Stochastic Overlapping Generations Model Research Articles

Financing universal health care: Premiums or payroll taxes?

This paper presents a stochastic overlapping generations model with endogenous health investment to study the transition from the existing hybrid health insurance system in Germany towards a uniform system, financed by either funded or unfunded premiums or payroll taxes.Our simulation results highlight the insurance properties of payroll taxes, but also their cost in terms of labor supply distortions and moral hazard. We find that compulsory deductibles decrease aggregate welfare in Germany, although they reduce moral hazard and increase private health investment. Reform models with premiums also induce precautionary behavior and increase labor supply, but at the same time increase exposure to productivity risk. Since the introduction of a funded system is costly for transitional cohorts, unfunded premiums provide the highest efficiency gains in our framework.

Optimality in an OLG model with nonsmooth preferences

AbstractIt is a well‐known observation that, in the overlapping generations (OLG) model with the complete market, we can judge optimality of an equilibrium allocation by examining the associated equilibrium price. Motivated by recent development in decision theory under ambiguity, this study reexamines the above observation in a stochastic OLG model with convex but not necessarily smooth preferences. It is shown that optimality of an equilibrium allocation depends on the set of possible supporting prices, not necessarily on the associated equilibrium price itself. Therefore, observations of an equilibrium price do not necessarily tell us precise information on optimality of the equilibrium allocation.

Climate Justice in an Intergenerational Sustainability Framework: A Stochastic OLG Model

Climate justice is conceived as the intertemporal climate equity and equality exchange amongst generations. Sustainability—intended as the interplay amongst the economy, the society, the environment, and the governance—is essential to forge the climate justice theoretical framework. On this base, the study attempts to model the intertemporal choice of the status quo amongst generations in these four domains, making use of an overlapping generations (OLG) model making use of an intertemporal choice framework. The proxies detected are GDP growth (economy), environmental quality (environment), and labor growth, and environmental investment (society) as assumptions. The governance dimension is captured by the difference in wealth between young and old generations. The work aims at replying to the following research question: Which are the conditions for sustainable development such that climate justice holds? The intra-intergenerational exchange is defined in two periods, while the individual provides their preferred economic and environmental choice mix as consumption-saving. This study shows that keeping the business-as-usual scenario, young generations will have to bear the brunt of sustainable development. Additionally, reduced emissions are only achievable with increased efforts by the youth by reducing their leisure and consumption. These facts call for enhanced intergenerational sustainability and climate justice policies.

“TIME-RELEASE” OUTPUT RESPONSES TO PUBLIC EDUCATION EXPENDITURES

This paper argues that output can respond to public education spending in a delayed and persistent manner through human capital accumulation. We refer to this as a “time-release” response, reflecting that the output response grows as students exposed to increased expenditures sequentially enter the labor market. We first develop and calibrate a stochastic overlapping generations model to formalize the propagation of spending shocks over a long time horizon. We then empirically explore this time-release aspect of shocks to government education expenditures on output using US state-level data for the period 1963–2016 and a panel structural vector autoregression methodology. Consistent with the model, our empirical results show that the dynamic response of output to shocks to government education expenditures is positive, significant, and long-lasting.

A characterization of Markov equilibrium in stochastic overlapping generations models

This paper characterizes the Markov equilibrium in stochastic overlapping generations models with both pure exchange and production using the theory of linear iterated function systems. We provide conditions for the linearized Markov equilibrium to have an absolutely continuous invariant measure or a singular invariant measure. We also examine relationships between the linear equilibrium system and the model parameters. This analysis identifies the set of economies for each type of invariant measure. We show that the attractor of the singular invariant measure exhibits fractal patterns, which supports the proposition that self-affinity patterns in financial data can be explained via rational expectations equilibrium as an economic mechanism.

Stock vs. Bond yields and demographic fluctuations

Abstract This paper analyzes the strong comovement between real stock and nominal bond yields at generational frequencies. Using a stochastic overlapping generations model with cash-in-advance constraints, we show that the simulated life-cycle patterns in savings behavior make both real stock and nominal bond yields comove with the changing population age structure. These persistent comovements account for the equilibrium relation between stock and bond markets. A stochastic Fisher decomposition of nominal bond yields reveals that, while having a moderate effect on both the inflation risk premium and expected inflation, demographic changes affect nominal yields mainly through real bond yields. Using both U.S. data and a cross-country panel, we find empirical support for these theoretical predictions. Finally, we show that the strength of the demographic effect on real yields explains cross-country differences in the comovement between stock and bond markets, while alternative demographic channels fail to explain such cross-country heterogeneity.

Self-Justified Equilibria: Existence and Computation

In this paper, we introduce the concept of as a tractable alternative to rational expectations equilibria in stochastic general equilibrium models with heterogeneous agents. A self-justified equilibrium is a temporary equilibrium where, in each period, agents trade in assets and commodities to maximize the sum of current utility and expected future utilities that are forecasted on the basis of current endogenous variables and the current exogenous shock. Agents' characteristics include a loss function that prescribes how the agent trades off the accuracy and the computational complexity of possible forecasts. We provide sufficient conditions for the existence of self-justified equilibria, and we develop a computational method to approximate them numerically. For this, we focus on a convenient special case where we use Gaussian process regression coupled to active subspaces to model agents' forecasts. We demonstrate that this framework allows us to solve stochastic overlapping generations models with hundreds of heterogeneous agents and very accurate forecasts.

The age-specific burdens of short-run fluctuations in government spending

We study the impact of government spending shocks on the distribution of income and wealth between cohorts and the associated welfare effects in a dynamic stochastic overlapping generations model with two types of households, Ricardian households and rule-of-thumb consumers. We demonstrate that an unexpected increase in government spending decreases income and wealth inequality. In contrast to the conventional wisdom that the financing of government expenditures by debt rather than taxes especially burdens young generations, we find that debt-financing also harms Ricardian households during retirement. The crucial element in our analysis is a wealth effect that results from the decline in the price of capital due to higher government debt.

Life in shackles? The quantitative implications of reforming the educational financing system

We conduct a quantitative analysis of educational financing systems in a stochastic overlapping generations model in which human capital can be enhanced through both formal schooling and learning-by-doing. The model is calibrated to the United States economy, including a stylized version of its student loan system. We find that moving to an income-contingent educational financing system, whereby transfers to students are financed from taxes on labor income, generates aggregate welfare gains. Such a system improves risk-sharing among college graduates and incentivizes individuals to obtain more education. These positive effects overturn the negative impact from labor supply distortions. Reforming the educational financing system towards income contingency, however, generates a considerable amount of transitional dynamics, so that welfare gains and losses are distributed unevenly across generations.

The Burden of Unanticipated Government Spending

We study the impact of a government spending shock on the distribution of income and wealth between cohorts in a dynamic stochastic Overlapping Generations model with two types of households, Ricardian households and rule-of-thumb consumers. We demonstrate that an unexpected increase in government spending increases income inequality and decreases wealth inequality. In contrast to the conventional wisdom that the financing of additional expenditures by debt rather than taxes especially burdens young generations, we find that a debt-financed increase in government spending also harms Ricardian households during retirement, while workers close to retirement benefit. The crucial element in our analysis is a wealth effect that results from the decline in the price of capital due to higher government debt.

Indeterminacy in stochastic overlapping generations models: real effects in the long run

Indeterminate equilibria are known to exist for overlapping generations models, though recent research has been limited to deterministic settings in which all equilibria converge to a steady state in the long run. This paper analyzes stochastic overlapping generations models with three-period-lived representative consumers and adopts a novel computational algorithm to numerically approximate the entire set of competitive equilibria. In a stochastic setting with incomplete markets, indeterminacy has real effects in the long run. Our numerical simulations reveal that indeterminacy is an order of magnitude more important than endowment shocks in explaining long-run consumption and asset price volatility.

Efficiency and Lack of Commitment in an Overlapping Generations Model with Endowment Shocks

This paper considers a pure exchange stochastic overlapping generations model in which, on each date, an economy faces an aggregate endowment shock. On each date, a young agent and an old agent simultaneously decide how much of their respective endowments to transfer to the other agent; however, a young agent cannot make promises about how much he or she will give when old. In this sense, an economy faces a limited commitment constraint. This paper characterizes an efficient intergenerational risk sharing allocation that satisfies a limited commitment constraint, and also studies the role of money and history in a stochastic overlapping generations economy.

Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models

In this paper, we study intergenerational stochastic games that can be viewed as a special class of overlapping generations models under uncertainty. Making use of the theorem of Dvoretzky, Wald and Wolfowitz [27] from the statistical decision theory, we obtain new results on stationary Markov perfect equilibria for the aforementioned games, with a general state space, satisfying rather mild continuity and compactness conditions. A novel feature of our approach is the fact that we consider risk averse generations in the sense that they aggregate partial utilities using an exponential function. As a byproduct, we also provide a new existence theorem for intergenerational stochastic game within the standard framework where the aggregator is linear. Our assumptions imposed on the transition probability and utility functions allow to embrace a pretty large class of intergenerational stochastic games analysed recently in macroeconomics. Finally, we formulate a set of assumptions under which the stochastic process induced by the stationary Markov perfect equilibrium possesses an invariant distribution.

A NOTE ON THE EXISTENCE AND UNIQUENESS OF STATIONARY MONETARY EQUILIBRIUM IN A STOCHASTIC OLG MODEL

This paper directly shows the equivalence between the existence of stationary monetary equilibrium and the conditional Pareto suboptimality of the initial endowment in a stochastic overlapping generations model. Especially, it gives short and constructive proofs for existence and uniqueness.

Computing minimal state space recursive equilibrium in OLG models with stochastic production

Using order-theoretic methods, we derive sufficient conditions for the existence, characterization, and computation of minimal state space recursive equilibrium (RE), as well as Stationary Markov equilibrium (SME) for various classes of stochastic overlapping generations models. In contrast to previous work, our methods focus on constructive methods. Our existence results are obtained for models that include public policy (e.g., social security policies, transfers, taxes, etc), production nonconvexities, elastic labor supply, non-monotone income processes, and long-lived agents. We distinguish conditions under which there exist various subclasses of minimal state space RE, including bounded, monotone, non-monotone, semicontinuous, Lipschitz continuous RE. Finally, we provide monotone equilibrium comparative statics results on the space of economies for some RE.

Golden rule optimality in stochastic OLG economies

This study examines conditional golden rule optimality (CGRO) in stochastic overlapping generations models to complement the existing results on conditional Pareto optimality (CPO). Although an example in which CPO implies CGRO is presented, it is shown that such a situation is avoidable under strictly convex preferences. Under such preferences, both CPO and CGRO are characterized by the conditions on the dominant root for the agents’ common matrix of marginal rates of substitution. We demonstrate that CGRO requires the dominant root being exactly equal to one, whereas CPO allows it to be less than one. By adopting CGRO rather than CPO, we provide welfare theorems in the financial economy.

Income Inequality, Mobility, and the Welfare State: A Political Economy Model

In this paper, we set up a three-period stochastic overlapping generations model to analyze the implications of income inequality and mobility for demand for redistribution and social insurance. We model the size of two different public programs under the welfare state. We investigate bidimensional voting on the tax rates that determine the allocation of government revenues among transfer payments and old-age pensions. We show that the coalitions formed, the resulting political equilibria, and the demand for redistribution crucially depend on the level of income inequality and mobility.

Life-Cycle Portfolio Choice, the Wealth Distribution and Asset Prices

This paper examines a canonical stochastic overlapping generations model with dynamically complete markets. Belief differences lead agents to place bets against each other and so wealth shifts across agents and across generations. Such changes in the wealth distribution strongly affect prices of long-lived assets since older generations have a lower propensity to save than younger generations. Contrary to the prices of long-lived assets, prices of short-lived assets are much less affected by the wealth distribution. Therefore, belief heterogeneity and life-cycle concerns are major forces contributing to the large gap between the volatility of stock returns and of the risk-free rate found in U.S. data.

Should Public Retirement Provision Be Means-Tested?

The complex matrix of retirement policy trade-offs -encompassing elements of paternalism, market failure, and overlaying incentives in a life-cycle context- have received much attention in the literature. But the issue of whether publicly-funded retirement provision should be means-tested, and if so how, has received limited attention, although it has been highlighted from time to time. This paper examines the economic welfare effects of means testing using a stochastic overlapping generations model calibrated to the UK economy. A labor-leisure choice is incorporated, with multiple individuals with different endowments of effective labor. Our results indicate that a change in the taper rate has implications for both welfare and economic aggregates. In particular, with a second tier pension in place, it is welfare improving to strictly means-test the first pillar. In contrast to much received wisdom, higher taper rates increase social welfare.

The Business Cycle and the Life Cycle

Our paper documents the differences in the variability of hours worked over the business cycle across several demographic groups and shows that these differences are large. We argue that understanding these differences should be useful in understanding the forces that account for aggregate fluctuations in hours worked. In particular, it is well known that standard models of the business cycle driven by technology shocks do not account for all of the variability in hours of work. This raises the following question: To what extent can the forces in this model account for the differences across demographic groups? We explore this in the context of hours fluctuations by age groups by formulating and analyzing a stochastic overlapping generations model. Our analysis shows that the model does a good job of accounting for hours fluctuations for prime-age workers but not for young or old workers. We conclude that a key issue is to understand why fluctuations for young and old workers are so much larger.