reaches an age equal to its own life expectancy, and for the gap between the period life expectancy in a certain year and the cohort life expectancy for the cohort born that year. Furthermore, we establish a relation between the period life expectancy in a certain year t, and the lag λ that leads to an equally large cohort life expectancy for a cohort born in year t – λ. This is the number of years it takes a period life expectancy to reach the current level of cohort life expectancy. Finally, using formulae for the second moment of the AADD, we derive expressions for lags and gaps in the standard deviations of the period and cohort AADDs. The latter measures are useful for describing trends in the compression of mortality. Our data show that under this model, as long as cohort life expectancies are lower than 94 years of age for Norwegian men and lower than 92 years of age for Norwegian women, their cohort life expectancies will be below period life expectancies a number of years later, where the time interval equals the cohort’s life expectancy. When cohort life expectancies are higher, they will exceed the period life expectancies at this particular lag. The gap between cohort and period life expectancies will grow by roughly half a year for every one-year increase in cohort life expectancy – or by about one year of age for every period of 6-7 years. The lag λ defined above widens rapidly for Norwegian men and women, by approximately three to four years for every one-year increase of the cohort life expectancy. For women we find that compression of morbidity, as judged by the standard deviation of the AADD above age 30, went more than twice as fast in reality (i.e. in birth cohorts) than what we see by inspecting period data only.

• Keilman, Nico; Pham, Quang Dinh & Syse, Astri (2017). Mortality shifts and mortality compression in Norway 1900-2100: periods and cohorts. Full text in Research Archive Show summary

  BACKGROUND: Life expectancies and compression indicators from period life tables give a distorted picture of average life times and concentration of time of death. Cohort life tables reflect reality better. OBJECTIVE: To derive expressions for life expectancy and variance of age at death in period and cohort life tables METHODS: Focus on d_x-columns of period and cohort life tables. When radix l_0 = 1, d_x is the Age at Death Distribution (AADD). RESULTS: We derived translation formulae for period life expectancy and variation in period age at death as a function of the moments of the cohort AADD.

• Keilman, Nico (2016). A two-sex model for first marriage. Full text in Research Archive
• Keilman, Nico (2016). Probabilistic demographic forecasts. Full text in Research Archive
• Keilman, Nico (2016). Tar SSB høyde for den usikre demografiske utviklingen i framtiden? Full text in Research Archive
• Keilman, Nico (2016). Barnefamilier, fruktbarhetsnivå og samfunnsplanlegging. Full text in Research Archive
• Keilman, Nico (2016). Befolkning: Statistisk sentralbyrå bør endre praksis og publisere sannsynlighetsprognoser. Samfunnsøkonomen. ISSN 1890-5250. p. 59–66. Full text in Research Archive Show summary

  Med jevne mellomrom beregner Statistisk sentralbyrå (SSB) prognoser for befolkningen fram til 2100: alderssammensetningen for hvert år, årlige antall fødsler og dødsfall, størrelsen på inn- og utvandringsstrømmene, antall innvandrere med ulik landbakgrunn, osv. Publisering av en ny prognose er planlagt for den 21. juni i år. I denne kommentaren bruker jeg resultater fra SSBs forrige befolkningsprognose fra 2014 for å gjøre rede for et viktig poeng: den framtidige befolkningsutviklingen er (som alle prognoser) usikker, men noen utviklinger er mer sannsynlige enn andre. Derfor bør SSB publisere sannsynlighetsprognoser, og ikke bare befolkningstall for framtidige år uten at brukeren vet hvor stor sjanse SSB knytter til den ene eller den andre befolkningsutviklingen.

• Keilman, Nico (2016). Probabilistic household forecasts for Denmark, Finland, and the Netherlands 2011-2041: Combining the Brass relational method with a Random Walk model. Full text in Research Archive Show summary

  Probabilistic household forecasts to 2041 are presented for Denmark, Finland, and the Netherlands. Future trends in fertility, mortality and international migration are taken from official population forecasts. Time series of shares of the population in six different household positions are modelled as Random Walks with a Drift. Brass’ relational model preserves the age patterns of the household shares. Probabilistic forecasts for households are computed by combining predictive distributions for the household shares with predictive distributions of the populations, specific for age and sex. If current trends in the three countries continue, we will witness a development towards more and smaller households, often driven by increasing numbers of persons who live alone. We can be quite certain that by 2041, there will be between two and four times as many persons aged 80 and over who live alone when compared with the situation in 2011.

• Keilman, Nico (2015). Dimension reduction by Brass' Relational Model: Household Dynamics in Five European Countries. Full text in Research Archive Show summary

  We use techniques of data dimension reduction to model and predict age patterns of household dynamics in a multi-country context. Probabilistic household forecasts are computed to 2041 for Denmark, Finland, Germany, the Netherlands and Norway. Time series of shares of the population by household position are modelled as Random Walk with Drift. Brass’ relational model preserves the age patterns of the household shares. Predictive distributions for the household shares are combined with predictive distributions of the populations. The predicted continuation of current trends towards more and smaller households is driven by increasing numbers of persons who live alone. Relative prediction uncertainty in more numerous household types is smaller than that in less numerous types.

• Bijak, Jakub; Alberts, Isabel; Alho, Juha; Bryant, John; Buettner, Thomas & Falkingham, Jane [Show all 16 contributors for this article] (2015). Letter to the Editor: Probabilistic Population Forecasts for Informed Decision Making. Journal of Official Statistics. ISSN 0282-423X. 31(4), p. 537–544. doi: 10.1515/JOS-2015-0033. Full text in Research Archive Show summary

  Demographic forecasts are inherently uncertain. Nevertheless, an appropriate description of this uncertainty is a key underpinning of informed decision making. In recent decades, various methods have been developed to describe the uncertainty of future populations and their structures, but the uptake of such tools amongst the practitioners of official population statistics has been lagging behind. In this letter we revisit the arguments for the practical uses of uncertainty assessments in official population forecasts, and address their implications for decision making. We discuss essential challenges, both for the forecasters and forecast users, and make recommendations for the official statistics community.

• Keilman, Nico (2015). Stochastic household forecasts for Denmark, Finland, Germany, Netherlands, Norway. Full text in Research Archive
• Keilman, Nico (2015). Jordens befolkning, "antall munner å mette". Full text in Research Archive
• Keilman, Nico (2014). Norway’s new public pension system: Is it robust against unexpected life expectancy developments? Full text in Research Archive Show summary

  Norway introduced a new system for public old age pensions in January 2011. The new system leads to lower pension expenditures than the old system, because annual pension benefits under the new system are inversely proportional to the remaining life expectancy of those who retire. We can expect public pension expenditures equal to 170 billion Norwegian crowns (NOK) in 2030 and 288 billion NOK in 2050. But expenditures will be larger if retirees live longer than expected. We cannot be certain about the pace of mortality decline in the future. Therefore we have computed a probabilistic population forecast for Norway to 2050 and analysed the consequences of population growth for public old age pension expenditures. A new insight is that the new system is much less robust against unexpected longevity shocks than what was assumed earlier, in spite of the longevity adjustment. The reason is that annual pension benefits are determined when a person retires. After retirement, a retiree’s annual benefits remain the same, even when mortality changes.

• Keilman, Nico (2014). Dimension reduction of household parameter time series by the Brass logit model. Full text in Research Archive
• Keilman, Nico (2014). Probabilistic population and household forecasts. Full text in Research Archive
• Keilman, Nico (2013). Uncertainty in population projections - with special reference to the UK. Full text in Research Archive
• Keilman, Nico (2013). Pensjonsreformen kan bli mye dyrere enn mange tror. Full text in Research Archive Show summary

  Det nye pensjonssystemet medfører lavere offentlige utgifter enn det gamle systemet. Statistisk sentralbyrå forventer en innsparing på 31 mrd. kroner i 2030 og 50 mrd. kroner i 2050. Hvis pensjonistenes levealder øker fortere enn forventet blir innsparingene mindre. Det er usikkert hvor høy denne levealderen kommer til å bli i fremtiden. Derfor har vi laget en sannsynlighetsprognose for befolkningsutviklingen fram til 2050 og beregnet konsekvensene for pensjonsutgifter. Vi finner at de forventede pensjonsutgifter i 2050 er langt fra sikre.

• Keilman, Nico (2013). "What is happening in modern demography: life course analysis, policy evaluation, dimension reduction, prediction intervals in demographic forecasting". Full text in Research Archive
• Keilman, Nico (2013). Probabilistic demographic projections. Full text in Research Archive
• Christiansen, Solveig Tobie Glestad & Keilman, Nico (2012). Probabilistic household forecasts based on register data: the case of Denmark and Finland. Full text in Research Archive
• Keilman, Nico (2012). Integrated modelling of European migration flows: Methodology and main results. Full text in Research Archive
• Keilman, Nico (2012). Onzekerheid in demografische prognoses. Full text in Research Archive
• Keilman, Nico (2012). Missing girls in China will lead to fewer future births than previously thought. Full text in Research Archive
• Keilman, Nico (2012). College huishoudensprognoses. Full text in Research Archive
• Keilman, Nico (2012). Challenges for statistics on households and families. Full text in Research Archive
• Keilman, Nico (2012). Missing girls in China will lead to fewer future births than previously thought. Full text in Research Archive
• Keilman, Nico & Duin, Coen Van (2012). Stochastic household forecasts by coherent random shares predictions. Full text in Research Archive
• Keilman, Nico (2010). On future households. Full text in Research Archive Show summary

  We develop a method for computing probabilistic household forecasts which quantifies uncertainty in the future number of households of various types in a country. A probabilistic household forecast helps policy makers, planners and other forecast users in the fields of housing, energy, social security etc. in taking appropriate decisions, because some household variables are more uncertain than others. Deterministic forecasts traditionally do not quantify uncertainty. We apply the method to data from Norway.We find that predictions of future numbers of married couples, cohabiting couples and one-person households are more certain than those of lone parents and other private households. Our method builds on an existing method for computing probabilistic population forecasts, combining such a forecast with a random breakdown of the population according to household position (single, cohabiting, living with a spouse, living alone etc.). In this application, uncertainty in the total numbers of households of different types derives primarily from random shares, rather than uncertain future population size. A similar method could be applied to obtain probabilistic forecasts for other divisions of the population, such as household size, health or disability status, region of residence and labour market status.

• Keilman, Nico (2009). Failure and success: In-sample and out-of-sample demographic forecasts. Full text in Research Archive Show summary

  There is a growing literature on the quality of population forecasts. All of these forecasts relate to the future, and their accuracy can be established ex post facto. However, a large literature is concerned with explanation and prediction of current, not future behaviour. This paper explores the predictive success of those in-sample predictions. Likelihood statistics for 96 life course analyses published in key demographic journals are investigated. To what extent does predictive success depend on subject matter, on sample size, on type of dependent variable? We find that variables for fertility/reproduction and pair formation/dissolution are difficult to explain, in particular events. For mortality and health variables the situation is somewhat better.

• Keilman, Nico (2008). Uncertain population forecasts. Full text in Research Archive
• Keilman, Nico (2008). Using deterministic and probabilistic population forecasts. Interdisciplinary Communications. ISSN 0809-8735. Full text in Research Archive
• Keilman, Nico (2008). Concern in the European Union about Low Birth Rates. European View. ISSN 1781-6858. 7, p. 333–340. doi: 10.1007/s12290-008-0055-5. Full text in Research Archive Show summary

  While the European Union recognizes the importance of ageing and falling populations in a number of official documents, the findings require focus. In this article, the author first identifies the documents’ failure to name a target birth rate. Second, he stresses that the often mentioned fertility level of an average of 1.5 children per woman underestimates the real figure. Thirdly, he points out the futility of fertility policies when ageing processes will continue regardless of birth rate changes. In response, policies must be coordinated in a number of areas including gender policy, employment policy, immigration policy, housing policy, family policy and economic policy.

• Keilman, Nico & Veløy, Chris (2008). Europa kan halveres på to generasjoner. [Internet]. http://nrk.no/programmer/tv/schrodingers_katt/1.6224278. Full text in Research Archive
• Keilman, Nico (2008). Emerging family and household types in Europe: Issues, definitions and classifications. Full text in Research Archive Show summary

  Earlier work in connection with the preparation of the 2010 round of Population and Housing Censuses for member countries of the United Nations Economic Commission of Europe revealed that in the 2000 round countries experienced difficulties in collecting data for reconstituted families and same-sex couples. Other problematic issues were the distinction between private and institutional households, and the notions of de facto and legal marital status. In addition to problems encountered in population censuses, some emerging family and household types pose problems when mapped by means of sample surveys. The UNECE Task Force on Families and Households has identified a number of additional types for which problems exist. In this paper I shall briefly discuss the problems mentioned above, and refer to possible definitions and classifications for reconstituted families, same-sex couples and couples in a LAT-relationship (Living Apart Together).

• Keilman, Nico (2008). Scenarios of demographic change: the role of probabilistic approaches in population projection. Full text in Research Archive Show summary

  This brief note first summarizes the four main demographic trends that are expected for the coming decades, and discusses two techniques that demographers use for mapping future population trends, namely scenarios and probabilistic projections.

• Keilman, Nico & Veløy, Chris (2008). AFP en ulykke for landet. [Internet]. http://nrk.no/programmer/tv/schrodingers_katt/1.6224469. Full text in Research Archive
• Keilman, Nico (2006). Livslängd och invandring spräckte prognoserna. Välfärd. ISSN 1651-6710. p. 6–7. Full text in Research Archive Show summary

  En analys av befolkningsprognosernas träffsäkerhet i 18 europeiska länder har visat att demograferna har varit för försiktiga i sina antaganden. I Europa har både medellivslängden och invandringen ökat kraftigare under de senaste decennierna än vad demograferna räknade med.

• Keilman, Nico (2006). European demographic forecasts have not become more accurate during the past 25 years. Full text in Research Archive Show summary

  Nowadays, demographers, population statisticians, and population forecasters have richer data, more refined theories of demographic behaviour, and more sophisticated methods of analysis than they had two or three decades ago. This scientific progress should have made it easier to predict demographic behaviour. But my analyses of the errors in old forecasts show that demographic forecasts published by statistical agencies in 14 European countries have not become more accurate over the past 25 years. My findings demonstrate that scientific progress in population studies during the previous two to three decades might have been too slow to keep up with less predictable demographic behaviour of populations in European countries. There is no reason to be more optimistic about US Census Bureau forecasts. I argue that population forecasts are intrinsically uncertain, and hence should be couched in probabilistic terms.

• Keilman, Nico; Cruijsen, Harri & Alho, Juha (2006). Diverging views of future demographic trends. Full text in Research Archive
• Alho, Juha; Cruijsen, Harri & Keilman, Nico (2006). Empirically-based specification of forecast uncertainty. Full text in Research Archive
• Alho, Juha; Alders, Maarten; Cruijsen, Harri; Keilman, Nico; Nikander, Timo & Pham, Quang Dinh (2005). Population decline postponed in Europe. Statistical Magazine. Full text in Research Archive Show summary

  The United Nations and Eurostat recently predicted that the population in 18 European countries will fall in the future. However, the results of a new forecast show that there is reason to expect higher immigration and lower mortality than that predicted by the UN and Eurostat. Hence, the population decline will happen later, and perhaps as late as 2050. For Norway, a population of 5.75 million is anticipated by 2050, slightly higher than the official forecast by Statistics Norway in 2002.

• Alders, Maarten; Keilman, Nico & Cruijsen, Harri (2005). Assumptions for national stochastic population forecasts in 18 European countries. Full text in Research Archive Show summary

  In order to develop and implement stochastic population forecasting for European countries, the European Commission has commissioned the project �Changing population of Europe: uncertain future� to researchers from Joensuu University and the statistical offices of Finland, the Netherlands and Norway. The objective was to develop a general methodology for assessing predictive distributions for fertility, mortality and migration. Generally speaking the assumptions underlying stochastic population forecasts can be assessed by means of analyses of errors of past forecasts, model-based estimates of forecast errors, and expert judgement. All these approaches have been thoroughly investigated in the project. The paper summarises and discusses the results of the different approaches. It demonstrates how the, sometimes conflicting, results can be synthesised into a consistent set of assumptions. Finally, the paper presents the main assumptions about the total fertility rate, life expectancy at birth of men and women, and net migration for 18 European countries.

• Keilman, Nico (2004). Long term public old age pension obligations in a stochastic demographic setting in Norway. Full text in Research Archive
• Keilman, Nico & Vogt, Yngve (2004). Utrygg pensjonsreform: Samfunnet kan tape skyhøye beløp. Full text in Research Archive Show summary

  Datasimuleringer viser at pensjonskommisjonen og politikerne er naive. De har ikke tatt hensyn til usikkerhetsanalyser i befolkningsutviklingen under planleggingen av det nye pensjonssystemet. Det kan koste samfunnet dyrt.

• Keilman, Nico Willem (2003). Model based errors and empirical errors in fertility and mortality forecasts for the Nordic countries. Full text in Research Archive
• Keilman, Nico Willem (2003). Do Cause of Death analyses improve the accuracy of mortality forecasts? Full text in Research Archive
• Keilman, Nico Willem & Pham, Quang Dinh (2002). Time series based errors and empirical errors in fertility forecasts in the Nordic countries. Full text in Research Archive Show summary

  We use time series models to derive model based prediction intervals for the Total Fertility Rate (TFR) in Norway, Sweden, Finland, and Denmark up to 2050. For the short term (5-10 yrs), expected TFR-errors are compared with empirical forecast errors observed in historical population forecasts prepared by the statistical agencies in these countries since 1969. Moreover, we analyse medium-term and long-term (up to 50 years) error patterns based on so-called naïve forecasts, i.e. forecasts that assume that recently observed TFR-levels also apply for the future.

• Keilman, Nico Willem (2002). DEMOGRAPHIC AND SOCIAL IMPLICATIONS OF LOW FERTILITY FOR FAMILY STRUCTURES IN EUROPE. Full text in Research Archive Show summary

  This text is a progress report for the study on ¿Demographic and social implications of new patterns in the family and non-family sectors¿ undertaken for the Council of Europe. The study investigates the relationship between low fertility and new patterns in the family and non-family sectors. The non-family sector is to be understood as consisting of one-person households and childless couples (i.e. couples who have not, or not yet, given birth to any children). The study discusses also the social implications of childlessness, single child families, and other family sizes, thereby focusing on social cohesion. The study is limited to birth order-specific fertility, and couples, thereby not distinguishing between married and cohabiting couples. First, a theoretical perspective on childlessness is given. Next, the impact of changes in birth order-specific fertility on family size is analysed, by using the results from a simulation study, in which I analyse how family sizes change when the quantum and tempo of age- and birth order-specific fertility change. The model applied here is a multidimensional life table. The final section discusses possible consequences for social cohesion and social exclusion of the trends identified in the previous section.

• Keilman, Nico Willem (2002). Book review of S. K. Smith, J. Tayman, and D. Swanson ¿ State and Local Population Projections: Methodology and Analysis¿. Population Studies. ISSN 0032-4728. 56(3), p. 340–341. Full text in Research Archive
• Keilman, Nico Willem; Pham, Dinh Quang & Hetland, Arve (2001). Norway's uncertain demographic future. Full text in Research Archive Show summary

  The demographic future of any country is uncertain. There is not just one possible future, but many. Some of these are more probable than others. Therefore, an exploration of a country's demographic future should include two elements: first, a range of possible outcomes, and second, a probability attached to that range. Together, these two constitute a predictive interval for the variable concerned. The current paper presents predictive intervals for the future size and age-sex composition of Norway's population up to the year 2050. These intervals have been obtained by stochastic simulation, on the basis of repeated runs of the cohort-component model. We describe the method briefly. We also compare our results with those of the official population forecast computed by Statistics Norway, and explain why the latter forecast does not give an appropriate indication of forecast uncertainty.

• Keilman, Nico Willem (2001). Age structural transitions in historical perspective: What can we learn from the past? Full text in Research Archive Show summary

  The paper reviews what can we learn from age structures, and changes therein, when using stable population theory, inverse/back projections and generalizations thereof, variable growth rate method, and old population forecasts. Following the discussion of the accuracy of age structure forecasts for the elderly, I also speculate how we can improve the accuracy of mortality forecasts. The focus is on industrialized countries.

• Keilman, Nico Willem (2001). Population Forecasting. Full text in Research Archive Show summary

  Cohort component method, ratio method, empirical forecast accuracy, stochastic forecasts, use of population forecasts

• Keilman, Nico Willem (2001). Types of models for projecting mortality. Full text in Research Archive Show summary

  The short paper presents a systematic overview of various types of models for projecting mortality. The framework is that of population forecasts of the cohort-component type for the elderly at the national level.I distinguish between demographic and non-demographic models. Demographic models are rather mechanistic, although they include various degrees of judgement. Demographic models can be divided further into extrapolation models and interpolation models. Non-demographic models build on epidemiology and biomedical sciences, and thus are much more of a causal nature than the demographic ones. I distinguish between macro models and micro models.

• Keilman, Nico Willem (2000). Andrew Hinde, Demographic Methods. London: Arnold Publishers 1998. European Journal of Population. ISSN 0168-6577. 16(2), p. 187–188. Full text in Research Archive
• Keilman, Nico (2023). A probabilistic forecast of the immigrant population of Norway. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: We present a probabilistic forecast for the immigrant population of Norway and their Norwegian-born children (“second generation”) broken down by age, sex, and three types of country background: 1. West European countries plus the United States, Canada, Australia, and New Zealand; 2. East European countries that are members of the European Union; 3. other countries. First, we compute a probabilistic forecast of the population of Norway by age and sex, but irrespective of migration background. The future development of the population is simulated 3 000 times by stochastically varying parameters for mortality, fertility and international migration to 2060. We add migrant group detail using stochastically varying random shares to split up each result from the previous step into six sub-groups with immigration background, and one for the non-immigrants. The probabilistic forecast is calibrated against the Medium Variant of Statistics Norway’s official population projection.

• Keilman, Nico & Aristotelous, Georgios (2021). Expert opinion on migration data. QuantMig Deliverable D6.1. ingen. Full text in Research Archive
• Keilman, Nico; Pham, Quang Dinh & Syse, Astri (2018). Mortality shifts and mortality compression: The case of Norway, 1900-2060. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Historically, official Norwegian mortality projections computed by Statistics Norway have consistently under-predicted life expectancy. The projected age distribution of deaths may be used to check if the official mortality projections are plausible. The aim of the paper is to verify whether the projections predict a continuation of the ongoing compression in mortality and of the steady upward shift in the ages at which people die. We use official period data on observed (1900-2015) and projected (2016- 2060) sex- and age-specific mortality to estimate the age distribution of life table deaths. We analyse trends in life expectancy at birth, modal and median ages at death, and standard deviation of the age distribution at ages > 30. The historical shifts towards longer longevity are projected to continue into the future. The projections suggest a steady increase in the modal and the median age at death for men and women towards values between 90 and 94 years in 2060. At present these ages are in the range 83-90 years. Simultaneously, deaths become more concentrated around the mean, as the standard deviation of the age distribution is projected to fall continuously. Statistics Norway’s projection methodology is capable of tracking ongoing processes of mortality shifts towards higher ages and a compression of mortality around the modal and mean ages. Mortality projections could potentially benefit from including assessments of the age distribution of deaths.

• Kastrati, Avni; Uka, Sanije; Sojeva, Arijeta & Keilman, Nico (2017). Kosovo Population Projection 2017-2061. Kosovo Agency of Statistics. ISSN 9789951224208. Full text in Research Archive
• Keilman, Nico (2016). Fødsler og fruktbarhet i Norge. Akademika AS. Full text in Research Archive Show summary

  I dette vedlegget gjøres det rede for at fruktbarhetsnivået i Norge er høyere enn det Samlet fruktbarhetstall (SFT) har vist de siste årene. Samtidig er det meget sannsynlig med en økning i årlig antall fødsler fra rundt 60 000 nå til i underkant av 70 000 om ti år. En tilfredsstillende forklaring for dagens fruktbarhetsnivå er vanskelig å gi. Derfor er predikeringer av framtidens fruktbarhet usikre. En viktig konsekvens er at Statistisk sentralbyrå bør publisere sine befolkningsprognoser i form av sannsynlighetsprognoser. Hvis vi ønsker å løse de problemene en aldrende befolkning medfører med hensyn til vårt velferdssystem, er ikke fruktbarhetsnivået av stor betydning. I denne sammenhengen er det viktig at politikere og samfunnsplanleggere vurderer tiltak innenfor arbeidsmarkedet samt skatte-, helse-, og pensjonssystemene.

• Keilman, Nico (2015). Probabilistic household forecasts for five countries in Europe. ingen. Full text in Research Archive Show summary

  We show how techniques of data dimension reduction can be used to predict patterns of household dynamics in a multi-country context. Probabilistic household forecasts are presented for Denmark, Finland, Germany, the Netherlands, and Norway, spanning the period 2011-2041. Starting point is the population of each country broken down by age, sex, and household position as reported in the census round of 2011. Future trends in fertility, mortality and international migration are taken from official population forecasts. For changes in household structure we rely on time series of household data. Long series of household data, in which the population is broken down by household position, age, and sex, are available for Denmark (1981-2007) and Finland (1988-2009) from the population registers in these countries. For the Netherlands the series are rather short (1995-2011). Annual shares of the population by household position, age, and sex for the three time series countries are modeled using an approach that builds on Brass’ relational model originally developed to model the age pattern of mortality. We find that the household shares can be modelled as Random Walks with Drifts (RWD), independent of country. The Brass approach preserves the age patterns of the household shares. Future household shares are found by extrapolating the RWD processes. This results in household share forecasts, as well as standard errors of the forecasts. Correlations across ages and between men and women are estimated from model residuals. No time series data are available for Germany or Norway. For Germany, we use household transition rates borrowed from Denmark and Finland, but adjusted to cohabitation and marriage levels from the German Generation and Gender Survey. For Norway, we have household transition rates for the year 2010 from the population register. Future household patterns for these two countries are computed by using the multistate household model LIPRO, in which the household transition rates are applied to the household pattern from the census. Uncertainty parameters are borrowed from the time series analyses for Denmark, Finland and the Netherlands. The results show a continuation of current trends towards more and smaller households, often driven by increasing numbers of persons who live alone. The number of households increases faster than population size, which leads to falling average household size. A very consistent finding is that larger households are easier to predict than smaller households, at least when uncertainty is considered in a relative sense.

• Wisniowski, Arkadiusz; Keilman, Nico; Bijak, Jakub; Christiansen, Solveig; Forster, Jonathan & Smith, Peter [Show all 7 contributors for this article] (2011). Augmenting migration statistics with expert knowledge. NORFACE. Full text in Research Archive
• Graziani, Rebecca & Keilman, Nico (2010). The sensitivity of the Scaled Model of Error with respect to the choice of the correlation parameters: A Simulation Study. Økonomisk institutt. Full text in Research Archive Show summary

  Abstract: The Scaled Model of Error has gained considerable popularity during the past ten years as a device for computing probabilistic population forecasts of the cohort-component type. In this report we investigate how sensitive probabilistic population forecasts produced by means of the Scaled Model of Error are for small changes in the correlation parameters. We consider changes in the correlation of the age-specific fertility forecast error increments across time and age, and changes in the correlation of the age-specific mortality forecast error increments across time, age and sex. Next we analyse the impact of such changes on the forecasts of the Total Fertility Rate and of the Male and Female Life Expectancies respectively. For age specific fertility we find that the correlation across ages has only limited impact on the uncertainty in the Total Fertility Rate. As a consequence, annual numbers of births will be little affected. The autocorrelation in error increments is an important parameter, in particular in the long run. Also, the autocorrelation in error increments for age specific mortality is important. It has a large effect on long run uncertainty in life expectancy values, and hence on the uncertainty around the elderly population in the future. In empirical applications of the Scaled Model of Error, one should give due attention to a correct estimation of these two parameters. Key words: Scaled model of error, Stochastic population forecast, Probabilistic cohort component model, Sensitivity, Correlation JEL classifications: C15, C49, C63, J41

• Keilman, Nico Willem & Pham, Quang Dinh (2004). Empirical errors and predicted errors in fertility, mortality and migration forecasts in the European Economic Area. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  We analyse empirical errors observed in historical population forecasts produced by statistical agencies in 14 European countries since 1950. The focus is on forecasts for three demographic variables: fertility (Total Fertility Rate - TFR), mortality (life expectancy at birth), and migration (net migration). We inspect forecast bias and forecast accuracy in the historical forecasts, as well as the distribution of the errors. Finally, we analyse for each of the three variables correlation patterns in forecast errors across countries and, for mortality, the correlation between errors for men and women. In the second part of the report we use time series model to construct prediction intervals to 2050 for the TFR, the life expectancy for men and women, and net migration in 18 European countries. GARCH models are used for fertility and mortality, while net migration is modelled as an autoregressive process. Keywords: stochastic population forecast, empirical forecast errors, prediction intervals, GARCH-models, TFR, life expectancy, net migration, EEA. JEL classification: C22, J11.

• Keilman, Nico Willem (2004). Conséquences démographiques et sociales d'une faible fécondité pour les structures familiales en Europe. Council of Europe Publishing/Editions du Conseil de l'Europe. ISSN 9789287154415. Full text in Research Archive
• Keilman, Nico & Kinsella, Kevin (2004). Families and households in the 2000 round of censuses in ECE member countries. UNECE. Full text in Research Archive
• Keilman, Nico Willem (2003). Demographic and social implications of low fertility for family structures in Europe. Council of Europe Publishing. ISSN 9789287153425. Full text in Research Archive Show summary

  The study sets out to investigate the relationship between low fertility and new patterns in the family and non-family sectors. It examines the social implications of childlessness, single child families, and other family sizes, with an emphasis on questions of social cohesion. Firstly a theoretical perspective on childlessness is given. This is followed by an analysis of the impact of changes in birth order-specific fertility on family size using the results from a simulation study which analyses how family sizes change when the level and timing of age- and birth order-specific fertility change. The final section discusses possible consequences for social cohesion and social exclusion of the trends identified in the previous sections with a focus on poverty.

• Keilman, Nico Willem (2003). Demographic implications of low fertility for family structures in Europe. Strasbourg: Council of Europe. Full text in Research Archive Show summary

  This text reports the findings from the study on �Demographic and social implications of new patterns in the family and non-family sectors� undertaken for the Council of Europe. The study investigates the relationship between low fertility and new patterns in the family and non- family sectors. The study discusses also the social implications of childlessness, single child families, and other family sizes, thereby focusing on social cohesion. The study is limited to birth order-specific fertility, and couples, thereby not distinguishing between married and cohabiting couples. First, a theoretical perspective on childlessness is given. Next, the impact of changes in birth order-specific fertility on family size is analysed, by using the results from a simulation study, in which I analyse how family sizes change when the quantum and tempo of age- and birth order-specific fertility change. The model applied here is a multidimensional life table. The final section discusses possible consequences for social cohesion and social exclusion of the trends identified in the previous section, with a focus on poverty.

• Keilman, Nico Willem (2001). Children and time: The Norwegian model. Netherlands Interdisciplinary Demographic Institute. Full text in Research Archive Show summary

  Norway's family policy has received widespread attention in the Netherlands in recent years. The extremely generous parental leave arrangements and reasonable level of childcare facilities are designed to make it easier for Norwegian women to combine a family and a professional career. In this lecture I shall look into the impact of this family policy on the labour force participation and fertility of women in Norway. The more unintentional effects, such as the time pressures this places on many families with young children, will also be dealt with. Should the Netherlands follow Norway's example?

• Keilman, Nico Willem; Pham, Quang Dinh & Hetland, Arve (2001). Norway's Uncertain Demographic Future. Statistics Norway. ISSN 9788253750026. Full text in Research Archive Show summary

  This report presents prediction intervals for the future population of Norway broken down by age and sex to the horizon 2050. We combined Monte Carlo simulation with a cohort-component population projection model to obtain 5,000 simulations of the population. The odds are four to one (80 per cent chance) that Norway's population, now 4.5 million, will number between 4.3 and 5.4 million in the year 2025, and 3.7-6.4 million in 2050. There is a clear trade-off between greater accuracy (higher odds) and higher precision (narrower intervals). Odds of 19 to one (95 per cent chance) result in a wider interval: 4.1-5.7 million in 2025, and 3.2-7.3 million in 2050. The probabilistic population forecasts of the youngest and the oldest age groups show largest uncertainty, because fertility and mortality are hard to predict. As a result, prediction intervals in 2030 for the population younger than 20 years are so wide, that the forecast is not very informative. International migration shows large prediction intervals around expected levels, but its impact on the age structure is modest. In 2050, uncertainty has cumulated so strongly, that intervals are very large for virtually all age groups, in particular when the intervals are judged in a relative sense (compared to the median forecast). According to our statistical model, the expected accuracy of the total population size forecast published by Statistics Norway is somewhat below two-thirds on the long run, and a little above that level on the short run.

• Keilman, Nico Willem (2000). Demographic Translation: From Period To Cohort Perspective And Back. Department of Economics, University of Oslo. Full text in Research Archive Show summary

  [Internet http://www.sv.uio.no/sosoek/memo/memopdf/memo0600.pdf] When successive birth cohorts of women get their children at progressively lower ages, births that would have occurred during a certain period without changes in the timing, are now "squeezed" into a shorter period. This pushes period fertility up, and the period Total Fertility Rate (TFR) will be inflated, compared to the TFR that would have occurred without changes in the timing. In general, even when the number of children per woman is constant over successive birth cohorts, period fertility levels may vary - they are inflated in years in which childbearing is accelerated, and deflated when women postpone childbearing. Thus period fertility cannot be used as a reliable indicator for the level of cohort fertility: period fertility may be "distorted" in times of tempo changes in cohort fertility. At the same time cohort fertility cannot be fully understood without studying periods. These qualitative links between period and cohort fertility are straightforward. But the detailed interplay between period and cohort fertility, both its quantum (level) and tempo (timing) aspects, can be formalized mathematically. The resulting expressions constitute the core of what has become known as the theory of demographic translation, a term coined by Norman Ryder. This chapter gives a brief general overview of demographic translation theory. It integrates Ryder's findings from the 1960s that he applied to age-specific fertility, with more recent insights, which can be used for analysing other demographic processes, such as childlessness, first marriage, and divorce.

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