This paper addresses the various methodological issues surrounding vector autoregressions, simultaneous equations, and chain reactions, and provides new evidence on the long-run inflation-unemployment tradeoff in the US. It is argued that money growth is a superior indicator of the monetary environment than the federal funds rate and, thus, the focus is on the inflation/unemployment responses to money growth shocks. SVAR (structural vector autoregression) and GMM (generalised method of moments) estimations confirm earlier findings in Karanassou, Sala and Snower (2005, 2008b) obtained from chain reaction structural models: the slope of the US Phillips curve is far from vertical, even in the long-run, which implies that the nominal and real sides of the economy are symbiotic. In the light of the significant and robust long-run inflation-unemployment tradeoffs, policy makers should reconsider the classical dichotomy thesis.