Identification in (Endogenously) Nonlinear SVARs Is Easier Than You Think

TL;DR

This paper demonstrates that identification in nonlinear SVARs with endogenous variables is as straightforward as in linear models, allowing existing methods to extend to more complex nonlinear settings.

Contribution

It shows that nonlinear SVARs with endogenous nonlinearity are identifiable up to an orthogonal transformation, simplifying analysis and extending linear identification schemes.

Findings

Identification in nonlinear SVARs is similar to linear cases.

Most linear SVAR identification schemes extend to nonlinear models.

Application finds significant state-dependent 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.