The role of empirical verification in the mathematized economics of the Samuelson era was supposed to be played by econometrics, a field, curiously enough, in which Samuelson himself rarely, if ever, worked. With some economic data traditional statistical methods work very well. I remember Richard Ruggles showing a slide of what appeared to be a perfect bell curve in a talk, and remarking that it was in fact a visualization of real census data points. With macroeconomic time series, however, several problems gang up on econometrics to make life very difficult.
First, although it may appear that there are a lot data points in macroeconomic time series, a little acquaintance with the data shows that it is highly “autocorrelated”, which means in practical terms that the amount of independent information is much smaller than the number of measured data points. For example there may have been twelve or thirteen separate business cycles since 1929, which suggests that at business cycle frequency the effective statistical sample size is only on that order, which greatly limits the power of any statistical methods to find reliable regularities.
Second, econometrics was born under some unlucky scientific stars. Though economic theory (of all schools) bristles with inherently nonlinear relationships, the dominant and best-developed statistical methods available in the first decades of serious econometric investigation firmly rested on linear specifications.
Linear regression is best adapted to understand equilibrium systems undergoing small perturbations from stable equilibrium configurations, a situation where the small size of the variations makes the assumption of linearity plausible. This is emphatically not a good description of macroeconomic fluctuations in industrial capitalist economies. The particular “frequentist” philosophy that dominated econometric thinking and teaching frames statistical inference as a problem of “estimating” models, and generally evaluates procedures by their “asymptotic consistency”, that is, their theoretical performance with unboundedly large samples from “stationary”, that is, essentially, unchanging repetitive experiments. This is cold comfort for a science where data points are scarce, and a recipe for disaster in macroeconomic
research where history is in principle unrepeatable. Early econometric theory remained blissfully innocent of the problem of over-fitting limited data with excessively parameterized specifications, so that its methods tended to confirm pretty much any theory whatsoever. The absence of any theory of fluctuations in the optimizing mathematics that underlies the various flavors of general equilibrium theory means that theory itself offers no guide to the statistical specification of econometric models, further opening the floodgates to whatever method supports the point of view of the investigator.
The wild-west character of econometric investigations into macroeconomic problems from the 1940s to the 1970s led to a swing of the pendulum, exploited by the advocates of “rational expectations” macroeconomic modeling, in which the traditional scientific role of empirical confirmation in policing theoretical speculation was usurped by philosophical/theoretical general principles. The filter for publication of macroeconomic research became, not the ability of the theory to explain real features of the data (of which there wasn’t that much to begin with), but the fidelity of the theory to strictures of modeling purity announced ex cathedra by leading senior authorities. The test of the ability of theories to explain data, which was never very strong in macroeconomics, was further watered-down to ad hoc procedures such as “calibration”, which have essentially no protections against over-fitting built into them.