Endogenous Cycles in Optimal Monetary Policy with a Nonlinear Phillips Curve

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy with sticky prices a la Calvo and forward looking behavior. In this paper we extend this standard model by introducing nonlinearity into the Phillips curve. As the linear Phillips curve may be questioned on theoretical grounds and seems not to be favoured by empirical evidence, a similar procedure has already been undertaken in a series papers over the last few years, e.g., Schaling (1999), Semmler and Zhang (2004), Nobay and Peel (2000), Tambakis (1999), and Dolado et al. (2004). However, these papers were mainly concerned with the analysis of the problem of inflation bias, by deriving an interest rate rule which is nonlinear, leaving the issues of stability and the possible existence of endogenous cycles in such a framework mostly overlooked. Under the specific form of nonlinearity proposed in our paper (which allows for both convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into a fully deterministic structure of the standard model produces significant changes to the major conclusions regarding stability and the efficiency of monetary policy in the standard model. We should emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable and chaotic fixed points (endogenous cycles); (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem interesting. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate may have a lower mean and is certainly less volatile; secondly, for changes in the degree of price stickiness the results are not are clear cut as in the previous case, however, we can also observe that when such stickiness is high the inflation rate tends to display a somewhat larger mean and also higher volatility; and thirdly, it shows that the target values for inflation and the output gap (π^,x^), both crucially affect the dynamics of the economy in terms of average values and volatility of the endogenous variables --- e.g., the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility --- while in the linear case only the π^ does so (obviously, only affecting in this case the level of the endogenous variables). Moreover, the existence of endogenous cycles due to chaotic motion may raise serious questions about whether the old dictum of monetary policy (that the Central Bank should conduct policy with discretion instead of commitment) is not still very much in the business of monetary policy.Optimal monetary policy, Interest Rate Rules, Nonlinear Phillips Curve, Endogenous Fluctuations and Stabilization

New geochemical and isotopic constraints on the genesis of the Oliveira Azeméis granitoid melts (Porto-Tomar Shear Zone, Iberian Variscan Chain, Central-Western Portugal).

The Porto-Tomar Shear Zone (PTSZ) is a very important tectonic structure that separates, in central-western Portugal, two of the major tectonic units of the Iberian Variscan Chain: the Ossa-Morena Zone, to the west, and the Central Iberian Zone, to the east. The Oliveira de Azeméis area lies in the northern sector of the PTZC and it is characterized by the occurrence of strongly deformed granitoids. Country rocks are dominantly pelitic metasediments which, according to recent geological mapping (Pereira et al., 2007), belong to the Precambrian Lourosa Formation and the Ordovician São João de Ver Formation. Using Rb-Sr whole-rock isotopic data, Pinto (1979) proposed an age of 379 12 Ma for the Oliveira de Azeméis granitoids. In this work, new results were obtained on these granitoids in the area between the villages of Travanca and Curval, especially in the Sacramento quarry. In this critical outcrop, strongly deformed two-mica granite (displaying S-C structures, with dextral NNW-SSE shear planes) pass into diatexites and metatexites with garnet, cordierite and sillimanite-bearing melanosomes. Leucosomes seem to have mainly granitic s.s. compositions, but cm-thick bands of leucotonalite were also found. Major element geochemistry of granite samples shows the following ranges: 71.4% SiO2 74.2%; 0.74% Fe2O3t 2.48%; 0.35% MgO 0.60%; 0.49% CaO 1.32%; 2.90% Na2O 3.11%; 4.70% K2O 5.47%; 1.17 ASI 1.36. Trace element data reveal a strong fractionation between highly incompatible LILE and less incompatible HFSE (248 PM normalized Rb/Y 671) and between LREE and HREE (18.6 PM normalized La/Lu 54.7). These features, in particular the peraluminous composition, the high K contents and the distinct rare-earth fractionation suggest that the Oliveira de Azeméis granites are mostly the result of partial melting of metasediments with a large pelitic component and that garnet is a likely residual phase. Isotope geochemistry data show that the previously reported isochron should not correspond to a true age since the 87Sr/86Sr(380Ma) obtained in the granite samples analysed in the present work are very low, varying from 0.6978 to 0.7063, with an average value of 0.7023, which are unrealistic in S-type granitic melts. Probably, the 380 Ma date is the consequence of mixing of different melt source components in the samples used in its calculation. Using the granite whole-rock samples collected in this work, a 328 28 Ma errorchron (MSWD=4.0; initial 87Sr/86Sr=0,7106 0.0045) is now obtained. Assuming a typical syn-tectonic Variscan age of 320 Ma for the studied granites, 87Sr/86Sr and "Nd range from 0.7100 to 0.7133 and from -6.5 to -7.9, respectively. A micaschist sample collected in this area displays 87Sr/86Sr(320Ma) = 0.7146 and "Nd(320Ma) = -9.2. Therefore, the Sr and Nd isotope composition agrees with the clearly dominance of a melt component derived by anatexis of a metapelitic source. Two samples of a garnet-bearing (and comparatively zircon-rich) diatexite show 87Sr/86Sr(320Ma) values (0.7120 and 0.7102) similar to those found in granites, but have higher "Nd(320Ma): -2.0 and -1.6. This may be explained by either (a) the involvement of a different source in the genesis of this diatexite or (b) the occurrence of Nd isotope disequilibrium during the melting process, with the preservation of high 143Nd/144Nd ratios in refractory phases such as garnet and/or zircon. A Rb-Sr wr-feldspar-biotite-muscovite isochron of 301.2 5.6 Ma (MSWD=0.42; initial 87Sr/86Sr=0,71516 0.00074) in a granite sample is interpreted as recording the final stage of the operation of the shear zone, which was accompanied by mica recrystallization. Funding: projects Petrochron (PTDC/CTE-GIX/112561/2009) and Geobiotec (PEst-C/CTE/UI4035/2011). References Pereira E. et allia (2007) – Carta Geológica 1/50000 de Oliveira de Azeméis. INETI, Lisboa. Pinto M.S. (1979) – PhD Thesis. Univ. Leed