Shifting from Ramsey optimal policy to time-consistent policy or optimal simple rule corresponds to a saddle-node bifurcation of the dynamic system of the economy. A pre-test of Ramsey optimal policy versus time-consistent policy rejects time-consistent policy and optimal simple rule for the U.S. Fed during 1960 to 2006, assuming the reference new-Keynesian Phillips curve transmission mechanism with auto-correlated cost-push shock. The number of reduced form parameters is larger with Ramsey optimal policy than with time-consistent policy although the number of structural parameters, including central bank preferences, is the same. The new-Keynesian Phillips curve model is under-identified with Ramsey optimal policy (one identifying equation missing) and hence under-identified for time-consistent policy (three identifying equations missing). Estimating a structural VAR for Ramsey optimal policy during Volcker-Greenspan period, the new-Keynesian Phillips curve slope parameter and the Fed's preferences (weight of the volatility of the output gap) are not statistically different from zero at the 5% level.