Wicksell's Classical Dichotomy: Is the natural rate of interest independent of the money rate of interest?

According to Wicksell's Classical Dichotomy the money rate of interest depends on the natural rate of interest, but the latter does not depend on the former. If this Classical Dichotomy is false monetary policy may induce hysteresis because the natural rate of interest would depend upon the money rate of interest. We use data for Israel to test Wicksell's Classical Dichotomy. We proxy the natural rate of interest by the forward yield to maturity on indexed-linked treasury bonds. If the null hypothesis is false it is difficult to suggest persuasive instruments that would identify the causal effect of the money rate on the natural rate of interest. Our identification strategy is therefore built around quasi-experimentation and event analysis. Large and seemingly orthogonal shocks to the natural rate of interest have no measurable effect on the natural rate of interest according to non-parametric and parametric tests. Therefore, Wicksell's Classical Dichotomy is empirically valid.