Solving the Multi-Country Real Business Cycle Model Using Ergodic Set Methods

We use the stochastic simulation algorithm, described in Judd, Maliar and Maliar (2009), and the cluster-grid algorithm, developed in Judd, Maliar and Maliar (2010a), to solve a collection of multi-country real business cycle models. The following ingredients help us reduce the cost in high-dimensional problems: an endogenous grid enclosing the ergodic set, linear approximation methods, fixed-point iteration and efficient integration methods, such as non-product monomial rules and Monte Carlo integration combined with regression. We show that high accuracy in intratemporal choice is crucial for the overall accuracy of solutions and offer two approaches, precomputation and iteration-on-allocation, that can solve for intratemporal choice both accurately and quickly. We also implement a hybrid solution algorithm that combines the perturbation and accurate intratemporal-choice methods.

Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. It consists in constructing a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably large, then the actual approximation errors are even larger, and hence, the approximation is inaccurate. Our lower‐bound error analysis is complementary to the conventional upper‐error (worst‐case) bound analysis, which provides a sufficient condition for accuracy. As an illustration of our methodology, we assess approximation in the first‐ and second‐order perturbation solutions for two stylized models: a neoclassical growth model and a new Keynesian model. The errors are small for the former model but unacceptably large for the latter model under some empirically relevant parameterizations.Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution and Department of Economics at Stanford University, Santa Clara University, Ivie, University of Alicante, and the MINECO/FEDER Grant ECO2015-70540-P

How to Solve Dynamic Stochastic Models Computing Expectations Just Once

We introduce a technique called "precomputation of integrals" that makes it possible to compute conditional expectations in dynamic stochastic models in the initial stage of the solution procedure. This technique can be applied to any set of equations that contains conditional expectations, in particular, to the Bellman and Euler equations. After the integrals are precomputed, we can solve stochastic models as if they were deterministic. We illustrate the benefits of precomputation of integrals using one- and multi-agent numerical examples.

A Cluster-Grid Projection Method: Solving Problems with High Dimensionality

We develop a projection method that can solve dynamic economic models with a large number of state variables. A distinctive feature of our method is that it operates on the ergodic set realized in equilibrium: we simulate a model, distinguish clusters on simulated series and use the clusters’ centers as a grid for projections. Making the grid endogenous to the model allows us to avoid costs associated with finding a solution in areas of state space that are never visited in equilibrium. On a standard desktop computer, we calculate linear and quadratic solutions to a multi-country growth model with up to 400 and 80 state variables, respectively. Our solutions are global, and their accuracy does not rapidly decline away from steady state.

ОСОБЛИВОСТІ КЛІНІЧНОГО ПЕРЕБІГУ ЗАПАЛЬНИХ ЗАХВОРЮВАНЬ ГЕНІТАЛІЙ НА ТЛІ ВНУТРІШНЬОМАТКОВИХ СПІРАЛЕЙ

In the conditions of the course of inflammatory diseases of genitals on bodies of inwardly-uterine spirals. It is established, that long stay in a inwardly-uterine spirals conducts no typical to a course of inflammatory diseases of genitals with occurrence of tumor-like formations which demand operative intervention.В условиях клиники изучено течение воспалительных заболеваний гениталий на фоне внутриматочных спиралей (ВМС). Установлено, что длительное пребывание в матке ВМС ведет к атипичному течению воспалительных заболеваний гениталий с возникновением опухолеподобных образований, которые требуют оперативного вмешательства.В умовах клініки вивчено перебіг запальних захворювань геніталій на тлі внутрішньоматкових спіралей (ВМС). Встановлено, що тривале перебування в матці ВМС веде до атипового перебігу запальних захворювань геніталій з виникненням пухлиноподібних утворень, які вимагають оперативного втручання

Raman Scattering:From Structural Biology to Medical Applications

This is a review of relevant Raman spectroscopy (RS) techniques and their use in structural biology, biophysics, cells, and tissues imaging towards development of various medical diagnostic tools, drug design, and other medical applications. Classical and contemporary structural studies of different water-soluble and membrane proteins, DNA, RNA, and their interactions and behavior in different systems were analyzed in terms of applicability of RS techniques and their complementarity to other corresponding methods. We show that RS is a powerful method that links the fundamental structural biology and its medical applications in cancer, cardiovascular, neurodegenerative, atherosclerotic, and other diseases. In particular, the key roles of RS in modern technologies of structure-based drug design are the detection and imaging of membrane protein microcrystals with the help of coherent anti-Stokes Raman scattering (CARS), which would help to further the development of protein structural crystallography and would result in a number of novel high-resolution structures of membrane proteins—drug targets; and, structural studies of photoactive membrane proteins (rhodopsins, photoreceptors, etc.) for the development of new optogenetic tools. Physical background and biomedical applications of spontaneous, stimulated, resonant, and surface- and tip-enhanced RS are also discussed. All of these techniques have been extensively developed during recent several decades. A number of interesting applications of CARS, resonant, and surface-enhanced Raman spectroscopy methods are also discussed

Active learning and optimal climate policy

This paper develops a climate-economy model with uncertainty, irreversibility, and active learning. Whereas previous papers assume learning from one observation per period, or experiment with control variables to gain additional information, this paper considers active learning from investment in monitoring, specifically in improved observations of the global mean temperature. We find that the decision maker invests a significant amount of money in climate research, far more than the current level, in order to increase the rate of learning about climate change. This helps the decision maker make improved decisions. The level of uncertainty decreases more rapidly in the active learning model than in the passive learning model with only temperature observations. As the uncertainty about climate change is smaller, active learning reduces the optimal carbon tax. The greater the risk, the larger is the effect of learning. The method proposed here is applicable to any dynamic control problem where the quality of monitoring is a choice variable, for instance, the precision at which we observe GDP, unemployment, or the quality of education