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Keywords:Stochastic analysis 

Journal Article
How good is what you've got? DSGE-VAR as a toolkit for evaluating DSGE models
In the constant search for better models to help guide policy decisions, central banks have begun to use and develop dynamic stochastic general equilibrium (DSGE) models. Although such models were until recently considered theoretically sound but overly restrictive, newly developed methods have proved successful in specifying DSGE models that fit the macroeconomic data well. ; Policy institutions that use DSGE models in policymaking need a reliable method for evaluating the models? effectiveness. This article reviews a procedure recently proposed by the authors and their colleagues. The article first describes how the linear DSGE model can be nested in a vector autoregression (VAR) and then outlines a procedure that can systematically relax the restrictions the DSGE model imposes on the VAR. ; Using the resulting DSGE-VAR specification as a framework, the authors compare the fit and forecasting performance of a DSGE model with several nominal and real rigidities. They use the DSGE-VAR framework to assess the relative importance of different frictions, with particular emphasis on wage and price indexation and habit formation. The DSGE-VAR framework also provides a benchmark that can reveal in what dimensions a DSGE model needs to be improved. ; This DSGE-VAR procedure, the authors believe, shows some promise in delivering robust evaluations of DSGE models.>
AUTHORS: Schorfheide, Frank; Del Negro, Marco
DATE: 2006

Journal Article
Take your model bowling: forecasting with general equilibrium models
During the past two decades, dynamic stochastic general equilibrium (DSGE) models have taken center stage in academic macroeconomics. Nonetheless, these models are still rarely used in policy-making and forecasting. ; This article describes the workings of the DSGE-VAR, a procedure that combines DSGE models and vector autoregressions (VARs). The procedure uses DSGE models as priors to restrict the VAR?s parameters. Since the VAR?s parameters are imprecisely estimated unless a very long time series of data is available, using DSGE priors can improve the VAR?s forecasting performance. Moreover, the Lucas critique implies that DSGE priors can be particularly useful when forecasting the impact of policy changes. ; The authors assess DSGE-VAR?s forecasting performance in terms of three variables that most interest monetary policymakers: real output growth, inflation, and the federal funds rate. Their results show that the DSGE-VAR forecast is superior to that of unrestricted VARs and comparable to that of VARs with Minnesota priors. ; The article also discusses how DSGE-VAR can be used to identify the fundamental shocks that hit the economy and to forecast the impact of changes in the policy rule followed by the monetary authorities. ; Perhaps in the not-too-distant future, practitioners and policymakers will be able to use a full-fledged DSGE model for both forecasting and policy assessment. In the meantime, the authors argue, DSGE-VAR may provide a viable alternative to the models currently used.
AUTHORS: Schorfheide, Frank; Del Negro, Marco
DATE: 2003

Working Paper
Business cycles and remittances: can the Beveridge-Nelson decomposition provide new evidence?
In this paper, I analyze the business cycle properties of remittances and output series for three pairs of countries: United States-Mexico, United States-El Salvador, and Germany-Turkey. Using an unobserved components state-space model (via the Beveridge-Nelson decomposition), I decompose the remittances and output series into stochastic permanent and cyclical components. I then use the resulting stationary cyclical components to estimate co-movements between remittances and output series. Empirical results indicate that remittances are countercyclical with all the home countries: Mexico, El Salvador, and Turkey. With respect to source countries, remittances to Mexico are countercyclical with the United States business cycle, while remittances from the United States to El Salvador and remittances from Germany to Turkey are strongly procyclical with output fluctuations in the source country. The contribution of this paper to the literature is twofold: (1) I use high-frequency data (quarterly) for a relatively long period of time; and (2) I employ more recent and sophisticated econometric techniques in the decomposition of the series into stochastic permanent and cyclical components. The existing literature lacks both of these important aspects of my analysis. I show that once both of these factors are incorporated into the analysis, empirical results are more aligned to those predicted by economic theory.
AUTHORS: Coronado, Roberto
DATE: 2009

Working Paper
Bayesian semiparametric stochastic volatility modeling
This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, we use nonparametric Bayesian methods to flexibly model the skewness and kurtosis of the distribution while continuing to model the dynamics of volatility with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. We present a Markov chain Monte Carlo sampling approach to estimation with theoretical and computational issues for simulation from the posterior predictive distributions. The new model is assessed based on simulation evidence, an empirical example, and comparison to parametric models.
AUTHORS: Jensen, Mark J.; Maheu, John M.
DATE: 2008

Working Paper
Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities
This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment suggests that the procedure works well in practice. Implementing the procedure with actual S&P 500 option-implied volatilities and high-frequency five-minute-based realized volatilities results in significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of underlying macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.
AUTHORS: Bollerslev, Tim; Gibson, Michael S.; Zhou, Hao
DATE: 2004

Working Paper
Documentation of the Research and Statistics Division’s estimated DSGE model of the U.S. economy: 2006 version
This paper provides documentation for the large-scale estimated DSGE model of the U.S. economy used in Edge, Kiley, and Laforte (2007). The model represents part of an ongoing research project (the Federal Reserve Board's Estimated, Dynamic, Optimization-based--FRB/EDO--model project) in the Macroeconomic and Quantitative Studies section of the Federal Reserve Board aimed at developing a DSGE model that can be used to address practical policy questions and the model documented here is the version that was current at the end of 2006. The paper discusses the model's specification, estimated parameters, and key properties.
AUTHORS: Edge, Rochelle M.; Kiley, Michael T.; Laforte, Jean-Philippe
DATE: 2007

Working Paper
Solving stochastic money-in-the-utility-function models
This paper analyzes the necessary and sufficient conditions for solving money-in-the-utility-function models when contemporaneous asset returns are uncertain. A unique solution to such models is shown to exist under certain measurability conditions. Stochastic Euler equations, whose existence is normally assumed in these models, are then formally derived. The regularity conditions are weak, and economically innocuous. The results apply to the broad range of discrete-time monetary and financial models that are special cases of the model used in this paper. The method is also applicable to other dynamic models that incorporate contemporaneous uncertainty.
AUTHORS: Nesmith, Travis D.
DATE: 2005

Working Paper
Stochastic volatility
Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.
AUTHORS: Andersen, Torben G.; Benzoni, Luca
DATE: 2009

Working Paper
The Chicago Fed DSGE model
The Chicago Fed dynamic stochastic general equilibrium (DSGE) model is used for policy analysis and forecasting at the Federal Reserve Bank of Chicago. This article describes its specification and estimation, its dynamic characteristics and how it is used to forecast the US economy. In many respects the model resembles other medium scale New Keynesian frameworks, but there are several features which distinguish it: the monetary policy rule includes forward guidance, productivity is driven by neutral and investment specific technical change, multiple price indices identify inflation and there is a financial accelerator mechanism.
AUTHORS: Brave, Scott; Campbell, Jeffrey R.; Fisher, Jonas D. M.; Justiniano, Alejandro
DATE: 2012

Working Paper
Realized volatility
Realized volatility is a nonparametric ex-post estimate of the return variation. The most obvious realized volatility measure is the sum of finely-sampled squared return realizations over a fixed time interval. In a frictionless market the estimate achieves consistency for the underlying quadratic return variation when returns are sampled at increasingly higher frequency. We begin with an account of how and why the procedure works in a simplified setting and then extend the discussion to a more general framework. Along the way we clarify how the realized volatility and quadratic return variation relate to the more commonly applied concept of conditional return variance. We then review a set of related and useful notions of return variation along with practical measurement issues (e.g., discretization error and microstructure noise) before briefly touching on the existing empirical applications.
AUTHORS: Andersen, Torben G.; Benzoni, Luca
DATE: 2008

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