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), unemployment rate, the real rate of interest, productivity growth, price inflation, and wage inflation. The ingredients of our model are in part motivated by economic theory and, in part, by the empirical features necessitated due to the changing economic environment. Following 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 our large multivariate model, we use a recently developed precision sampler that relies on Bayesian methods. Our approach's by-products are the time-varying estimates of the wage and price
Phillips curves, passthrough between prices and wages, which provide new insights into these empirical relationships' instability in US data. Generally, the contours of our 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. Lastly, we document the competitive real-time forecasting properties of our model and, separately, the usefulness of stars' estimates if they were used as steady-state values in external models.