Collaborative Research: Piecewise Linear Approximations for DSGE Models With Occasionally-Binding Constraints: Solution, Estimation, Model Evaluation, and Applications

中央银行的监管者使用数学模型来理解经济活动的波动和银行政策的影响。目前用于分析政策变化对大规模经济变量（如总产出、通货膨胀和利率）之间关系的一般影响的方法，要么无法捕捉某些极端事件的影响，如将利率降至零，要么实施起来太慢，成本太高。该研究项目将开发新的、更快、更便宜和更好的方法来分析政策变化对经济中大规模变量的影响。因此，这项研究项目的结果将有助于经济科学，更重要的是，可以更好地了解政策变化或外部影响如何在整个更大的经济中传播。这将使经济学家能够向决策者提供更明智的建议，从而促进经济增长，提高美国人的生活水平。该项目开发的工具也可以应用于世界任何地方，从而确立了美国在经济分析工具开发方面的全球领导者地位。在大衰退之前，美联储和其他监管机构使用的宏观变量之间的线性关系模型能够捕捉总时间序列的最重要特征，并产生准确的预测。然而，在大衰退期间和之后，由偶尔具有约束力的约束（如名义利率的有效下限约束）产生的非线性已成为常态。本研究项目将开发新的技术来构建宏观经济模型的非线性解，其中偶尔约束起着重要作用。拟议研究的目标是开发和应用一种分段线性解决方法，该方法可以在计算速度和准确性之间进行折衷，并且可以扩展到中央银行使用的大型模型。该项目还将开发一类灵活的模型，这些模型可用于评估施加强大理论限制的模型是否得到了很好的规定。该项目的成果将为研究人员提供新的分析工具，以提高政策建议和监管的质量。这可以促进美国的经济增长，改善公民的生活。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Central banks regulators use mathematical models to understand fluctuations in economic activity and the effects of the bank's policies. Current methods used to analyze the general effects of policy changes on relationships among large-scale economic variables, such as total output, inflation, and interest rate are either not able to capture the effects of some extreme events, such as decreasing interest to zero, or are too slow and costly to implement. This research project will develop new, faster, cheaper, and better methods to analyze the effects of policy changes on large-scale variables in the economy. The results of this research project will therefore contribute to economic science, and more important, allow for a better understanding of how policy changes or external influences are transmitted throughout the larger economy. This will allow economist to provide more informed advice to police makers and in so doing, enhance economic growth and improve the living standards of Americans. The tools developed in this project can also be applied anywhere in the world, thus establishing the U.S. as the global leader in the development of economic analytical tools.Prior to the Great Recession, models of linear relationship among macro variables used by the Fed and other regulatory agencies were able to capture the most important features of aggregate time series and generate accurate predictions. However, during and after the Great Recession, nonlinearities generated by occasionally-binding constraints such as an effective lower bound constraint on nominal interest rates, have become the norm. This research project will develop new techniques to construct nonlinear solutions to macroeconomic models in which occasionally-binding constraints play an important role. The goal of the proposed research is to develop and apply a piecewise-linear solution method that trades off a little of accuracy against computational speed and is scalable to large models used by central banks. The project will also develop a class of flexible models that can be used to assess whether models that impose strong theoretical restrictions are well specified. The results of this project will provide researchers with new analytical tools that will improve the quality of policy advice as well as regulation. This could increase economic growth in the U.S. and improve the lives of citizens.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.