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Indirect Inference for the Identification of Star Variables in Macroeconomic Models

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Abstract

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.

Suggested Citation

  • Minford, Patrick & Xu, Yongdeng, 2025. "Indirect Inference for the Identification of Star Variables in Macroeconomic Models," Cardiff Economics Working Papers E2025/8, Cardiff University, Cardiff Business School, Economics Section.
  • Handle: RePEc:cdf:wpaper:2025/8
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    Keywords

    Star variables; identification; indirect inference; structural models; neutral real rate; potential output;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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