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We present a flexible and scalable method for computing global solutions of high-dimensional stochastic dynamic models. Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance, in regions with steep gradients or at non-differentiabilities. To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high-performance computing architectures. To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high-dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu-cost models with temporary sales and economies of scope in price setting.

International financial integration helps to diversify risk but also may spread crises across countries. We provide a quantitative analysis of this trade-off in a two-country general equilibrium model with collateral-constrained borrowing using a global solution method. Borrowing constraints bind occasionally, depending upon the state of the economy and levels of inherited debt. We examine different degrees of international financial integration, moving from financial autarky, to bond and equity market integration. Financial integration leads to a significant increase in global leverage, substantially escalates the probability of crises for any one country, and dramatically increases the degree of “contagion” across countries. Outside of crises, the impact of financial integration on macroeconomic aggregates is relatively small. But the impact of a crisis with integrated international financial markets is much less severe than that under financial market autarky. Thus, a trade-off emerges between the probability of crises and the severity of crises. Using a large cross-country database of financial crises in developing and developed economies over a forty-year period, we find evidence in support of the model.

Unscheduled charging of plenty of electric vehicles (EVs) might exert an adverse effect on the existing power grid, especially when the charging coincides with daily peak load at distribution level. In this study, a scalable real-time scheduling scheme for EV charging in low-voltage residential distribution system is proposed. Since most often, voltage drop would become a binding constraint when a distribution feeder is subject to a high EV penetration level, a scheduling method is first developed to increase the voltage safety margin. Then, a novel factor is derived to allow the scheduling to shift from voltage-safety-oriented to loss-minimisation-oriented, or vice versa, on demand of the EV penetration level. A number of charging scenarios were simulated to evaluate the proposed scheduling scheme. Simulation results verified that the proposed scheduling scheme is fast and efficient with circuit losses close to optimal at a low EV penetration level and voltage drops maintained within the tolerable limit at a high EV penetration level. The high scalability and effectiveness of the proposed scheme has made it suitable for coordinating large number of EV charging activities in real-time.

This paper presents an algorithm for simulating multiple equilibria in otherwise-linear dynamic models with occasionally-binding constraints. Our algorithm extends the guess-and-verify approach of Guerrieri and Iacoviello (2015) to detect and simulate multiple perfect foresight equilibria, and allows arbitrary “news shocks” up to a finite horizon. When there are multiple equilibria, we show how to compute expected paths using a “prior probabilities” approach and we provide an approach for running stochastic simulations with switching between equilibria on the simulated path. A policy application studies a New Keynesian model with a zero lower bound on nominal interest rates and multiple equilibria, including a “bad” solution based on self-fulfilling pessimistic expectations. A price-level targeting rule does not always eliminate the bad solution, but it shrinks the indeterminacy region substantially and improves stabilization and welfare relative to more conventional interest rate rules or forward guidance.

We introduce a novel simulated certainty equivalent approximation (SCEQ) method for solving dynamic stochastic problems. Our examples show that SCEQ can quickly solve high-dimensional finite- or infinite-horizon, stationary or non- stationary dynamic stochastic problems with hundreds of state variables, a wide state space, and occasionally binding constraints. With the SCEQ method, a desk- top computer will suffice for large problems, but it can also use parallel tools ef- ficiently. The SCEQ method is simple, stable, and can utilize any solver, making it suitable for solving complex economic problems that cannot be solved by other algorithms.

We present a model in which banks and other financial intermediaries face both occasionally binding borrowing constraints, and costs of equity issuance. Near the steady state, these intermediaries can raise equity finance at no cost through retained earnings. However, even moderately large shocks cause their borrowing constraints to bind, leading to contractions in credit offered to firms, and requiring the intermediaries to raise further funds by paying the cost to issue equity. This leads to the occasional sharp increases in interest spreads and the countercyclical, positively skewed equity issuance that are characteristics of the credit crunches observed in the data.

This paper compares the implications of tax system and public borrowing limit asymmetries for the welfare cost of business cycles and interregional consumption risk sharing in a two-region fiscal union. We identify the welfare-improving and risk-sharing-improving designs of the regional tax systems and borrowing limits. We find that the choice of public borrowing limits is more consequential than is the choice of a tax regime for union welfare. It also serves as an argument for the harmonization of fiscal policies adopted in the fiscal union, as it would internalize fiscal externalities and improve consumption risk-sharing across the union regions. The key parameter determining the merits of alternative regional tax systems and possible limits to public borrowing in the fiscal union is the productivity of public good. Other aspects of the economy, such as the type of technology process, or the nature of the productivity shock do not affect the union public finance system design significantly. Extensive simulations suggest that if the productivity of public capital lies within the range of plausible empirical estimates, allowing both regions to have flexible borrowing limits and to choose whatever tax system they prefer will reduce the overall welfare costs of business fluctuations. However, for very low productivity of public capital, the welfare-improving regional public finance reforms that would prohibit public borrowing and tax labor income can produce limited benefits.

We develop a new model of cycles and crises in emerging markets, featuring an occasionally binding borrowing constraint and stochastic volatility, and estimate it with quarterly data for Mexico since 1981. We propose an endogenous regime-switching formulation of the occasionally binding borrowing constraint, develop a general perturbation method to solve the model, and estimate it using Bayesian methods. We find that the model fits the Mexican data well without systematically relying on large shocks, matching the typical stylized facts of emerging market business cycles and Mexico's history of sudden stops in capital flows. We also find that interest rate shocks play a smaller role in driving both cycles and crises than previously found in the literature.

Consumption-saving models with adjustment costs or discrete choices are typically hard to solve numerically due to the presence of non-convexities. This paper provides a number of tools to speed up the solution of such models. Firstly, I use that many consumption models have a nesting structure implying that the continuation value can be efficiently pre-computed and the consumption choice solved separately before the remaining choices. Secondly, I use that an endogenous grid method extended with an upper envelope step can be used to solve efficiently for the consumption choice. Thirdly, I use that the required pre-computations can be optimized by a novel loop reordering when interpolating the next-period value function. As an illustrative example, I solve a model with non-durable consumption and durable consumption subject to adjustment costs. Combining the provided tools, the model is solved almost 50 times faster than with standard value function iteration for a given level of accuracy. Software is provided in both Python and C++.

When the economy experiences a sharp economic downturn, credit spreads widen and project financing costs for firms rise as funding sources begin to dry up. The economy experiences a lengthy recovery, with unemployment rates slow to return to “full employment” levels. We develop a model that displays these features. It relies on an interaction between labor search frictions and firm-level moral hazard that is accentuated during recessions. The model is capable of addressing the “Shimer puzzle,” with labor market variables exhibiting significantly more volatility on average as a result of the heightened moral hazard concerns during these episodes that significantly deepen and prolong periods of high unemployment, as vacancy postings fall dramatically and the job-finding rate declines. Our mechanism is also found to induce internal shock propagation causing the peak response of output, unemployment, and wages to occur with a several quarter delay relative to a model without such frictions. Many other labor market variables also show slower recovery—their return to preshock level occurs at a slower pace for a number of periods after the peak response.