Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application

Abstract

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.

Monetary Policy Options at the Effective Lower Bound: Assessing the Federal Reserve's Current Policy Toolkit

“…We find that moderate deviations from the SEP-baseline assumption about r LR The seven measures used to construct Figure 1 are based on the time-series models of Del Negro and others (2017), Holston and others (2017), Johannsen and Mertens (2018), Kiley (2015), Laubach and Williams (2015), Lewis and Vazquez-Grande (2017), and Lubik and Matthes (2015). We thank the authors of these studies for providing updated estimates.…”

Real Rates and Consumption Smoothing in a Low Interest Rate Environment: The Case of Japan

“…Throughout this period the correlation remains below 0.3 and is thus lower than the correlation at the beginning of our sample. 12 We also look at the behavior of measures of labor input over the sample period. As we will show below, economic theory allows us to link the behavior of consumption growth and the real rate to changes in employment via the intertemporal Euler-equation.…”

“…The 12 Lubik and Matthes (2015b) highlight the importance of modeling time variation explicitly in aggregate time series. They advocate the use of time-varying parameter VARs with stochastic volatility to delineate different sources of time variation and apparent breaks in data.…”

Beveridge Curve Shifts and Time-Varying Parameter VARs

“…Our speci…c time-series model builds on Cogley and Sargent (2005) and Primiceri (2005). The exposition below follows Lubik and Matthes (2015), who provide further details on the implementation.…”

“…In TVP-VARs the choice of priors is of special importance because, with standard sample sizes, they have a substantial impact on how much of the variation in observables is attributed to stochastic volatility versus time variation in other coe¢ cients. 4 At the same time, there is a growing sense, e.g., Lubik and Matthes (2015), that the conclusions drawn from the TVP-VAR literature warrant skepticism. More speci…cally, TVP-VARs often …nd not much time variation in the lag coe¢ cients.…”