Macroeconomic Models before the Transformation
Macroeconomic models were systems of equations that determined current
outcomes given the values of the current policy actions, values of predetermined
variables, and values of any stochastic shocks. Thus, physical models and
pre-transformation macro models have the same mathematical structure.
The basic mathematical structure of both is
xt+1= f (xt,ut,t ).
The state or position of the dynamic system at the beginning of period t is xt,
the control or policy variables are ut , and the stochastic shocks are t .
With the system-of-equations approach, each equation in the system is
determined up to a set of parameters. The simple prototype system-of-equations
macro model has a consumption function, an investment equation, a money
demand function, and a Phillips curve. Behind all these equations were a rich
empirical literature and, in the case of the consumption function, money
demand function, and investment equation, some serious theoretical work.
The final step was to use the tools of statistical estimation theory to select the
parameters that define the function f.
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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