Indirect inference for the identification of star variables in macroeconomic models

Star variables, such as potential output and the neutral real interest rate, are fundamental to economic policymaking but challenging to identify due to their latent nature. Buncic, Pagan, and Robinson (2023) highlight the difficulty of identifying star variables within short macroeconomic models, which typically contain more shocks than observable variables. To address this challenge, we propose an indirect inference method that assesses identification by examining how changes in these latent variables impact the behavior of observable economic data. Specifically, we simulate data from structural economic models, summarize their behavior using simplified statistical descriptions (VAR models), and evaluate the consistency between simulated and actual data. If the star variables are identifiable, even small deviations in their specifications will result in significant rejections in our indirect inference test. Applying our method to a standard three-equation New Keynesian model and the widely used Laubach-Williams model, we demonstrate that modest inaccuracies in specifying star variables clearly increase rejection rates. These results support the identification of star variables and indicate that indirect inference provides a reliable method to assess their identification in structural macroeconomic models.