What is the natural rate of interest? The natural rate is the equilibrium real interest rate consistent with price stability. The natural rate is an idea that originated with Knut Wicksell in 1896 and has been made use of by more recent studies of monetary policy like Michael Woodfords' mind bending Interest and Prices: Foundations of a Theory of Monetary Policy. Unfortunately for everyone the natural rate cannot actually be observed which makes it pretty unpractical in terms of actual monetary policy, but it can still be used as a nice theoretical tool to help explain output fluctuations. The New Keynesian natural rate is an equilibrium rate consistent with period-by-period price stability as opposed to a deviation towards a longer term trend. Some New Keynesian models emphasize the "real rate gap"-which is the difference between the actual short-term real interest rate and the natural rate- as a principle source of Aggregate Demand driven imbalances. When output is equal to natural GDP, the natural rate is equal to the equilibrium real interest rate. This implies that real rigidities that prevent GDP from approaching natural GDP also prevent the real rate from approaching the natural rate.
A typical New Keynesian model has firms engaged in Monopolistic Competition and prices are assumed to be sticky. This leads to the horizontal short-run aggregate supply curve so output is demand determined. Household's and firms are assumed to act rationally, which implies they form expectations rationally. Consumption and investment decisions cause output to be affected by the private sectors expectations of future interest rates and future values of the natural rate. This framework is in equilibrium when current and expected real rate gaps are zero, GDP and natural GDP are equal and the price level has no tendency to change. The only reason i like the idea of a natural rate of interest is because it can be used to explain how imperfections in the financial markets can impact the real economy. Various market imperfections (including risk premia and credit rationing due to asymmetric information, incomplete indexation, and expectational errors by market participants) cause the real rate to deviate from the natural rate leading to a misallocation of credit.