Extracting a Robust U.S. Business Cycle Using a Time-Varying Multivariate Model-Based Bandpass Filter

In this paper we investigate whether the dynamic properties of the U.S. business cycle have changed in the last fifty years. For this purpose we develop a flexible business cycle indicator that is constructed from a moderate set of macroeconomic time series. The coincident economic indicator is based on a multivariate trend-cycle decomposition model that accounts for time variation in macroeconomic volatility, known as the great moderation. In particular, we consider an unobserved components time series model with a common cycle that is shared across different time series but adjusted for phase shift and amplitude. The extracted cycle can be interpreted as the result of a model-based bandpass filter and is designed to emphasize the business cycle frequencies that are of interest to applied researchers and policymakers. Stochastic volatility processes and mixture distributions for the irregular components and the common cycle disturbances enable us to account for all the heteroskedasticity present in the data. The empirical results are based on a Bayesian analysis and show that time-varying volatility is only present in the a selection of idiosyncratic components while the coefficients driving the dynamic properties of the business cycle indicator have been stable over time in the last fifty years.

A General Framework for Observation Driven Time-Varying Parameter Models

We propose a new class of observation driven time series models that we refer to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled likelihood score. This provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity and single source of error models. In addition, the GAS specification gives rise to a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.dynamic models, time-varying parameters, non-linearity, exponential family, marked point processes, copulas

The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks

Many researchers believe that the Beveridge-Nelson decomposition leads to permanent and transitory components whose shocks are perfectly negatively correlated. Indeed, some even consider it to be a property of the decomposition. We demonstrate that the Beveridge-Nelson decomposition does not provide definitive information about the correlation between permanent and transitory shocks in an unobserved components model. Given an ARIMA model describing the evolution of U.S. real GDP, we show that there are many state space representations that generate the Beveridge-Nelson decomposition. These include unobserved components models with perfectly correlated shocks and partially correlated shocks. In our applications, the only knowledge we have about the correlation is that it lies in a restricted interval that does not include zero. Although the filtered estimates of the trend and cycle are identical for models with different correlations, the observationally equivalent unobserved components models produce different smoothed estimates.

Evaluating Structural Models for the U.S. Short Rate Using EMM and Particle Filters

We combine the efficient method of moments with appropriate algorithms from the optimal filtering literature to study a collection of models for the U.S. short rate. Our models include two continuous-time stochastic volatility models and two regime switching models, which provided the best fit in previous work that examined a large collection of models. The continuous-time stochastic volatility models fall into the class of nonlinear, non-Gaussian state space models for which we apply particle filtering and smoothing algorithms. Our results demonstrate the effectiveness of the particle filter for continuous-time processes. Our analysis also provides an alternative and complementary approach to the reprojection technique of Gallant and Tauchen (1998) for studying the dynamics of volatility.

The European and American immigration struggle: How two continents endeavor to solve the immigration question

Both the European Union and the United States experienced an immigration crisis in the Early 2000\u27s. Each has reacted with policies and judicial opinions based on their culture, circumstances, and geography. I conduct a comparative policy-based analysis with a multi-faced lens that will be analyzed with emphasis on the consequences of immigration and how each judicial system endeavors to solve the most pressing challenge of their times. Specifically, I compare various case law, directives, and precedent to provide a more in-depth narrative on how each system has reacted to circumstances before their respective Courts. An in-depth examination of both EU and US response to their crises helps provide relevant and accurate context to their current immigration challenges

Full Circle

School of Art and Design: Integrative Project ThesisArt and Design, School ofUniversity of MichiganUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/60485/1/IPThesis_Creal.pd

The effect of the great moderation on the US business cycle in a time-varying multivariate trend-cycle model

a time-varying multivariate trend-cycle mode

A General Framework for Observation Driven Time-Varying Parameter Models

We propose a new class of observation driven time series models referred to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled score of the likelihood function. This approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the autoregressive conditional intensity, and the single source of error models. In addition, the GAS specification provides a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions, and models for time-varying higher order moments. We study the propertie