🤖 AI Summary
This study addresses the identification problem in structural vector autoregressive (SVAR) models when endogenous variables enter the left-hand side of equations nonlinearly, thereby relaxing the conventional restriction that nonlinearity must stem solely from exogenous or predetermined variables. Under mild regularity conditions, it establishes that model parameters and structural shocks are nonparametrically identified up to an orthogonal transformation, with the number of required identifying restrictions matching that of linear SVARs. Leveraging nonparametric identification theory, the analysis focuses on two classes of endogenous nonlinear SVARs—piecewise affine and smooth transition specifications—and demonstrates that existing linear identification strategies extend directly to these nonlinear settings. Applied to a nonlinear Phillips curve, the framework yields a robust test for identification assumptions, providing empirical evidence of pronounced state dependence in inflation dynamics.
📝 Abstract
We study identification in structural vector autoregressions (SVARs) in which the endogenous variables enter nonlinearly on the left-hand side of the model, a feature we term endogenous nonlinearity, to distinguish it from the more familiar case in which nonlinearity arises only through exogenous or predetermined variables. This class of models accommodates asymmetric impact multipliers, endogenous regime switching, and occasionally binding constraints. We show that, under weak regularity conditions, the model parameters and structural shocks are (nonparametrically) identified up to an orthogonal transformation, exactly as in a linear SVAR. Our results have the powerful implication that most existing identification schemes for linear SVARs extend directly to our nonlinear setting, with the number of restrictions required to achieve exact identification remaining unchanged. We specialise our results to piecewise affine SVARs, which provide a convenient framework for the modelling of endogenous regime switching, and their smooth transition counterparts. We illustrate our methodology with an application to the nonlinear Phillips curve, providing a test for the presence of nonlinearity that is robust to the choice of identifying assumptions, and finding significant evidence for state-dependent inflation dynamics.