Paul Samuelson's ways to macroeconomic dynamics

Samuelson kept optimization-based problems separated from macroeconomic dynamics in his Foundations, where dynamics were defined in terms of difference and differential equations. Despite some criticism of his "correspondence principle" of stability analysis by D.F. Gordon, D. Patinkin and others, it was only in the 1970s that Samuelson's separation was effectively challenged, particularly by R. Lucas. After the Foundations, Samuelson developed dynamic optimization models, sometimes featuring representative agents, but he did not extend that to the study of macroeconomic fluctuations. Neither did he accept market clearing inter-temporal maximization as a solution to the microfoundations problem that beset his models of macroeconomic dynamics. His last contribution to macro dynamics was his 1988 nonlinear non-optimizing business cycle model. Eventually, he disentangled his 1965 "efficient market hypothesis" from rational expectations and claimed that the former should form one of the pillars of macroeconomic dynamics, together with imperfectly competitive markets for goods and labour.