I need to read this:
Testing Models of Low-Frequency Variability, by Ulrich Mueller and Mark W. Watson, NBER WP 12671, November 2006: Abstract We develop a framework to assess how successfully standard times series models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle. ... Conclusions ... Three main findings stand out. First, despite the narrow focus, very few of the series are compatible with the I(0) model. ... Most macroeconomic series and relationships thus exhibit pronounced non-trivial dynamics below business cycle frequencies. In contrast, the unit root model is often consistent with the observed low-frequency variability. Second, our theoretical results on the similarity of the low-frequency implications of alternative models imply that it is essentially impossible to discriminate between these models based on low-frequency information using sample sizes typically encountered in empirical work. ... Third, maybe the most important empirical conclusion is that for many series there seems to be too much low-frequency variability in the second moment to provide good fits for any of the models. From an economic perspective, this underlines the importance of understanding the sources and implications of such low-frequency volatility changes. From a statistical perspective, this finding motivates further research into methods that allow for substantial time variation in second moments. [Open link]
Linear-Quadratic Approximation of Optimal Policy Problems, by Pierpaolo Benigno and Michael Woodford , NBER WP 12672, November 2006: Abstract We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The LQ approximate problem is computationally simple to solve, even in the case of moderately large state spaces and flexibly parameterized disturbance processes, and its solution represents a local linear approximation to the optimal policy for the exact model in the case that stochastic disturbances are small enough. We derive the second-order conditions that must be satisfied in order for the LQ problem to have a solution, and show that these are stronger, in general, than those required for LQ problems without forward-looking constraints. We also show how the same linear approximations to the model structural equations and quadratic approximation to the exact welfare measure can be used to correctly rank alternative simple policy rules, again in the case of small enough shocks. [Open link]
I don't expect much if any interest in these papers (though open links are included for the curious), just putting them in the archive for easy access later.