Overlapping-Generations | Macro Paper Warehouse

The Life-Cycle Implications of Temporary Employment Contracts

Thu, 01 Jan 2026 00:00:00 +0000

Many countries, primarily in Europe, apply dismissal protections to permanent employment contracts but not to temporary ones, creating a two-tiered labor market in which younger and less educated workers disproportionately hold the precarious jobs; this paper asks what eliminating that second tier would do to output, employment and income, and how the answer differs across ages. Using Dutch data — the European Union Labour Force Survey for 2019 and the LISS household panel for 2008 to 2019 — the author documents that more than half of all transitions from unemployment into employment, at every age, are transitions into temporary contracts; that the annual rate of moving from employment to unemployment is higher in temporary contracts; and that, after controlling for worker and job characteristics, temporary workers earn about 5.8% less per hour and those who stay in temporary contracts experience about 1.5% lower annual growth in real per-hour income. She then builds a directed-search model with overlapping generations in which workers of differing age, human capital and education choose which job type to search for, accumulate human capital while employed, and can lose it during unemployment, and calibrates it to sixteen Dutch labor-market moments. In that model, abolishing firing costs raises the quarterly job-finding rate of the unemployed by roughly 13 percentage points but also raises job destruction by more, so the unemployment rate rises by 6.3 to 6.7 percentage points, average human capital falls by 9.2% to 10.4%, and GDP net of search and firing costs falls by 5.8% to 6.5% at the new steady state — a qualitative reversal of earlier structural results, which the author traces directly to the human capital channel: stripping human capital dynamics out of the same model restores the older finding that removing firing costs lowers unemployment and raises output. The effects are strongly age-dependent: average wages and consumption are higher for younger workers after the reform but lower from roughly age 40 to 45 onward, and the sign of the welfare verdict — a gain of 1.05% if protections do nothing for skill accumulation, a loss only if the probability of a human capital gain falls by around 20% — depends on an incentive effect the paper deliberately does not try to pin down.

An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money

This 1958 Journal of Political Economy paper by Paul Samuelson builds a deliberately stripped-down model of a world in which goods cannot be stored or invested – nothing “keeps” – so people can only shift consumption across their lifetime by trading with other, differently-aged people currently alive, an arrangement he calls the consumption-loan model. Assuming three-period overlapping lifetimes (working, working, retired) and a population that may be stationary or growing at a constant rate, Samuelson shows that if such consumption loans clear competitively period by period, the interest rate that would maximize a representative person’s lifetime welfare exactly equals the population’s biological growth rate, so that in a stationary population the socially optimal interest rate is exactly zero. He then proves, in an “impossibility theorem,” that this social optimum can never actually be reached by a genuinely free, decentralized market relying only on voluntary bilateral trade between generations, because a young lender’s eventual repayment must come from someone who was never party to the original exchange; in a worked numerical example the free market instead settles permanently on a substantially negative real interest rate, leaving every generation worse off than the optimum. Samuelson identifies two escapes from this market failure: an explicit Hobbes-Rousseau social contract that guarantees support for the aged by drawing on the yet-unborn (a forerunner of social security), or the spontaneous emergence of a durable, intrinsically worthless money that successive generations agree to accept and pass on, whose real value can adjust as population changes so that its return replicates the optimal biological rate. The paper’s larger claim is that this reframes one function of money – not as a mere convenience for barter, but as a social compact that a purely competitive, atomistic market cannot generate on its own.

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

A popular argument — the “asset market meltdown” of the 1990s, revived as the “great demographic reversal” — holds that once the old start running down their savings, aging will push interest rates back up. This paper argues the opposite, and its central object is the compositional effect: the direct impact of a changing age distribution on log wealth-to-GDP, holding the age profiles of wealth and labor income fixed. In the authors’ baseline overlapping-generations model that statistic is a sufficient statistic for the change in wealth-to-GDP in a small open economy, and aggregated across countries — combined with asset supply and demand semielasticities obtained from further sufficient-statistic formulas — it pins down the general equilibrium effect on returns, wealth and global imbalances. Measuring it from 2019 UN population projections and household surveys for 25 countries, they find it positive everywhere between 2016 and 2100, ranging from 17 log points in Sweden to 45 in China and 56 in India, with a wealth-weighted global average of 31.7; the driver is that the old hold much more wealth than the young and on average do not dissave much as they age. In their central case, with an elasticity of intertemporal substitution of 0.5 and a unit elasticity of capital-labor substitution, the world return falls by 1.07 percentage points by 2100, global wealth-to-GDP rises by 8.9 log points (456% to 498% of world GDP), and net foreign asset positions diverge sharply — India’s rising by 179 percentage points of GDP and Germany’s falling by 56. The magnitudes depend on those two parameters (the return falls by between 0.58 and 2.45 percentage points across the range considered), the projections are taken as given rather than explained, indirect effects such as changes in technology or market structure are ruled out, and the authors report that rising government debt “can mitigate or even undo” the effect on real interest rates.

National Debt in a Neoclassical Growth Model

This 1965 American Economic Review paper by Peter Diamond extends Samuelson’s pure consumption-loan model by adding a produced, durable capital good, so that people can provide for retirement either by lending to other people or by holding physical capital, and asks what happens to the economy’s long-run competitive equilibrium once a government issues debt. Working with two-period-lived overlapping generations, a constant-returns aggregate production function, and a population growing at a constant rate n, Diamond first characterizes the “Golden Rule” capital-labor ratio that would maximize steady-state per-capita consumption for a central planner, then shows that the decentralized competitive equilibrium – in which the young lend their unconsumed wages to entrepreneurs at an interest rate equal to capital’s marginal product – need not coincide with it. His central theoretical result is that the free-market solution can settle at a capital-labor ratio permanently above the Golden Rule level, meaning the interest rate falls permanently below the population growth rate; in that case the economy is dynamically inefficient, since it would be possible to make every future generation better off simply by holding less capital, even though the model has no monopoly power, taxes, externalities, or any other conventional source of inefficiency. Diamond then introduces government debt into this framework and shows that externally held debt reduces long-run individual welfare (in the efficient case) purely through the taxes needed to service it, while internally held debt does so by an even larger amount, because it additionally substitutes government paper for productive physical capital in individual portfolios, further shrinking the capital stock. In the dynamically inefficient case, by contrast, both forms of debt can raise welfare by moving the interest rate closer to the growth rate.