Threshold endogeneity in vector autoregressions: reassessing monetary state dependence

We develop an endogenous threshold VAR that addresses contemporaneous dependence between the threshold variable and reduced-form innovations— a pervasive issue when regime indicators are jointly determined with system dynamics. A regime-specific copula-based control function removes this dependence instrument-free, without parametric assumptions on the threshold’s marginal distribution, while preserving the linear regime-wise least-squares structure. We characterize the resulting misspecification through excess sensitivity and excess propagation errors in impulse responses, clarify structural and proxy-SVAR identification under endogenous regimes, and establish conditions under which Chan-type threshold asymptotics remain valid with generated controls. A Hermite sieve extension accommodates tail-dependent and asymmetric dependence. Monte Carlo evidence documents large distortions from ignoring endogeneity. Applied to monetary transmission, the framework avoids the price and persistence puzzles displayed by the linear VAR, delivers regime-dependent sacrifice ratios, and aligns estimated regimes with historical inflation episodes. JEL Classification: C32, C34, E52