The evolutionary vision in which history matters is of an evolving economy driven by bursts of technological change initiated by agents facing uncertainty and producing long term, path-dependent growth and shorter-term, non-random investment cycles. The alternative vision in which history does not matter is of a stationary, ergodic process driven by rational agents facing risk and producing stable trend growth and shorter term cycles caused by random disturbances. We use Carlaw and Lipsey’s simulation model of non-stationary, sustained growth driven by endogenous, path-dependent technological change under uncertainty to generate artificial macro data. We match these data to the New Classical stylized growth facts. The raw simulation data pass standard tests for trend and difference stationarity, exhibiting unit roots and cointegrating processes of order one. Thus, contrary to current belief, these tests do not establish that the real data are generated by a stationary process. Real data are then used to estimate time-varying NAIRU’s for six OECD countries. The estimates are shown to be highly sensitive to the time period over which they are made. They also fail to show any relation between the unemployment gap, actual unemployment minus estimated NAIRU and the acceleration of inflation. Thus there is no tendency for inflation to behave as required by the New Keynesian and earlier New Classical theory. We conclude by rejecting the existence of a well-defined a short-run, negatively sloped Philips curve, a NAIRU, a unique general equilibrium, short and long-run, a vertical long-run Phillips curve, and the long-run neutrality of money.