Estimating and accounting for the output gap with large Bayesian vector autoregressions

Abstract

Summary We consider how to estimate the trend and cycle of a time series, such as real gross domestic product, given a large information set. Our approach makes use of the Beveridge–Nelson decomposition based on a vector autoregression, but with two practical considerations. First, we show how to determine which conditioning variables span the relevant information by directly accounting for the Beveridge–Nelson trend and cycle in terms of contributions from different forecast errors. Second, we employ Bayesian shrinkage to avoid overfitting in finite samples when estimating models that are large enough to include many possible sources of information. An empirical application with up to 138 variables covering various aspects of the US economy reveals that the unemployment rate, inflation, and, to a lesser extent, housing starts, aggregate consumption, stock prices, real money balances, and the federal funds rate contain relevant information beyond that in output growth for estimating the output gap, with estimates largely robust to substituting some of these variables or incorporating additional variables.

Time-Varying Uncertainty of the Federal Reserve's Output Gap Estimate

“…The Tealbook potential estimate is judgmental, combining estimates of potential output from growth accounting models, trend-cycle decompositions, especially those containing a Phillips curve relationship, and DSGE models (Mishkin 2007). That these more comprehensive approaches produce output gaps that are more cyclically sensitive (in the sense that economic variables are respond strongly to the factor innovations) is consistent with other economic variables carrying information relevant to the output gap (Fleischmann & Roberts, 2011;Morley & Wong, 2020). Alternatively, it may also be that explicitly modeling slowly trending variables helps to calibrate the amount of signal taken from a given surprise to estimates of real output, see Kamber et al (2018).…”

Large Hybrid Time-Varying Parameter VARs

“…As a comparison, we also report the corresponding long-run trend estimates for a small system (n = 3) with real GDP, PCE inflation and unemployment, as well as a medium system (n = 7) with four additional variables: Fed funds rate, industrial production, real average hourly earnings in manufacturing and M1 money stock. These variables are similar to those used in Morley and Wong (2019) for estimating the output gap. It is evident from the figure that that there is substantial time variation in the trend output growth under the large hybrid TVP-VAR over the past six decades.…”

A Unified Framework to Estimate Macroeconomic Stars

“…8 Morley and Wong (2020) and Chan (2019) propose an alternative modeling framework based on VARs to estimate the long-run equilibrium values. The advantage of the VAR-based framework is the ability to handle larger amounts of information conveniently and flexibly compared to UC models.…”

“…Second, to improve the econometric estimation of the output gap, we enrich the IS equation by bringing in information from the unemployment gap (from the unemployment block) as an explanatory variable. 20 This latter addition is motivated by the approach taken in a long list of papers (e.g., Morley and Wong, 2020;Grant and Chan, 2017a;Fleischman and Roberts, 2011;Sinclair, 2009;Clark, 1987) that demonstrate the usefulness of the unemployment rate in improving the econometric estimation of the output gap. As mentioned earlier, in the equation for the unemployment gap, we add the output gap to improve the former's estimation.…”