IMPLEMENTATION AND TESTING OF SHEAFIFICATION OF GOODWIN MODELS

Economics and mathematics have always been interrelated. This paper examines one such instance of overlapping: the Goodwin model of endogenous growth. Goodwin illustrates the dynamic interaction between employment rate and workers’ share of national income through differential equations exhibiting nuanced and complex behavior. Theories and models are refined over time; an important update to Goodwin’s model is Ishiyama’s (2001), who extends it to include two countries engaged in horizontal trade. Using sheaf theory, this paper provides a means for testing the original’s validity through synthesis and analysis of real-world data. Sheaves provide visual representations of complex variable relationship structures once the model’s equations are properly encoded via a dependency diagram. This paper attempts such analyses, focusing mainly on local sheaf sections, extensions to global sections, and quantifying data fit. To this end we implement a Pysheaf encoding of data from the Federal Reserve as a Section for the Sheafified Goodwin Model, examining the output and fit over various sliding windows. We conduct our analyses to test the original model’s validity and lay the groundwork for quantitatively comparing and judging other models in the future.