Revisiting the Dollar-Euro Permanent Equilibrium Exchange Rate: Evidence from Multivariate Unobserved Components Models

We propose an alterative approach to obtaining a permanent equilibrium exchange rate (PEER), based on an unobserved components (UC) model. This approach offers a number of advantages over the conventional cointegration-based PEER. Firstly, we do not rely on the prerequisite that cointegration has to be found between the real exchange rate and macroeconomic fundamentals to obtain non-spurious long-run relationships and the PEER. Secondly, the impact that the permanent and transitory components of the macroeconomic fundamentals have on the real exchange rate can be modelled separately in the UC model. This is important for variables, where the long and short-run effects may drive the real exchange rate in opposite directions, such as the relative government expenditure ratio.Permanent Equilibrium Exchange Rate; Unobserved Components Model; Exchange rate forecasting.

Realised and Optimal Monetary Policy Rules in an Estimated Markov-Switching DSGE Model of the United Kingdom

This paper conducts a systematic investigation of parameter instability in a small open economy DSGE model of the UK economy over the past thirty-five years. Using Bayesian analysis, we find a number of Markov-switching versions of the model provide a better fit for the UK data than a model with time-invariant parameters. The Markov-switching DSGE model that has two independent Markov-chains - one governing the shifts in UK monetary policy and nominal price rigidity and one governing the standard deviations of shocks - is selected as the best fitting model. The preferred model is then used to evaluate and design monetary policy. For the latter, we use the Markov-Jump-Linear-Quadratic (MJLQ) model, as it incorporates abrupt changes in structural parameters into derivations of the optimal and arbitrary policy rules. It also reveals the entire forecasting distribution of the targeted variables. To our knowledge, this is the first paper that attempts to evaluate and design UK monetary policy based on an estimated open economy Markov-switching DSGE model.DSGE models; Markov-switching; Bayesian analysis

Measuring the Euro area output gap using multivariate unobserved components models containing phase shifts

This paper analyses the impact of using different macroeconomic variables and output decompositions to estimate the euro area output gap. We estimate twelve multivariate unobserved components models with phase shifts being allowed between individual cyclical components. As output decomposition plays a central role in all multivariate models, three different output decompositions are utilised; these are a first-order stochastic cycle combined with either a local linear trend or a damped slope trend, and a second-order cycle plus an appropriate trend specification (a trend following a random walk with a constant drift is generally preferred). We also extend the commonly used trivariate models of output, inflation and unemployment to incorporate a fourth variable, either investment or industrial production. We find that the four-variate model incorporating industrial production produces the most satisfactory output gap estimates, especially when the output gap is modelled as a first-order cycle. In addition, measuring phase shifts and calculating contemporaneous correlations between individual cyclical components provides a better understanding of the different gap estimates. We conclude that the output gap estimate in all models leads the cyclical components of inflation and unemployment, but lags those of industrial production and investment. Furthermore, the output gap estimates obtained from the four-variate model including investment present the longest leads-and-lags with respect to other cyclical components, implying that investment appears to be more of a leading indicator than a coincident variable for the euro area.output gap, higher-order cycle, industrial production, state-space, Kalman filter.

Matrix effects in inductively coupled plasma mass spectrometry

The inductively coupled plasma is an electrodeless discharge in a gas (usually Ar) at atmospheric pressure. Radio frequency energy generated by a RF power source is inductively coupled to the plasma gas through a water cooled load coil. In ICP-MS the {open_quotes}Fassel{close_quotes} TAX quartz torch commonly used in emission is mounted horizontally. The sample aerosol is introduced into the central flow, where the gas kinetic temperature is about 5000 K. The aerosol is vaporized, atomized, excited and ionized in the plasma, and the ions are subsequently extracted through two metal apertures (sampler and skimmer) into the mass spectrometer. In ICP-MS, the matrix effects, or non-spectroscopic interferences, can be defined as the type of interferences caused by dissolved concomitant salt ions in the solution. Matrix effects can be divided into two categories: (1) signal drift due to the deposition of solids on the sampling apertures; and/or (2) signal suppression or enhancement by the presence of the dissolved salts. The first category is now reasonably understood. The dissolved salts, especially refractory oxides, tend to deposit on the cool tip of the sampling cone. The clogging of the orifices reduces the ion flow into the ICP-MS, lowers the pressure in the first stage of ICP-MS, and enhances the level of metal oxide ions. Because the extent of the clogging increases with the time, the signal drifts down. Even at the very early stage of the development of ICP-MS, matrix effects had been observed. Houk et al. found out that the ICP-MS was not tolerant to solutions containing significant amounts of dissolved solids

The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally H\"older continuous with exponent $\delta\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $\delta\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.Comment: Keywords: local martingales, local stochastic solutions, degenerate Cauchy problems, Feynman-Kac formula, necessary and sufficient condition for uniqueness, comparison principl

Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model

This paper employs an unobserved component model that incorporates a set of economic fundamentals to obtain the Euro-Dollar permanent equilibrium exchange rates (PEER) for the period 1975Q1 to 2008Q4. The results show that for most of the sample period, the Euro-Dollar exchange rate closely followed the values implied by the PEER. The only significant deviations from the PEER occurred in the years immediately before and after the introduction of the single European currency. The forecasting exercise shows that incorporating economic fundamentals provides a better long-run exchange rate forecasting performance than a random walk process