Contributions published at Financial Economics (Felix Kübler)

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I provide a new way to model bounded rationality and show the existence of recur-sive equilibria with bounded rational agents. The existence proof applies to dynamic stochastic general equilibrium models with infinitely lived heterogeneous agents and incomplete markets. In this type of models, recursive methods are widely used to compute equilibria, yet recursive equilibria do not exist generically with rational agents. I change the rational expectation assumption and model bounded rationality as fol-lows. Different from a rational agent, a bounded rational agent does not know the true Markov transition of the state space of the economy. In order to make decisions, the bounded rational agent would try to compute a stationary distribution of the state space using a numerical method and then use the Markov transition associated with it to maximize utility. For a certain distribution of the current period, given other agents’ strategies, the agent would get its next-period transition: the distribution of the state space in the next period that results from the competitive equilibrium in the next period. However, if a distribution stays “closer” to its next-period transition than the minimum error the numerical method can observe, the agent would consider it as computational stationary. In equilibrium, each agent maximizes utility with a computational stationary distribution and markets clear. I use the Kantorovich-Rubinshtein norm to characterize the distance between distributions of the state space. With this set up, usual convergence criteria used in the literature can be incorporated and thus many computed equilibria in the literature using recursive methods can be categorized as bounded rational recursive equilibria in the sense of this paper.

In this paper we introduce "self-justified" equilibrium as a solution concept in stochastic general equilibrium models with a large number of heterogeneous agents. In each period agents trade in assets to maximize the sum of current utility and forecasted future utility. Current prices ensure that markets clear and agents forecast the probability distribution of future prices and consumption on the basis of current endogenous variables and the current exogenous shock. The forecasts are self-justfied in the sense that agents use forecasting functions that are optimal within a given class of functions and that can be viewed as optimally trading o˙ the accuracy of the forecast and its complexity. We show that self-justified equilibria always exist and we develop a computational method to approximate them numerically. By restricting the complexity of agents' forecasts we can solve models with a very large number of heterogeneous agents. Errors can be directly interpreted.

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We propose a massively parallelized and optimized framework to solve high-dimensional dynamic stochastic economic models on modern GPU- and MIC-based clusters. First, we introduce a novel approach for adaptive sparse grid index compression alongside a surplus matrix reordering, which significantly reduces the global memory throughput of the compute kernels and maps randomly accessed data onto cache or fast shared memory. Second, we fully vectorize the compute kernels for AVX, AVX2 and AVX512 CPUs, respectively. Third, we develop a hybrid cluster oriented work-preempting scheduler based on TBB, which evenly distributes the time iteration workload onto available CPU cores and accelerators. Numerical experiments on Cray XC40 KNL “Grand Tave” and on Cray XC50 “Piz Daint” systems at the Swiss National Supercomputer Centre (CSCS) show that our framework scales nicely to at least 4,096 compute nodes, resulting in an overall speedup of more than four orders of magnitude compared to a single, optimized CPU thread. As an economic application, we compute global solutions to an annually calibrated stochastic public finance model with sixteen discrete, stochastic states with unprecedented performance. Index Terms—High-Performance Computing, Macroeconomics, Public Finance, Adaptive Sparse Grids, Heterogeneous Systems, CUDA, GPU, MIC

We propose a massively parallelized and optimized framework to solve high-dimensional dynamic stochastic economic models on modern GPU- and MIC-based clusters. First, we introduce a novel approach for adaptive sparse grid index compression alongside a surplus matrix reordering, which significantly reduces the global memory throughput of the compute kernels and maps randomly accessed data onto cache or fast shared memory. Second, we fully vectorize the compute kernels for AVX, AVX2 and AVX512 CPUs, respectively. Third, we develop a hybrid cluster oriented work-preempting scheduler based on TBB, which evenly distributes the time iteration workload onto available CPU cores and accelerators. Numerical experiments on Cray XC40 KNL “Grand Tave” and on Cray XC50 “Piz Daint” systems at the Swiss National Supercomputer Centre (CSCS) show that our framework scales nicely to at least 4,096 compute nodes, resulting in an overall speedup of more than four orders of magnitude compared to a single, optimized CPU thread. As an economic application, we compute global solutions to an annually calibrated stochastic public finance model with sixteen discrete, stochastic states with unprecedented performance. Index Terms—High-Performance Computing, Macroeconomics, Public Finance, Adaptive Sparse Grids, Heterogeneous Systems, CUDA, GPU, MIC

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Economists have previously made little use of high-performance computers (HPC) in their research. This is despite the fact that the complex interactions and heterogeneity of their models can quickly cause them to reach hundreds of dimensions, which cannot be calculated using conventional methods. In the past, simplified models were therefore often formulated for answering complex questions. These models solved some problems, but they could also provide false predictions, explains Simon Scheidegger, Senior Assistant at the University of Zurich's Department of Banking and Finance. For example, quantitatively studying optimal monetary policy in the wake of a financial crisis cannot be properly achieved using the conventional methods. However, calculating high-dimensional models on a supercomputer is not easy either. Until recently, researchers lacked appropriate numerical analysis and highly efficient software. Read more at: https://phys.org/news/2018-02-economists-cash-efficient-high-performance-method.html#jCp

Economists have previously made little use of high-performance computers (HPC) in their research. This is despite the fact that the complex interactions and heterogeneity of their models can quickly cause them to reach hundreds of dimensions, which cannot be calculated using conventional methods. In the past, simplified models were therefore often formulated for answering complex questions. These models solved some problems, but they could also provide false predictions, explains Simon Scheidegger, Senior Assistant at the University of Zurich's Department of Banking and Finance. For example, quantitatively studying optimal monetary policy in the wake of a financial crisis cannot be properly achieved using the conventional methods. However, calculating high-dimensional models on a supercomputer is not easy either. Until recently, researchers lacked appropriate numerical analysis and highly efficient software

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