Demographics, Wealth, and Global Imbalances in the Twenty-First Century

Not whether aging matters, but by how much and in which direction going forward. The authors describe a “widespread view” that aging raises saving and so explains falling returns on private wealth, rising private wealth-to-GDP ratios, and — insofar as it differs across countries — rising global imbalances. “Beyond this qualitative consensus lies substantial disagreement about magnitudes”: structural estimates of the effect of demographics on interest rates over 1970–2015 run “from a moderate decline of less than 1 percentage point (pp, Gagnon, Johannsen and López-Salido 2021) to a large decline of over 3 pp (Eggertsson, Mehrotra and Robbins 2019).” On the future, economists split on sign. The paper quotes Larry Summers directly: “Once people have aged and they’re retiring, then they draw down their savings and spend. And so I think we’re making a transition from more saving because of aging, to less saving because aging has happened.” The authors state their position as flatly as the claim: “Our paper refutes this argument and shows that, instead, demographics will continue to push strongly in the same direction.”

It is the direct impact of the changing age distribution on log wealth-to-GDP, holding the age profiles of wealth and labor income fixed — a shift-share, but one the paper ties to a general equilibrium counterfactual. In the baseline overlapping-generations model it “is a sufficient statistic for the actual change in wealth-to-GDP for a small open economy” facing a fixed return. For the world economy, the compositional effect aggregated across countries, “combined with elasticities of asset supply and demand that we obtain with other sufficient statistic formulas—fully pins down the general equilibrium effect on returns, wealth-to-GDP, and global imbalances.” The authors position this against two existing reduced-form traditions — Mankiw and Weil (1989) and Poterba (2001) computing changing age distributions over fixed asset profiles, and Cutler, Poterba, Sheiner and Summers (1990) and the demographic-dividend literature doing the same over fixed income profiles — noting that such calculations “are very intuitive, but are not tied to specific general equilibrium counterfactuals”, and that what they show is that “a ratio of two such shift-shares is the driver of equilibrium outcomes in a fully specified OLG model.”

UN population projections crossed with household survey age profiles of wealth and labor income, for 25 countries, with 2016 as the base year. Age distributions come from the 2019 United Nations World Population Prospects in five-year buckets, under the baseline, high-fertility and low-fertility scenarios. Labor income profiles come from the Luxembourg Income Study — total pretax labor income of individuals of a given age, including wages, salaries, bonuses, fringe benefits and self-employment income before social security and labor income taxes, divided by the number of individuals of that age. Wealth profiles come from a collection of wealth surveys including the US Survey of Consumer Finances and the European Household Finance and Consumption Survey, measured as total assets net of liabilities with housing and defined-contribution pension wealth included and mortgages deducted; for the United States the authors add age-specific estimates of the funded component of private defined-benefit plans from Sabelhaus and Volz (2019). Household wealth is mapped to individuals by splitting it equally across the head of household, the spouse, and any other household members at least as old as the head, with the appendix reporting robustness to other splitting rules.

Positive everywhere, averaging 31.7 log points globally to 2100, and ranging by more than a factor of three across countries. Between 1950 and 2016 the effect was positive everywhere, 23 log points on average and 25 in the United States — against an actual change in wealth-to-GDP of 59 log points for the average country and 32 in the US, which reflects other forces and general equilibrium adjustment as well. Looking forward from 2016 to 2100 the effect is larger on average and more dispersed: 17 log points in Sweden, 28 in the United States, 45 in China, 56 in India. Fertility assumptions move it substantially — under high fertility the effect falls to 29 in China and 16 in the US, under low fertility it “swells to 69 log points in China and 43 in the United States.” The authors attribute the cross-country dispersion mainly to demography rather than to differences in profiles: “countries with large effects are those whose demographic transitions are later and faster”, and recomputing every country’s effect using US asset and income profiles raises the levels slightly while leaving the heterogeneity similar.

That the old hold much more wealth than the young and, on average, do not spend it down much as they age. The authors describe this as “remarkably robust across countries and time”, and it is what makes an older age distribution mechanically raise wealth-to-GDP. The effect has two parts, which the paper separates: shifting the population into high-wealth ages pushes up assets, while the same shift first pushes up aggregate labor income as the baby boomers reach middle age — the demographic dividend of Bloom, Canning and Sevilla (2003) — and later pushes it down as more people reach old age. Both the numerator and the denominator of wealth-to-GDP therefore move in the same direction over the century.

Both from closed-form sufficient-statistic formulas requiring only aggregates and two standard parameters. Asset supply responds to the required return in proportion to the initial global capital-wealth ratio and the inverse of the user cost: with a capital-wealth ratio of 0.79 and a user cost of 9.5%, the supply semielasticity runs from 4.1 to 12.4 for capital-labor substitution between 0.5 and 1.5, and equals 8.3 under Cobb-Douglas. Asset demand decomposes into a substitution term of 43.7, an income term of −0.6 and a labor-share term of 5.8; with an elasticity of intertemporal substitution of 0.5 and Cobb-Douglas production this gives 21.2, meaning “a decrease in r by one percentage point would reduce households’ desired wealth relative to GDP by around 21%.” The authors note the dominant positive substitution term makes demand upward-sloping “unless σ is extremely low” — positive as long as the elasticity exceeds 0.014 under Cobb-Douglas — and offer a back-of-the-envelope reconstruction: consumption-to-wealth of roughly one eighth times the variance of the age of consumption, about 44 if consumption were spread uniformly from age 20 to 85, close to the measured 43.7. As an external check they cite Moll et al.’s (2022) survey of capital-tax studies, which finds demand semielasticities between 1.25 and 35, none negative.

The return falls unambiguously, wealth-to-GDP rises by considerably less than the compositional effect, and both magnitudes depend on the two elasticities. In the central case with capital-labor substitution of 1 and an intertemporal elasticity of 0.5, the return falls by 31.7/(21.2 + 8.3) = 1.07 percentage points by 2100; across the grid considered the fall ranges from 0.58 to 2.45 percentage points, larger when either elasticity is small “since this limits the responsiveness of asset supply and demand to falling returns.” The sign is robust rather than calibrated: the fall follows because the compositional effect and the sum of the two semielasticities are both positive “for any plausible combination” of the parameters. Wealth-to-GDP rises by 8.9 log points, from 456% to 498% of world GDP — much less than the 31.7-point compositional effect, because the equilibrium response is multiplied by the supply share of adjustment, roughly one third. The authors place this “between the predictions by Piketty (2014) and Krusell and Smith (2015)”: Piketty’s identity with a stable savings rate would imply about 40 log points, while Krusell and Smith argue for roughly constant wealth-to-GDP.

They diverge substantially, and this prediction is less sensitive to the elasticities than the others. Applying the formula country by country, India’s net foreign asset position rises by 179 percentage points of GDP between 2016 and 2100, China’s by 60, and Germany’s falls by 56, with the United States also declining to absorb the asset demand. What drives the pattern is the demeaned compositional effect — how much a country’s aging exceeds the world average — which is why the elasticities matter less here: “semielasticities only affect global imbalances insofar as they differ across countries”, and varying the two parameters “primarily moves semielasticities in parallel across countries.” Projecting dynamically, the authors expect existing imbalances to widen in the next few decades as China’s position rises and the US declines, the trends to flatten mid-century, and the second half of the century to feature “a conspicuous rise in India’s net foreign assets, offset partly by a decline in Germany and Japan, whose demographic transitions at that point are nearly complete.”

It explains about half the interest-rate decline since 1950 and much less of the wealth increase, and the net-foreign-asset test is suggestive rather than decisive. Running the same formulas backward, in the central case demographics explain “half of the historical interest rate decline (112 of 215 basis points) and 15% of the wealth increase (7 of 47 log points) since 1950”; with a lower intertemporal elasticity and higher capital-labor substitution these rise to 65% and 30%. The authors read the gap as evidence that other forces matter too, especially for wealth, and infer through a demand-supply accounting exercise that demographics account for 30% of the historical asset demand shift. On net foreign assets, regressing valuation-free changes over 1970–2015 on the predicted values gives a coefficient of 0.44 with a standard error of 0.38, and the authors are careful about what that licenses: “While the result does not directly reject our theory, since the theoretically predicted slope of ‘1’ is inside the confidence interval, it does not provide strong support for it either.” In a shorter 1993–2015 sample admitting six more countries the coefficient is 1.19 with a standard error of 0.45. Japan and Greece are clear outliers, both having run up government debt, which in the theory reduces net foreign assets one-for-one; adding the change in debt to the regression gives coefficients close to the theoretical +1 and −1 and statistically significant, “somewhat sensitive to removing prominent outliers”. Their own verdict: “historical changes in NFAs are generally consistent with the predictions from our model, but that there is not enough data for a decisive verdict.”

It adds the mechanisms the baseline rules out — bequests, income risk, perceived mortality, retirement and fiscal adjustment — and agrees qualitatively everywhere and quantitatively except under one-sided fiscal adjustment. The extended model gives a return decline of 1.24 percentage points against the sufficient statistic’s 1.07, and a wealth-to-GDP rise of 12.3 log points against 8.9. The authors decompose the gap step by step. Dropping annuitization and adding bequests, then matching bequests received to bequests given along the transition (a “bequest concentration” effect, as bequests are spread among fewer young people), then adding income risk — which shortens effective horizons through buffer-stock behavior and reduces the demand semielasticity — together take the decline to 1.41 percentage points. Letting individuals perceive the true falling path of mortality moves it only to 1.43. Raising the retirement age by five years pulls it back to 1.25, “because later retirement attenuates the decline in labor supply from an aging population, causing the denominator of wealth-to-GDP to fall by less.” Letting the government raise taxes and cut benefits rather than only cutting consumption does little on top of that, to 1.24 — but the authors stress this is not because fiscal adjustment is irrelevant: closing deficits entirely through higher taxes gives 0.96, and entirely through lower social security benefits gives 1.49, because taxes leave workers fewer resources to save while benefit cuts force them to save more.

Because matching the limited decumulation of assets in old age forces the calibration to lean on bequest motives rather than on retirement consumption. The authors describe the standard story — assets are held to finance old-age consumption, so a longer old age means more assets — and note that life-cycle models “struggle to match the limited decumulation of assets in old age (De Nardi, French and Jones 2016).” Once their model is calibrated to the empirical wealth-by-age profile, “most old-age assets must be held for reasons other than personal consumption—which the model captures with a bequest motive.” The consequence is direct: “Even after the mortality decline, people still die and leave bequests with probability one, and pushing that date later in life does not dramatically change the incentive to save.” They report that perceived mortality can matter more in a version with no bequest motive, “but that this comes at the cost of a poor fit to the age-wealth profile.” They also note that the large mortality effects found in Krueger and Ludwig (2007), Carvalho et al. (2016) and others partly include the compositional channel already counted here. This distinction is consequential for the projection, since “a large share of population aging will come from falling fertility rather than longevity.”

It looks at flows but forgets that population aging also lowers the growth rate, so net investment falls by more than saving. The authors concede the premise: in their own model the compositional effect on savings rates to 2100 is negative in every country except Germany. The error is in the equilibrium reasoning. On a balanced growth path net saving equals net investment plus net public borrowing, both of which scale with the growth rate; demographic change shifts the savings curve left, which on its own looks like a rise in the return, but it also lowers population growth and so shifts the net investment curve left by more. Viewed in stocks rather than flows, only asset demand shifts — to the right — “and the unambiguous implication is a decline in r.” The authors’ conclusion is that the flow view “is in principle just as valid” provided the effect of growth on net investment is kept in view, and that “ignoring this effect in the context of demographic change … may give the wrong sign for the change in r.” They name the analyses they take this to affect: “This effect is missed by Summers, Lane (2020), and Mian et al. (2021).” They also note the inflation corollary: a lower real rate implies less inflationary pressure “in any standard model in which this pressure is captured by the natural interest rate”, against Goodhart and Pradhan’s (2020) prediction.

Allowing safe and risky assets, or capitalized rents, changes the headline little. With households investing in both safe and risky assets — government bonds supplying the safe asset and capital the risky one — the effect on the average return stays “quantitatively close” to the baseline for a plausible range of the elasticity of the risky share to the risk premium. Demographic change does push the risk premium up by 0.37 percentage points in the central case, as older households shift toward safety, but this is “largely orthogonal to the effect on the average return, which now falls by 1.12pp rather than 1.07pp.” Allowing rents from markups or land also changes the central predictions little: capitalizing rents raises the supply semielasticity, but that is roughly offset by slower population growth lowering the value of future rents.

It takes the demographics as given and rules out several channels, and the authors say so. “We do not explain the sources of this change; instead, we take demographic projections as given.” Indirect effects of aging such as changes in technology or market structure are ruled out, with the relevant debates cited rather than resolved — Maestas, Mullen and Powell (2023) against Acemoglu and Restrepo (2017) on aging and total factor productivity, Bornstein (2021) against Peters and Walsh (2022) on demographics and markups. The main model attributes the growing gap between wealth and measured capital to unmeasured capital, with rising markups explored only as an extension. And the baseline holds government debt-to-GDP policy fixed, while the authors show that rising government debt “can mitigate or even undo the effect of demographic change on real interest rates, while increasing the effect on wealth-to-GDP” — which, given the fiscal trajectories many of these countries face, is a large caveat attached to the headline 1.07 percentage points.

That aging will keep pushing in the direction it has been pushing, with capital deepening everywhere and imbalances financed by India and China. The conclusion is compact: “This effect is positive, large and heterogeneous across countries. According to our model, this will lead to capital deepening everywhere, falling real interest rates, and rising net foreign asset positions in India and China financed by declining asset positions in the United States.” The load-bearing qualifier is “according to our model” — the projections are conditional on the UN scenarios, on the two elasticity parameters, on government debt ratios holding, and on the age profiles of wealth and income staying as they are measured in 2016.