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Effects of Long-Run Demographic Changes in a Multi-Country Model*

Author(s):
Paul Masson
Published Date:
December 1991
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I. Introduction

Demographic developments have important macroeconomic effects that are, in principle, forecastable far in advance of their occurrence, because changes in birth rates have effects on the age structure of the population for decades. Indeed, because “baby booms” produce echoes as the baby boomers reach child-bearing age, demographic transitions may take more than a lifetime to work through. Webb and Zia (1989) present simulations for developing countries in which attainment of net reproductive rates (i.e., the number of female children per woman that survive to child-bearing age) of one, so that zero population growth eventually results, still has not produced a stable age structure 70 years later. They also state that “French demography echoes the Napoleonic wars throughout the whole 19th century” (Webb and Zia (1989), p. 11). Consistent with this, long-term demographic projections are available from statistical agencies of many countries extending beyond the middle of the next century.

Macroeconomic effects of the age-structure of the population can be far-reaching. An increase in the dependent population (conventionally defined as those under 15 and 65 and over, divided by those between 15 and 64) will lead to lower labor supply and employment, and higher consumption out of a given national income. It can also be expected to lead to higher government expenditure per capita, on education of the young and medical care of the old; the payment of pensions may also involve large inter-generational transfers.

A number of studies have analyzed the economic effects of aging, but usually in the context of partial equilibrium models, e.g., of consumption, or simple theoretical models. Yet this is an area in which empirical macroeconomic models may have useful long-term predictions—provided of course that these models are constructed in such a way that they have a coherent long-term structure. In particular, it is important that they impose long-run homogeneity properties, are consistent with steady-state growth, and impose full stock-flow equilibrium.

It is also important to consider population aging in a multi-country context, for two reasons. First, increases in dependency ratios in industrial countries (and, to a lesser extent, in developing countries) are so widespread that global effects can be expected. In particular, the level of interest rates world-wide can be expected to change as a result of changes in global saving relative to investment. Second, effects on exchange rates and current account balances will depend on differences in the extent and speed of aging across countries; clearly, in order to gauge effects on these variables it is not sufficient to look at one country in isolation—even if it is a small open economy facing exogenous interest rates and import demand, since those variables will be influenced by population aging in other countries.

Because MULTIMOD, the IMF’s multi-region model (see Masson, Symansky, and Meredith (1990)) is a global model, and careful attention has been paid in its construction to long-run simulation properties, it is a good vehicle for studying the effects of demographic changes. MULTIMOD was used for this purpose in IMF (1990), in which projections for dependency ratios and government spending were simulated from 1996–2025 for each of the Group of Seven countries (i.e., the seven largest industrial countries); a more complete discussion was presented in Masson and Tryon (1990).

From that exercise emerged a dramatic contrast in the implications of demographic changes for Japan and Germany on the one hand, and for the United States (and to a lesser extent Canada) on the other. The former countries experienced a more extreme increase in their dependency ratios, resulting in large declines in saving rates, exchange rate appreciation, and current balance deterioration. In the United States, because of a more moderate (and later) increase in the dependency ratio, saving rates declined much less, the dollar depreciated in real terms, and the current balance improved. The simulations produced sizable shifts in net foreign asset positions of these countries over the period 1996–2025 as a result.

In this paper, the focus is on the causes, and likely magnitudes, of changes in net foreign asset positions resulting from changes in dependency ratios. It is important to stress some of the limitations of the analysis. The paper does not consider the effects of permanent changes in either population size or population growth—it just considers the effects of different age structures. More wide-ranging studies include van Dalen (1991) and Brander and Dowrick (1990). A general treatment of a population growth slowdown is complex because it involves several phases, as the smaller new cohorts progress through the population age structure, and also because long-run effects may depend on a Malthusian “dilution” of fixed factors such as land (Brander and Dowrick (1990)). These issues are not treated here. In Section II of the paper, the age structure of the population is introduced into a simple theoretical model based on the model of Yaari (1965) and Blanchard (1985). In that model, the age structure depends in a simple way on birth and death rates. We illustrate how the age structure changes gradually over time in response to a permanent decline in both birth and death rates, leaving population growth unchanged. The economy’s adjustment to such a demographic transition depends in a key way on wealth effects in consumption and the contribution of net foreign assets to wealth accumulation. The adjustment process to equilibrium is very slow and involves potentially very sizable accumulations of net foreign assets. Section III presents two sets of empirical evidence on these effects: estimates of consumption equations that include dependency ratios and wealth as separate variables, and cointegration results for net foreign assets as ratios to GDP. The consumption estimates are compared to other studies that have attempted to explain differences in saving behavior across countries.

In Section IV simulation results for the G-7 using the estimated consumption equation are discussed, and additional estimates using plausible parameters are presented for Australia. Whether the implications for net foreign asset positions are reasonable or not is then considered. It has been argued that large net positions are unlikely to develop because of risk of confiscation (a point made by Dooley and Isard (1987) and Krugman (1989)), and suggestions are made in a concluding section for extending the model to make the results more plausible.

II. Theoretical Model

The model of Yaari (1965) and Blanchard (1985) can be extended by the addition of dependency ratios to provide a tractable framework for analyzing the effects of demographic changes on consumption. As noted by Blanchard, the model does not allow easy treatment of life cycle considerations. 1/ However, its advantage is that it captures a key feature of overlapping generations models—expected mortality and the birth of new cohorts, which leads to greater discounting of the future—in a very simple setup. Moreover, given its assumptions—that mortality is independent of age—a simple relationship links the age structure of the population to birth and death rates. In our empirical work, 2/ we used this to justify inclusion of a dependency ratio in the consumption equation; the estimates imply a statistically significant positive effect of this variable on the wealth/consumption ratio.

Since the Yaari-Blanchard model is well known, its derivation from individual optimizing behavior will not be presented. The model for a single open economy is presented in Table 1, using similar notation to that in Masson and Tryon ((1990), Appendix), which gives a closed economy version. It is assumed that the birthrate β is exogenous; population is assumed to grow at rate n=β−λ, where λ is a constant mortality rate, and ρ is the pure rate of time preference for any given individual. For the model presented here, monetary factors are ignored.

Table 1.Single Country Model of Demographic Effects
Variable notation:
  • B = real government bond stock (in units of home good)

  • C = real consumption (in units of consumption bundle)

  • E = real exchange rate (increase = depreciation)

  • F = net foreign asset position (in units of foreign good)

  • G = real government spending (falls on domestic output)

  • H = real human capital (in units of home good)

  • K = capital stock (takes the form of home good)

  • L = labor force

  • r = real interest rate (r* is foreign rate)

  • T = real taxes (in units of home good)

  • X = real exports (units of home good)

  • Y = output of home good

Parameters
  • ρ = pure rate of time preference

  • λ = mortality rate

  • Δ = dependency ratio

  • β = birth rate

  • δ = depreciation rate for capital

  • μ = expenditure share for home goods

Aggregation across surviving consumers gives equation (1), which differs from the standard model only in making the ratio of consumption to wealth depend on the variable A, the dependency ratio, through its link with the mortality rate λ. Utility of domestic and foreign goods is assumed to be Cobb-Douglas, so that spending shares are constant—assumed to be μ and l−μ, respectively. (Correspondingly, the consumer price index is Cobb-Douglas, with those same weights.) Human capital, H, discounts future output net of depreciation on the capital stock and lump-sum taxes; households earn both their labor income and the return to capital. Equations (3) and (4) are based on the production function (it assumes that there are constant returns to scale) and the first-order conditions for the optimal capital stock (investment is assumed to take the form of accumulation of home goods) in the absence of adjustment costs. The dependence of the labor force on the dependency ratio (for given population) is made explicit. Open interest parity, equation (5), is assumed, making the domestic real interest rate equal to the foreign rate plus real exchange rate depreciation. Goods market equilibrium, equation (6), makes the sum of domestic and export demand equal to aggregate supply; government spending is assumed to fall solely on home goods. From equation (7), a current account surplus corresponds to accumulation of net claims on foreigners F, assumed to be denominated in units of foreign goods. Equation (8) is the government’s budget constraint.

What is the justification for including the dependency ratio in the consumption equation? In the Yaari-Blanchard model, it is assumed that mortality rates (i.e., the probability of dying in a given period) are independent of age; this allows aggregation across all age groups. However, we can add a feature of life cycle models, the shortening of individuals’ horizons as they age (and hence a higher propensity to consume), by including the dependency ratio as an influence on the consumption/wealth ratio—ρ+λ (which, in the standard model, is constant). Note that, if we are comparing steady states with the same population growth, under the assumptions of the Yaari-Blanchard model, there is a simple relationship linking the mortality rate and the dependency ratio (see Appendix). However, the dependency ratio captures features of a demographic transition related to the life cycle, while the average mortality rate does not. Empirically, the dependency ratio provides a better explanation of consumption—at the cost of introducing, it must be admitted, an element of ad hockery into the elegance of the Yaari-Blanchard model.

What is the effect of a demographic shift for a small open economy facing a given demand function for its exports and an exogenous world interest rate? Consider a situation in which the economy, starting from a steady state, experiences a permanent fall in both birth and death rates by the same amount (leaving population growth unchanged). Figure 1 illustrates the path of the dependency ratio, when the population grows at 1 percent per annum, and birth and death rates decline as of period 0 from 0.02 and 0.01, respectively, to 0.017 and 0.007. This produces first a fall in the dependency ratio since fewer newborn add to those under 15. The trough occurs 15 years after the shift; thereafter, there are fewer and fewer people of working age, lowering the denominator of the dependency ratio. The new higher long-run level of that ratio is achieved after 65 years, when the demographic transition is complete (though not its economic effects). It should be noted that the effect on the overall dependency ratio of an equal decline in birth and mortality rates is ambiguous, though, as pointed out in Masson, Kremers, and Horne (1991), effects on youth and elderly dependency ratios separately are not: the former declines, and the latter increases. 3/

Figure 1.A Demographic Transition to Lower Birth Kates and Death Rates.

Let us now consider the effect of the demographic shift in the model of Table 1—which allows for a positive effect of the overall dependency ratio on the consumption/wealth ratio. Note that if we are comparing steady states with the same real growth rates then the experiment we are considering also involves a fall in the birth rate β, which changes the discounting of wealth in equation (2). However, we may also want to consider changes in the dependency ratio alone.

In a new steady state, lower mortality and birth rates lead to an older population and higher consumption out of wealth. During the demographic transition, however, dependency ratios lead to greater saving and asset accumulation, and, at least for a time, a larger labor force. The labor force L can be written as follows, where POP is total population and PART is the participation rate of those 15–64 (and it is assumed that only they participate in the labor force):

Increases in Δ lower the working age population, which, for a given participation rate, leads to a fall in the labor force that is proportionate to 1+Δ.

In the later stages of the demographic transition, the rise of consumption and fall in labor force both lead to excess demand for the home good; by equation (6), this will mean that the real exchange rate must appreciate, achieving goods market equilibrium by crowding out foreign demand. The current account will deteriorate, since exports decline and imports rise; over time, this will lead to increased net indebtedness to foreigners.

Thus, net foreign assets are expected to increase initially, and be run down later. The ultimate steady-state effect on net foreign positions is complicated, and we will rely on simulations below to gauge the net effects and adjustment paths. First, we will consider the empirical evidence for demographic effects on consumption and net foreign assets.

III. Empirical Evidence

The adjustment process described above depends fundamentally on two mechanisms: a direct effect of the dependency ratio on consumption, and the feedback of net foreign assets through wealth onto consumption (producing a stabilizing effect on the change in net foreign assets). We will examine some empirical evidence for both channels. First, empirical estimates of a consumption equation based on the Yaari-Blanchard model (with the addition of liquidity constraints and lagged adjustment in the form of error correction) are presented. Next, some evidence is given on whether net foreign assets for major industrial countries seem to stabilize as ratios to GNP.

1. Estimated consumption equation

The following describes an updated version of the consumption equation included in MULTIMOD, a preliminary version of which was presented in Masson and Tryon (1990) and which was used in the demographic simulations reported there. The model includes the change in disposable income in addition to wealth, consistent with the strong co-movements in consumption and disposable income observed in aggregate time-series data (see, for instance, Campbell and Mankiw (1989)). Such co-movement could be due both to liquidity constraints and to the fact that consumption as measured includes purchases of consumer durables, rather than their consumption services. The estimated model implements dynamic adjustment in an error-correction framework, as in Davidson and others (1978) and Hendry and von Ungern-Sternberg (1981). As discussed above a dependency ratio is added to capture effects of differences in age structure on consumption and saving. The data for human wealth discount future potential output, which is also affected by future demographic changes: it is the discounted value of future disposable income (see Masson, Symansky, and Meredith (1990), pp. 3–4).

The equation was estimated using instrumental variables 4/ with annual data from 1970 to 1988 pooled across the G-7 countries. The estimated equation, which is used in the simulations described below, is as follows:

where the numbers in parentheses are t-statistics, 5/ and where C is real consumption expenditure, W is real wealth, RLR is the real long-term interest rate (expected inflation is proxied for estimation purposes by a centered ten-year moving average of actual inflation), YD is real, after-tax net domestic product, DEM3 is the overall dependency ratio (the ratio of dependents to the working age population), 6/ and DUM80 is a dummy variable equal to 1.0 after 1980. This variable was included because of evidence of an upward shift in the consumption function in the 1980 for many industrial countries; Auerbach, Cai, and Kotlikoff (1990) also include such a variable in their reduced-form estimates for the United States. 7/ Total wealth W is the sum of the discounted present value of future (noninterest) disposable income and the real value of financial wealth, held in the form of domestic outside money, government bonds, and net claims on foreigners. The disposable income variable YD is constrained by the error-correction specification to have only transitory effects, as liquidity constraints are assumed to operate only in the short to medium term.

The estimated equation attributes a significant positive effect on consumption of an increase in the overall dependency ratio. Including the youth and elderly dependency ratios separately did not significantly increase the explanatory power of the equation, hence they were constrained to have the same coefficient. It was also the case that the data could not reject the constraint of a common coefficient on the overall dependency ratio across countries. There is some evidence from these results that increases in the dependency ratio may have been associated historically with increases in consumption relative to income and wealth, a conclusion that emerges more strongly from the quarterly estimation using U.S. data of a similar specification by Bovenberg and Evans (1990). 8/Auerbach, Cai, and Kotlikoff (1990) also find significant demographic effects on consumption in the United States.

From the equation, a 1 percentage point increase in the dependency ratio, holding other explanatory variables constant, is estimated to cause an increase in consumption of 0.159 percent in the short run and 1.06 percent in the long run. It is of interest to compare these results to those found in other studies. Heller (1989) surveys saving equations that include estimated effects of dependency ratios. Though the definitions of variables differ, as do sample periods, a rough comparison can be made with the equation estimated for MULTIMOD, after converting it to an equation for gross private saving, i.e., to an equation for s = 1 − C/GDP.

Table 2 gives estimates for MULTIMOD as well as for five other models. 9/ It can be seen that MULTIMOD is near the center of the range of available estimates. Each estimate gives a powerful effect on saving of an increase in the elderly as a proportion of the working age population. 10/ It would seem therefore that there is considerable additional support for the hypothesis that the aging of the population projected for the next century is likely to increase consumption relative to income. However, it must be stressed that other studies (Aaron and others (1989), for instance, examining U.S. evidence), have failed to find a significant effect. Graham (1987) cites econometric results that suggest that female labor force participation is a much more important demographic influence on saving rates; and Koskela and Viren (1989), in a comment on Graham’s work, argue that demographic influences are not robust either to data sample or time period. Simulations of MULTIMOD are presented below of the effects of aging on macroeconomic variables, that capture the implications of our estimated consumption equation, as well as effects through the labor force channel mentioned above. First, however, we consider the role of net foreign assets in the adjustment process.

Table 2.Long-Run Effects of an Increase in the Elderly Dependency Ratio on the Private Saving Rate in Various Models
Modigliani (1970)-0.88
Modigliani and Sterling (1980)-0.51
Feldstein (1980)-1.21
Horioka (1989)-1.61
Bateman, and others (1990)-0.53
MULTIMOD-0.85

2. Long-run stability of net foreign assets

It was noted above that a crucial feature of the model presented in Section II is that wealth affects consumption positively, so that net foreign asset accumulations are self-correcting: they do not tend to feed upon themselves and lead to boundless accumulation or decumulation of net foreign debt. What is the evidence in the data on this point? In Masson, Kremers, and Horne (1991), cointegration techniques were used to examine whether there was a long-run relationship between net foreign assets, as a ratio to GNP, and other variables predicted by the model: dependency ratios and government debt. Table 3 summarizes that evidence, for the United States, Germany, and Japan.

Table 3.Cointegration Tests 1/
Coefficients of:Tests
ConstantB/YRDEM1RDEM2Sargan-BhargavaAugmented Dickey-Fuller
United States
0.62-0.440.46-0.870.62-3.51
(0.06)(0.05)(0.08)(0.09)
Japan
0.43-0.210.18-0.390.94-4.22*
(0.06)(0.06)(0.02)(0.03)
Germany
0.360.24-0.810.36-3.04
(0.06)(0.11)(0.25)
Data sources: Masson, Kremers, and Home (1991), Appendix II.

This table reports static OLS regressions of the ratio of net foreign assets to GNP on: a constant; the ratio of government debt to GNP (B/Y) (except for Germany); the foreign ratio of the population aged under 15 years to that from 15 to 64 years relative to the corresponding ratio in the home country (RDEM1); and the foreign ratio of the population aged 65 years and over to that aged from 15 to 64 years relative to the corresponding ratio for the home country (RDEM2). Conventionally computed standard errors are in parentheses. The data are annual for the period 1956-86 (1954-86 for Germany). The tests for non-stationarity of the residuals from these regressions are given by the Sargan-Bhargava test statistic, with critical values in Sargan and Bhargava (1983, Table I), and the Augmented Dickey-Fuller statistic, with critical values in Engle and Yoo (1987, Table 3). Statistics suggesting rejection of non-stationarity at the 5 percent significance level are marked by an asterisk (*). The ADF auxiliary test regressions (not reported) were checked for the absence of autocorrelation.

Data sources: Masson, Kremers, and Home (1991), Appendix II.

This table reports static OLS regressions of the ratio of net foreign assets to GNP on: a constant; the ratio of government debt to GNP (B/Y) (except for Germany); the foreign ratio of the population aged under 15 years to that from 15 to 64 years relative to the corresponding ratio in the home country (RDEM1); and the foreign ratio of the population aged 65 years and over to that aged from 15 to 64 years relative to the corresponding ratio for the home country (RDEM2). Conventionally computed standard errors are in parentheses. The data are annual for the period 1956-86 (1954-86 for Germany). The tests for non-stationarity of the residuals from these regressions are given by the Sargan-Bhargava test statistic, with critical values in Sargan and Bhargava (1983, Table I), and the Augmented Dickey-Fuller statistic, with critical values in Engle and Yoo (1987, Table 3). Statistics suggesting rejection of non-stationarity at the 5 percent significance level are marked by an asterisk (*). The ADF auxiliary test regressions (not reported) were checked for the absence of autocorrelation.

The results suggest some support for the hypothesis that there is a long-run relationship that explains net foreign assets. For Japan, nonstationarity of the error is rejected at the 5 percent level in a static regression of the net foreign asset ratio on government debt and relative dependency ratios. For Germany and the United States, significance levels are somewhat higher than 10 percent. The model of Section II does not distinguish between young dependents and elderly dependents, nor did our estimates of a consumption equation. Here, the two variables—which are measured as other countries’ values divided by the home country’s dependency ratio—have opposite effects on the net foreign asset to GNP ratio, as the steady-state derivations suggest they should. The coefficient on the elderly dependency ratio implies that an increase in the proportion of elderly in the home country would lead to higher net foreign assets, because the elderly accumulate assets during their working lives, allowing them to dissave in their retirement years. This is consistent with the implications of the Blanchard-Yaari model (see Appendix I to Masson, Kremers, and Home (1991)). In any case, the cointegration results provide weak evidence that feedback mechanisms may exist that prevent net foreign assets and liabilities from growing without bounds relative to output. Reinforcing this result, we found that error correction models could be estimated for domestic absorption in which the error from the cointegration equation entered significantly, that is, higher net foreign assets tended to increase domestic absorption (Masson, Kremers, and Home (1991)). The increase in domestic absorption relative to output reduces the current account balance, tending to stabilize net foreign assets.

IV. Simulations of Population Aging

1. A demographic transition due to a fall in birth and death rates

Given the fact that MULTIMOD has well-designed long-run properties that reflect full stock/flow equilibrium, it is possible to use the model, with the estimated consumption equation reported above, to simulate the impact of population aging in industrial countries. We first consider a stylized demographic transition, in which the path induced by a fall in birth and death rates is simulated, leading to a fall and then a rise in the dependency ratio in a single country (as plotted in Figure 1). Such a transition occurred after the post-war baby boom; with the subsequent birth rate decline, the earlier larger cohorts have major effects on the dependency ratio as they move through the population age structure. In this first simulation, we do not use actual data for dependency ratios, however; they are generated by the birth and death rate assumptions described above (the birth rate decline is also taken into account in the human wealth calculation). In the next subsection, actual demographic projections are simulated, but relative to where we are now, not to the position when the demographic transition started two decades ago. 11/

The demographic transition is assumed to occur in the United States only, and to start in 1985. It can be seen that U.S. net foreign assets first rise and later fall (Figure 2). The fact that the demographic transition takes a very long time is illustrated here. In principle, the simulation horizon should probably extend well beyond the point where the dependency ratio has settled down, but our projections of exogenous variables arbitrarily stop in 2050. We have recently updated the data and extrapolated them further, however, and plan to use them in the future to simulate beyond 2050.

Figure 2.Simulated Demographic Transition Starting in 1985.

(deviations from baseline)

2. Simulating projected changes in dependency ratios for G-7 countries

Instead of using assumed paths for birth and death rates (or actual historical data on dependency ratios extending back several decades), we may want to simulate only part of the demographic transition. Since the initial stages of the demographic transition related to the baby boom are history, of more immediate relevance for the future is what further changes are built in. Consistent with this, in the next set of simulations the lower birth rate is taken as a given, and the effect of only the subsequent path for dependency ratios is simulated, not the decline in β.

Available projections for the dependency ratios of the young and elderly are presented in Table 4 for industrial countries. It can be seen that the youth dependency ratio, which declined sharply from 1965 to 1985, is projected to remain roughly constant from 1995 to 2025. In contrast, the elderly dependency ratio is projected to rise in all countries. The overall dependency ratio, which is the variable that appears in MULTIMOD, increases dramatically as a result. The asset accumulation phase, which would be associated with a decline in dependency ratios, is thus largely behind us—except possibly for the United States.

Table 4.Major Industrial Countries: Selected Demographic Variables; 1965–2025

(In percent)

Projections
1965197519851995200520152025
(Population under 15/Population 15–64)
United States51393334292930
Japan38363225282827
Germany 1/35342223221923
France41383231282628
Italy25252224
United Kingdom36372931313131
Canada57413230272528
Australia3633313030
(Population 65 and over/Population 15–64)
United States16161819182129
Japan9121519263332
Germany 1/18232124293137
France19222022242733
Italy22252832
United Kingdom19222323222428
Canada13131518192534
Australia1617182126
(Overall Dependency Ratio)
United States67555152475059
Japan48484744546159
Germany 1/54564347515160
France61605253525361
Italy 2/52544547505055
United Kingdom55595254535559
Canada70544848465061
Australia5250495156
Sources: OECD Labor Force Statistics, 1964–84 and 1967–87, and Demographic Databank projections, Social Affairs, Manpower and Education Directorate, OECD. Australia’s data interpolated from Bateman and others (1990), Table 2.1.

West Germany only.

Fund staff estimates for 1965–85.

Sources: OECD Labor Force Statistics, 1964–84 and 1967–87, and Demographic Databank projections, Social Affairs, Manpower and Education Directorate, OECD. Australia’s data interpolated from Bateman and others (1990), Table 2.1.

West Germany only.

Fund staff estimates for 1965–85.

Our simulations use the year 1995 as a base, and examine what is the effect of the increase in dependency ratios over the period 1996–2025, compared to a simulation in which they remain unchanged at their 1995 values. 12/ Increases of 13–15 percentage points are projected for Japan and Germany (our data for Germany just refer to West Germany, before unification with the former GDR). In contrast, the ratio for the United States increases by just 7 percentage points over that period, and actually declines in the 1996–2015 period. Other G-7 countries have projections that are intermediate between them. Data for Australia (interpolated from those presented in Bateman and others (1990)), are close to those for the United States. Simulations for Australia will be discussed in the next section.

In doing the simulations here, only effects on consumption and on labor supply (and hence on potential output) are considered. 13/ Results of the simulation are presented in Table 5 for each of the G-7 countries and the remaining industrial countries as a group. It can be seen that population aging produces quite large effects in most countries by 2025. In the United States, the early decline in the dependency ratio leads to a rise in GNP, while the opposite is true of Japan and Germany. Mirroring the decline in the population of working age, the capital stock per worker rises strongly in the early decades of the next century in Japan and Germany, and private saving as a ratio to GNP falls.

Table 5.Simulation of Changes in Dependency Ratios, 1996–2025
200020052010201520202025
United States
Real GNP (In percent)0.93.95.54.92.7-0.3
Real interest rate0.2-1.4-2.8-3.1-2.3-0.3
Real effective exchange rate (In percent)-8.314.4-15.9-13.6-9.0-4.3
GDP per worker (In percent)0.93.24.33.51.1Ȓ2.1
Capital stock per worker (In percent)0.33.06.58.67.52.5
(As a percent of GNP)
Current account balance0.92.22.92.82.42.2
Private saving1.53.54.74.53.00.8
Gross private investment0.61.52.01.50.2-1.8
Net foreign assets2.49.318.726.430.632.2
Japan
Real GNP (In percent)-0.1-2.0-4.0-6.0-7.9-10.0
Real interest rate-2.9-2.7-1.9-0.50.81.6
Real effective exchange rate (In percent)14.929.742.847.842.430.6
GDP per worker (In percent)0.3-0.9-2.5-4.2-5.7-7.0
Capital stock per worker (In percent)3.36.06.54.81.4-2.9
(As a percent of GNP)
Current account balance-1.5-2.8-3.5-3.7-3.8-4.0
Private saving-0.0-2.0-3.6-4.6-5.0-5.3
Gross private investment1.41.00.2-0.7-1.3-1.6
Net foreign assets-7.9-17.5-27.6-37.3-46.4-54.7
Germany1/
Real GNP (In percent)-0.2Ȓ1.8-2.5-2.9-4.4-6.9
Real interest rate-0.9-1.2-1.8-2.0-1.6-0.6
Real effective exchange rate (In percent)1.42.92.60.6-0.40.3
GDP per worker (In percent)-0.5-1.0-1.0-1.2-3.0-6.3
Capital stock per worker (In percent)0.92.63.84.02.2-2.5
(As a percent of GNP)
Current account balance0.1-1.3-2.0-1.8-1.3-0.9
Private saving1.00.3-0.2-0.4-1.1-2.9
Gross private investment1.01.51.71.2-0.2-2.4
Net foreign assets-0.8-4.4-9.9-14.4-16.2-16.2
United Kingdom
Real GNP (In percent)-0.21.21.91.5-0.1-2.2
Real interest rate-0.4-1.0-1.9-1.9-1.5-0.4
Real effective exchange rate (In percent)-3.0-5.3-7.3-8.8-10.5-11.5
GDP per worker (In percent)-0.21.01.51.0-0.6-2.7
Capital stock per worker (In percent)0.11.83.54.12.3-2.0
(As a percent of GNP)
Current account balance-0.10.50.80.80.50.5
Private saving0.71.82.31.90.7-1.0
Gross private investment0.81.31.40.8-0.2-1.9
Net foreign assets0.11.53.75.66.26.5
France
Real GNP (In percent)0.11.42.32.00.1-2.2
Real interest rate-0.3-0.9-2.2-2.4-1.8-0.5
Real effective exchange rate (In percent)-1.6-3.6-5.6-6.1-5.3-4.5
GDP per worker (In percent)0.11.42.21.9-0.3-2.9
Capital stock per worker (In percent)0.32.24.45.94.70.6
(As a percent of GNP)
Current account balance0.30.81.01.10.80.7
Private saving0.91.92.72.61.4-0.3
Gross private investment0.61.21.61.30.2-1.4
Net foreign assets1.23.57.010.111.711.7
Italy
Real GNP (In percent)-0.3-0.3-0.10.0-1.3-3.4
Real interest rate-1.0-0.7-1.4-1.7-1.5-0.9
Real effective exchange rate (In percent)1.63.21.3-1.5-3.9-5.2
GDP per worker (In percent)-0.2-0.4-0.3-0.3-1.7-3.9
Capital stock per worker (In percent)1.02.43.44.12.8-0.9
(As a percent of GNP)
Current account balance-0.00.30.50.70.91.0
Private saving0.50.91.72.12.01.0
Gross private investment0.80.81.00.80.1-1.3
Net foreign assets0.61.32.44.06.28.6
Canada
Real GNP (In percent)0.42.53.72.6-0.0-3.7
Real interest rate-0.0-1.6-2.8-3.0-2.3-0.5
Real effective exchange rate (In percent)-2.5-4.9-5.3-4.1-1.71.7
GDP per worker (In percent)0.52.22.91.7-1.0-4.8
Capital stock per worker (In percent)1.04.17.79.57.71.7
(As a percent of GNP)
Current account balance0.10.81.61.81.81.7
Private saving1.12.73.93.71.9-1.0
Gross private investment1.12.22.51.5-0.5-3.3
Net foreign assets0.93.07.813.317.720.7
Smaller Industrial Countries
Real GNP (In percent)0.00.91.20.4-1.5-4.1
Real interest rate-0.7-1.3-2.0-2.0-1.5-0.3
Real effective exchange (In percent)0.1-0.3-0.7-1.1-1.4-1.7
GDP per worker (In percent)0.10.80.9-0.0-1.9-4.5
Capital stock per worker (In percent)1.03.04.75.23.3-1.4
(As a percent of GNP)
Current account balance-0.20.20.60.70.70.8
Private saving0.81.72.21.80.5-1.4
Gross private investment1.11.61.60.9-0.6-2.7
Net foreign assets0.40.81.93.34.86.6

West Germany only.

West Germany only.

Because of differences in the extent of population aging, there are large effects on exchange rates and current account balances. As discussed above, the countries with the largest increases in dependency ratios have the largest declines in their saving ratios, exchange rate appreciation, and large falls in current account balances. Over the period 1996–2025, the exchange rate of Japan appreciates by 30 percent in real effective terms, while its current account balance shows a reduced surplus (or increased deficit) relative to baseline by as much as 4 percent of GNP. Germany sees its currency appreciate by a much more modest amount, and its current balance deteriorate by less also—a peak of 2 percent of GNP in 2010 relative to baseline. In contrast, the U.S. dollar appreciates in real terms, and the U.S. current account balance improves significantly. Interestingly enough, these tendencies go in opposite directions to recent current balance developments, which saw persistent U.S. current account deficits and Japanese and German surpluses in the second half of the 1980s. 14/ Over these 30 years, the current account effects cumulate into large changes of net foreign asset positions: a fall of 55 percent of GNP for Japan and 16 percent of GNP for Germany, and an increase of 32 percent of GNP for the United States. It is important to remember that these are not projections, since other factors will also affect the evolution of net foreign asset positions; however, the resulting effects are large, as can be judged by the levels of net foreign asset or liability ratios for these three countries at the end of the decade of the 1980s: a net debtor position of roughly 13 percent of GNP for the United States, and net creditor positions for Japan and Germany of 14 and 26 percent of their respective GNP levels. 15/

3. Simulation results for Australia

Since Australia is not separately included in MULTIMOD (it is included in a group of non-G-7 industrial countries), the same simulation methodology could not be directly applied. Instead, a model similar in structure to the country models (including the consumption equation reported above), was simulated with the changes in dependency ratio projected in Table 4 for Australia, and the variables for other countries generated by the simulation reported in Table 5 were used as inputs. In other words, Australia is treated as a small open economy, with the effects of dependency ratios on other countries taken into account as they affect Australia, but not the effects of Australia on the rest of the world—the Australian economy is taken to be recursive with respect to MULTIMOD. These results are reported in Table 6.

Table 6.Simulation of Changes in Dependency Ratio for Australia
200020052010201520202025
Real GNP (in percent)0.11.22.21.60.1-2.1
Real interest rate-0.5-1.1-1.9-1.9-1.5-0.3
Real effective exchange rate (in percent)0.3-0.8-2.2-3.0-4.0-4.5
GDP per worker (in percent)0.21.11.91.1-0.6-3.0
Capital stock per worker (in percent)1.13.04.85.43.6-0.9
(As a percent of GNP)
Current account balance-0.30.31.01.41.42.2
Private saving0.71.72.72.61.60.0
Gross private investment1.11.51.60.9-0.5-2.7
Net foreign assets-0.10.22.76.911.517.3

It can be seen from a comparison with Table 5 that Australia, like the United States, experiences a rise in real GNP over the period 1996–2020, as its dependency ratio initially falls slightly. 16/ Australia’s real effective exchange rate depreciates and the current balance improves. Only in the 2020–2025 period does Australia’s GNP decline relative to baseline. The cumulative increase in net foreign assets to 2025, about 17 percent of GNP, is considerably smaller than for the United States, but is still sizable. The demographic transition in Australia, which is less severe than in some other industrial countries, does not seem likely to involve major macroeconomic disruption. Indeed, the model simulations suggests that it might tend to offset recent large current account deficits. 17/

4. Are large net foreign asset positions likely to emerge?

The simulations reported above imply large changes in net foreign asset positions, especially for the United States and Japan—unless offset by other factors. In addition, the horizon of the simulations, to 2025, leaves out subsequent projected aging of populations. In any case, cumulated changes on net foreign assets would continue even in the absence of further demographic shifts, if effects on saving and investment persisted. Therefore, the question arises as to whether changes of such magnitude are likely to occur.

A quite different projection exercise was undertaken by Hamada and Iwata (1989), who simulated various hypothesized saving relationships for the United States, Japan, and Germany until 2030. In their study, demographic influences on saving were assumed to operate in some of the scenarios; however, they did not reverse existing differences in saving rates—the United States continued to save less than the other two countries. A scenario in which capital moves to equate rates of return—that is, perfect capital mobility is assumed—leads to projections of foreign ownership equal to 30–40 percent of the U.S. capital stock by 2030. Assuming a capital/output ratio of 2.5, this yields net foreign liability ratios of some 75–100 percent of GNP.

In commenting on this article, Krugman (1989) argues that such large changes in net foreign asset positions are unlikely in fact to emerge:

I do not believe that really massive net holdings of claims by one industrial country against another are possible in the modern world … The late twentieth century is a time of highly politicized economies, in which sovereign states cannot credibly guarantee that they will keep hands off…. [S]uppose that the U.S. had a net external debt of 50 percent of GNP. Can we be sure that the U.S. would not consider a moratorium on debt service? (see Krugman (1989), p. 1085).

What is at issue is the assumption that capital is perfectly mobile, that current account deficits can be always be financed provided that borrowing can be justified by rate of return considerations. 18/ The contrary position is argued by Feldstein and Horioka (1980), who point to the strong correlation between domestic investment and saving: as a result, current account deficits, and reliance on foreign saving, are limited.

It is important to point out the differences between the approach underlying the MULTIMOD simulations and that used by Hamada and Iwata (1989). Our simulations were not intended to be projections, but rather to give the partial effects of changes in a particular variable, the dependency ratio; it is quite conceivable that other exogenous variables would lead to offsetting effects. In particular, slower population aging in the United States than in Japan may do no more than partially reverse the large gap in saving rates that prevails at present between the two countries. To the extent that current account deficits involving running down assets (as is the case for Japan in our simulations), rather than incurring large net foreign liabilities, they would be less subject to the criticism expressed by Krugman. In contrast, Hamada and Iwata attempt to make unconditional projections of actual saving rates and the implied paths for net foreign assets, which imply a considerable widening of the U.S. net liability position.

Our model also differs from their analysis in incorporating terms of trade changes. One of Krugman’s criticisms of the model in Hamada and Iwata was that it was a one-good model; changes in saving behavior, Krugman argues, should lead to changes in terms of trade that would at least partially offset the net impact on current balances. Our simulations allow for this channel, but nevertheless suggest that large changes in current balances and net foreign assets could result from demographic changes.

If it is true that large changes in net foreign asset positions are not plausible, how should the models be changed in order to achieve greater realism? Ideally, we should have a theory of investor behavior that would reflect fears of the increased likelihood of confiscation or expropriation as net liability positions increased; this avenue has been explored by Dooley and Isard in several articles. 19/ Empirical application of such a theory is limited by the relative absence of large net external positions, at least for the largest industrial countries, though Canada is a net external debtor to the extent of at least 50 percent of its GNP, and Australia’s net debt has exceeded 30 percent of GNP. Moreover, the initial empirical promise of models in which interest rate differentials depended on net foreign asset positions has not survived extensive testing.

The stabilizing mechanism that would come into play in such a model is that higher net foreign liabilities would lead to increased borrowing costs, which would tend to crowd out domestic investment and bring it more closely into line with available domestic saving. Whether this mechanism would effectively stabilize the stock of net foreign assets is however questionable, because higher borrowing costs increase the interest service component of the current account deficit, which in itself increases the accumulation of foreign liabilities. Moreover, the empirical evidence suggests that within a fairly wide range, interest rates respond little, if at all, to changes in net foreign assets. Currie, Levine, and Vidalis (1987) found that making interest rates respond to contemporaneous net foreign asset positions (in a small model based on the OECD’s INTERLINK, and in which a portfolio balance model is implemented), gave very long adjustment periods—several centuries. Stabilizing net foreign assets through this channel requires both a strong response of borrowing costs to net foreign assets and a strong interest rate response of domestic absorption—features that are not present in most empirical macroeconomic models. Therefore, modeling limits to perfect capital mobility in the traditional portfolio-balance framework may not give the desired results.

It would seem that the effect of net foreign assets is a nonlinear one; it is only when net liabilities approach a level that is considered unsustainable is the supply of financing affected. In addition, investors react not just to the current stock, but to projections of what net debt will become in the future. Consistent with this reasoning, a possible approach involves imposing a terminal condition on net foreign asset positions, such that risk premiums in interest rates respond not to the current value of net foreign assets but rather to values at an end point that is sufficiently far ahead. This is an approach implemented experimentally in MULTIMOD by Chadha and Symansky (1990). Another possibility, suggested by Warwick McKibbin, is to model government reactions—for instance the taxation of nonresidents by the home country. With model-consistent expectations, this will provide a disincentive to international capital flows, limiting net foreign asset positions. More work is certainly needed, but in any case both seem to be promising avenues. Unfortunately, we still lack a theory of the sustainability of current account positions—and net debt—in the long run.

V. Concluding Remarks

Demographic developments constitute an important influence on the long-run evolution of economies. Because those developments can in principle be anticipated far in advance, and because they have predictable effects on aggregate demand and supply, they constitute an important application of empirical macroeconomic models. This paper has described simulations of changes in dependency ratios in industrial countries, using a global multi-country model, MULTIMOD.

The magnitude of resulting changes in GNP, current balances, and net foreign assets that emerge from the simulations is quite large. Indeed, some have questioned whether net foreign asset changes of this size are plausible—casting doubt on one of the features of the model, the existence of perfect capital mobility, as implemented in the model through uncovered interest parity. Relaxing this assumption naturally leads to consideration of other aspects of the long-run equilibrium that are important to model. In particular, issues of the sustainability of balance of payments positions and the responses of investors to risks of expropriation and confiscation in foreign countries come into play. However, these issues go beyond the scope of the present paper.

APPENDIX: Dependency Ratios in a Demographic Transition

Assume that we are initially in a steady state with constant birth rate βo= λo + n and death rate λo (where n is the population growth rate). At time 0, both birth and death rates decline by the same amount (where λ1 is the new mortality rate). As in Yaari (1965) and Blanchard (1985), at a point in time death rates are the same for all ages. Consider the subsequent path for the dependency ratio Δ(t), defined as those under 15 and over 65 divided by those between 15 and 65. It can be shown that in a first phase, for 0 < t ≤ 15,

In a middle phase, for 15 < t ≤ 65,

Finally, after the transition is completed, i.e., for 65 < t,

It can be seen that the last expression is independent of t (and of the previous mortality rate λo).

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This can be done by simulation of overlapping generations models, as in Auerbach and others (1989), but absence of detailed data makes the calibration of such models difficult; their analysis, moreover, does not allow for global effects.

See Masson and Tryon (1990), updated below.

The combined effect thus depends on the size of these two age groups. The ambiguity of the net effect suggests including the two ratios separately in a consumption equation. They are included together in the estimation results reported below because the data accepted the restriction of a common coefficient.

Instruments used were the total population, foreign absorption, the 1980 dummy, and lagged variables of the nominal interest rate, consumption, the ratio of government spending to potential output, and inflation.

Equation standard errors range from 0.013 to 0.033, and R-squares from 0.23 to 0.55.

Expressed as a decimal fraction, rather than in percent as in Table 4 below.

In further work, we will test whether the timing of the shift in consumption differs across countries.

Their measure of wealth is household net worth, and they include separate population variables to capture dependents below age 20 and over age 65.

The estimate for MULTIMOD assumes a consumption income ratio (C/Y) of 0.8.

These studies also estimate a separate effect of the proportion of the young in the population; in each case, this variable has the same sign but a smaller coefficient.

Data limitations prevented us from starting simulations that far back.

Changes in the size of the population are not considered, just in its age structure.

In Masson and Tryon (1990), projections of government spending changes due to demography were also simulated, with an earlier version of MULTIMOD that had larger interest elasticities of saving and investment.

However, by 1991, current account imbalances of these three countries had been much reduced, and Germany was even running a current account deficit as a result of unification.

These net asset positions are presumably the reflection, in part, of the earlier phases of the post-war demographic transition.

Dowrick (1988) projects increasing aggregate participation rates over the period 1991–2001, which would imply that dependency ratios corrected for labor force participation would decline even more.

It would thus tend to reinforce the view expressed by Pitchford (1990) that Australia’s foreign debt is not cause for concern.

Alternatively, a proper incorporation of government confiscation through taxation or default would adjust downward expected returns, discouraging capital inflows.

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