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I don't follow. What is identity form? And why did you group (employment, credit, policy, etc...) under growth but (agency, management, input factors, etc...) under productivity.Yes, the accounting necessary to aggregate is in identity form. That still does not negate the relationship between economic growth (employment, credit, policy, etc...) and productivity (agency, management, input factors, etc...) being a multi-dimensional paradigm which primarily determine inflation.
Inflation has many causes, and economic systems have many inputs (meaning you can represent them with multi-dimensional manifolds). But I'm not sure that inflation is a multi-dimensional paradigm. It's kind of a one dimensional scalar.