Despite intense scrutiny, estimates of the government spending multiplier remain highly uncertain, with values ranging from 0.5 to 2. While an increase in government spending is generally assumed to have the same (mirror-image) e¤ect as a decrease in government spending, we show that relaxing this assumption is important to understand the e¤ects of …scal policy. Regardless of whether we identify government spending shocks from (i) a narrative approach, or (ii) a timing restriction, we …nd that the contractionary multiplier-the multiplier associated with a negative shock to government spending-is above 1, while the expansionary multiplier-the multiplier associated with a positive shock-is substantially below 1. The multiplier is largest in recessions, as found in previous studies, but only because the contractionary multiplier is largest in recessions. The expansionary multiplier is always below 1 and not larger in recessions. We argue that our results help understand the wide range of multiplier estimates found in the literature.

Highly volatile transition dynamics can emerge when a central bank disinflates while operating without full transparency. In our model, a central bank commits to a Taylor rule whose form is known but whose coefficients are not. Private agents learn about policy parameters via Bayesian updating. Under McCallum's (1999) timing protocol, temporarily explosive dynamics can arise, making the transition highly volatile. Locally unstable dynamics emerge when there is substantial disagreement between actual and perceived feedback parameters. The central bank can achieve low average inflation, but its ability to adjust reaction coefficients is more limited.

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T ime-varying parameter vector autoregressions (TVP-VARs) have become an increasingly popular tool for analyzing the behavior of macroeconomic time series. TVP-VARs di¤er from more standard …xed-coe¢ cient VARs in that they allow for coe¢ cients in an otherwise linear VAR model to vary over time following a speci…ed law of motion. In addition, TVP-VARs often include stochastic volatility (SV), which allows for time variation in the variances of the error processes that a¤ect the VAR.The attractiveness of TVP-VARs is based on the recognition that many, if not most, macroeconomic time series exhibit some form of nonlinearity. For instance, the unemployment rate tends to rise much faster at the start of a recession than it declines at the onset of a recovery. Stock market indices exhibit occasional episodes where volatility, as measured by the variance of stock price movements, rises considerably. As a third example, many aggregate series show a distinct change in behavior in terms of their persistence and their volatility around the early 1980s when the Great In ‡ation of the 1970s turned into the Great Moderation, behavior that is akin to a structural shift in certainWe are grateful to Pierre-Daniel Sarte, Daniel Tracht, John Weinberg, and Alex Wolman, whose comments greatly improved the exposition of this paper. The views expressed in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

SUMMARYWe propose two methods to choose the variables to be used in the estimation of the structural parameters of a singular DSGE model. The first selects the vector of observables that optimizes parameter identification; the second selects the vector that minimizes the informational discrepancy between the singular and non‐singular model. An application to a standard model is discussed and the estimation properties of different setups compared. Practical suggestions for applied researchers are provided. Copyright © 2014 John Wiley & Sons, Ltd.