This paper follows Harvie and Grasselli and Maheshwari's research program in testing both Goodwin's predator–prey model and the extension proposed by van der Ploeg. The aim of this paper is to provide a guideline for the bloc estimation and the backtesting strategy that can be applied to such a class of continuous-time non-linear macroeconomic models. The goal of this paper is to propose and test stochastic differential equations for Goodwin's model and one of its extensions by an estimation technique based on simulated maximum likelihood developed by Durham and Gallant. The data considered here are that of wage share and employment rate in the United States from 1948:Q1 to 2019:Q4. Results show that two structural breaks—at the beginning of the 80s' and late 90s'—are likely to have occurred and the Goodwin-type model endowed with Leontief production technology explains more accurately the data than the van der Ploeg's CES production function. These results are partly confirmed by a backtesting strategy, which highlights the predicting property of the van der Ploeg-like model on a purely statistical VAR model. Both the estimation and backtesting strategies can be used to assess the empirical improvement on any extensions of the models investigated in this paper.

中文翻译：

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用随机微分法测试古德温——美国（1948-2019）

本文遵循 Harvie 和 Grasselli 以及 Maheshwari 在测试 Goodwin 的捕食者-猎物模型和 van der Ploeg 提出的扩展方面的研究计划。本文的目的是为可应用于此类连续时间非线性宏观经济模型的集团估计和回测策略提供指导。本文的目标是通过基于 Durham 和 Gallant 开发的基于模拟最大似然的估计技术提出并测试 Goodwin 模型及其扩展之一的随机微分方程。这里考虑的数据是美国从 1948 年第一季度到 2019 年第四季度的工资份额和就业率。结果表明，在 80 年代初和 90 年代末，两次结构性断裂 ——很可能已经发生了，具有Leontief生产技术的Goodwin型模型比van der Ploeg的CES生产函数更准确地解释了数据。这些结果部分得到了回测策略的证实，该策略突出了 van der Ploeg-like 模型在纯统计 VAR 模型上的预测特性。估计和回测策略均可用于评估本文研究的模型的任何扩展的经验改进。