A novel robust framework for the identification of component weights in the Girton-Roper exchange market pressure index

This study introduces a novel estimation procedure for weight identification in composite indices, with a focus on regime-dependent persistence in exchange market pressure (EMP) indices. We propose a two-stage estimation framework, where persistence is modeled through an interaction between a fixed parameter ρ (0≤ρ≤1) and a regime-specific coefficient λ. Our methodology addresses three main challenges: (i) endogenous regressors, (ii) regime-dependent persistence in the error structure, and (iii) simultaneous equation bias. The asymptotic properties of our estimators are established within a regime-switching framework, proving consistency under weak regularity conditions and deriving limiting distributions. For identification, we employ generated instruments, providing formal proofs of asymptotic normality and deriving the variance-covariance matrix. Analytical derivations also confirm the efficiency of our estimators under various persistence structures and regime specifications. Combined with empirical relevance, this framework serves as a robust tool for policy analysis and empirical applications in composite indices with regime-dependent dynamics.