Endogenous threshold VAR solves price puzzles in monetary policy
An ECB working paper by Dimitris Christopoulos, Peter McAdam, and Elias Tzavalis introduces a copula-based control function for threshold vector autoregressions with endogenous state variables. The framework removes excess sensitivity and propagation errors in macroeconomic impulse responses without requiring external instruments.
Purging endogeneity with copula controls
Standard threshold vector autoregressions assume that regime-splitting threshold variables are predetermined.
Authors Dimitris Christopoulos, Peter McAdam, and Elias Tzavalis demonstrate that when threshold variables react contemporaneously to structural shocks, uncorrected models suffer from covariance inflation and dynamic coefficient bias.
These distortions create excess sensitivity in impact matrices and excess propagation in impulse responses.
To fix this, the authors derive a regime-specific copula-based control function using probability integral transforms.
The method orthogonalizes threshold variables and innovations without requiring external instruments or parametric assumptions on threshold distributions, maintaining linear regime-wise least-squares structures.
State dependence in American monetary history
Applied to US monetary transmission from 1973 to 2007, the endogenous threshold model locates the regime boundary at 3.53 percent expected inflation, splitting the sample into low and high inflation states.
Unlike linear VARs that generate price puzzles and sluggish adjustments, the corrected framework produces clear disinflationary dynamics following monetary tightening.
Peak output gap contraction reaches minus 0.08 in the high regime versus minus 0.05 in the low regime.
The dynamic sacrifice ratio drops from 5.0 in low-inflation periods to 1.6 in high-inflation states.
Essential patch with sample constraints
The paper provides a necessary methodological fix for threshold models where state exogeneity is unrealistic.
Yet the copula-based approach remains sensitive to sample size limitations when handling heavy-tailed data.
Applied researchers gain a practical tool to eliminate artificial price puzzles in monetary policy evaluation.