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- Wirtschaftswissenschaften (36) (remove)
We consider an additively time-separable life-cycle model for the family of power period utility functions u such that u0(c) = c−θ for resistance to inter-temporal substitution of θ > 0. The utility maximization problem over life-time consumption is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated agent and her naive counterpart is always identical for a logarithmic utility function (i.e., for θ = 1). As an extension of Pollak’s result we show that the sophisticated agent saves a greater (smaller) fraction of her wealth in every period than her naive counterpart whenever θ > 1 (θ < 1) irrespective of the specification of discount factors. We further show that this finding extends to an environment with risky returns and dynamically inconsistent Epstein-Zin-Weil preferences.
This paper studies discrete time finite horizon life-cycle models with arbitrary discount functions and iso-elastic per period power utility with concavity parameter θ. We distinguish between the savings behavior of a sophisticated versus a naive agent. Although both agent types have identical preferences, they solve different utility maximization problems whenever the model is dynamically inconsistent. Pollak (1968) shows that the savings behavior of both agent types is nevertheless identical for logarithmic utility (θ = 1). We generalize this result by showing that the sophisticated agent saves in every period a greater fraction of her wealth than the naive agent if and only if θ ≥ 1. While this result goes through for model extensions that preserve linearity of the consumption policy function, it breaks down for non-linear model extensions.
Using a structural life-cycle model, we quantify the long-term impact of school closures during the Corona crisis on children affected at different ages and coming from households with different parental characteristics. In the model, public investment through schooling is combined with parental time and resource investments in the production of child human capital at different stages in the children's development process. We quantitatively characterize both the long-term earnings consequences on children from a Covid-19 induced loss of schooling, as well as the associated welfare losses. Due to self-productivity in the human capital production function, skill attainment at a younger stage of the life cycle raises skill attainment at later stages, and thus younger children are hurt more by the school closures than older children. We find that parental reactions reduce the negative impact of the school closures, but do not fully offset it. The negative impact of the crisis on children's welfare is especially severe for those with parents with low educational attainment and low assets. The school closures themselves are primarily responsible for the negative impact of the Covid-19 shock on the long-run welfare of the children, with the pandemic-induced income shock to parents playing a secondary role.
Using a structural life-cycle model, we quantify the heterogeneous impact of school closures during the Corona crisis on children affected at different ages and coming from households with different parental characteristics. In the model, public investment through schooling is combined with parental time and resource investments in the production of child human capital at different stages in the children’s development process. We quantitatively characterize the long-term consequences from a Covid-19 induced loss of schooling, and find average losses in the present discounted value of lifetime earnings of the affected children of close to 1%, as well as welfare losses equivalent to about 0.6% of permanent consumption. Due to self-productivity in the human capital production function, skill attainment at a younger stage of the life cycle raises skill attainment at later stages, and thus younger children are hurt more by the school closures than older children. We find that parental reactions reduce the negative impact of the school closures, but do not fully offset it. The negative impact of the crisis on children’s welfare is especially severe for those with parents with low educational attainment and low assets. The school closures themselves are primarily responsible for the negative impact of the Covid-19 shock on the long-run welfare of the children, with the pandemic-induced income shock to parents playing a secondary role.
On average young people \undersave" whereas old people \oversave" with respect to the rational expectations model of life-cycle consumption and savings. According to numerous studies on subjective survival beliefs, young people also \underestimate" whereas old people \overestimate" their objective survival chances on average. We take a structural behavioral economics approach to jointly address both empirical phenomena by embedding subjective survival beliefs that are consistent with these biases into a rank-dependent utility (RDU) model over life-cycle consumption. The resulting consumption behavior is dynamically inconsistent. Considering both naive and sophisticated RDU agents we show that within this framework underestimation of young age and overestimation of old age survival probabilities may (but need not) give rise to the joint occurrence of undersaving and oversaving. In contrast to this RDU model, the familiar quasi-hyperbolic discounting (QHD), which is nested as a special case, cannot generate oversaving.
Using a structural life-cycle model and data on school visits from Safegraph and school closures from Burbio, we quantify the heterogeneous impact of school closures during the Corona crisis on children affected at different ages and coming from households with different parental characteristics. Our data suggests that secondary schools were closed for in-person learning for longer periods than elementary schools (implying that younger children experienced less school closures than older children), and that private schools experienced shorter closures than public schools, and schools in poorer U.S. counties experienced shorter school closures. We then extend the structural life cycle model of private and public schooling investments studied in Fuchs-Schündeln, Krueger, Ludwig, and Popova (2021) to include the choice of parents whether to send their children to private schools, empirically discipline it with data on parental investments from the PSID, and then feed into the model the school closure measures from our empirical analysis to quantify the long-run consequences of the Covid-19 school closures on the cohorts of children currently in school. Future earnings- and welfare losses are largest for children that started public secondary schools at the onset of the Covid-19 crisis. Comparing children from the topto children from the bottom quartile of the income distribution, welfare losses are ca. 0.8 percentage points larger for the poorer children if school closures were unrelated to income. Accounting for the longer school closures in richer counties reduces this gap by about 1/3. A policy intervention that extends schools by 3 months (6 weeks in the next two summers) generates significant welfare gains for the children and raises future tax revenues approximately sufficient to pay for the cost of this schooling expansion.
When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations and demonstrate that they interact over the life-cycle. The interactions appear even though the two risks are orthogonal and they amplify the welfare consequences of introducing social security. On the one hand, the interactions increase the welfare benefits from insurance. On the other hand, they can in- or decrease the welfare costs from crowding out of capital formation. This ambiguous effect on crowding out means that the net effect of these two channels is positive, hence the interactions of risks increase the total welfare benefits of social security.
When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations. We derive the equilibrium dynamics in closed form and show that joint presence of both risks leads to over-proportional risk exposure for households. This implies that the whole benefit from insurance through social security is greater than the sum of the benefits from insurance against each of the two risks in isolation. We measure this through interaction effects which appear even though the two risks are orthogonal by construction. While the interactions unambiguously increase the welfare benefits from insurance, they can in- or decrease the welfare costs from crowding out of capital formation. The net effect depends on the relative strengths of the opposing forces.
We develop a model of managerial compensation structure and asset risk choice. The model provides predictions about how inside debt features affect the relation between credit spreads and compensation components. First, inside debt reduces credit spreads only if it is unsecured. Second, inside debt exerts important indirect effects on the role of equity incentives: When inside debt is large and unsecured, equity incentives increase credit spreads; When inside debt is small or secured, this effect is weakened or reversed. We test our model on a sample of U.S. public firms with traded CDS contracts, finding evidence supportive of our predictions. To alleviate endogeneity concerns, we also show that our results are robust to using an instrumental variable approach.
Ongoing demographic change will lead to a relative scarcity of raw labor to the effect that output growth will be decreasing in the next decades, a secular stagnation. As physical capital will be relatively abundant, this decrease of output will be accompanied by reductions of asset returns. We quantify these effects for the US economy by developing an overlapping generations model with risky and risk-free assets. Without adjustments of human capital, risky returns decrease until 2035 by about 0.7 percentage point, and the risk-free rate by about one percentage point, leading to substantial welfare losses for asset rich households. Per capita output is reduced by 6%. Endogenous human capital adjustments strongly mitigate these effects. We conclude that human capital policies will be crucial in the context of labor shortages.
Alexander Ludwig: An expert commission makes sense – but why expert opinion only after 2025 and clientele policy before?
We characterize the optimal linear tax on capital in an Overlapping Generations model with two period lived households facing uninsurable idiosyncratic labor income risk. The Ramsey government internalizes the general equilibrium feedback of private precautionary saving. For logarithmic utility our full analytical solution of the Ramsey problem shows that the optimal aggregate saving rate is independent of income risk. The optimal time-invariant tax on capital is increasing in income risk. Its sign depends on the extent of risk and on the Pareto weight of future generations. If the Ramsey tax rate that maximizes steady state utility is positive, then implementing this tax rate permanently generates a Pareto-improving transition even if the initial equilibrium is dynamically efficient. We generalize our results to Epstein-Zin-Weil utility and show that the optimal steady state saving rate is increasing in income risk if and only if the intertemporal elasticity of substitution is smaller than 1.
We characterize the optimal linear tax on capital in an Overlapping Generations model with two period lived households facing uninsurable idiosyncratic labor income risk. The Ramsey government internalizes the general equilibrium effects of private precautionary saving on factor prices and taxes capital unless the weight on future generations in the social welfare function is sufficiently high. For logarithmic utility a complete analytical solution of the Ramsey problem exhibits an optimal aggregate saving rate that is independent of income risk, whereas the optimal time-invariant tax on capital implementing this saving rate is increasing in income risk. The optimal saving rate is constant along the transition and its sign depends on the magnitude of risk and on the Pareto weight of future generations. If the Ramsey tax rate that maximizes steady state utility is positive, then implementing this tax rate permanently induces a Pareto-improving transition even if the initial equilibrium capital stock is below the golden rule.
n this paper we compute the optimal tax and education policy transition in an economy where progressive taxes provide social insurance against idiosyncratic wage risk, but distort the education decision of households. Optimally chosen tertiary education subsidies mitigate these distortions. We highlight the importance of two different channels through which academic talent is transmitted across generations (persistence of innate ability vs. the impact of parental education) for the optimal design of these policies and model different forms of labor as imperfect substitutes, thereby generating general equilibrium feedback effects from policies to relative wages of skilled and unskilled workers. We show that subsidizing higher education has important redistributive benefits, by shrinking the college wage premium in general equilibrium. We also argue that a full characterization of the transition path is crucial for policy evaluation. We find that optimal education policies are always characterized by generous tuition subsidies, but the optimal degree of income tax progressivity depends crucially on whether transitional costs of policies are explicitly taken into account and how strongly the college premium responds to policy changes in general equilibrium.
Homeownership rates differ widely across European countries. We document that part of this variation is driven by differences in the fraction of adults co-residing with their parents. Comparing Germany and Italy, we show that in contrast to homeownership rates per household, homeownership rates per individual are very similar during the first part of the life cycle. To understand these patterns, we build an overlapping-generations model where individuals face uninsurable income risk and make consumption-saving and housing tenure decisions. We embed an explicit intergenerational link between children and parents to capture the three-way trade-off between owning, renting, and co-residing. Calibrating the model to Germany we explore the role of income profiles, housing policies, and the taste for independence and show that a combination of these factors goes a long way in explaining the differential life-cycle patterns of living arrangements between the two countries.
Homeownership rates differ widely across European countries. We document that part of this variation is driven by differences in the fraction of adults co-residing with their parents. Comparing Germany and Italy, we show that in contrast to homeownership rates per household, homeownership rates per individual are very similar during the first part of the life cycle. To understand these patterns, we build an overlapping-generations model where individuals face uninsurable income risk and make consumption-saving and housing tenure decisions. We embed an explicit intergenerational link between children and parents to capture the three-way trade-off between owning, renting, and co-residing. Calibrating the model to Germany we explore the role of income profiles, housing policies, and the taste for independence and show that a combination of these factors goes a long way in explaining the differential life-cycle patterns of living arrangements between the two countries.
We extend the canonical income process with persistent and transitory risk to shock distributions with left-skewness and excess kurtosis, to which we refer as higher- order risk. We estimate our extended income process by GMM for household data from the United States. We find countercyclical variance and procyclical skewness of persistent shocks. All shock distributions are highly leptokurtic. The existing tax and transfer system reduces dispersion and left-skewness of shocks. We then show that in a standard incomplete-markets life-cycle model, first, higher-order risk has sizable welfare implications, which depend crucially on risk attitudes of households; second, higher-order risk matters quantitatively for the welfare costs of cyclical idiosyncratic risk; third, higher-order risk has non-trivial implications for the degree of self-insurance against both transitory and persistent shocks.