Contributions published at Financial Economics (Felix Kübler)

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We present a flexible and scalable method to compute global solutions of high-dimensional non-smooth dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximal problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of MPI and OpenMP. This parallelization enables us to efficiently use modern high-performance computing architectures. Our time iteration algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.

It is standard in economics to assume that assets are normal goods and demand is downward sloping in price. This view has its theoretical foundation in the classic single period model of Arrow with one risky asset and one risk free asset, where both are assumed to be held long. However when short selling is allowed, we show that the risk free asset can not only fail to be a normal good but can in fact be a Gi¤en good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions. Distinct regions in the price-income space are identi?ed in which the risk free asset exhibits normal, inferior and Gi¤en behavior. Moreover for uility functions with decreasing relative risk aversion, such as the weighted average constant relative risk aversion (WACRRA) class introduced in this paper, the risk free asset can become a Gi¤en good only when it is held long. Examples are provided in which Gi¤en behavior occurs over multiple ranges of income. The analysis is also extended to a two period setting.

Marcet and Marimon (1994, revised 1998) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a flat region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through - one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal's choice set is not convex but where randomization is possible.

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This paper analyzes the effects of time-consistent capital taxation on the level of capital and welfare. We find that a commitment to a zero capital tax shifts the time inconsistency problem towards labor taxes and the provision of public consumption. By comparing the worst timeconsistent policies with and without a commitment to zero capital taxes, we find that the mere existence of a capital tax might lead to capital tax rates that are as high as 90% at steady state and capital stocks that are 84% lower. There the welfare gains of a commitment to zero capital taxes are about 7,4% of initial steady state consumption. At the other end, comparing the best time-consistent policies, we find that the welfare losses of a commitment to zero capital taxes are about 0,9% of consumption.

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This paper examines a dynamic stochastic economy with a benevolent government that cannot commit to future policies. Following Phelan and Stacchetti (2001), we consider sequential sustainable equilibria (SSE). We numerically solve for the set of equilibrium payoffs, and investigate whether the time consistency problem of capital income tax is quantitatively important. For a realistically calibrated economy, we find that the optimal sustainable capital income tax rate is pro-cyclical and close to zero on average, while the labor income tax is countercyclical. Moreover, the welfare cost of no commitment is very small (0:22%) when compared with the Ramsey allocation. We also find that the best sustainable equilibrium outcome may achieve substantially higher social welfare than the Markov-perfect equilibrium as considered by Klein, Krusell and Rios-Rull (2008).

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This paper examines a dynamic stochastic economy with a benevolent government that cannot commit to future policies. Following Phelan and Stacchetti (2001), we consider sequential sustainable equilibria (SSE). We numerically solve for the set of equilibrium payoffs, and investigate whether the time consistency problem of capital income tax is quantitatively important. For a realistically calibrated economy, we find that the optimal sustainable capital income tax rate is pro-cyclical and close to zero on average, while the labor income tax is countercyclical. Moreover, the welfare cost of no commitment is very small (0:22%) when compared with the Ramsey allocation. We also find that the best sustainable equilibrium outcome may achieve substantially higher social welfare than the Markov-perfect equilibrium as considered by Klein, Krusell and Rios-Rull (2008).

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