The Discovery of Age Structure I

The Discovery of Age Structure

The question of just how demographic change interacts with economic and social development has been debated in the social sciences since time immemorial. In the 18th century the mercantilists held that a large population stimulates economic growth, and this argument has continued to rear its head from time to time across the years, especially in its more refined form that population growth through stimulating demand and investment may stimulate development. In the 19th century Malthus advanced the argument that population growth, by producing decreasing returns in agriculture, leads to lower per capita income. Since this time both these arguments have tended to come and go, with the pendulum swinging now this way, now that.

In general, neo-malthusians (like the Swede Knut Wicksell at the end of the 19th century) have continued to argue that population growth is harmful, while Keynesians have tended to see population growth as a stimulus to investment demand and, thus, to income growth (Perlman 1975). A third, more neutralist view, which has gained considerable influence since the 1970s onwards, argues that population growth rates are not an economically determining factor, one way or the other, and is not a significant variable when it comes to understanding differences in per capita income growth.


More recently this view has been subjected to increasing criticism after having maintained considerable influence all through the 1990s as study after study seemed to reveal little cross-country evidence that would justify thinking there was any significant demographivc effect, either in the form of dividend or in that of penalty. One obvious limitation of much of this population 'neutralist' growth research they largely involved holding virtually every other factor which could conceivably infuence the situation constant in order to test exclusively for correlations between rates of population growth and per capita income growth.

Whether results obtained in this way truly reflect the unimportance of population growth, or, as some have argued, are the summative outcome of the impact of diffent, and mutually offsetting, negative and positive influences of population on economic growth still continues to be debated to this day.

Critics of such studies tend to cite the existence of inadequate control variables or other such model specification errors, or the relatively poor quality of the available data, or the presence of reverse causality, or all of these combined. As a result, and despite a not insignificant quantity of empirical work, the population issue continues to be a relatively open question.


Nonetheless, this earlier body of empirical research surely tended to support what has come to be known as the population neutralist view. This view has been the dominant academic belief in this area since the early 1980s, a state which critics claim has lead to the marginalization of population and reproductive health questions as instruments of economic development within key development agencies like the World Bank (Birdsall 2003, Kelley 2003).


However of late interest in the macroeconomic consequences of population change has renewed itself (and forcefully so). The change in attitudes can be traced to new evidence that comes in three forms.

First, a series of empirical studies based on aggregate level panel data have concluded that demographic factors do in fact have a strong, statistically significant effect on aggregate saving rates (Bloom and others, 2003; Deaton and others, 2000; Kelley and others, 1996; Kinugasa, 2004; Williamson and others, 2001) and on economic growth (Bloom and others, 2001; Bloom and others, 1998; Kelley and others, 1995).

Second, detailed case studies of the East Asian miracle have provided compelling and consistent evidence that what has come to be called the "demographic dividend" was an important element economic success of the region (Bloom and others, 1998; Mason, 2001b; Mason and others, 1999). In a study which really made it impossible to continue to ignore the relevance of demographic changes Bloom and Williamson (1998) using econometric techniques concluded that about one-third of East Asia’s increase in per capita income was due to the demographic dividend. While not everyone has accepted these conclusions at face value (Schultz, 2005), there is little doubt that an increase in the proportion of the population of working age was a significant factor in their growth tramnsition. In a similar vein, Mason (2001a), using growth accounting methods, estimates that the 'demographic dividend' accounted for about a quarter of the Tiger’s economic growth during the 'growth spurt'.

In the third place the combination of having a rapidly increasing proportion of the population over retirement age coupled with an unprecedentedly low level of fertility in the world's second and third largest economies (Japan and Germany) has concentrated attention on the "population topic" as never before.

While it should be obvious, it is perhaps worth noting here that all the above-cited authors argue that even though age-structure variables do have predictive power and can 'explain' a significant portion of economic growth during the development process, the relationship between demographic variables and the economy is not a deterministic one. Population matters, but policy matters to, and whether or not governments put in place an appropriate package of policies makes a big difference between whether the opportunity offered by the demographic dividend is put to productive use or simply frittered. The difference between the experiences of some Latin American countries and some Asian ones is clearly salutory here.


The Coale Hoover Hypothesis


The recent blossoming of interest in the demographic and age-structure related components of growth in fact date-back to the year 1958 and the publication of an influential book by Ansley J. Coale and Edgar Hoover - Population Growth and Economic Development in Low-Income Countries.

The Coale-Hoover hypothesis, as it has come to be called, was based on one simple but powerful intuition: rapid population growth arising from falling infant and child mortality swells the ranks of dependent young, and this single demographic event in and of itself increases consumption at the expense of saving.


Using simulation results from a mathematical model calibrated with Indian data, Coale and Hoover concluded that India's development would be substantially enhanced by lower rates of population growth.

Their analysis rested on two premises. Firstly, that in post initial-mortality-decline 'child-heavy' societies household and aggregate saving is reduced by the generalised presence of large families. And secondly, the existence of such high ratios of dependent children skews aggregate investment away from more self-evidently economically productive activities, since there is a continuous pressure for funds funds to be transferred towards so-called 'unproductive' population-sensitive social expenditures (like health and education).


The key novelty in the Coale Hoover model was to link this 'crowding out' process to the age composition of the high-fertility population, and not simply to its size, density, or growth, per se.

Pioneering in several dimensions, their book:

1) identified several possible theoretical linkages between population and economic growth which were in harmony with the economic-growth paradigms of the time (e.g., an emphasis on physical capital formation);

2) formalized these linkages into a mathematical model that was parameterized and simulated to generate forecasts of alternative fertility scenarios over the intermediate-run;

3) provided a case study of an important country whose prospects were considered by many analysts to be grim. The Coale-Hoover framework was transparent and easy to understand, the assumptions were made explicit and qualified, and the findings were clearly expounded and accessible to a wide readership.

The model identified, and the simulations quantified, three adverse impacts of population growth:

1) capital-shallowing--a reduction in the ratio of capital to labor because there is nothing about population growth per se that increases the rate of saving;

2) age-dependency--an increase in youth-dependency, which raises the requirements for household consumption at the expense of saving, while diminishing the rate of saving;

3) investment diversion--a shift of (mainly government) spending into areas such as health and education at the expense of (assumed-to-be) more productive, growth-oriented investments.

In particular it attracted attention a good deal of attention from economists since its principal focus was on physical capital (as distinct from the Malthusian focus which was on land). At the time physical capital accumulation was considered by many to be 'the' key to economic development.

Their work, which at the time had a substantial impact on U.S. population policy and thinking, did not go unchallenged. In fact over time its impact waned since subsequent empirical research failed to uncover the empirically strong and consistent impacts of population movements on saving in the developing and less developed world which the Coale Hoover thesis was thought to have anticipated.

Nathaniel Leff in an early study using a sample of 74 countries found the log of gross savings rates to be inversely related to the proportion of the population either under 15 or over 64 (Leff, 1969), a finding which appeared to place the youth dependency hypothesis on a solid empirical footing. Subsequent research, however, (Goldberger,1973, Ram, 1982) failed to find confirmation of the dependency hypothesis and researchers even cast doubt on the validity of the empirical methods employed in the initial Leff study.

Contemporaneous theoretical developments also seemed to undermine the foundations of the dependency hypothesis. The principal rival, Tobin’s (1967) life-cycle model, took it as axiomatic that the savings rate should increase with as population growth did. The reason for this is simple, at least in Tobin's original version of the model: faster population growth tilts the age distribution toward young, saving, households and away from older, dissaving ones.

The representative agent version of Robert Solow’s neoclassical growth model also pointed in the same direction, with faster population growth resulting in higher savings rates in response to heightened investment demand (Cass 1965, Phelps 1968, and Solow 1956). However, neither clas of model directly addressed the dynamics of the dividend implicit in the ongoing impact of the demographic transition.

The "age tilt" in Tobin’s steady-state model, while interesting in and of itself, occurs simply because the model takes the decision from the outset to describe a world restricted to active adults and retired dependents. Had the model incorporated the idea of youth dependency a very different tilt-effect would have been produced.

In similar fashion, the standard neoclassical growth models assume exogenously fixed labor participation rates, and, by implication, assume no change endogenously driven in the dependency ratio. Clearly this kind of assumption is strictly speaking 'necessary' if one's objective is the conceptualisation of "steady-state" behaviour, but it precisely fails to capture what one might argue are the key "transitional dynamics" of a continuing process of demographic change, and in so doing it seems to beg the very question it is expected to answer. In effect the whole neoclassical school of models gain in rigour precisely at the price of sacrificing the rich population dynamics which were implicit in Coale and Hoover’s early theorising on the East-Asian demographic transition.

The empirical findings which went against Coale and Hoover are not perhaps entirely surprising. At the household level, the saving impacts they attempted to describe are fundamentally based on a 'life-cycle' conceptualization of behaviour and such a conceptualisation requires a substantial 'forward looking' planning horizon. The behavioural transition which is required also involves a considerable evolution in institutional structure (developed capital markets, reliable pension options etc) in order to make the implementation of such lifetime plans feasible. At the time of Coale and Hoover these conditions simply did not pertain in the vast majority of the then third world countries. For many families living in an agricultural context spending on children represents a form of saving (e.g., parents may expect transfers from their children in old age) and, children, as many studies reveal, can be viewed as a productive asset both in the household and on the farm (Doepke 2004, Doepke and Zilibotti 2005).


New Wave Age Structure Theory

The climate at the end of the 80s, and the evaluation which was made of Coale and Hoover is perhaps well summed-up in the following observation by Angus Deaton (1992): "Although there are some studies that find ... demographic effects, the results are typically not robust, and there is no consensus on the direction of the effect on saving."

As has been said above, in recent years there has been a considerable revival of interest in the Coale-Hoover model, and this despite the known limitations (see eg Williamson 2001), and in fact a revised form of their dependency hypothesis has enjoyed something of a renaissance. The original hypothesis has now evolved into class of explicit economic models that, suitably calibrated, account tolerably well for cross-country savings variations in macro time-series. Almost all recent analyses of macro data confirm Coale-Hoover effects to a greater or lesser extent(Collins 1991; Harrigan 1996; Higgins 1994, 1998a; Kang 1994; Kelley and Schmidt 1995, 1996; Lee, Mason, and Miller 1997; Masson 1990; Taylor 1995; Taylor and Williamson 1994; Webb and Zia 1990; and Williamson 1993).

This succesful renaissance of the Coale Hoover hypothesis is in large measure due to the work of fairly limited number of researchers. What might be termed the 'new wave' of age-structure research possibly begins with a paper by Mason and Fry (1982) Subsequently elaborated further by Mason (1987,1988). These researchers developed what they called a 'variable rate-of-growth effect' model which sought to establish a link between youth dependency ratios and national saving rates. The model relied principally on the insight that given the existence of positive labor productivity growth, younger cohorts enjoy higher permanent incomes and higher consumption than their elders. If consumption is shifted from child-rearing to later, non-childrearing stages of the life cycle, aggregate savings rise with a strength that depends directly on the growth rate of national income. The dependency and lifecyle perspectives are thus unified through the effect that changes in the youth dependency ratio induce in the timing of life-cycle consumption.

A decline in the youth dependency ratio, for example, should cause consumption to be shifted from the childrearing years to later, non-childrearing stages of the lifecycle. As a result, according to their model, the saving rate depends on the product of the youth dependency ratio and the growth rate of national income (the Tobin 'growth-tilt effect'), as well as on the dependency ratio itself (the 'composition effect').

Their findings contained an important qualitative implication for the "classic" dependency model: the demographic "center of gravity" for investment demand should be located earlier in the age distribution than that for savings supply. In particular, investment demand should be more closely related to the share of young (through its connection with labor-force growth), while savings supply should be more closely related to share of mature adults (through its connection with retirement needs). The divergence between these centers of gravity implies that the effects of demographic change on savings and net capital flows will depend on the economy's degree of openness to capital flows.


In an open economy, a population with a heavily child-centred age distribution should exhibit a tendency towards current account deficits: savings are low due to the high youth dependency burden. Later as increasing numbers of young people enter the labour market investment rises in response to higher labour-force growth. Then as the age distribution shifts steadily upwards, the savings supply should increase pushing the current account into surplus.

It is also important to note that the negative coefficients for the elderly need not indicate that they are actually drawing down their stocks of assets. The burden of supporting the elderly (either directly or through transfer payments) might lead to lower saving by younger households. Alternatively, prime-age households with elderly parents might save less in anticipation of bequest receipts (Weil, 1994). The age coefficients are not behavioural parameters which describe the actions of agents belonging to different age groups, but instead capture the relationship between the age distribution and the behaviour of agents of all ages.



The Demographic Dividend



Use of the expression demographic dividend goes back an early Bloom and Williamson paper (1998). As stated above in the paper they use quantitative results from cross-country econometric regressions in an attempt to calculate the contribution made by age structure changes to the 'spurt' in East Asian economic growth. According to their argument the demographic "dividend" leads to opportunities for growth of output per capita for two reasons.

First, there is an impact on total GDP due to a "growth accounting effect": a rising share of the total population in the working-age group increases the ratio of "producers" to "consumers". Obviously this situation contributes positively to the growth of output per capita.

Secondly, they conjecture that age-distributions might also be associated with what they call "behavioral effects", and these in turn exert an influence on the growth of output per capita.

Formally the the accounting effect and the behavioral effects can be decomposed in that growth in per capita income is a function of both growth in the proportion of the population of working age and growth in productivity per worker. The former is what is termed the "compositional effect" and the latter the "behavioural effect".


Simply stated, the demographic dividend occurs when a fall in the birth rate following an initial mortality decline produces changes in the age distribution of a society, and these changes mean that fewer investments are required to meet the needs of the youngest age groups. Thus resources are released which may be used for investment in economic development and for improved family welfare. That is, a falling birth rate makes for a smaller population at the young, dependent, ages and for relatively more people in the adult age groups who comprise the productive labor force. It improves the ratio of productive workers to child dependents in the population. That makes for faster economic growth and fewer burdens on families.

The demographic dividend, however, does not last forever. There is a limited window of opportunity. In time, the age distribution changes again, as the large adult population moves into the older, less-productive age brackets and is followed by the smaller cohorts born during the fertility decline. When this occurs, the dependency ratio rises again, this time involving the need to care for the elderly, rather than the need to take care of the young.

In addition, the dividend is not automatic. While demographic pressures are normally eased when fertility initially falls, some countries will take better advantage of this easing than others. Some countries will act to capitalize upon the released resources and use them effectively, while others will not. However, in time, the window of opportunity closes, those that who have not found the way to take ample advantage of the demographic dividend may well face renewed resource pressures at a time when their ability to respond is weaker than ever.

The demographic dividend is delivered through the operation of several interconnected mechanisms.

Labor Supply

As the demographic transition follows its course the generations of children born during the high fertility years enter adult life and become workers. Women who are now having fewer children than before are released from childrearing responsibilities and are able to take jobs outside of the home; also, as the transition moves forward and years of compulsory education increase youngerwomen tend to be better educated than those in the older cohorts, and are thus more productive once inside the labor force.


Savings

Working-age adults tend to earn more and thus can potentially save more than new-entrants to the labour market. Thus the larger generations who work their way through the labour force as the age pyramid changes favors greater personal and national savings. This ability to save becomes even greater as these "thick cohorts" move into their 40s, especially as in the first instance the generation-span is smaller, and their own children rapidly become wage-earners themselves and hence require less support. Thus personal savings continue to grow and are able to serve as a source of investment funds. Countries thus steadily move from being heavily dependent on external finance, to a position of relative financial self-sufficiency.

Human Capital

Having fewer children normally enhances the health of both mother and child. Female participation in the labor force, in turn, enhances the social status and personal and financial independence of women. Also fewer children normally means fewer and better educated. More investment is allocated to each individual child.


Theory and Modeling

The more general awareness of these issues among economists coincided with the emergence in the 1990s of the empirical "convergence" models of economic growth. Pioneered by Robert Barro, these empirical paradigms postulate the existence of either a universal, or a country-specific, long-run steady state and then proceed to attempt to identify the factors (economic, political, social, institutional, geographic etc) that determine each country's long-run growth rate, and in the shorter-to-intermediate-run the transition to this longer-run state. These models lend themselves to demographic investigation due to the differentiation between short- and long-run impacts.


Three approaches dominate the extensive literature on economic-demographic modeling: simple correlations, production functions, and convergence patterns.


Simple-correlations studies hypothesize that per capita output growth is influenced by various dimensions of demography in the following fashion: Y/Ngr = f(D),


Production Functions

Production-function studies are based on estimating variants of a model:
Y = g(K, L, H, R, T),

Convergence Patterns

Convergence-patterns studies, rooted in neoclassical growth theory, explore the relationships between economic growth and the level of economic development. They focus on the pace at which countries move from their current level of labor productivity to their long-run, or steady-state equilibrium level of labor productivity.

A revealing feature of the convergence-patterns models can be seen if we take a closer look at some of the variables which have been omitted by Barro and those working in this tradition. In the majority of papers authors emphasize variables that determine longrun, or "potential" labor productivity, and downplay variables that bring about the "adjustment" or transition to long-run equilibrium. An example of one such omitted variable would be the investment share. Leaving aside for the moment the issue of endogeneity, investment can be viewed as an adjustment variable.

Indeed investment might be considered to be the first variable one would think to include in a model which focuses on labour productivity. Levine and Renelt (1992) surveyed numerous empirical growth studies to identify a common set of influential variables and found, somewhat unsurprisingly, that investment rates constituted the single most robust variable. Rather than implying that the investment rate is a viable Z variable for predicting long-run capital-to-output ratios, however, the significance of this finding is that it suggests an incomplete set of Z variables. If the convergence hypothesis were correct and the list of Z variables were complete, the investment coefficient would in theory be insignificant (see Bloom, Canning, and Malaney (2001), Higgins and Williamson (1994), and Kelley and Schmidt (1994)).


The gap between current and long-run labor force productivity largely dictates the return to investment. In theory investment should flow to those countries which exhibit the highest returns. So, rather than investment accounting for growth per se, it could be argued that the it is the "structural" features of a country (among which one could incorporate its demographic strucure) which either impede or facilitate investment that ultimately determine growth.


Attempts to incorporate demography into convergence models have been few and normally relaively ad hoc. Demographic variables that qualify are those that affect long run labour productivity, and those that condition the transition to it. The nature of these two types of demographic variables can be illustrated by examining Barro (1997) and Kelley and Schmidt (1994), both of which highlight long-run impacts of demography but exclude a role for transitions, Kelley and Schmidt (1995) which examines both long-run and transition impacts,and Bloom and Williamson (1998), which captures primarily the transition impacts.

Empirical analysis was enrichened in the 1990s with the emergence of a theoretical framework by Robert J. Barro (Barro 1991) that incorporates demography into convergence (or technologygap) models. He and collaborators concluded that high fertility, population growth, and mortality all exert negative impacts on per capita output growth. In 1994 Kelley and Schmidt extended this list to include population density and size, which revealed positive impacts, although a net negative assessment of combined demographic trends represented the bottom line.


Barro (1997) focuses on a single demographic variable, the Total Fertility Rate (TFR). This variable captures both the adverse capital-shallowing impact of more rapid population growth, and the resource costs of raising children versus producing other goods and services. By its very nature the TFR exerts its impacts mainly on long-run labor productivity, to the detriment of the short-run transitions en route to equilibrium. TFR is, after all, a hypothetical construct that represents what the fertility rate "would be" if the current age-specific fertility rates were maintained over a long period of time.

Bloom and Williamson

In the late 1990s there was a further evolution in the convergence modeling of demography by several Harvard economists (e.g., David Bloom, David Canning, Jeffrey Sachs, and Jeffrey Williamson). Building on the Barro setup (albeit with a different choice of core variables), the Harvard framework focused on population impacts that take place due to imbalanced age-structure changes over the Demographic Transition. Their modeling compactly captured these impacts by just two variables: population growth (Ngr) and working-age growth (WAgr). Such a specification neatly follows from an identity that “translates” a traditional neoclassical model formulated in output per worker growth into a comparable model formulated in output per capita growth. While by construction such a translation represents accounting, it nevertheless provides a way of exposing some shorter-period “population impacts” within the usual long-run neoclassical framework. Assessments of such accounting impacts of demography in numerous Harvard empirical papers are shown to be sizeable, especially in East Asia.


Much of this work takes as its starting point an alternative methodology for exposing such dynamic relationships which was advanced by Bloom and Williamson (Bloom and williamson, 1998, BW hereafter). Demography in the BW model follows neatly from a definition that translates the convergence model from one that explains productivity growth into one that explains per capita output growth. In the Bloom and Williamson version of the demographic dividend thesis, the accounting and behavioral effects of the age transition can be decomposed using fairly straightforward econometric techniques which involve the formulation of an identity function, the taking of natural logarithms of output per capita and the differentiation of the resulting expression with respect to time.

Starting with the definition of output per labor hour, it can be shown that the basic model can be transformed into one which describes the growth process in per-capita terms. Now the impacts of working-hour growth and population growth cancel each other out when they change at the same rate, something which certainly occurs in a steady-state growth situation with a static age pyramid. This condition is normally imposed by assumption in most empirical studies. BW note that the 1960s, 1970s, and 1980s were periods of demographic transition for most developing countries. As a result, neither condition held and differential growth rates should be observed. This of course is what in parctice was the case.

In the BW setup, the workforce share in fact has no impact on output growth. BW replace labour force growth with a pure demographic proxy, the growth rate of the working-age population. That is, as if the only determinant of hours worked were the age-distribution of the population, hence the relative growth of the working-age versus full population constitutes the sole impact of demography in their model. Following the BW setup, sometimes the impact of demography will be positive, sometimes negative, and sometimes zero. The model thus highlights the reality that demographic impacts vary during the transition but is silent on the issue of possible demographic impacts on long-run labor productivity; i.e., demography does not affect the Barro Z's.

As a result, the BW model has a narrower interpretation than most renderings in the recent literature, which often admit both short- and long-run impacts of demographic change as a part of their theoretical structure. On the other hand, it has the desirable attribute of clarity in its interpretation.

Second, consider the focus of the BW model on the transitional impacts of demographic change. The postulated relations between population growth and working age growth, respectively, allow a clear interpretation for the role of demography: relatively rapid growth of the working-age population will speed the transition to long-run economic prosperity. However, two countries with the same Z’s will ultimately arrive at the same level of labour productivity growth, irrespective of their demography.

BW acknowledge the possibility that the rates of growth of working age and total population might impact long run labour productivity, but they fail to model this explicitly. Nor do they include other demographic variables among the Z’s. Rather, they limit themselves to noting that long run influences could result in coefficient estimates which deviate from unity.



While Bloom & Williamson (1998) focus on output per capita as the dependent variable, the recent literature argues that an understanding of international differences in output per worker is needed, since only workers contribute to production. From regressions with the growth rate of output per capita as the dependent variable it is rather complicated to assess behavioral effects (see Bloom et al. (2001) for an assessment of behavioral effects from such regressions).


Kelley and Schmidt (2001) for example demonstrated the implication of this point by evaluating the net impact of demographic change on economic growth in eight empirical renderings.

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