A Unified Framework to Estimate Macroeconomic Stars

We develop a flexible semi-structural time-series model to estimate jointly several macroeconomic "stars" -- i.e., unobserved long-run equilibrium levels of output (and growth rate of output), the unemployment rate, the real rate of interest, productivity growth, price inflation, and wage inflation. The ingredients of the model are in part motivated by economic theory and in part by the empirical features necessitated by the changing economic environment. Following the recent literature on inflation and interest rate modeling, we explicitly model the links between long-run survey expectations and stars to improve the stars' econometric estimation. Our approach permits time variation in the relationships between various components, including time variation in error variances. To tractably estimate the large multivariate model, we use a recently developed precision sampler that relies on Bayesian methods. The by-products of this approach are the time-varying estimates of the wage and price Phillips curves, and the pass-through between prices and wages, both of which provide new insights into these empirical relationships' instability in US data. Generally, the contours of the stars echo those documented elsewhere in the literature -- estimated using smaller models -- but at times the estimates of stars are different, and these differences can matter for policy. Furthermore, our estimates of the stars are among the most precise. Last, we document the competitive real-time forecasting properties of the model and, separately, the usefulness of stars' estimates as steady-state values in external models.