Optimal Monetary Policy Under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach

We study the design of optimal monetary policy under uncertainty in a dynamic stochastic general equilibrium model. We use a Markov jump-linear-quadratic (MJLQ) approach to study policy design, proxying the uncertainty by different discrete modes in a Markov chain, and by taking mode-dependent linear-quadratic approximations of the underlying model. This allows us to apply a powerful methodology with convenient solution algorithms that we have developed. We apply our methods to a benchmark new-Keynesian model, analyzing how policy is affected by uncertainty, and how learning and active testing affect policy and losses.

Essays on functional coefficient models

This dissertation is composed of three essays on functional coefficient models (also referred to as varying-coefficient models) in the time series context. The first essay proposes two estimators for a functional coefficient model with discontinuities in the coefficient functions. One is based on the weighted residual mean squared error, which works well only if the conditional error variance is continuous. The other estimator is based on the local Wald test statistics which is applicable even if the conditional error variance contains discontinuities. In the second essay, we introduce a new model – the semiparametric transition model, and propose an iterative estimation procedure which is based on the straightforward application of (local) least squares. Simulations demonstrate that the proposed estimation provides precise estimates for many types of transition functions. The third essay proposes an estimator for a functional coefficient model with endogenous variables. In contrast to the existing functional coefficient IV literature, our estimator is adapted to the case that coefficients are functions of an endogenous variable. To illustrate the utility of our approach, we provide an empirical example based on the relationship among the hourly wage rate, education level, and work experience

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Bayesian mapping of brain regions using compound Markov random field priors

Human brain mapping, i.e. the detection of functional regions and their connections, has experienced enormous progress through the use of functional magnetic resonance imaging (fMRI). The massive spatio-temporal data sets generated by this imaging technique impose challenging problems for statistical analysis. Many approaches focus on adequate modeling of the temporal component. Spatial aspects are often considered only in a separate postprocessing step, if at all, or modeling is based on Gaussian random fields. A weakness of Gaussian spatial smoothing is possible underestimation of activation peaks or blurring of sharp transitions between activated and non-activated regions. In this paper we suggest Bayesian spatio-temporal models, where spatial adaptivity is improved through inhomogeneous or compound Markov random field priors. Inference is based on an approximate MCMC technique. Performance of our approach is investigated through a simulation study, including a comparison to models based on Gaussian as well as more robust spatial priors in terms of pixelwise and global MSEs. Finally we demonstrate its use by an application to fMRI data from a visual stimulation experiment for assessing activation in visual cortical areas