This volume includes 29 papers, all but one of which have appeared previously as journal articles. The authors have made a good selection, and the collection provides a sense of topics that have engaged economists concerned with population ageing. The papers focus on macroeconomic effects of population ageing on the standard of living (how well we live). Much of the popular concern is whether public pension and health-care systems will be sustainable. What economists bring to this discussion – their comparative advantage – is to focus attention on issues of supply (such as the productive capacity of the economy, or the size of the pie) as well as those concerned with demand (such as the claims made on the pie by older members of the population). On the supply side, for example, are behavioural responses to changes in market conditions that could affect productive capacity induced by population ageing?

In the shorthand of economists, the average standard of living can be represented by consumption per capita (C/N). It in turn can be expressed as an identity, , the component parts of which are associated with the three sections of the volume. They are ‘productivity and growth’ (Y/L, output per employed person), ‘consumption, saving and investment’ (C/Y, the fraction of aggregate output that is consumed, the balance being saved and invested) and, with somewhat more of a stretch, ‘labour and fiscal effects’ (L/N, the fraction of the population that is employed). The decision to organise the volume in this way means that much research is excluded, for example, that concerned with migration, female labour-force participation, health care and environmental aspects. Even so, the range of topics covered and approaches identified is substantial, and the editors provide a satisfying though brief overview explaining what they have focused on and why. The papers reflect the tendency among economists to think in structural and general equilibrium terms. Thus, for example, the income-fertility relationship is central to many chapters: causality runs from the economy to the population as well as in the opposite (and more familiar) direction.

The papers were all written by economists and, in most cases, for economists. While some were intended to reach a broader audience, such as Chapters 6 (Lee), 13 (Elmendorf and Sheiner), 18 (Weil), 24 (Flodén) and 28 (MacKellar), interested readers will find it rewarding to peruse all chapters, even those in which the technical demands are greatest, to gain an impression of the range of population phenomena that have been the subject of economic analysis. The big question in Section 1 is whether we would be better off if fertility were higher or lower. Ahituv (Chapter 1) concludes that, after accounting for income-fertility interactions, a one per cent drop in fertility would lead to a three per cent increase in output per capita. Slower population growth could mean, however, that fewer ideas are generated and hence productivity and, in consequence, income growth would be reduced. Jones (Chapter 7) argues that increases in research intensity and education could provide only temporary offsets. However, declining productivity may not be inevitable. Becker and colleagues (Chapter 3) develop a model in which the rate of return to human capital increases with the stock of human capital, at least after a point, thereby encouraging further investment and increasing the rate of growth, and in the model of Dalgaard and Kreiner (Chapter 4) we find that making the stock of human capital endogenous offsets productivity decline. In another perspective on the importance of education, de la Croix and Doepke (Chapter 5) explore the impact of income distribution and conclude that increasing income inequality tends to reduce the average level of education and hence economic growth. Weil's contribution (Chapter 18) is concerned, in part, with the optimal rate of population growth and would appear to fit better in this section.

Section 2 explores the relationship between population ageing and the share of income devoted to consumption, an issue framed by economists as the impact on the aggregate saving rate. The analysis is based on the ‘life cycle model’ where people borrow while young, save in mid-life, and dis-save in old age. Population ageing is thus seen as a change in the relative proportions of savers and dis-savers in overlapping generations models. Auerbach and Kotlikoff (Chapter 10) and Miles (Chapter 17) use this theoretical framework to simulate the evolution of the future saving rate and conclude that it will fall. Cutler and colleagues (Chapter 12) and Elmendorf and Sheiner (Chapter 13) ask a more ambitious question: what is the optimal saving rate in an ageing population? Both studies find that the lower saving rate predicted by Auerbach and Kotlikoff would be close to optimal. Cutler et al. also emphasise the importance of technical change and observe that technical change itself may be induced by a relative scarcity of labour. Miles (Chapter 17) and Kelley and Schmidt (Chapter 20) raise the important issue of whether the life cycle model is supported by the evidence. They summarise the debate, noting how the lack of support in early empirical studies has evolved into more robust support in recent work. Chapters 11 (Brooks), 14 (Guest and McDonald), 15 (Jansen), 16 (Kenc and Sayan), and 19 (Higgins) use a variety of approaches to analyse the consequences for capital mobility of differential ageing across regions; all conclude that dis-saving in older economies will be partially financed by saving in younger economies in Asia and Latin America.

The introduction anticipates that Section 3 will help readers to understand the causes and consequences of changes in the fraction of the population in the labour force, but only Chapter 23 (Elmeskov) focuses on the causes. It appears that differences across countries greatly exceed the within-country changes over time, something that he attributes to differing (dis)incentives to work (such as income replacement rates, tax rates, and unemployment benefits). Most of the remaining chapters in the Section are concerned with the consequences. Among the issues addressed are whether public budgets are better balanced or, at least in part, deficit financed (Chapter 26, Ono), the impact on intergenerational equity (Chapter 22, Buiter; 29, von Weizsäcker), the lessons from the optimal taxation literature (Chapter 24, Flodén), and what difference it makes how open the economy is to international trade (Chapter 27, Sadka and Tanzi). In addition, Lee and Edwards (Chapter 25) draw attention to the uncertainty of future population change itself and provide probabilistic projections of a variety of fiscal effects.

What do we learn from the collection? Population ageing is often seen as a threat: age-related expenditures will increase, productive capacity will decline. The authors in this volume provide a much more balanced view of what lies ahead, and how legitimate concerns might be addressed. Understanding the effects of existing policies and anticipating the effects of policy changes is important. So, too, is identifying the many margins on which incentive structures could change through market-based adjustments as well as policy initiatives.