In the paper, we provide a critical and selective survey of arguments relevant for the assessment of the case for price level path stability (PLPS). Using a standard hybrid new Keynesian model we argue that price level stability provides a natural framework for monetary policy under commitment. There are two main arguments in favour of a PLPS regime. First, it helps overall macroeconomic stability by making expectations operate like automatic stabilizers. Second, under a price level path stability regime, changes in the price level operate like an intertemporal adjustment mechanism, reducing the magnitude of required changes in nominal interest rates. Such a property is particularly relevant as a means to alleviate the importance of the zero bound on nominal interest rates. We also review and discuss the arguments against price level path stability. Finally, we also found, using the Smets and Wouters (2003) model which includes a wide variety of frictions and is estimated for the euro area, that the price level is stationary under optimal policy under commitment. The results obtain when the quasi-difference of inflation is used in the loss function, as in the hybrid new Keynesian model. Overall, the arguments in favour of or against price level path stability depend on the degree of dependence of private sector expectations on the characteristics of the monetary policy regime.