Working Papers 2022
2022-01: Identifying Proxy VARs with Restrictions on the Forecast Error Variance
Tilmann Härtl
Abstract
The proxy VAR framework requires additional restrictions to disentangle the structural shocks when multiple shocks are identified using multiple instruments. I propose to employ restrictions on the forecast error variance (FEV). Less restrictive assumptions that bound the contributions to the FEV can replace or accompany inequality restrictions on e.g. the impulse responses. This enables to sharpen the set identification of the structural parameters. Furthermore, assuming one shock maximizes the contribution to the FEV of a target variable (Max-Share) can be used to point identify the structural parameters. I show under which circumstances this strategy succeeds and propose an augmentation to the Max-Share framework in cases it is prone to bias concerns. Point identification is achieved without the need for strict equality restrictions, but limited to the case of two proxies which identify two shocks.