I worked in this tradition. In my dissertation, I formulated the optimal policy
selection problem as a Bayesian sequential decision problem. The problem is
a difficult one because the policy actions taken today affect the distribution of
the posterior distribution of the values of the coefficients of the equations.
The macroeconometric models organized the field. Success in macroeconomics
was to have your equation incorporated into the macroeconometric
models. Indeed, Lucas and I were searching for a better investment equation
when in 1969 we wrote our paper “Investment under Uncertainty,” a paper that
was published two years later in 1971.
A key assumption in the system-of-equations approach is that the equations
are policy invariant. As Lucas points out in his critique, which I delivered in 1973,
this assumption is inconsistent with dynamic economic theory. His insight made
it clear that there was no hope for the neoclassical synthesis – that is, the development
of neoclassical underpinnings of the system-of-equations macro models.
Fortunately, with advances in dynamic economic theory an alternative set
of tractable macro models was developed for drawing scientific inference.
The key development was recursive competitive equilibrium theory in Lucas
and Prescott (1971) and Lucas (1972). Equilibrium being represented as a
set of stochastic processes with stationary transition probabilities was crucial
to the revolution in macroeconomics.