An extensive literature has argued that stochastic returns to capital at the level of individual household portfolios are needed to account for observed wealth inequality. How should capital income, labor income, and wealth be taxed in an economy with stochastic returns? To answer this question, I develop a model in which these stochastic returns arise from optimal incentive-compatible contracts with private information. To provide appropriate incentives, optimal contracts expose entrepreneurs partially to the idiosyncratic risk of the firms they manage. The government has access to linear taxes on consumption, capital income, labor income and wealth. It must use these revenues both to redistribute among consumers and to finance government consumption. Analytically, the intertemporal wedge is shown to be zero in the steady-state of the Ramsey allocation. A quantitative version of the model is consistent with key features of the US data. I compute the time path of optimal policies starting from a calibrated steady state with taxes similar to the current US tax system. Quantitatively, the intertemporal wedge is close to zero at all times and the labor wedge is essentially constant. When consumption tax is not available as an instrument to the planner, the intertemporal wedge is large for a short duration before dropping close to zero. These results are qualitatively close to neoclassical models without financial frictions.
This paper studies optimal fiscal policy in an economy with heterogeneous returns to capital and exogenously incomplete markets. Two commonly used models of incomplete markets are considered. In the first model, entrepreneurs differ in the known returns of their investment and face collateral constraints. In the second model, the returns of entrepreneurs are subject to ex-post investment risk. In both models, optimal fiscal policy achieves the complete markets Ramsey allocation with a rich tax system. Optimal policy requires a large amount of public debt that satisfies the demand for safe and liquid assets by entrepreneurs. The government funds large interest payments by levying large consumption taxes and subsidizing labor income.
We consider an economy with perpetual youth and inelastic labor supply that grows endogenously. Consumers are subject to idiosyncratic capital accumulation risk and markets are incomplete. The government purchases consumption goods, makes transfers in the form of baby bonds, and it can use consumption and wealth taxes. The wealth distribution is given in closed form. When the intertemporal elasticity of substitution ɛ is equal to 1, the government can run a permanent primary deficit, up to a finite upper bound, if the coefficient of relative risk aversion is high enough and the factor share of labor is not too close to 1. This causes the risk-free rate r to be below the growth rate g of the economy. But the government can implement Pareto improvements when r - g does not exceed zero by enough. If ɛ ≠ 1, then there may not be an upper bound on the permanent primary deficits of the government. If ɛ Є (0,1), this happens when the economy is relatively unproductive, and then taking deficits to be very large makes all consumers worse off. If ɛ Є (1,∞), very large deficits are possible if the economy is sufficiently productive, and then they imply unbounded Pareto improvements.
In an economy with incomplete markets and consumers who are sufficiently risk averse, we show that the government can uniquely implement a permanent primary deficit using nominal debt and continuous Markov strategies for primary deficits and payments to debtholders. But this result fails if there are also useless pieces of paper (bitcoin for short) that can be traded. If there is trade in bitcoin, then there is no continuous Markov strategy for the government that leads to unique implementation. Instead, there is a continuum of equilibria with distinct real allocations in which the price of bitcoin converges to zero. And there is a balanced budget trap: continuous government policies designed for a permanent primary deficit cannot eliminate an alternative steady state in which r - g = 0 and the government is forced to balance its budget. A legal prohibition against bitcoin can restore unique implementation of permanent primary deficits, and so can a tax on bitcoin at the rate -(r - g) > 0.
We consider an economy with overlapping generations of relatively patient consumers who live for two periods. There is within-cohort heterogeneity in old-age endowments that depends on an aggregate state. That state is independent and identically distributed across generations. We assume consumers in their old age cannot be forced to give up any real resources. A stationary equilibrium in which state-contingent claims can be sold against the collateral of a single safe bubble security is efficient. The same allocation is also an equilibrium outcome in an economy with a sufficient number of stochastic bubble securities that can be traded subject to collateral constraints. When consumers cannot sell any securities short at all, the same efficient allocation can be implemented with a stochastic bubble forest: a continuum of Lucas trees that bear no fruit, with prices that evolve stochastically. Dynamic spanning is a potential rationale for the existence of distinct bubble assets.
The rich literature on Pay-As-You-Go (PAYG)-type pensions provides a notion that when pension return is dominated by the market return, generally it is impossible to phase pension out without hurting any generation. We show that PAYG pensions can indeed be phased out in a much richer framework where fertility is endogenous and general equilibrium effects are present. Interestingly, the factor that helps us to phase the pension out in a Pareto way is hidden in the structure of PAYG pension itself. Individualistic agents fail to recognize the benefits of their fertility decision on these programs and, therefore, end up in an allocation that is strictly dominated by the allocations that internalize this externality. Exploiting this positive externality, competitive economy can improve its allocations and can reach the planner's steady-state in finite time where each generation secures as much utility as in the competitive equilibrium. Clearly, it is possible to transition in a Pareto way to an economy either with no pension or with pensions whose return is not dominated by market return.