### Chaotic dynamics in optimal monetary policy

For instance, if the nominal interest rate is above the inflation-augmented natural rate[2] then monetary conditions are too tight and the economy is underutilizing its available labor and capital resources. Conversely, a real interest rate below the natural rate leads to overutilization of productive resources and, in consequence, inflation above its target. Although the natural rate is not directly observable, it can be estimated from a hypothetical economic model in which prices and wages are perfectly flexible, and devoid of shocks to the markup on goods and labor markets.

In this hypothetical economy, the resulting equilibrium interest rate is the natural rate of interest, as stressed by Woodford The below Figure represents the historical path of the estimated natural rate plus expected inflation obtained from this model for the euro area, along with the EONIA.

## Chaotic dynamics in optimal monetary policy | The European Physical Journal B (EPJ B)

For comparison purposes, the natural rate is, in black, displayed in nominal terms that is, the sum of the real natural rate plus expected inflation. In consequence, the aggressive monetary easing measures conducted by ECB have not allowed the nominal interest rate to follow the estimated natural rate. Based on this estimated natural rate, monetary policy was too tight over that period. Of course, EONIA does not take into account all unconventional monetary policy measures forward guidance, long term refinancing operations, quantitative easing, ….

In a recent empirical study, Wu and Xia have constructed a shadow interest rate taking into account both conventional and unconventional measures so as to quantify the stance of ECB monetary policy at the zero lower bound. This is what shows the below Figure from to The dotted blue line reports the four-quarter moving average of the nominal natural rate of interest. EONIA is in red.

- Woodford, M.: Interest and Prices: Foundations of a Theory of Monetary Policy. | SpringerLink!
- American Economic Association.
- Handbook of Monetary Economics, Volume 3B.

Corresponding authors: a ogomes escs. There is by now a large consensus in modern monetary policy.

## Monetary economics: a reading list

This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e. Bernanke and J.

Rotemberg Cambridge, Mass. In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper which allows for convexity and concavity and secures closed form solutions , we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy.

Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility but this is sensitive to the values given to the parameters of the model ; and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.

PACS: Ac — Low-dimensional chaos. EPJ Appl.

B Eur. E Eur.