Sigma Point Filters For Dynamic Nonlinear Regime Switching Models

In this paper we take three well known Sigma Point Filters, namely the Unscented Kalman Filter, the Divided Difference Filter, and the Cubature Kalman Filter, and extend them to allow for a very general class of dynamic nonlinear regime switching models. Using both a Monte Carlo study and real data, we investigate the properties of our proposed filters by using a regime switching DSGE model solved using nonlinear methods. We find that the proposed filters perform well. They are both fast and reasonably accurate, and as a result they will provide practitioners with a convenient alternative to Sequential Monte Carlo methods. We also investigate the concept of observability and its implications in the context of the nonlinear filters developed and propose some heuristics. Finally, we provide in the RISE toolbox, the codes implementing these three novel filters

Dynare: Reference Manual Version 4

Dynare is a software platform for handling a wide class of economic models, in particular dynamic stochastic general equilibrium (DSGE) and overlapping generations (OLG) models. The models solved by Dynare include those relying on the rational expectations hypothesis, wherein agents form their expectations about the future in a way consistent with the model. But Dynare is also able to handle models where expectations are formed differently: on one extreme, models where agents perfectly anticipate the future; on the other extreme, models where agents have limited rationality or imperfect knowledge of the state of the economy and, hence, form their expectations through a learning process. Dynare offers a user-friendly and intuitive way of describing these models. It is able to perform simulations of the model given a calibration of the model parameters and is also able to estimate these parameters given a dataset. Dynare is a free software, which means that it can be downloaded free of charge, that its source code is freely available, and that it can be used for both non-profit and for-profit purposes.Dynare; Numerical methods; Perturbation; Rational expectations

Efficient Perturbation Methods for Solving Regime-Switching DSGE Models

In an environment where economic structures break, variances change, distributions shift, conventional policies weaken and past events tend to reoccur, economic agents have to form expectations over different regimes. This makes the regime-switching dynamic stochastic general equilibrium (RS-DSGE) model the natural framework for analyzing the dynamics of macroeconomic variables. We present efficient solution methods for solving this class of models, allowing for the transition probabilities to be endogenous and for agents to react to anticipated events. The solution algorithms derived use a perturbation strategy which, unlike what has been proposed in the literature, does not rely on the partitioning of the switching parameters. These algorithms are all implemented in RISE, a flexible object-oriented toolbox that can easily integrate alternative solution methods. We show that our algorithms replicate various examples found in the literature. Among those is a switching RBC model for which we present a third-order perturbation solution.publishedVersio

Conditional Forecasts in DSGE Models

New-generation DSGE models are sometimes misspecified in dimensions that matter for their forecasting performance. The paper suggests one way to improve the forecasts of a DSGE model using a conditioning information that need not be accurate. The technique presented allows for agents to anticipate the information on the conditioning variables several periods ahead. It also allows the forecaster to apply a continuum of degrees of uncertainty around the mean of the conditioning information, making hard-conditional and unconditional forecasts special cases. An application to a small open-economy DSGE model shows that the benefits of conditioning depend crucially on the ability of the model to capture the correlation between the conditioning information and the variables of interest.publishedVersio

Efficient Perturbation Methods for Solving Regime-Switching DSGE Models

In an environment where economic structures break, variances change, distributions shift, conventional policies weaken and past events tend to reoccur, economic agents have to form expectations over different regimes. This makes the regime-switching dynamic stochastic general equilibrium (RS-DSGE) model the natural framework for analyzing the dynamics of macroeconomic variables. We present efficient solution methods for solving this class of models, allowing for the transition probabilities to be endogenous and for agents to react to anticipated events. The solution algorithms derived use a perturbation strategy which, unlike what has been proposed in the literature, does not rely on the partitioning of the switching parameters. These algorithms are all implemented in RISE, a flexible object-oriented toolbox that can easily integrate alternative solution methods. We show that our algorithms replicate various examples found in the literature. Among those is a switching RBC model for which we present a third-order perturbation solution

Implementing the Zero Lower Bound in an Estimated Regime-Switching DSGE Model

The Zero Lower Bound (ZLB) on policy rates is one of the key monetary policy issues du jour. In this paper we investigate the problem of modelling and estimating the ZLB in a simple New Keynesian model with regime switches. The key features of the model include switches in the time preference shock, productivity growth rate and the steady state rate of inflation leading to two steady states: a normal steady state and a ZLB steady state. The model is fittted to US data using Bayesian methods and is found to match the US experience over the great moderation and the ZLB periods very well. The key features of the model allow us to test competing theories about the determinants of the ZLB steady state. Our results suggest that the ZLB steady state is driven by precautionary savings behavior. It is also found that expectations over different regimes crucially matter for the dynamics of the system.publishedVersio

Conditional Forecasts in DSGE Models

New-generation DSGE models are sometimes misspecified in dimensions that matter for their forecasting performance. The paper suggests one way to improve the forecasts of a DSGE model using a conditioning information that need not be accurate. The technique presented allows for agents to anticipate the information on the conditioning variables several periods ahead. It also allows the forecaster to apply a continuum of degrees of uncertainty around the mean of the conditioning information, making hard-conditional and unconditional forecasts special cases. An application to a small open-economy DSGE model shows that the benefits of conditioning depend crucially on the ability of the model to capture the correlation between the conditioning information and the variables of interest

Modeling production and employment in the Norwegian private services

After discussing the choice of an appropriate production function for the Norwegian private services, we use quarterly data to estimate models for production and labor demand over 1979Q1-2001Q3. The results show that in the long-run the production function is consistent with a profit-maximizing behavior. Moreover, Norwegian private services are labor intensive, which accords with the stylized facts of the literature on services economics. However, due to its sluggish movements, the role of capital in the production process is difficult to grasp. Finally, not only the models presented track the data pretty well, they also are serious contenders to the rival explanations of the current models in RIMINI, the Norwegian Central Bank macro-model

Conditional forecasts in DSGE models

New-generation DSGE models are sometimes misspecified in dimensions that matter for their forecasting performance. The paper suggests one way to improve the forecasts of a DSGE model using a conditioning information that need not be accurate. The technique presented allows for agents to anticipate the information on the conditioning variables several periods ahead. It also allows the forecaster to apply a continuum of degrees of uncertainty around the mean of the conditioning information, making hard-conditional and unconditional forecasts special cases. An application to a small open-economy DSGE model shows that the benefits of conditioning depend crucially on the ability of the model to capture the correlation between the conditioning information and the variables of interest.DSGE model, conditional forecast

Loose Commitment in Medium-Scale Macroeconomic Models: Theory and an Application

This paper proposes a method and a toolkit for solving optimal policy with imperfect commitment in linear quadratic models. As opposed to the existing literature, our method can be employed in medium- and large-scale models typically used in monetary policy. We apply our method to the Smets and Wouters (2007) model, where we show that imperfect commitment has relevant implications for the interest rate setting, the sources of business cycle fluctuations, and welfare.publishedVersio