Identification by Heteroskedasticity or Non-Gaussianity

Abstract

Introduction As we have seen in Chapters 8 and 10, the identification of structural VAR models typically relies on economically motivated identifying restrictions. Another strand of the literature exploits certain statistical properties of the data for identification. In particular, changes in the conditional or unconditional volatility of the VAR errors (and hence of the observed variables) can be used to assist in the identification of structural shocks. For example, Rigobon (2003), Rigobon and Sack (2003), and Lanne and Lutkepohl (2008) rely on unconditional heteroskedasticity, whereas Normandin and Phaneuf (2004), Bouakez and Normandin (2010), and Lanne, Lutkepohl, and Maciejowska (2010) exploit conditional heteroskedasticity. In this chapter, we explain the principle of identification by heteroskedasticity. In Section 14.2, the general modeling strategy is presented and its advantages and limitations are discussed. The central idea is that in a conventional structural VAR analysis the structural shocks are recovered by transforming the reduced-form residuals. As we have seen in previous chapters, this is typically done through exclusion restrictions. The current chapter considers the question of how changes in the volatility of the model errors can be used for this purpose. We show that the assumption that the structural impulse responses are time invariant, as the volatility of the reduced-form shocks changes, provides additional restrictions that can be used to uniquely pin down mutually uncorrelated shocks. There is nothing in this purely statistical identification procedure, however, that ensures that these shocks are also economically meaningful, making it difficult to interpret them as structural VAR shocks. One way to assess whether all or some of the shocks identified by heteroskedasticity correspond to economic shocks and, hence, can be interpreted as proper structural shocks is to treat conventional identifying restrictions as overidentifying restrictions within the heteroskedastic model, facilitating formal tests of these restrictions. In some cases it may also be possible to infer the economic interpretation of these shocks informally from comparisons of the implied impulse responses with impulse response estimates based on conventional structural VAR models, as illustrated in Lutkepohl and Netsunajev (2014). A necessary condition for such comparisons is that the structural impulse responses in the VAR model based on conventional identifying restrictions can be estimated consistently under the assumptions maintained in the explicitly heteroskedastic VAR model.