In this article, we analyze the short term real interest rate series for the last five decades in the framework of a M-SETAR model (Momentum - Self Exciting Threshold Auto-Regressive). With the aim of disentangling the non-linearity from the non-stationarity cases, we use threshold integration tests against a stationary but non-linear alternative hypothesis. One innovation consists in the introduction of a structural break in the deterministic component of the process as well as threshold effects for the volatility (TARCH). Therefore, our model allows for shifting regimes both in the deterministic part (mean shift) and in the stochastic part (threshold effects). The empirical application concerns the gap between the ex post real interest rate and its natural level which changes after the break date. Our empirical results for the US and the euro-zone show some evidence that the real interest gap follows a two-regimes threshold process. Furthermore, the process seems to behave as a martingale in one of the regimes, highlighting the 'reactive' characteristics of the monetary policy during these corresponding periods.

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